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LME for Pocket PC User Manual

1. 3 39 Graphical Functions for Dynamical Systems 4 1 Serial Port Functions 000 5 1 stdlibj oeras a et RA ee ee bee ea 22 SUA ais te Meck Bere wh idl acs ith aren Bio ot al a ewe wa ho 5 3 ClASSCS nag aa of ect amp Ble aged pak dees XA Ee ee 5 4 PATIO se oe se cee a eee he See ee kN wd GA GD We a aes 5 5 Hield eea ok ee Gees Be ee ks oti ek eae ee Mee ee ee ee re ee re wee he 57 tih eae te quence hg a Ree a an A Ge an ee ee eae ee 5 8 SIQDENC pee ee eee ba eee ee eee de ee ee eee D9 Wades kde ew A RA ee ee he bak oie Be eB Peery Ge Maa A eh A Ae ea Dll CONnStants ss o hoe de we big the ew ee A he 6 1 Long Integers 2 00 eee eee es 6 2 Memory Mapping 0000222 e eae 6 3 Data Compression 0 0000 ee eee eas Sarl Contents 5 6 4 ImageFiles 0000002 564 6 5 MAT files 0 0 0 a 567 IGG a ne A ee ee ak ee dee Pate ae Bk eA 569 Aad ka WM Baa ee A Se 569 6 8 Functions 0 0 00 aa eta aah deoa eee 570 6 9 Sockets 0 ee 575 6 10 Launch URL 0 00000 eee 580 6 11 Download URL 0 00000 eae 581 6 12 Web Services ies sso on oe dc ee Bed Bee Bee 582 6 13 Serial port 0 00000 2c eee 597 6 14 Audio output 2 66 shea eee bee ea ee ee es 600 6 15 Audio INputl ce scence dee OA dae hee we Ee a 602 604 Chapter 1 Introduction LME for Pocket PC is LME t
2. cellfun Function evaluation for each cell of a cell array Syntax A cellfun fun C A cell fun C Description cellfun fun C evaluates function fun for each cell of cell array C Each evaluation must give a scalar result of numeric logical or char acter type results are returned as a non cell array the same size as C First argument is a function reference an inline function or the name of a function as a string With more than two input arguments cellfun calls function fun as feval fun C i other where C i is each cell of C in turn and other stands for the remaining arguments of cellfun 242 LMEPPC User Manual 1999 2008 Calerga Sarl cellfun differs from map in two ways the result is a non cell array and remaining arguments of cellfun are provided directly to fun Examples cellfun isempty 1 ones 5 FT TF map isempty 1 ones 5 2x2 cell array cellfun size 1 ones 5 2 10 05 See also diag Creation of a diagonal matrix or extraction of the diagonal elements of a matrix Syntax M diag v M diag v k v diag M v diag M k Description With a vector input argument diag v creates a square diagonal ma trix whose main diagonal is given by v With a second argument the diagonal is moved by that amount in the upper right direction for pos itive values and in the lower left direction for negative values With a matrix in
3. chebyl n w0 high chebyl n wl wh stop chebyl s Description chebyl calculates a Chebyshev type 1 filter The result is given as zeros poles and gain if there are three output arguments or as nu merator and denominator coefficient vectors if there are two output arguments cheby1 n w0 where w0 is a scalar gives a nth order digital low pass filter with a cutoff frequency of w0 relatively to half the sampling frequency cheby1 n wl wh where the second input argument is a vector of two numbers gives a 2nth order digital bandpass filter with pass band between wl and wh relatively to half the sampling frequency cheby1 n w0 high gives a nth order digital highpass filter with a cutoff frequency of w0 relatively to half the sampling frequency cheby1 n wl wh stop where the second input argument is a vector of two numbers gives a 2nth order digital bandstop filter with stopband between wl and wh relatively to half the sampling frequency With an additional input argument which is the string s cheby1 gives an analog Chebyshev type 1 filter Frequencies are given in rad s Libraries filter 515 See also cheby2 Chebyshev type 2 filter Syntax use filter Z k cheby2 n w0 num den cheby2 n w0 cheby2 n wl wh cheby2 n w0 high cheby2 n wl wh stop cheby2 s Descr
4. interval See also circle Add circles to the figure Syntax circle x y r circle x y r style circle x y r style id 384 LMEPPC User Manual 1999 2008 Calerga Sarl Description circle x y r draws a circle of radius r centered at x y The argu ments can be vectors to display several circles Their dimensions must match scalar numbers are repeated if necessary The optional fourth and fifth arguments are the style and object ID cf their above In mouse handlers _x0 and _y correspond to the projection of the mouse click onto the circle _nb is the index of the circle in x y and r and _ix is empty Circles are displayed as circles only if the scales along the x and y axis are the same and linear With different linear scales circles are displayed as ellipses With logarithmic scales they are not displayed Examples circle 1 2 5 r 1 circle zeros 10 1 zeros 10 1 1 10 See also colormap Current colormap from scalar to RGB Syntax colormap clut clut colormap Description Command colormap clut changes the color mapping from scalar values to RGB values used by commands such as pcolor image and surf Colormaps are arrays of size n by 3 Each row corresponds to a color the first column is the intensity of red from 0 no red component to 1 maximum intensity the second column the intensity of green and the third column the intensity of blue Input values are mapped
5. Description sensor3 type param id specifies how a 3D element can be dragged interactively Contrary to 2D graphics where the mapping between the mouse cursor and the graphical coordinates depends on two separate scaling factors manipulation in 3D space must use a surface as an additional constraint sensor3 specifies this surface for a graphical object whose ID is the same as argument id The constraint surface is specified with string type and numeric array param It always contains the selected point For instance if the user clicks the second point of plot3 1 2 5 3 2 4 1 and sensor3 defines a horizontal plane the move lies in horizontal plane z 4 In addition to position _p1 parameters specific to the constraint surface are provided in special variable _g a vector of two elements type plane The constraint surface is the plane defined by the selected point _p0 and two vectors vxl vyl vz1 and vx2 vy2 vz2 given in argument param vxl vyl vzl vx2 vy2 vz2 During the drag q contains the coefficients of these two vectors such that _p1 _p0 _q param type sphere The constraint surface is a sphere whose center is defined by a point param px py pz Its R is such that the surface contains the selected point _p0 During the drag q contains the spherical coordinates phi and theta such that _pl param R cos q_ 1 cos q_ 2 sin q_ 1 cos q_ 2 sin q_ 2 With five input argu
6. P H hess A H hess A Description hess A reduces the square matrix A A to the upper Hessenberg form H using an orthogonal similarity transformation P H P A The result H is zero below the first subdiagonal and has the same eigenvalues as A Example P H hess 1 2 3 4 5 6 7 8 9 P 1 0 0 0 0 4961 0 8682 0 0 8682 0 4961 H 1 3 597 0 2481 8 0623 14 0462 2 8308 0 0 8308 4 6154e 2 PxHxP ans 1 2 3 4 5 6 7 8 9 See also 216 LMEPPC User Manual 1999 2008 Calerga Sarl inv Inverse of a square matrix Syntax M2 inv M1 Description inv M1 returns the inverse M2 of the square matrix M1 i e a matrix of the same size such that M2 M1 M1 M2 eye size M1 M1 must not be singular otherwise its elements are infinite To solve a set of linear of equations the operator is more efficient Example inv 1 2 3 4 2 1 1 5 0 5 See also kron Kronecker product Syntax M kron A B Description kron A B returns the Kronecker product of matrices A size m1 by n1 and B size m2 by n2 i e an m1 m2 by n1 n2 matrix made of m1 by n1 submatrices which are the products of each element of A with B LME Reference linear algebra Example kron 1 1 2 3 4 ones 2 1 2 1 2 1 2 3 4 3 4 W W e A ANNS See also kurtosis Kurtosis of a set of values Syntax k kurtosis A k kurtosis A dim Description 217 kurtosis A gives the kurtos
7. Syntax use stdlib S corrcoef X S corrcoef X1 X2 Description corrcoef X calculates the correlation coefficients of the columns of the m by n matrix X The result is a square n by n matrix whose diag onal is 1 corrcoef X1 X2 calculates the correlation coefficients of X1 and X2 and returns a 2 by 2 matrix It is equivalent to corrcoef X1 X2 Example use stdlib corrcoef 1 3 2 5 4 4 7 10 1 0 8915 0 8915 1 corrcoef 1 5 5 1 1 1 1 1 1 See also COV cumtrapz Cumulative numerical integration with trapezoidal approximation Libraries stdlib 467 Syntax use stdlib S cumtrapz Y S cumtrapz X Y S cumtrapz X Y dim Description cumtrapz Y calculates an approximation of the cumulative integral of a function given by the samples in Y with unit intervals The trape zoidal approximation is used If Y is neither a row nor a column vector integration is performed along its columns The result has the same size as Y The first value s is are 0 cumtrapz X Y specifies the location of the samples A third argu ment may be used to specify along which dimension the integration is performed Example use stdlib cumtrapz 2 3 5 0 2 5 6 5 cumtrapz 1 2 5 2 3 5 0 2 5 14 5 See also factor Prime factors Syntax use stdlib v factor n Description factor n gives a row vector which contains the prime factors of n in ascending order Mult
8. ment Example range rand 1 100 0 9602 See also squareform Resize the output of pdist to a square matrix Syntax use stat D squareform d 490 LMEPPC User Manual 1999 2008 Calerga Sarl Description squareform d resize d which should be the output of pdist into a symmetric square matrix D so that the distance between observations iand jisD i j See also pdist trimmean Trimmed mean of a set of values Syntax use stat m trimmean A prc m trimmean A prc dim Description trimmean A prc gives the arithmetic mean of the columns of array A or of the row vector A once prc 2 percent of the values have been re moved from each end The dimension along which trimmean proceeds may be specified with a third argument trimmean is less sensitive to outliers than the regular arithmetic mean See also zscore Z score normalized deviation Syntax use stat Y zscore X Y zscore X dim Libraries classes 491 Description zscore X normalizes the columns of array X or the row vector X by subtracting their mean and dividing by their standard deviation The dimension along which zscore proceeds may be specified with a sec ond argument 5 3 classes Library classes implements the constructors and methods of two classes polynom for polynomials and ratfun for rational functions Basic arithmetic operators and functions are overloaded to support expressions with the same syntax
9. sv w dsigma Description dsigma Ad Bd Cd Dd Ts plots the singular values of the frequency response of the discrete time state space model Ad Bd Cd Dd de fined as zX z AgX zZ BgU z Y zZ CgX z DgU Z where z e 7s and Ts is the sampling period Further options can be provided in a structure opt created with responseset field Range is utilized The optional arguments style and id have their usual meaning dsigma is the equivalent of dbodemag for multiple input systems For single input systems it produces the same plot LME Reference graphics for dynamical systems 431 The range of frequencies is selected automatically or can be speci fied in an optional argument w a vector of frequencies With output arguments dsigma gives the singular values and the frequency as column vectors No display is produced See also dbodemag dbodephase sigmal responseset dstep Step response plot of a discrete time linear system Syntax dstep numd dend Ts dstep numd dend Ts opt dstep Ad Bd Cd Dd Ts A a Bd Cd Dd Ts opt a style dstep oe id y t dstep Description dstep numd dend Ts plots the step response of the discrete time transfer function numd dend with sampling period Ts Further options can be provided in a structure opt created with responseset field Range is utilized The optional arguments style and id have their usual meaning dstep Ad Bd Cd D
10. tf gain where gain is a matrix creates a matrix of gains Examples Simple continuous time system with variable p p is used only for dis play use lti sc tf 1 1 2 3 4 p sc continuous time transfer function 1 p 3 2p 2 3p 4 Matrix of discrete time transfer functions for one input and two out puts with a sampling period of 1ms sd tf 0 1 0 15 1 0 8 1 0 78 le 3 sd discrete time transfer function Ts le 3 yl ul 0 1 s 0 8 y2 ul 0 15 s 0 78 See also SS i SS Iti append Append the inputs and outputs of systems Libraries lti 523 Syntax use lti b append al a2 Description append al a2 builds a system with inputs ul u2 and outputs yl y2 where ul and u2 are the inputs of al and yl and y2 their outputs respectively append accepts any number of input arguments See also ti connect ss augstate Extend the output of a system with its states Syntax use lti b augstate a Description augstate a extends the ss object a by adding its states to its out puts The new output is y x where y is the output of a and x is its states See also Uti append Iti beginning First index Syntax use lti var beginning 524 LMEPPC User Manual 1999 2008 Calerga Sarl Description In an expression used as an index between parenthesis beginning a gives the first valid value for an index It is always 1 See also
11. y acsch x LME Reference mathematical functions 147 Description acsch x gives the inverse hyperbolic cosecant of x which is complex if x is See also angle Phase angle of a complex number Syntax phi angle z Description angle z gives the phase of the complex number z i e the angle be tween the positive real axis and a line joining the origin to z angle 0 is O Examples angle 1 3j 1 2490 angle 0 1 1 0 3 1416 See also asec Inverse secant Syntax y asec x Description asec x gives the inverse secant of x which is complex if x is complex or is in the range 1 1 148 LMEPPC User Manual 1999 2008 Calerga Sarl See also asech Inverse hyperbolic secant Syntax y asech x Description asech x gives the inverse hyperbolic secant of x which is complex if x is complex or strictly negative See also sech asec acosh asin Arc sine Syntax y asin x Description asin x gives the arc sine of x which is complex if x is complex or if abs x gt 1 Examples asin 5 0 5236 asin 2 1 5708 1 317j See also LME Reference mathematical functions 149 asinh Inverse hyperbolic sine Syntax y asinh x Description asinh x gives the inverse hyperbolic sine of x which is complex if x is complex Examples asinh 2 1 4436 asinh 0 1 2j 0 1 8055 1 7359j See also Sinh lacosh asin atan Arc tangent Sy
12. Examples Sine between 0 and 27 xX 2 x pi gt x 0 100 0 01 y sin x plot x y Ten random crosses plot rand 1 10 rand 1 10 x LME Reference base graphics 395 A complete SQ file for displaying a red triangle whose corners can be moved interactively on Sysquake variables x y x and y are 1 by 3 vectors init x y init init handler figure Triangle draw drawTri x y mousedrag x y dragTri x y ix _xl _yl functions function x y init x 1 1 0 y 1 1 2 subplots Triangle function drawTri x y scale equal 3 3 3 3 plot x y rf 1 filled red triangle with ID 1 function x y dragTri x y ix x1 yl if isempty ix cancel not a click over a point end x ix xl y ix yl See also plotoption Set plot options Syntax plotoption str Description plotoption sets the initial value of one of the plot options the user can change Its single argument a character string can take one of the following values frame Rectangular frame with tick marks and a white background around the plot noframe No frame no tickmarks no white background 396 LMEPPC User Manual 1999 2008 Calerga Sarl label Subplot name above the frame nolabel legend nolegend trlegend tllegend brlegend bllegend margin nomargin No subplot name Legend if
13. Projection kind Syntax camproj str str camproj 408 LMEPPC User Manual 1999 2008 Calerga Sarl Description camproj str sets the projection mode string str can be either orthographic or o for a parallel projection or perspective or p for a projection with a view point at a finite distance With an output argument camproj gives the current projection Camera roll around view direction Syntax camroll dalpha Description camroll dalpha rotates the up vector by angle dalpha around the vector from view position to target dalpha is given in radians A positive value makes the scene rotate counterclockwise See also candotly CamvVa CamZOOm camtarget Target position Syntax camtarget p camtarget auto camtarget manual p camtarget LME Reference 3D graphics 409 Description camtarget p sets the target to p p is a 3D vector camtarget auto sets the target to automatic mode so that it fol lows the center of the objects which are drawn camtarget manual sets the target to manual mode With an output argument camtarget gives the current target See also candolly camorbit Ccamzoom camup Up vector Syntax camup p camup auto camup manual p camup Description camup p sets the up vector to p p is a 3D vector camup auto sets the up vector to 0 0 1 camup manual does nothing With an output argument camup gives the current up vecto
14. d 2f 3E g n 1 3 pi 1 2 00 3 000E0 3 1416 22 Caveat Same limitations as sprintf See also fread Raw input Syntax a count a count a count fread fd fread fd size fread fd size precision Description fread fd reads signed bytes from the file descriptor fd until it reaches the end of file It returns a column vector whose elements are signed bytes between 128 and 127 and optionally in the second output argument the number of bytes it has read fread fd size reads the number of bytes specified by size If Size is a scalar that many bytes are read and result in a column vector If size is a vector of two elements m n mxn elements are read row by row and stored in an m by n matrix If the end of the file is reached before the specified number of elements have been read the number of rows is reduced without throwing an error The optional second output argument always gives the number of elements in the result 360 LMEPPC User Manual 1999 2008 Calerga Sarl With a third argument fread fd size precision reads inte ger words of 1 2 or 4 bytes or IEEE floating point numbers of 4 bytes single precision or 8 bytes double precision The meaning of the string precision is described in the table below precision meaning int8 signed 8 bit integer 128 lt x lt 127 char signed 8 bit integer 128 lt x lt 127 int16 signed 16 bit integer 32768 lt x lt 32767 int32
15. dard remote procedure calls using XML RPC and SOAP Hardware support Serial port Windows Mac Unix Communication with the se rial port I2C bus Linux Communication with devices on an I2C bus Joystick Windows Mac OS X Linux Support for reading the state of a joystick or other similar device Audio playback Windows Mac OS X Linux Audio output Serial port 457 Audio recording Windows Mac OS X Linux Audio input Speech Windows Mac Speech output Image Capture Mac OS X Support for getting images from dig ital cameras 4 1 Serial Port Functions Serial port functions enable communication with devices connected to the computer via an RS 232 interface Such devices include modems printers and many scientific instruments The operating system can also emulate RS 232 connections with other devices such as built in modems or USB Universal Serial Bus devices Functions described in this section include only those required for opening and configuring the connection They correspond to fopen for files Input output and control are done with the following generic functions Function Description fclose close the file fflush flush I O buffers fgetl read a line fgets read a line fprintf write formatted data fread read data fscanf read formatted data fwrite write data redirect redirect output Functions opendevice devicename closedevice and flushdevice are obsolete and may be removed in the f
16. profile fun profile report profile done profile function fun 84 LMEPPC User Manual 1999 2008 Calerga Sarl profile off profile on profile reset profile report format Description The purpose of the profiler is to measure the amount of time spent executing each line of code of a function This helps in evaluating where effort should be put in order to optimize the code With LME a single function can be profiled at any given time Command profile manages all aspects related to profiling from specifying which func tion is to be profiled to displaying the results and resuming normal operations The time measured for each line includes time spent executing sub functions called from that line Only the cumulative times are col lected lines of code in loops are likely to have a larger impact on the overall execution time The profile accuracy is limited mainly by two factors The resolution of the timer which is typically between 1e 9 and le 6 second This has obviously a larger effect on lines executed quickly Lines which contain scalar assignments or statements like if and for may completely escape from the timing The time overhead to perform the timing and add the data Here again its effect is more dramatic with fast lines To profile a function one usually proceeds in four steps Setup profile fun sets up profiling for function fun Room in memory is allocated and initialized for collecting the cumu
17. serial 599 Description serialdevopen portname opens a connection to the serial port whose name is portname and returns a file descriptor fd Names depend on the operating system and can be obtained with serialdevname Some platforms do not provide a complete list of all ports serialdevopen may accept additional device names and pass them directly to the corresponding function of the operating system The second argument of serialdevopen portname options isa structure which contains configuration settings It is set with serialdevset Once a connection has been opened the file descriptor fd can be used with functions such as fread fwrite fscanf and fprintf The connection is closed with fclose Example fd serialdevopen serialdevname 1 serialdevset BPS 19200 TextMode true Timeout 2 fprintf fd L d 2 n 1 reply fgetl fd fclose fd See also fclose serialdevname serialdevset fflush fscanf fgetli fgets fprintt serialdevset Configuration settings for serial port Syntax options serialdevset options serialdevset namel valuel options serialdevset options0O namel valuel Description serialdevset namel valuel creates the option argument used by serialdevopen Options are specified with name value pairs where the name is a string which must match exactly the names in the table below Case is significant Options which are not specified have a
18. ti end jlti subsasgn lti subsre Iti c2d Conversion from continuous time to discrete time Syntax se lti c2d a Ts c2d a Ts method u b b Description c2d a Ts converts the continuous time system a to a discrete time system with sampling period Ts c2d a Ts method uses the specified conversion method method is one of the methods supported by c2dm See also Iti connect Arbitrary feedback connections Syntax use lti b connect a links in out Libraries lti 525 Description connect a lLinks in out modifies lti object a by connecting some of the outputs to some of the inputs and by keeping some of the inputs and some of the outputs Connections are specified by the rows of matrix Link In each row the first element is the index of the system input where the connection ends other elements are indices to system outputs which are summed The sign of the indices to outputs gives the sign of the unit weight in the sum Zeros are ignored Arguments in and out specify which input and output to keep See also lti feedback Iti d2c Conversion from discrete time to continuous time Syntax use lti b d2c a b d2c a method Description d2c a converts the discrete time system a to a continuous time sys tem d2c a method uses the specified conversion method method is one of the methods supported by d2cm See also Uti c2d Iti end Last index Syntax us
19. 1 2 3 4 dbodemag numd dend Ts w opt dbodemag Ad Bd Cd Dd Ts dbodemag Ad Bd Cd Dd Ts w dbodemag Ad Bd Cd Dd Ts opt Seema a Bd Cd Dd Ts w opt dbodemag style dbodemag style id mag w dbodemag Description dbodemag numd dend Ts plots the magnitude of the frequency re sponse of the discrete time transfer function numd dend with sampling period Ts The range of frequencies is selected automatically or can be specified in an optional argument w a vector of frequencies Further options can be provided in a structure opt created with responseset field Range is utilized The optional arguments style and id have their usual meaning dbodemag Ad Bd Cd Dd Ts plots the magnitude of the frequency response Y jw UGw of the discrete time state space model Ad Bd Cd Dd defined as ZX zZ AgX z BgU z Y z CgX z DgU z LME Reference graphics for dynamical systems 423 where z e 7s With output arguments dbodemag gives the magnitude and the fre quency as column vectors No display is produced Example dbodemag 1 poly 0 9 0 7 0 6 0 7 0 6j 1 See also dbodephase Phase Bode diagram for a discrete time system Syntax dbodephase numd dend Ts dbodephase numd dend Ts w dbodephase numd dend Ts opt dbodephase numd dend Ts w opt dbodephase Ad Bd Cd Dd Ts dbodephase Ad Bd Cd Dd Ts w dbodephase Ad Bd Cd Dd Ts opt dbodephase Ad
20. 3 5x 2 1 See also polynom polynom ratfun disp Display a ratfun object Syntax use classes disp a Description disp a displays rational function a It is also executed implicitly when LME displays the ratfun result of an expression which does not end with a semicolon See also ratfun ratfun disp ratfun num Get the numerator of a ratfun as a vector of coefficients Syntax use classes coef num a 498 LMEPPC User Manual 1999 2008 Calerga Sarl Description num a gets the numerator of a as a row vector of descending power coefficients See also ratfun ratfun ratfun den Get the denominator of a ratfun as a vector of coefficients Syntax use classes coef den a Description den a gets the denominator of a as a row vector of descending power coefficients See also ratfun num ratfun ratfun ratfun diff Ratfun derivative Syntax use classes diff a Description diff a differentiates ratfun a Libraries classes 499 Example use classes r ratfun 1 3 0 1 2 5 q diff r 4x 3 21x 2 30x 2 4x 2 20x 25 a See also ratfun ratfun ratfun inline Conversion from ratfun to inline function Syntax use classes fun inline a Description inline a converts ratfun a to an inline function which can then be used with functions such as feval and ode45 See also ratfun ratfun ratfun feval ratfun feval Evalua
21. Access to any kind of file can be useful to analyze data which come from other applications such as experimental data and to generate results in a form suitable for other applications such as source code or HTML files Functions specific to files are described in this sec tion Input output and control are done with the following generic functions Function Description fclose close the file feof check end of file status fflush flush I O buffers fgetl read a line fgets read a line fprintf write formatted data fread read data fscanf read formatted data fseek change the current I O position ftell get the current I O position fwrite write data redirect redirect output fopen Open a file Syntax fd fd fopen path fopen path mode 370 LMEPPC User Manual 1999 2008 Calerga Sarl Description fopen opens a file for reading and or writing The first argument is a path whose format depends on the platform If it is a plain file name the file is located in the current directory what current means also depends on the operating system The output argument a real num ber is a file descriptor which can be used by many input output func tions such as fread fprintf or dumpvar The optional second input argument a string of one or two charac ters specifies the mode It can take one of the following values Mode Meaning none sameas r r r read only binary mode seek to beginning w rea
22. And you can develop yours in C It even supports multithreading But as a technology preview on the way to something more finished it has not received its own product name 8 LMEPPC User Manual 1999 2008 Calerga Sarl 1 1 LME Installation LME for Pocket PC is provided as a cab file One way to install it is to download it to your Pocket PC device to locate it in the File Explorer and to open it LME and all its support files are installed in Program Files Calerga with a shortcut to the application in the Programs folder At startup LME loads extensions in the subdirectory LMEExt exe cutes the contents of Imestartup txt if it exists and restores the his tory of past commands from the file Imehistory txt All these directo ries and files must be located in the same directory as LME exe All of them are optional Imehistory txt is created when LME exits if it does not exist LME comes with libraries files ending with the double suffix Iml txt which add useful functions in different domains such as statistics physical constants signal processing or control LME will find them only if they are in one of the directories enumerated in the Options When you run LME for the first time you should check in menu Tools gt Options that the Paths of Libraries include Program Files Calerga Lib 1 2 User interface When launched LME presents a basic user interface with the following elements Command input The text field at the
23. Flag Meaning left alignment default is right alignment display of a sign for positive numbers 0 zero padding instead of spaces alternate format see below space sign replaced with space for positive numbers n is the optional width of the field as one or more decimal digits default is the minimum width to display the data d is the number of digits after the decimal separator for a number displayed with a fractional part the minimum number of displayed digits for a number displayed as an integer or the number of characters for a string one or more decimal digits by default it is 4 for a number or the length of the string for a string and t is a single character denoting the type of conversion In most cases each control sequence corresponds to an LME Reference input output 365 additional argument All elements of arrays are used sequentially as if they were provided separately strings are used as a whole The table below gives the valid values of t A gt go Conversion single decimal number as an integer same as d hexadecimal number for integers between 0 and 2732 1 same as x with uppercase digits octal number for integers between 0 and 2 32 1 fixed number of decimals exp notation if abs x gt 1e18 same as f with an uppercase E scientific notation such as 1e5 scientific notation such as 1E5 engineering notation such as 100e3 engineering notation such as 100E3 decimal or scien
24. If ais of type double so is the result and n is limited to 32 Examples bitset 123 10 635 bitset 123 1 0 122 bitset 7uint8 1 8 1x8 uint8 array 7 7 7 15 23 39 71 135 See also bitshift Bit shift Syntax b bitshift a shift b bitshift a shift n Description The first input argument is converted to a 32 bit unsigned integer and shifted by shift bits to the left if shift is positive or to the right if it is negative With a third argument n only n bits are retained The inputs can be scalar arrays of the same size or a mix of both Examples bitshift 1 3 8 bitshift 8 2 2 2 4 8 16 32 LME Reference logical functions 341 bitshift 15 0 3 4 15 14 12 8 See also bitxor Bitwise exclusive OR Syntax c bitxor a b Description The input arguments are converted to 32 bit unsigned integers each bit of the result is the binary exclusive OR of the corresponding bits of the inputs The inputs can be scalar arrays of the same size or a scalar and an array Examples bitxor 1 3 2 bitxor 1 6 1 032547 bitxor 7uint8 1234int16 1237int16 See also false Boolean constant false Syntax b false B false n B false nl n2 B false nl n2 342 LMEPPC User Manual 1999 2008 Calerga Sarl Description The boolean constant false can be used to set the value of a variable It is equivalent to Logical 0 The constant 0 is equivalent
25. M1 M2 calculates M1 to the M2 power element wise Both arguments must have the same size unless one of them is a scalar power x y is equivalent to x y It can be used to redefine this operator for objects Examples 1 2 3 4 2 1 4 9 16 1 2 3 5 4 3 1 16 27 See also LME Reference operators 129 Operator Complex conjugate transpose Syntax M ctranspose M Description M is the transpose of the real matrix M i e columns and rows are per muted If Mis complex the result is the complex conjugate transpose of M If Mis an array with multiple dimensions the first two dimensions are permuted ctranspose M is equivalent to M It can be used to redefine this operator for objects Examples 1 2 3 4 1 3 24 1 2j 3 4j 1 2j 3 4j See also operator conj Operator Transpose Syntax M transpose M Description M is the transpose of the matrix M i e columns and rows are per muted M can be real or complex If Mis an array with multiple dimen sions the first two dimensions are permuted 130 LMEPPC User Manual 1999 2008 Calerga Sarl transpose M is equivalent to M It can be used to redefine this operator for objects Example 1 2 3 4 13 24 1 2j 3 4j 1 2j 3 4j See also Operator Equality Syntax xX y eq x y Description x y is true if x is equal to y and false otherwise Comp
26. See also lyap Continuous time Lyapunov equation LME Reference linear algebra 221 Syntax lyap A B C lyap A C Description lyap A B C calculates the solution X of the following continuous time Lyapunov equation AX XB C 0 All matrices are real With two input arguments lyap A C solves the following Lya punov equation AX XA C 0 Example 3 1 2 1 3 5 6 2 1 2 7 8 3 2 1 4 5 8 9 lyap A B C 0 1635 0 1244 0 2628 0 1311 0 7797 0 7645 A B C X XIN See also dlyap max Maximum value of a vector or of two arguments Syntax x max v v ind max v v As dim v ind max M dim M3 kr 1 M2 222 LMEPPC User Manual 1999 2008 Calerga Sarl Description max v returns the largest number of vector v NaN s are ignored The optional second output argument is the index of the maximum in v if several elements have the same maximum value only the first one is obtained The argument type can be double single or integer of any size max M operates on the columns of the matrix M and returns a row vector max M dim operates along dimension dim 1 for columns 2 for rows max M1 M2 returns a matrix whose elements are the maximum between the corresponding elements of the matrices M1 and M2 M1 and M2 must have the same size or be a scalar which can be compared against any matrix Examples mx ix max 1 3 2 5 8 7 mx 8 ix 5 max
27. Sign a gets the sign of bitfield a The result is 1 if the most significant bit of a is 1 0 if all bits of a are 0 or 1 otherwise Example use bitfield a bitfield 5 3 a 0b101 sign a 1 See also bitfield uint8 bitfield uint16 bitfield uint32 Convert a bitfield object to an unsigned integer number Libraries filter 509 Syntax use bitfield n uint8 a n uint16 a n uint32 a Description uint8 a uint16 a and uint32 a convert bitfield a to a uint8 uint16 or uint32 number respectively If a has more bits than the target integer most significant bits are ignored Example use bitfield a bitfield 1234 16 uint8 a 210 See also t uint32 bitfield int8 bitfield intl6 bitfield int32 bitfield double bitfield bitfield Cc H ee 5 6 filter filter is a library which adds to LME functions for designing analog continuous time and digital discrete time linear filters The following statement makes available functions defined in filter use filter This library provides three kinds of functions besselap buttap cheblap cheb2ap and ellipap which com pute the zeros poles and gain of the prototype of analog low pass filter with a cutoff frequency of 1 rad s They correspond respec tively to Bessel Butterworth Chebyshev type 1 Chebyshev type 2 and elliptic filters besself butter chebyl cheby2 and ellip which provide a hig
28. Syntax b bitget a n Description bitget a n gives the n th bit of integer a a can be an integer or a double The result has the same type as a n 1 corresponds to the least significant bit The inputs can be scalar arrays of the same size or a scalar and an array If a is of type double so is the result and n is limited to 32 Examples bitget 123 5 1 bitget 7 1 8 11100000 LME Reference logical functions 339 bitget 5uint8 2 Ouint8 See also bitset bitand bitor Bitwise OR Syntax c bitor a b Description The input arguments are converted to 32 bit unsigned integers each bit of the result is the binary OR of the corresponding bits of the inputs The inputs can be scalar arrays of the same size or a scalar and an array If the input arguments are of type double so is the result and the operation is performed on 32 bits Examples bitor 1 2 3 bitor 1 6 1 133557 bitor 7uint8 1234int16 1239int16 See also bitset Bit assignment Syntax b b bitset a n bitset a n v 340 LMEPPC User Manual 1999 2008 Calerga Sarl Description bitset a n sets the n th bit of integer a to 1 a can be an integer or a double The result has the same type as a n 1 corresponds to the least significant bit With 3 input arguments bitset a n v sets the bit to 1 if v is nonzero or clears it if v is zero The inputs can be scalar arrays of the same size or a mix of them
29. abs Absolute value Syntax x abs z Description abs takes the absolute value of each element of its argument The result is an array of the same size as the argument each element is non negative Example abs 2 3 0 3 4j 2305 See also acos Arc cosine Syntax y acos x Description acos x gives the arc cosine of x which is complex if x is complex or if abs x gt 1 LME Reference mathematical functions 145 Examples acos 2 0 1 3170j acos 1 2j 1 5708 1 1437 1 5286j See also acosh Inverse hyperbolic cosine Syntax y acosh x Description acosh x gives the inverse hyperbolic cosine of x which is complex if x is complex or if x lt 1 Examples acosh 2 1 3170 acosh 0 1 2j 0 1 5708j 1 5286 1 1437j See also cosh jasinh acos acot Inverse cotangent Syntax y acot x Description acot x gives the inverse cotangent of x which is complex if x is 146 LMEPPC User Manual 1999 2008 Calerga Sarl See also acoth Inverse hyperbolic cotangent Syntax y acoth x Description acoth x gives the inverse hyperbolic cotangent of x which is complex if x is complex or is in the range 1 1 See also coth acot acsc Inverse cosecant Syntax y acsc x Description acsc x gives the inverse cosecant of x which is complex if x is com plex or is in the range 1 1 See also acsch Inverse hyperbolic cosecant Syntax
30. both the x and y are fixed The values returned by scale reflect the zoom chosen by the user They can be used to limit the computation of data displayed by plot to the visible area LME Reference base graphics 401 Examples Here are some suggestions for the most usual graphics Time response default linlin is fine Bode mag scale logdb Bode phase scale loglin D bode mag scale lindb logdb 0 pi Ts D bode phase scale Linlin loglin 0 pi Ts Poles scale equal D poles scale equal 1 1 1 1 Nyquist scale equal 1 5 1 5 1 5 1 5 Nichols scale lindb Use of scale to display a sine in the visible x range scale 0 10 sc scale xmin sc 1 xmax sc 2 x xmin xmax xmin 0 0 01 1 101 values between xmin and xmax default x range between 0 and 10 maybe changed by the user 1x2 or 1x4 y sin x plot x y See also plotoption scalefactor Change the scale displayed in axis ticks and labels Syntax scalefactor f f scalefactor Description scalefactor f sets the factor used to display the ticks and the la bels Its argument f can be a vector of two real positive numbers to set separately the x axis and the y axis or a real positive scalar to set the same factor for both axis The normal factor value is 1 so that the ticks correspond to the graphical contents With a different factor the contents are displayed with the same scaling bu
31. char sl1 s2 concatenates vertically the arrays given as ar guments to produce a string matrix If the strings do not have the same number of columns blanks are added to the right LME Reference strings 301 Examples char 65 70 ABCDEF char 65 66 67 68 ABCD char ab cde ab cde char abc de fg abc de fg See also deblank Remove trailing blank characters from a string Syntax s2 deblank s1 Description deblank s1 removes the trailing blank characters from string s1 Blank characters are spaces code 32 tabulators code 9 carriage returns code 13 line feeds code 10 and null characters code 0 Example double tAB CD r n 0 32 9 65 66 32 32 67 68 13 10 0 double deblank tAB CD n r 0 32 9 65 66 32 32 67 68 See also findstr Find a substring in a string 302 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax pos findstr str sub Description findstr str sub finds occurrences of string sub in string str and returns a vector of the positions of all occurrences or the empty vector if there is none Occurrences may overlap Examples findstr ababcdbaaab ab 13 10 findstr ababcdbaaab ac findstr aaaaaa aaa 123 See also ischar Test for a string object Syntax b ischar obj Description ischar obj is true if the object obj is a character string fa
32. dbstack s dbstack dbstack all s dbstack all Description dbstack displays the chain of function calls which lead to the current execution point with the line number where the call to the subfunction is made It can be executed in a function or from the command line interface when execution is suspended with a breakpoint or dbhalt dbstack all or dbstack all displays the whole stack of function calls For instance if two executions are successively suspended at breakpoints dbstack displays only the second chain of function calls while dbstack all displays all functions With an output argument dbstack returns the result in a list of structures Each structure contains the function name or class and method names in field name and the line number in field Line Note that you cannot assign the result of dbstack to a new variable in sus pended mode Examples use stdlib dbstop primes isprime 113 lt primes 164 gt p ones 1 n dbstack stdlib primes 164 stdlib isprime 157 dumpvar stack dbstack stack struct name stdlib primes Line 164 struct name stdlib isprime Line 157 See also dbstop dbhalt LME Reference debugging commands 79 dbstatus Display list of breakpoints Syntax dbstatus dbstatus fun Description dbstatus displays the list of all breakpoints dbstatus fun displays the list of breakpoints in function fun See al
33. its elements bytes 16 bit words or 32 bit words can be accessed like a normal array thanks to virtual memory These functions are available only on Unix or Unix like systems such as Mac OS X mmap Map a file in memory 560 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax m mmap filename n m mmap filename n type m mmap filename n type perm m mmap filename n type perm offset Description mmap filename n maps in memory the n first bytes of file whose name is given by string filename It returns an object which can be used to read bytes with regular array indexing with the first byte at offset 0 The file is created if necessary mmap filename n type specifies the type of the elements type is one of the strings in the table below Type Range Description uint8 0 255 unsigned byte char char 0 char 255 character uint16 0O 65535 unsigned 16 bit word uint32 0O 4294967295 unsigned 32 bit word int8 128 127 signed byte int16 32768 32767 signed 16 bit word int32 2147483648 2147483647 signed 32 bit word By default multibyte words are encoded with the least significant byte first little endian The characters b can be appended to spec ify that they are encoded with the most significant byte first big en dian for symmetry U is accepted and ignored mmap filename n type perm specifies permission with string perm which takes one of th
34. mod moment 224 mpower mrdivide mtimes 114 munmap 561 nan 182 nancorrcoef 483 nancov 484 nanmean 485 nanmedian 485 nanstd 486 nansum 487 nargin 102 nargout 103 nchoosek 183 ndgrid 255 ndims 255 ne 114 ngrid 441 nichols 442 nnz 256 norm 225 not 114 null 225 num2cell 2 num2List 326 number nume 2 nyquist 443 Udi NI i Fai object ode23 2 ode45 2 Index odeset 289 ones operator amp 137 mmr Q Z20g py a p f OLN ea ra ee a ee He NPNIRINTRIN A SLANINE uy 0 E AN I gt pm ee NJ u Hl Golf NI coll Gal BSI u Uo Aolo ee EOT PI A Ha efek pa NINI ing w f ea m far a NL Oe F N n UJ F O UJ m m D O I i ais N 2 optimset 297 or 114 orderfields B29 orth 226 otherwise 68 permute 258 persistent pi 18 pinv plot plot3 plotoption plotpoly plotroots 444 plus 114 quaternion Quaternions quiver B97 rand 259 randn 260 range rare OT rdivide 114 real 185 611 612 LMEPPC User Manual 1999 2008 Calerga Sarl reallog 1 realmax 1 realmin 186 realpow Bue realegre ey ren eq rem 187 responseset 445 rethrow 104 return 71 rlocus 447 rmfield roots 233 rot90 262 round rpy2q sandbox sandboxtrust scale 398 scale of r
35. or be a scalar which can be compared against any matrix Examples mx ix min 1 3 2 5 8 7 mx 1 ix 1 min 1 3 5 nan 2 1 5 min 1 3 5 nan 2 12 22 See also max moment Central moment of a set of values Syntax m moment A order m moment A order dim Description moment A order gives the central moment moment about the mean of the specified order of the columns of array A or of the row vector A The dimension along which moment proceeds may be specified with a third argument Example moment randn 1 10000 3 3 011 See also LME Reference linear algebra 225 norm Norm of a vector or matrix Syntax x norm v x norm v kind x norm M x norm M kind Description With one argument norm calculates the 2 norm of a vector or the induced 2 norm of a matrix The optional second argument specifies the kind of norm Kind Vector Matrix none or2 sqrt sum abs v 2 largest singular value induced 2 norm 1 sum abs V largest column sum of abs inf or inf max abs v largest row sum of abs inf min abs v largest row sum of abs p sum abs V p 1 p invalid fro sqrt sum abs v 2 sqrt sum diag M M Examples norm 3 4 5 norm 2 5 9 3 10 2194 norm 2 5 9 3 1 11 See also null Null space Syntax Z null A 226 LMEPPC User Manual 1999 2008 Calerga Sarl Description null A returns a matrix Z whose columns are an
36. position ftell fd Description ftell fd gives the current file position associated with file descriptor fd The file position is the offset with respect to the beginning of the file at which the next input function will read or the next output function will write The offset is expressed in bytes With text files ftell may not always correspond to the number of characters read or written See also fseek feof fwrite Raw output Syntax write fd data write fd data precision coun coun t f t f Description fwrite fd data writes the contents of the matrix data to the out put referenced by the file descriptor fd The third parameter is the precision whose meaning is the same as for fread Its default value is 7uint8 See also Tread LME Reference input output 363 redirect Redirect or copy standard output or error to another file descriptor Syntax redirect fd fdTarget redirect fd fdTarget copy redirect fd R redirect fd redirect R redirect Description redirect fd fdTarget redirects output from file descriptor fd to fdTarget fd must be 1 for standard output or 2 for standard error If fdTarget fd the normal behavior is restored redirect fd fdTarget copy copies output to both fd and fdTarget if copy is true instead of redirecting it only to fdTarget If copy is false the result is the same as with two input arguments With zero or one input argument and wit
37. the other one a vector is reused for each line Automatic scaling is performed the same way as for cartesian plots after polar coordinates have been converted The figure axis ticks and grids are specific to polar plots Polar plots can be mixed with other graphical commands based on cartesian coordinates such as plot line and circle Example theta 0 0 01 20 pi rho exp 0 1 x theta sin 5 x theta polar theta rho See also plot quiver Quiver plot Syntax quiver x y u V quiver u v quiver scale quiver style 398 LMEPPC User Manual 1999 2008 Calerga Sarl Description quiver x y u V displays vectors u v starting at x y If the four arguments are matrices of the same size an arrow is drawn for each corresponding element If x and y are vectors they are repeated x is transposed to a row vector if necessary and repeated to match the number of rows of u and v and y is transposed to a column vector if necessary and repeated to match their number of columns The absolute size of arrows is scaled with the average step of the grid given by x and y so that they do not overlap if the grid is uniform If x and y are missing their default values are 1 2 m and 1 2 n respectively where m and n are the number of rows and columns of u and v With a 5th or 3rd argument quiver scale multiplies the arrow lengths by the scalar number scale If scale is zero arrows are no
38. ther after the last statement or because of the command return the current value of the output arguments as set by the function s state ments is given back to the caller All variables used in the function s statements are local their value is undefined before the first assign ment and it is illegal to use them in an expression and is not shared with variables in other functions or with recursive calls of the same LME Reference programming constructs 65 function Different kinds of variables can be declared explicitly with global and persistent When multiple functions are defined in the same code source for instance in a library the body of a function spans from its header to the next function or until the endfunction keyword whichever comes first Function definitions cannot be nested endfunction is required only when the function definition is followed by code to be executed outside the scope of any function This includes mixed code and function definitions entered in one large entry in a command line interface or applications where code is mainly provided as state ments but where function definitions can help and separate libraries are not wished note that libraries cannot contain code outside func tion definitions they do never require endfunction Like function endfunction must be the first element of a line Not all of the input and output arguments are necessarily used The caller fixes the number of inpu
39. w et t tdt 0 152 LMEPPC User Manual 1999 2008 Calerga Sarl Example betainc 0 2 1 2 0 36 See also betaln Logarithm of beta function Syntax y betaln z w Description betaln z w gives the logarithm of the beta function of z and w Ar guments and result are real imaginary part is discarded Example betaln 0 5 2 0 2877 See also ganmatn cast Type conversion Syntax Y cast X type LME Reference mathematical functions 153 Description cast X type converts the numeric array X to the type given by string type which can be double single int8 or any other signed or unsigned integer type char or logical The number value is preserved when possible conversion to integer types discards most significant bytes If X is an array conversion is performed on each element the result has the same size The imaginary part if any is discarded only with conversions to integer types Example cast pi int8 3int8 See also uint8 and related functions cdf Cumulative distribution function Syntax y cdf distribution x y cdf distribution x al y cdf distribution x al a2 Description cdf distribution x calculates the integral of a probability density function from oo to x The distribution is specified with the first argu ment a string case is ignored t and T are equivalent Additional arguments m
40. were passed by the caller to avoid accessing the undefined variables Note that if you want to have an optional argument before the end of the list you have to interpret the meaning of the variables yourself LME always sets the nargin first arguments There are two other ways to let a function accept a variable num ber of input arguments to define default values directly in the func tion header or to call varargin to collect some or all of the input arguments in a list LME Reference miscellaneous functions 103 With one argument nargin fun returns the maximum number of input arguments a function accepts fun may be the name of a built in or user function a function reference or an inline function Func tions with a variable number of input arguments such as fprintf give 1 Examples A function with a default value pi for its second argument function x multiplyByScalar a k if nargin lt 2 multiplyByScalar x k pi same as multiplyByScalar x pi end x kxta A function with a default value standard output for its first argument Note how you have to interpret the arguments function fprintstars fd n if nargin fprintstars n to standard output fprintf repmat 1 fd n is actually stored in fd else fprintf fd repmat 1 n end Number of input arguments of function plus usually written nargin plus 2 See also nargout varargin function nargout
41. z p k lp2hp z0 pO kO w0 num den lp2hp num0 den0 w0 Description lp2hp convert a lowpass analog filter prototype with unit angular fre quency to a highpass analog filter with the specified cutoff angular frequency w0 lp2hp z0 p0 k0 w0 converts a filter given by its ze ros poles and gain lp2hp num0 den0 w0 converts a filter given by its numerator and denominator coefficients in decreasing powers of s The new filter F s is 1 F s Fo _ Wos where Fo s is the filter prototype Libraries lti 519 See also Ip2ip Lowpass prototype to lowpass filter conversion Syntax use filter z p k lp2lp z0 pO kO w0 num den lp2lp num0 den0 w0 Description lp2lp convert a lowpass analog filter prototype with unit angular fre quency to a lowpass analog filter with the specified cutoff angular frequency w0 Lp2lp z0 p0 k0 w0 converts a filter given by its ze ros poles and gain Lp2lp num0 den w0 converts a filter given by its numerator and denominator coefficients in decreasing powers of s The new filter F s is S F s Fo gt Wo where Fo s is the filter prototype See also Up2hp lp2bp lp2bs 5 7 Iti Library lti defines methods related to objects which represent linear time invariant dynamical systems LTI systems may be used to model many different systems electro mechanical devices robots chemical processes filters etc LTI systems map one or more
42. 1 The empty array is a special case Since horzcat and vertcat also accept cell arrays brackets can be used to concatenate cell arrays too Examples 1 2 3 5 C1 1 2 C2 ab false C1 C2 2x2 cell array Compare this with the effect of braces where elements are not con catenated but used as cells C1 C2 1x2 cell array LME Reference operators 119 See also Operator Braces Syntax list_elements cells v index v indexl index2 v index expr fun v i Description A pair of braces is used to define a list or a cell array given by its elements In a list the operator is used to separate elements In a cell array the operator is used to separate cells on the same row the operator is used to separate rows Braces without semicolons produce a list braces with semicolon s produce a cell array v index is the element of list variable v whose index is given index must be an integer between 1 for the first element and length v for the last element v index may be used in an expression to extract an element or on the left hand side of the equal sign to assign a new value to an element Unless it is the target of an assignment v may also be the result of an expression If v is a cell array v index is the element number index v index1 index2 gives the specified cell of a cell array v itself may be an element or a field in a larger var
43. 1 1 1 1 1 valid 45 See also conv LME Reference linear algebra 201 cov Covariance Syntax M M M cov data cov data 0 cov data 1 Description cov data returns the best unbiased estimate m by m covariance ma trix of the n by m matrix data for a normal distribution Each row of data is an observation where n quantities were measured The co variance matrix is real and symmetric even if data is complex The diagonal is the variance of each column of data cov data Q is the same as cov data cov data 1 returns the m by m covariance matrix of the n by m matrix data which contains the whole population Example cov 1 2 2 4 3 5 11 5 1 5 2 3333 See also cross Cross product Syntax v3 v3 cross vl v2 cross vl v2 dim Description cross vl v2 gives the cross products of vectors v1 and v2 v1 and v2 must be row or columns vectors of three components or arrays of 202 LMEPPC User Manual 1999 2008 Calerga Sarl the same size containing several such vectors When there is ambi guity a third argument dim may be used to specify the dimension of vectors 1 for column vectors 2 for row vectors and so on Examples cross 1 2 3 0 0 1 2 1 0 cross 1 2 3 7 1 3 4 0 0 0 2 0 2 0 12 8 6 0 14 See also cumprod Cumulative products Syntax M2 cumprod M1 M2 cumprod M1 dim Description cumprod M1 returns a matrix M2 of the s
44. 159 cea ellip ellipam 608 endfunction 64 eps 163 eq erf erfc erfinv 165 erlocus 432 error eval 92 exist 92 factor 46 factorial 167 false 341 fclose 355 feof 355 feval fevalx 94 ff Lush 356 fft 209 fft2 210 fftn 210 fftshift 468 fgetl fgets fieldnames 327 filled shape filter filter2 468 find 244 findstr 301 fix flipdim fliplr LMEPPC User Manual 1999 2008 Calerga S rl flipud floor fminbnd 283 fminsearch 284 fontset B86 fopen 369 for format 357 fplot fprintf fread fscanf 360 fseek 361 ftell fun2str 94 function inline reference function 64 funm 212 fwrite 362 fzero 286 gamma 168 gammainc 169 gamma ln 169 gcd 170 geomean ao getfield 327 oS aoe gethostname 5 global 55 golden Te Graphic ID graycode 3 grid 379 griddata 2 griddatan gt 114 hankel 469 harmmean 482 hess 215 hgrid hist 469 Index horzcat 114 hstep hypot i 172 icdf 172 if 60 ifft 213 ifft2 214 ifftn 214 ifftshift 470 igraycode 343 imag image 388 imageread 564 include includeifexists 68 ind2sub 247 inf 174 inflate 563 info 95 initial 437 inline inmenm int16 2 int32 2 int64 int8 279 ee ay intersect 249 intmax 280 intmin 281
45. 19 Integer Functions uint8 uint16 uint32 uint64 int8 int16 int32 int64 Conversion to integer types 280 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax uint8 A uint16 A v vuv uvu wW tou ow id te ud 1 Description The functions convert a number or an array to unsigned or signed integers The name contains the size of the integer in bits To avoid a conversion from double to integer constant literal num bers should be written with a type suffix such as 12int32 This is the only way to specify large 64 bit numbers because double precision floating point numbers have a mantissa of 56 bits uint64 and int64 are not supported on platforms with tight mem ory constraints Examples uint8 3 3uint8 3uint8 3uint8 uint8 50 50 400 1x8 uint8 array 50 100 150 200 250 44 94 144 int8 50 50 400 1x8 int8 array 50 100 106 56 6 44 94 112 See also intmax Largest integer Syntax intmax intmax type i i LME Reference integers 281 Description Without input argument intmax gives the largest signed 32 bit inte ger intmax type gives the largest integer of the type specified by string type which can be uint8 uint16 uint32 uint64 int8 int16 int32 or int64 64 bit integers are not sup ported on all platforms The result has the corresponding integer type Examples intmax 2147483647int32 intmax uint16 65535uint
46. 2 5 and displays its value for x between 0 and 10 Examples Plot a sine fplot sin Plot x 0 3 a exp 3x in red for x 2 3 with a 7 2 and an identifier of 1 fun inline function y f x a y x 0 7 3 2 axexp 3 x 2 fplot fun 2 3 F L 2 See also image Raster RGB or grayscale image Syntax image gray image red green blue image rgb LME Reference base graphics 389 image xmin xmax ymin ymax image style image id Description image displays a raster image an image defined by a rectangular ar ray of patches of colors called pixels The raster image can be either grayscale or color A grayscale image is defined by a double matrix of pixel values in the range O black to 1 white or by a uint8 ma trix in the range 0 black to 255 white A color image is defined by three matrices of equal size corresponding to the red green and blue components or by an array with three planes along the 3rd dimen sion Each component is defined between 0 black to 1 maximum intensity with double values or between 0 black to 255 maximum intensity with uint8 values The position is defined by the the minimum and maximum coordi nates along the horizontal and vertical axis The raster image is scaled to fit The first line of the matrix or matrices is displayed at the top If style is e the raster image is scaled down such
47. 2 for its rows and so on fft f dim specifies the dimension without resizing the array fft is based on a mixed radix Fast Fourier Transform if the data length is non prime It can be very slow if the data length has large prime factors or is a prime number The coefficients of the DFT are given from the zero frequency to the largest frequency one point less than the inverse of the sampling 210 LMEPPC User Manual 1999 2008 Calerga Sarl period If the input f is real its DFT has symmetries and the first half contain all the relevant information Examples fft 1 4 10 2 2j 2 2 2j fft 1 4 3 6 1 5 0 866j 1 5 0 866j See also fft2 2 d Fast Fourier Transform Syntax F fft2 f F fft2 f size F fft2 f nr nc F fft2 f n Description fft2 f returns the 2 d Discrete Fourier Transform DFT along dimen sions 1 and 2 of array f With two or three input arguments fft2 resizes the two first dimen sions by cropping or by padding with zeros fft2 f nr nc resizes first dimension to nr rows and second dimension to nc columns In fft2 f size the new size is given as a two element vector nr nc fft2 F n is equivalent to fft2 F n n If the first argument is an array with more than two dimensions fft2 performs the 2 d DFT along dimensions 1 and 2 separately for each plane along remaining dimensions fftn performs an DFT along each dimension See also ifft2 fft FF tn fftn n dimension Fast Fourie
48. 493 Syntax use classes coef double a Description double a converts polynomial a to a row vector of descending power coefficients Example use classes p polynom 3 0 1 4 2 double p 301 42 See also polynom polynom polynom subst Substitute the variable of a polynom object with another polynomial Syntax use classes subst a b Description subst a b substitutes the variable of polynom a with polynom b Example use classes p polynom 1 2 3 p X 24 3x 9 q polynom 2 0 2x r subst p q 4x 2 6x 9 494 LMEPPC User Manual 1999 2008 Calerga Sarl See also polynom polynom polynom feval polynom diff Polynom derivative Syntax use classes dif f a Description diff a differentiates polynomial a Example use classes p polynom 3 0 1 4 2 q diff p 12x 3 2x 4 See also polynom polynom polynom int polynom int Polynom integral Syntax use classes int a Description int a integrates polynomial a Libraries classes 495 Example use classes p polynom 3 0 1 4 2 q int p 0 6x 5 0 3333x 3 2x 2 2x See also polynom polynom polynom diff polynom inline Conversion from polynom object to inline function Syntax use classes fun inline a Description inline a converts polynomial a to an inline function which can then be used with functions such as feval and ode45 Exa
49. Bc Cc Dc w bodemag Ac Bc Cc Dc opt ea Bc Cc Dc w opt bodemag bodemag mag w style style id bodemag Description bodemag numc denc plots the magnitude of the frequency response of the continuous time transfer function numc denc The range of fre quencies is selected automatically or can be specified in an optional argument w a vector of frequencies Further options can be provided in a structure opt created with responseset field Range is utilized The optional arguments style and id have theirjusual meaning bodemag Ac Bc Cc Dc plots the magnitude of the frequency response Y jw U jw of the continuous time state space model Ac Bc Cc Dc defined as jwX jw A X jw B UGw Yw CX jw DCUGwW With output arguments bodemag gives the magnitude and the fre quency as column vectors No display is produced 420 LMEPPC User Manual 1999 2008 Calerga Sarl scale logdb bodemag 1 1 2 3 4 Figure 3 9 scale logdb bodemag 1 1 2 3 4 Examples Green plot for 1 s 2s 3s 4 with s jw see Fig 3 9 bodemag 1 1 2 3 4 g The same plot between w 0 and w 10 scale 0 10 bodemag 1 1 2 3 4 g See also bodephase dbodemag bodephase Phase Bode diagram for a continuous time system Syntax bodephase numc denc bodephase numc denc w bodephase numc denc opt bodephase numc denc w opt bodephase Ac
50. Bd Cd Dd Ts w opt dbodephase style dbodephase style id phase w dbodephase Description dbodemag numd dend Ts plots the phase of the frequency response of the discrete time transfer function numd dend with sampling period Ts The range of frequencies is selected automatically or can be spec ified in an optional argument w a vector of frequencies Further options can be provided in a structure opt created with responseset field Range is utilized The optional arguments style and id have their usual meaning dbodephase Ad Bd Cd Dd Ts plots the phase of the frequency response Y jw UGw of the discrete time state space model Ad Bd Cd Dd defined as ZX z AgX z BgU z Y z CgX z DaU z 424 LMEPPC User Manual 1999 2008 Calerga Sarl where z e 7s With output arguments dbodephase gives the phase and the fre quency as column vectors No display is produced Example dbodephase 1 poly 0 9 0 7 0 6j 0 7 0 6j 1 See also bodephase dbodemag dimpulse Impulse response plot of a discrete time linear system Syntax dimpulse numd dend Ts dimpulse numd dend Ts opt dimpulse Ad Bd Cd Dd Ts dimpulse Ad Bd Cd Dd Ts opt dimpulse style dimpulse style id y t dimpulse Description dimpulse numd dend Ts plots the impulse response of the discrete time transfer function numd dend with sampling period Ts Further options can be provided i
51. Manual 1999 2008 Calerga Sarl only one library which is searched at the same locations as use They can be used only in libraries Since LME replaces include with the contents of lib one should be cautious about the public or private context which is preserved between the libraries It is possible to include a fragment of function without a function header See also includeifexists Include library if it exists Syntax includeifexists lib Description includeifexists lib inserts the contents of the library file Lib if it exists if the library does not exists it does nothing See also otherwise Conditional execution of statements depending on a number or a string See also private Mark the beginning of a sequence of private function definitions in a library LME Reference programming constructs 69 Syntax private Description In a library functions which are defined after the private keyword are private private may not be placed in the same line of source code as any other command comments are possible though In a library functions are either public or private Private functions can only be called from the same library while public functions can also be called from contexts where the library has been imported with a use command Functions are public by default Example Here is a library for computing the roots of a second order polynomial Only function roots2 may be called from the outs
52. Output Purpose 0 Input Standard input from keyboard 1 Output Standard output to screen 2 Output Standard error to screen 3 Output Prompt for commands 38 LMEPPC User Manual 1999 2008 Calerga Sarl You can use these file descriptors without calling any opening func tion first and you cannot close them For instance to display the value of m you can use fprintf fprintf 1 pi 6f n pi pi 3 141593 Some functions use implicitly one of these file descriptors For in stance disp displays a value to file descriptor 1 and warning displays a warning message to file descriptor 2 File descriptors for files and devices are obtained with specific func tions For instance fopen is used for reading from or writing to a file These functions have as input arguments values which specify what to open and how file name host name on a network input or output mode etc and as output argument a file descriptor Such file de scriptors are valid until a call to fclose which closes the file or the connection 3 6 Error Messages When an error occurs the execution is interrupted and an error mes sage explaining what happened is displayed unless the code is en closed in a try catch block The whole error message can look like gt factor 2 Wrong type stdlib primes 164 ones gt stdlib factor 174 The first line contains an error message the location in the source code where the error occurred and the nam
53. The result is a vector of bit positions in ascending order the least significant bit is number 0 Example use bitfield a bitfield 123 16 a 0b0000000001111011 ix find a ix 013456 See also bitfield int8 bitfield int16 bitfield int32 Convert a bitfield object to a signed integer number with sign exten sion Libraries bitfield 507 Syntax use bitfield n int8 a n int16 a n int32 a Description int8 a int16 a and int32 a convert bitfield a to an int8 int16 or int32 number respectively If a has less bits than the target integer and the most significant bit of a is 1 sign extension is performed i e the most significant bits of the result are set to 1 so that it is negative If a has more bits than the target integer most significant bits are ignored Example use bitfield a bitfield 9 4 a 0x1001 i int8 a 210 b bitfield i 0b11111001 See also t uint32 bitfield int8 bitfield int16 bitfield int32 bitfield doubLle bitfield bitfield Cc H ee bitfield length Word length of a bitfield Syntax use bitfield wordlength length a Description Llength a gives the number of bits of bitfield a 508 LMEPPC User Manual 1999 2008 Calerga Sarl Example use bitfield a bitfield 123 16 Llength a 16 See also bitfield sign Get the sign of a bitfield Syntax use bitfield s sign a Description
54. The syntax for field access var field is defined for the following fields for state space models A B C and D matrices of the state space model for transfer functions num and den cell arrays of co efficients for both var string and Ts scalar or empty array for continuous time systems The syntax with braces var i is not supported See also t1 subsasgn joperator subsasgn Iti tfdata Get transfer functions Syntax use lti num den tfdata a num den Ts ssdata a Description tfdata a where a is any kind of LTI object gives the numerator and denominator of the transfer function model and optionally the sampling period or the empty array for continuous time systems Libraries lti 539 The numerators and denominators are given as a cell array of power descending coefficient vectors the rows of the cell arrays correcpond to the outputs and their columns to the inputs See also Iti uminus Negative Syntax use lti b a b uminus a Description a multiplies all the outputs or all the inputs of system a by 1 If a is a transfer functions or a matrix of transfer functions this is equivalent to the unary minus See also ti minus ti uplus Iti uplus Negative Syntax use lti b a b uplus a Description a gives a See also Uti uminus lti plus 540 LMEPPC User Manual 1999 2008 Calerga Sarl zpk LTI transfer function co
55. a b a ellipse false S ellipse pixaxb 4 ax b function S area a b ellipse if nargin lt 2 b a end if nargin lt 3 ellipse false end S ellipse pi x xaxb 4 axb See also if elseif else end Conditional execution depending on the value of one or more boolean expressions Syntax if expr s1 end if expr s1 else s2 end if expr1 s1 elseif expr2 LME Reference programming constructs 67 s2 else s3 end Description If the expression following if is true nonempty and all elements dif ferent from 0 and false the statements which follow are executed Otherwise the expressions following elseif are evaluated until one of them is true If all expressions are false the statements following else are executed Both elseif and else are optional Example if x gt 2 disp large elseif x gt 1 disp medium else disp small end See also include Include libraries Syntax include lib Description include lib inserts the contents of the library file lib Its effect is similar to the use statement except that the functions and constants in lib are defined in the same context as the library where include is located Its main purpose is to permit to define large libraries in multiple files in a transparent way for the user include statements must not follow other statements on the same line and can reference 68 LMEPPC User
56. a row vector A row vector was expected but a more general array was found Non matrix array A matrix was expected but an array with more than 2 dimensions was found Non square matrix A square matrix was expected but a rectan gular matrix was found Index out of range Index negative or larger than the size of the array Wrong type String or complex array instead of real etc Non integer argument An argument has a fractional part while an integer is required Argument out of range An argument is outside the permitted range of values Non scalar argument An argument is an array while a scalar number is required Non object argument An object is required as argument Not a permutation The argument is not a permutation of the integers from 1 to n Bad argument A numerical argument has the wrong site or the wrong value Unknown option A string option has an invalid value 40 LMEPPC User Manual 1999 2008 Calerga Sarl Object too large An object has a size larger than some fixed limit Undefined variable Attempt to retrieve the contents of a variable which has not been defined Undefined input argument Attempt to retrieve the contents of an input argument which was neither provided by the caller nor defined in the function Undefined function Attempt to call a function not defined Too few or too many input arguments Less or more arguments in the call than what the function accepts Too few or too many output
57. also be computed as the union of a and b minus the intersection of a and b setdiff union a b intersect a b a aa de z See also Setditt unique Keep unique elements Syntax v2 unique vl list2 unique list1 b ia ib unique a 272 LMEPPC User Manual 1999 2008 Calerga Sarl Description With an array argument unique v1 sorts its elements and removes duplicate elements Unless v1 is a row vector v1 is considered as a column vector With an argument which is a list of strings unique list sorts its elements and removes duplicate elements The optional second output argument is set to a vector of indices such that if b ia unique a then b is a ia The optional third output argument is set to a vector of indices such that if b ia ib unique a then ais b ib Examples b ia ib unique 4 7 3 8 7 1 3 b 13478 ia 63124 ib 3425412 unique def ab def abc ab abc def See also setdiff zeros Null array Syntax zeros n zeros nl n2 zeros n1 n2 A A A A zeros type Description zeros builds an array whose elements are 0 The size of the array is specified by one integer for a square matrix or several integers either as separate arguments or in a vector for an array of any size An additional input argument can be used to specify the type of the result It must be the
58. and plus or minus 1 millisecond on Windows Example clock 1999 3 11 15 37 34 9167 See also tic Start stopwatch Syntax tic 372 LMEPPC User Manual 1999 2008 Calerga Sarl Description tic resets the stopwatch Typically tic is used once at the beginning of the block to be timed See also toc Elapsed time of stopwatch Syntax elapsed_time toc Description toc gets the time elapsed since the last execution of tic Typically toc is used at the end of the block of statements to be timed On multi tasking operating systems like Windows Mac OS X and Unix toc measures only the time spent in the LME application Other processes do not have a large impact For instance typing tic at the command line prompt waiting 5 seconds and typing toc will show a value much smaller than 5 Example tic x eig rand 200 toc 0 3046 See also 3 31 Date Conversion Functions Date functions perform date and time conversions between the calen dar date and the julian date The calendar date is the date of the proleptic Gregorian calendar i e the calendar used in most countries today where centennial years are not leap unless they are a multiple of 400 This calendar was introduced by Pope Gregory XIII on October 5 1582 Julian Calendar LME Reference date conversion 373 the calendar used until then which became October 15 The calendar used in this library is proleptic which means the rule for leap
59. are an alternative more compact syntax for inline functions In args expr args is a list of input arguments and expr is an expression which contains two kinds of variables input arguments provided when the anonymous expression is executed captured variables all variables which do not appear in the list of input arguments which have the value of variables of the same name existing when and where the anonymous function is created These values are fixed Anonymous functions are a convenient way to provide the glue be tween functions like fzero and ode45 and the function they accept as argument Additional parameters can be passed directly in the anony mous function with captured variables instead of being supplied as additional arguments the code becomes clearer Examples Function reference quad sin 0 pi 2 Anonymous function a 2 fun x sin a x fun 3 0 2794 quad fun 0 2 0 8268 Without anonymous function parameter a should be passed as an additional argument after all the input arguments defined for quad including those which are optional when parameters are missing quad inline sin a x x a 0 2 false a 0 8268 Anonymous functions are actually stored as inline functions with all captured variables dumpvar fun inline function y f a x y sin a x 2 144 LMEPPC User Manual 1999 2008 Calerga Sarl See also 3 15 Mathematical Functions
60. arguments Less or more left side variables in an assignment than the function can return Syntax error Unspecified compile time error function keyword without function name Incomplete func tion header Bad function header Syntax error in a function header Missing expression Statement such as if or while without ex pression Unexpected expression Statement such as end or else followed by an expression Incomplete expression Additional elements were expected dur ing the compilation of an expression such as right parenthesis or a sub expression at the right of an operator for not followed by a single assignment for is followed by an expression or an assignment with multiple variables Bad variable name The left hand part of an assignment is not a valid variable name e g 2 3 String without right quote The left quote of a string was found but the right quote is missing Unknown escape character sequence Ina string the backslash character is not followed by a valid escape sequence Unexpected right parenthesis Right parenthesis which does not match a left parenthesis Unexpected right bracket Right bracket which does not match a left bracket LME Reference 41 Unrecognized or unexpected token An unexpected character was found during compilation such as 1 end not in an index expression end was used outside of any index sub expression in an expression beginning not in an index expression beginning
61. as for numbers and matrices The following statement makes available functions defined in classes use classes polynom polynom Polynom object constructor Syntax use classes a polynom a polynom coef Description polynom coef creates a polynom object initialized with the coeffi cients in vector coef given in descending powers of the variable Without argument polynom returns a polynom object initialized to 0 The following operators and functions may be used with polynom arguments with results analog to the corresponding functions of LME minus plus mpower rem mldivide roots mrdivide uminus mtimes uplus 492 LMEPPC User Manual 1999 2008 Calerga Sarl Examples use classes p polynom 3 0 1 4 2 p 3x 4 x 2 4x 2 q 3 p2 8 27X 8 18x 6 72x 5 39x 4 24x 3 60x 2 48x 20 See also polynom disp polynom diff jratfun ratfun polynom double polynom int polynom inline polynom subst polynom feval polynom disp Display a polynom object Syntax use classes disp a Description disp a displays polynomial a It is also executed implicitly when LME displays the polynom result of an expression which does not end with a semicolon Example use classes p polynom 3 0 1 4 2 3x 4 x 2 4x 2 See also polynom polynom polynom double Convert a polynom object to a vector of coefficients Libraries classes
62. b is true and y otherwise Like with if and while state ments b is true if it is a nonempty array with only non zero elements Only one of x and y is evaluated depending on b Operators and have the same priority parenthesis or brackets should be used if e g x or y is a range Example Element of a vector v or default value 5 if the index ind is out of range ind lt 1 ind gt length v 5 v ind See also operator amp amp operator Operator Horizontal matrix concatenation Syntax M1 M2 M1 M2 horzcat M1 M2 Description Between brackets the comma is used to separate elements on the same row in a matrix Elements can be scalars vector or matrices their number of rows must be the same unless one of them is an empty matrix Outside brackets or between parenthesis the comma is used to separate statements or the arguments of functions 140 LMEPPC User Manual 1999 2008 Calerga Sarl horzcat M1 M2 is equivalent to M1 M2 It can be used to rede fine this operator for objects Between braces the comma separates cells on the same row Examples 1 2 12 3 5 ones 2 311 5 Ll abc def abcdef See also Operator Vertical matrix concatenation Syntax M1 M2 vertcat M1 M2 Description Between brackets the semicolon is used to separate rows in a matrix Rows can be scalars vector or matrices their number of columns must be the same unle
63. between each elements of the columns of matrix A or between each elements of A if it is a row vector diff A n calculates the n th order differences i e it repeats n times the same operation Up to a scalar factor the result is an ap proximation of the n th order derivative based on equidistant samples diff A n dim operates along dimension dim If the second argu ment n is the empty matrix the default value of 1 is assumed Examples diff 1 3 5 4 8 2 2 14 diff 1 3 5 4 8 2 0 35 diff 1 3 5 4 8 2 3 9 8 1 2 HONA i 2 4 6 See also cumsum dlyap Discrete time Lyapunov equation Syntax X dlyap A C LME Reference linear algebra 207 Description dlyap A C calculates the solution X of the following discrete time Lyapunov equation AXA X C 0 All matrices are real 3 1 2 7 1 2 dlyap KL 4 A XI ol N 1 0505 3 2222 1 2117 3 2317 11 213 4 8234 1 4199 5 184 2 7424 See also dot Scalar product Syntax v3 dot v1 v2 v3 dot v1 v2 dim Description dot v1 v2 gives the scalar products of vectors v1 and v2 v1 and v2 must be row or columns vectors of same length or arrays of the same size then the scalar product is performed along the first dimension not equal to 1 A third argument dim may be used to specify the dimension the scalar product is performed along Examples dot 1 2 3 0 0 1 3 dot 1 2 3 7 1 3 4 0 0 0
64. called directly or indirectly by statements in str The purpose of sandbox is to permit the evaluation of code which comes from untrusted sources such as the Internet sandbox str varin evaluates the statements in string str ina context with local variables equal to the fields of structure varin With an output argument sandbox collects the contents of all vari ables in the fields of a single structure An error is thrown when the argument of sandbox attempts to exe cute one of the functions which are disabled This error can be caught by a try catch construct outside sandbox but not inside its argument so that unsuccessful attempts to circumvent the sandbox are always reported to the appropriate level Examples Evaluation of two assignments the second value is displayed and the variables are discarded at the end of the evaluation sandbox a 2 b 3 5 b 345 Evaluation of two assignments the contents of the variables are stored in structure result result sandbox a 2 b 3 5 result a 2 b real 1x3 Evaluation with local variables x and y initialized with the field of a structure Variable z is local to the sandbox in x 12 in y 1 10 sandbox z x y in Zz 13 14 15 16 17 18 19 20 21 22 Attempt to execute the untrusted function fopen and to hide it from the outside Both attempts fail fopen is trapped and the security violation error is propagated outside the sandbox 112 LME
65. can use standard operator notations such as or constants constants defines physical constants in SI units date date implements functions for date and time manipulation and conversion to and from strings filter filter implements functions for the design of analog and digital filters lti lti implements constructors and methods for Linear Time Invariant models whcih may represent dynamical systems as continuous time or discrete time state space models or transfer functions With them you can use standard operator notations such as or array building operators such as A B C D connection functions such as parallel or feedback and much more 462 LMEPPC User Manual 1999 2008 Calerga Sarl ratio ratio implements constructors and methods for rational numbers based on long integers Standard arithmetic and boolean operators can be used Sigenc sigenc implements functions related to signal encoding to and decoding from a digital representation stat stat provides more advanced statistical functions stdlib stdlib is the standard library of general purpose functions for LME Functions span from array creation and manipulation to coordinates transform and basic statistics wav wav implements functions for reading and writing WAV files or encoding and decoding data encoded as WAV in memory wsserver wsserver implements a server for web services using the XML RPC or SOAP protocol It requires the TCP IP and WebSer vic
66. day 2005 Apr 18 year month and day 18 Apr 2005 day month and year 04 18 2005 month day and year 04 18 00 month day and year 18 04 2005 day month and year 18 04 05 day month and year 16 26 03 hour minute and second 16 26 hour and minute PM afternoon Unrecognized characters are ignored If the year is given as two digits it is assumed to be between 1951 and 2050 Examples use date datevec Date and time 20050418T162603 2005 4 18 16 26 3 datevec 03 57 PM 0 0 0 15 57 0 datevec 1 Aug 1291 1291 8 1 0 0 0 datevec At 16 30 on 11 04 07 2007 11 4 16 30 0 See also weekday Week day of a given date Syntax use date num str weekday year month day num str weekday datetime num str weekday jd Description weekday finds the week day of the date given as input The date can be given with three input arguments for the year the month and the Libraries constants 555 day or with one input argument for the date or date and time vector or julian date The first output argument is the number of the day from 1 for Sunday to 7 for Saturday and the second output argument is its name as a string of 3 characters such as Mon for Monday Example Day of week of today use date num str weekday clock num 2 str Mon See also cal2julian 5 11 constants constants is a library which defines physical constants in SI units me ter kilogram
67. de z Set exclusive or can also be computed as the union of a and b minus the intersection of a and b setdiff union a b intersect a b a aa de z See also size Size of an array Syntax v size A m n size A m size A i Description Size A returns the number of rows and the number of elements along each dimension of array A either in a row vector or as scalars if there are two output arguments or more size A i gives the number of elements in array A along dimen sion i size A 1 gives the number of rows and size A 2 the num ber of columns Examples M ones 3 5 size M 266 LMEPPC User Manual 1999 2008 Calerga Sarl w azul wi own Il size M 3 3 size M 1 3 size M 2 5 See also sort Array sort Syntax A_sorted ix sort A A_sorted ix sort A dim A_sorted ix sort A dir A_sorted ix sort A dim dir list_sorted ix sort list list_sorted ix sort list dir Description sort A sorts separately the elements of each column of array A or the elements of A if it is a row vector The result has the same size as A Elements are sorted in ascending order with NaNs at the end For complex arrays numbers are sorted by magnitude The optional second output argument gives the permutation array which transforms A into the sorted array It can be used to reorder elements in another array or to s
68. default initial state is the zero vector Options can be provided in a structure opt created with responseset 440 LMEPPC User Manual 1999 2008 Calerga Sarl lsim 0 2 Figure 3 18 lsim 1 1 2 3 4 u t Range The range is a vector of two elements the start time and the end time Such an explicit time range is required when the response is not displayed in a plot where the x axis represents the time tOnly When opt tOnly is true Lsim produces output only at the time instants defined in t The logical value false gives the default interpolated values The optional arguments style and id have their usual meaning With output arguments lsim gives the output and the time as col umn vectors or an array for the output of a multiple output state space model where each row represents a sample No display is produced Example Response of continuous time system given by its transfer function with an input defined by linear segments see Fig 3 18 t 0 10 20 30 50 u 1 1 0 1 1 lsim 1 1 2 3 4 u t b See also LME Reference graphics for dynamical systems 441 Figure 3 19 scale lindb 4 pi 0 0 01 100 ngrid ngrid Nichols chart grid Syntax ngrid ngrid style Description ngrid plots a Nichols chart in the complex plane of the Nichols dia gram see Fig B 19 The Nichols chart is a set of lines which corre spond to the same magnitude of the clo
69. empty or contains only separator characters the result is the empty string The optional second output is set to what follows immediately the token including separators If no token is found it is the same as str An optional second input argument contains the separators in a string Examples Strings are displayed with quotes to show clearly the separators strtok ab cde ab t r strtok ab cde r strtok 2 5 3 310 LMEPPC User Manual 1999 2008 Calerga Sarl See also strtrim Remove leading and trailing blank characters from a string Syntax s2 strtrim s1 Description strtrim s1 removes the leading and trailing blank characters from string s1 Blank characters are spaces code 32 tabulators code 9 carriage returns code 13 line feeds code 10 and null characters code 0 Example double tAB CD r n 0 32 9 65 66 32 32 67 68 13 10 0 double strtrim tAB CD n r 0 65 66 32 32 67 68 See also deblank upper Convert all lowercase letters to lowercase Syntax s2 upper s1 LME Reference strings 311 Description upper s1 converts all the lowercase letters of string s1 to uppercase Currently only ASCII letters without diacritic are converted Example upper abcABC123 ABCABC123 See also utf8decode Decode Unicode characters encoded with UTF 8 Syntax str utf8decode b Description utf8decode b deco
70. equality with a case string ex pression or any element of a case list expression Example switch option case arithmetic m mean data case geometric m prod data 1 length data otherwise error unknown option end See also LME Reference programming constructs 73 try Error recovery Syntax try end l try catch end Description The statements after try are executed If an error occurs execution is switched to the statements following try if any or to the statements following end The error message can be retrieved with lasterr or lasterror If no error occurs the statements between try and end are ignored try ignores two errors the interrupt key Control Break on Windows Command on Mac OS X Control C on other operating systems with a keyboard timeout in Sysquake Remote an attempt to execute an untrusted function in a sandbox The error can be handled only outside the sandbox Examples a l a 2 555 Index out of range try a 2 end 555 555 try a 2 catch 333 end 555 333 555 try a catch 333 end 555 a Fat a Or il 55 74 LMEPPC User Manual 1999 2008 Calerga Sarl See also lasterr Lasterror jerror until End of repeat until loop See also use Import libraries Syntax use lib use libl lib2 Description Functions may be defined in separate files called ibraries use makes them available in the
71. for objects Example 1 2 3 5 3 10 3 4 2 6 8 See also Operator Matrix right division Syntax a b A B A b mrdivide a b Description a b divides the first operand by the second operand If the second operand is a scalar it divides each element of the first operand If the second operand is Otherwise it must be a square matrix M1 M2 is equivalent to M1 inv M2 mrdivide x y is equivalent to x y It can be used to redefine this operator for objects LME Reference operators Example 9 3 3 2 6 1 2 3 4 5 1 4 10 2 25 See also Operator Scalar right division Syntax x y M1 M2 M X x JM rdivide x y Description 125 The first operand is divided by the second operand If both operands are matrices with a size different from 1 by 1 their size must be equal the division is performed element wise If one operand is a scalar it is repeated to match the size of the other operand rdivide x y is equivalent to x y It can be used to redefine this operator for objects Examples 3 10 3 5 12 See also 126 LMEPPC User Manual 1999 2008 Calerga Sarl Operator Matrix left division Syntax x y M1 M2 x M mldivide x y Description x y divides the second operand by the first operand If the first operand is a scalar it divides each element of the second operand Otherwise it must be a square matrix M1 M2
72. gt r xl x2 x1 x O n 1 n 1 dbtype 6 function r Llinspace xl x2 n 7 8 if nargin lt 3 9 n 100 10 end gt 11 r xl x2 x1 x O n 1 n 1 See also echo Echo of code before its execution Syntax echo on echo off echo fun on echo state echo state fd echo fun state echo fun state fd nannan Description echo on enables the display of an echo of each line of function code before execution The display includes the function name and the line LME Reference profiler number echo off disables the echo The argument can also be passed as a boolean value with the func tional form echo state echo on is equivalent to echo true echo fun on enables echo for function named fun only echo fun off disables echo the function name is ignored echo off has the same effect By default the echo is output to the standard error channel file descriptor 2 Another file descriptor can be specified as an additional numeric argument with the functional form only Example Trace of a function use stdlib echo on C compan 2 5 4 compan 26 if min size v gt 1 compan 29 v v compan 30 n length v compan 31 M v 2 end v 1 eye n 2 n 1 Echo stored into a file log txt fd fopen log txt w echo true fd echo off fclose fd See also 3 11 Profiler profile Install remove or display a function profile Syntax
73. in the range 0 for a null frequency to n for the Nyquist frequency the line is generated by e where v is such that the curve is inside the unit circle The whole grid is displayed only if the user selects it in the Grid menu or after the command plotoption fullgrid By default only the unit circle the stability limit is displayed Example Typical use for poles or zeros displayed in the z plane scale equal 1 2 1 2 1 2 1 2 zgrid plotroots pol See also Chapter 4 Extensions Extensions are additional functions usually developed in C or Fortran which extend the core functionality of LME the programming language of Sysquake Extensions are grouped in so called shared libraries or dynamically linked libraries DLL files At startup Sysquake loads all extensions it finds in the folder LMEExt in the same location as the Sysquake program file Each extension initializes itself and usually displays a line of information in the Command window No further action is needed in order to use the new functions You can also develop and add your own extensions as explained in the next chapter Here is the list of the extensions currently provided with Sysquake Mathematics Lapack Windows Mac Unix LAPACK based linear algebra functions Long integers Windows Mac Unix Arithmetic on arbitrary length integer numbers File input output and data compression Memory mapping Mac OS X Unix Mapping of f
74. in the same order deal can be used to assign a value to multiple variables to swap the contents of two variables or to assign the elements of a list to different variables Examples Swap variable a and b deal b a 90 LMEPPC User Manual 1999 2008 Calerga Sarl Copy the same random matrix to variables x y and z x y z deal rand 5 Assign the elements of list l to variables v1 v2 and v3 l 1 abc 3 5 v1 v2 v3 deal l vl See also operator 1 dumpvar Dump the value of an expression as an assignment to a variable Syntax dumpvar value dumpvar name value dumpvar fd name value str dumpvar value str dumpvar name value Description dumpvar fd name value writes to the channel fd the standard out put by default a string which would set the variable name to value if it was evaluated by LME If name is omitted only the textual represen tation of value is written With an output argument dumpvar stores result into a string and produces no output LME Reference miscellaneous functions 91 Examples dumpvar 2 3 a i 6 dumpvar a a S 2 tapers dumpvar string s string abc See also error Display an error message and abort the current computation Syntax error str error format argl arg2 error identifier format argl arg2 Description Outside a try block error str displays string str as an e
75. instance gt lt SOAP ENV Body gt lt m fun xmlns m ns gt lt x xsi type xsd double gt 3 1415926535898 lt x gt lt y xsi type xsd boolean gt 1 lt y gt lt m fun gt lt SOAP ENV Body gt lt SOAP ENV Envelope gt See also soapwriteresponse soapreadcall soapreadresponse Extensions Web Services 589 soapwritefault Encode a SOAP call response fault Syntax soapwritefault fd faultCode faultString soapwritefault faultCode faultString str soapwritefault faultCode faultString Description soapwritefault fd faultCode faultString writes to file descrip tor fd a complete SOAP response fault including the HTTP header If fd is missing the response is written to standard output file descrip tor 1 since the output contains carriage return characters it may not be displayed correctly on all platforms The faultCode argument is the fault code as an integer or a string and the faultString is the fault message With an output argument soapwritefault returns the response as a string without any output See also soapwriteresponse soapreadresponse soapwriteresponse Encode a SOAP call response Syntax soapwriteresponse fd method ns value soapwriteresponse method ns value str soapwriteresponse method ns value Description soapwriteresponse fd method ns value writes to file descriptor fd a complete SOAP response including the HTTP header If fd is missing t
76. integer int16 16 bit signed integer uint8 8 bit unsigned integer int8 8 bit signed integer uint64 64 bit unsigned integer int64 64 bit signed integer LME Reference 31 64 bit integer numbers are not supported by all applications on all platforms These basic types can be used to represent many mathematic ob jects Scalar One by one matrix Vector n by one or one by n matrix Functions which return vec tors usually give a column vector i e n by one Empty object 0 by 0 matrix 0 by n or n by 0 matrices are always converted to 0 by 0 matrices Polynomial of degree d 1 by d 1 vector containing the coeffi cients of the polynomial of degree d highest power first List of n polynomials of same degree d n by d 1 matrix con taining the coefficients of the polynomials highest power at left List of n roots n by 1 matrix List of n roots for m polynomials of same degree n n by m matrix Single index One by one matrix List of indices Any kind of matrix the real part of each element taken row by row is used Sets Numerical array or list or cell array of strings see below Boolean value One by one logical array 0 means false and any other value including nan means true comparison and logical operators and functions return logical values In programs and expressions constant boolean values are entered as false and true Scalar boolean values are displayed as false or true in arrays respectively as F o
77. it has been set with Legend Hidden legend Legend in top right corner default Legend in top left corner Legend in bottom right corner Legend in bottom left corner Margin space for title and labels No margin xgrid Grid of vertical lines for the x axis noxgrid No grid for the x axis ygrid Grid of horizontal lines for the y axis noygrid xygrid noxygrid No grid for the y axis Grid of vertical and horizontal lines for the x and y axis No grid for the x and y axis grid Normal details for grids displayed by sgrid zgrid etc nogrid fullgrid fill3d figure Example Removal of grids displayed by sgrid zgrid etc More details for grids displayed by sgrid zgrid etc In 3D graphics zoom in so that the bounding box fills the Display of a photographic image without frame plotoption noframe image photo See also legend LME Reference base graphics 397 polar Polar plot Syntax polar theta rho polar style polar style id Description Command polar displays graphical data in the current figure with po lar coordinates The data are given as two vectors of coordinates theta in radians and rho Depending on the style the points are displayed as individual marks or are linked with lines If x and y are matrices each row is considered as a separate line or set of marks if only one of them is a matrix
78. kinds with phi pi 2 can be obtained with ellipke See also ellipf ellipke ellipf Jacobi elliptic integral of the first kind Syntax u ellipf phi m LME Reference mathematical functions 161 Description ellipf phi m gives the Jacobi elliptic integral of the first kind de fined as Fom m sin Complete elliptic integrals of first and second kinds with phi pi 2 can be obtained with ellipke See also ellipj Jacobi elliptic functions Syntax sn cn dn sn cn dn ellipj u m ellipj u m tol Description ellipj u m gives the Jacobi elliptic function sn cn and dn Parame ter m must be in 0 1 These functions are based on the Jacobi elliptic amplitude the inverse of the Jacobi elliptic integral of the first kind which can be obtained with ellipam u F m sn u m sin cn u m cos dn u m 1 msin 9 ellipj u m tol uses tolerance tol the default tolerance is eps 162 LMEPPC User Manual 1999 2008 Calerga Sarl Examples sn cn dn ellipj 2 7 0 6 sn 0 8773 cn 0 4799 dn 0 7336 sin ellipam 2 7 0 6 0 8773 ellipj 0 5 0 3 0 0000 0 8188 0 9713 0 4114 0 5341 0 9930 See also ellipke Complete elliptic integral Syntax K E ellipke m K E ellipke m tol Description K E ellipke m gives the complete elliptic integrals of the first kind K F m and second kind E E m defined as 1 2 dt
79. last operand which is false remain ing operands are not evaluated or the last one Example Boolean value which is true if the vector v is made of pairs of equal values mod length v 2 0 amp amp v 1 2 end v 2 2 end The second operand of amp amp is evaluated only if the length is even See also Operator Or Syntax b1 b2 or bl1 b2 138 LMEPPC User Manual 1999 2008 Calerga Sarl Description b1 b2 performs the logical OR operation between the corresponding elements of b1 and b2 the result is false logical 0 if both operands are false or 0 and true logical 1 otherwise or b1 b2 is equivalent to b1 b2 It can be used to redefine this operator for objects Example false false true true false true false true FTTT See also Operator Or with lazy evaluation Syntax b1 b2 Description b1 b2 is b1 if b1 is true and b2 otherwise Like with if and while statements b1 is true if it is a nonempty array with only non zero elements b2 is evaluated only if b1 is false b1 b2 bn returns the last operand which is true remaining operands are not evaluated or the last one Example Boolean value which is true if the vector v is empty or if its first ele ment is NaN isempty v isnan v 1 See also operator amp amp LME Reference operators 139 Operator Alternative with lazy evaluation Syntax b x y Description b x y is x if
80. list of arguments and the URL as a string xmLrpcreadcall str decodes its string argument which must be a whole XML RPC call Extensions Web Services 593 Example str xmlrpcwritecall rpc remote com rpc getPressure method arglist url xmlrpcreadcall str method getPressure arglist url rpc See also xml rpcreadresponse xmlrpcwriteca xmirpcreadresponse Decode an XML RPC call response Syntax fault value fault value xmLrpcreadresponse fd xmlrpcreadresponse str Description xmLrpcreadresponse fd where fd is a file descriptor reads a com plete XML RPC response and decodes it In case of success it returns true in the first output argument and the decoded response value in the second output argument In case of failure it returns false and the fault structure which contains the fields faultCode error code as an int32 and faultString error message as a string xmlrpcreadresponse str decodes its string argument which must be a whole XML RPC response Examples str xmlrpcwriteresponse 123 fault value xmlrpcreadresponse str fault false value 123 strf xmlrpcwritefault 12int32 No power fault value xmlrpcreadresponse strf fault true 594 LMEPPC User Manual 1999 2008 Calerga Sarl value faultCode 12int32 faultString No power See also xmlrpcreadcall xmlrpcwriteresponse xmLrpcwritefault xmIirpcw
81. matrices M1 and M2 column by columns conv M1 M2 dim convolves along the dimension dim 1 for columns and 2 for rows If one of the matrices has only one column or one row it is repeated to match the size of the other argument Example conv 1 2 1 2 3 1476 conv 1 2 1 2 3 4 5 6 2 147 6 4 13 16 12 200 LMEPPC User Manual 1999 2008 Calerga Sarl See also conv2 Two dimensions convolution of matrices Syntax M M conv2 M1 M2 conv2 M1 M2 kind Description conv2 M1 M2 convolves the matrices M1 and M2 along both directions The optional third argument specifies how to crop the result Let nl1 ncl size M1 and nl2 nc2 size M2 With kind full default value the result M has nl1 nl2 1 lines and ncl nc2 1 columns With kind same the result M has nl1 lines and ncl columns this options is very useful if M1 represents equidistant samples in a plane e g pixels to be filtered with the finite impulse response 2 d filter M2 With kind valid the result M has nl1 nl2 1 lines and ncl nc2 1 columns or is the empty matrix if M1 represents data filtered by M2 the borders where the convolution sum is not totally included in M1 are removed Examples conv2 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 13 65 3 5 12 21 16 9 12 27 45 33 18 11 24 39 28 15 7 15 24 17 9 conv2 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 same 12 21 16 27 45 33 24 39 28 conv2 1 2 3 4 5 6 7 8 9 1 1 1 1
82. mimics mathe matical arithmetic operations like the addition and the multiplication They can be infix Such as x y separating their two arguments called operands prefix such as x placed before their unique operand or postfix such as M placed after their unique operand In Sysquake their arguments are always evaluated from left to right Since they do not require parenthesis or comma their priority matters Priority specifies when subexpressions are considered as a whole as the argu ment of some operator For instance in the expression at b c where x denotes the multiplication the evaluation could result in a b c or at b c however since operator s priority is higher than operator s the expression yields a b c without ambiguity Here is the list of operators from higher to lower priority unary J J lt gt lt gt Most operators have also a functional syntax for instance a b can also be written plus a b This enables their overriding with new definitions and their use in functions such as feval which take the name of a function as an argument Here is the correspondence between operators and functions 114 LMEPPC User Manual 1999 2008 Calerga Sarl a b vertcat a b a b minus a b a b horzcat a b axb mtimes a b a b colon a b a b mrdivide a b a b c colon a b c a b mldivide a b alb or a b a b times a b a amp b and a b a b rdivide a b a lt
83. model Examples use lti sc ss 1 1 2 2 5 0 Sc continuous time LTI state space system A Libraries lti 1 B 1 2 C 2 5 D 0 0 0 0 sd ss tf 1 1 2 3 4 0 1 sd discrete time LTI state space system Ts 0 1 A 2 3 4 1 0 0 0 1 0 B 1 0 0 C 0 0 1 D 0 See also tf tf LTI transfer function constructor Syntax lti f num den a denlist f Ts f TS var f b f gain f b eo tou ud tt uo ou ut to u a a a a a a a a 521 522 LMEPPC User Manual 1999 2008 Calerga Sarl Description tf num den creates an LTI object which represents the continuous time transfer function specified by descending power coefficient vec tors num and den tf num den Ts creates an LTI object which repre sents a discrete time transfer function with sampling period Ts In both cases num and den may be replaced with cell arrays of coef ficients whose elements are the descending power coefficient vectors The number of rows is the number of system outputs and the number of columns is the number of system inputs An additional argument var may be used to specify the variable of the Laplace s default or p or z transform z default or q tf b6 where b is an LTI object creates a transfer function of the same kind continuous discrete time sampling time and variable as b tf b converts the LTI object b to a transfer function
84. month day hour minute and second with more output arguments values are given separately Example Date 1000 days after April 18 2005 julian2cal cal2julian 2005 4 18 1000 2006 11 14 0 0 80 See also cal2julian 3 32 Graphics LME provides low level commands for basic shapes as well as high level commands for more specialized plots Low level commands Low level commands add simple shapes such as lines marks polygons circles and images With them you can display virtually everything you want Arguments of these commands are such that it is very easy to work globally with ma trices without computing each value sequentially in a loop High level commands High level commands perform some com putation of their own to process their arguments before displaying the result This has two benefits first the code is simpler more compact and faster to develop Second command execution is faster because the additional processing is not interpreted by LME but implemented as native machine code The information related to interactive manipulation is often easier to use too Most of these functions are related to automatic control and signal processing Here is the list of these commands 2D low level drawing commands LME Reference graphics activeregion colormap area contour bar fplot barh image circle line 375 pcolor plot polar quiver text 2D high level drawing commands bodemag dsigma bodephase ds
85. n columns and t has n 1 columns The result is a column vector with one element for each row of xi which is the row index in t of the first simplex which contains the point or NaN if the point is outside all simplices i e outside the convex hull of points x if t is a proper triangulation of x such as the one computed with delaunayn Example Search for simplices containing points 0 0 and 0 1 corresponding to Delauny triangulation of 20 random points x randn 20 2 t delaunayn x xi 0 0 0 1 ix tsearchn x t xi 278 LMEPPC User Manual 1999 2008 Calerga Sarl See also delaunayn voronoin voronoi 2 d Voronoi tessalation Syntax v p voronoi x y Description voronoi x y calculates the Voronoi tessalation of the set of 2 d points given by arrays x and y Both arrays must have the same number of values m The first output argument v is an array of two columns which contains the coordinates of the vertices of the Voronoi cells one row per vertex The first row contains infinity and is used as a marker for unbounded Voronoi cells The second output argument p is a list of vectors of row indices in v each element describes the Voronoi cell corresponding to a point in x In each cell vertices are sorted counterclockwise Voronoi tessalation is a tessalation a partition of the plane such that each region is the set of points closer to one of the initial point than to any other one Two
86. nanstd A p dim Description nanstd v returns the standard deviation of vector v with NaN values ignored normalized by one less than the number of non NaN values With a second argument nanstd v p normalizes by one less than the number of non NaN values if p is true or by the number of non NaN values if p is false nanstd M gives a row vector which contains the standard devi ation of the columns of M With a third argument nanstd M p dim operates along dimension dim In all cases NaN values are ignored Example use stat nanstd 1 2 nan nan 6 7 10 11 12 6 3640 4 5092 3 5355 See also Libraries stat 487 nansum Sum after discarding NaNs Syntax use stat y nansum A y nansum A dim Description nansum v returns the sum of the elements of vector v NaN values are ignored nansum A returns a row vector whose elements are the sums of the corresponding columns of array A nansum A dim returns the sum of array A along dimension dim the result is a row vector if dim is 1 or a column vector if dim is 2 See also pdist Pairwise distance between observations Syntax use stat pdist M pdist M metric pdist M metric p a ou oul Description pdist calculates the distance between pairs of rows of the observation matrix M The result is a column vector which contains the distances between rows i and j with i lt j It can be resized to a square matrix with squareform By default the
87. negative or noninteger the result is NaN The imag inary part is ignored Examples factorial 5 120 factorial nan 1 See also fix Rounding towards 0 Syntax y f1ix x Description fix x truncates the fractional part of x If the argument is a complex number the real and imaginary parts are handled separately Examples fix 2 3 2 fix 2 6 2 168 LMEPPC User Manual 1999 2008 Calerga Sarl See also floor Rounding towards infinity Syntax y floor x Description floor x gives the largest integer smaller than or equal to x If the argument is a complex number the real and imaginary parts are han dled separately Examples floor 2 3 2 floor 2 3 3 See also gamma Gamma function Syntax y gamma x Description gamma x gives the gamma function of x Argument and result are real imaginary part is discarded The gamma function is defined as Cc roo P le t dt 0 For positive integer values n n 1 LME Reference mathematical functions 169 Examples gamma 5 24 gamma 3 inf gamma 3 5 0 2701 See also gammainc Incomplete gamma function Syntax y gammainc x a Description gammainc x a gives the incomplete gamma function of x and a Ar guments and result are real imaginary part is discarded x must be nonnegative The incomplete gamma function is defined as 1 x gammainc x a t 16 dt r a Jo
88. of the over determined system M1 x y Examples 0 2 0 4 1 2 M2 x 1 2 1 2 M2 x 1 2 M2 0 2 0 4 See also poly Characteristic polynomial of a square matrix or polynomial coefficients based on its roots 228 LMEPPC User Manual 1999 2008 Calerga Sarl Description With a matrix argument poly M returns the characteristic polyno mial det x eye size M M of the square matrix M The roots of the characteristic polynomial are the eigenvalues of M With a vector argument poly r returns the polynomial whose roots are the elements of the vector r The first coefficient of the polynomial is 1 If the complex roots form conjugate pairs the result is real Examples poly 1 2 3 4 1 5 2 roots poly 1 2 3 4 5 3723 0 3723 eig 1 2 3 4 0 3723 5 3723 poly 1 3 1 6 11 6 See also polyder Derivative of a polynomial or a polynomial product or ratio Syntax Al polyder A Cl polyder A B N1 D1 polyder N D Description polyder A returns the polynomial which is the derivative of the poly nomial A Both polynomials are given as vectors of their coefficients highest power first The result is a row vector LME Reference linear algebra 229 With a single output argument polyder A B returns the derivative of the product of polynomials A and B It is equivalent to polyder conv A B With two output arguments N1 D1 polyder N D returns the derivative of the
89. or equal to the interpo lated value Examples One dimension interpolation LME Reference arrays 249 interpn 1 2 5 8 0 1 0 2 0 5 1 0 2 3 7 nan 0 2000 0 3000 0 8333 interpn 1 2 5 8 0 1 0 2 0 5 1 0 2 3 7 0 nan 0 2000 0 2000 1 0000 Three dimension interpolation D cat 3 0 1 2 3 4 5 6 7 interpn 0 1 0 1 0 1 D 0 2 0 7 0 5 3 1000 Image rotation we define original coordinates between 0 5 and 0 5 in vector c and arrays X and Y and the image as a linear gradient between 0 and 1 0 5 X interpn c c D Xi Yi isnan E 0 5 c 5 0 01 0 5 X repmat c 101 1 Y X phi 0 2 Xi cos phi X sin phi Y Yi sin phi X cos phi Y D E E intersect Set intersection Syntax c intersect a b c ia ib intersect a b Description intersect a b gives the intersection of sets a and b i e it gives the set of members of both sets a and b Sets are any type of nu merical character or logical arrays or lists or cell arrays of character strings Multiple elements of input arguments are considered as single members the result is always sorted and has unique elements The optional second and third output arguments are vectors of in dices such that if c ia ib intersect a b then cis a ia as well as b ib 250 LMEPPC User Manual 1999 2008 Calerga Sarl Example a a bc bbb
90. p k lp2bp z0 pO kO wc ww num den lp2bp num0 denO wc ww Description Lp2bp convert a lowpass analog filter prototype with unit angular fre quency to a bandpass analog filter with the specified center angular frequency w0 and bandwidth ww lp2bp z0 p0 k0 wc ww converts a filter given by its zeros poles and gain lp2bp num0 den0 wc ww converts a filter given by its numerator and denominator coefficients in decreasing powers of s The new filter F s is et ee S2 Ww w 4 ra ro c WwS where Fo s is the filter prototype The filter order is doubled See also Up2lp tp2hp lp2bs Ip2bs Lowpass prototype to bandstop filter conversion 518 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax use filter z p k lp2bs z0 pO kO wc ww num den lp2bs num0 denO wc ww Description lp2bs convert a lowpass analog filter prototype with unit angular fre quency to a bandstop analog filter with the specified center angular frequency w0 and bandwidth ww lp2bs z0 p0 k0 wc ww converts a filter given by its zeros poles and gain lp2bs num0 den0 wc ww converts a filter given by its numerator and denominator coefficients in decreasing powers of s The new filter F s is F s F te S Fo S w w2 4 where F o s is the filter prototype The filter order is doubled See also Ip2hp Lowpass prototype to highpass filter conversion Syntax use filter
91. plus star triangle up triangle down square diamond gt X O A7 lt LME Reference remarks on graphics 377 Miscellaneous String stairs S fill f arrow at end a arrows at beginning and end A Color h rrggbb specifies a color by its red green and blue components each of them is given by two hexadecimal digits from 00 minimum brightness to ff maximum brightness Color h rgb specifies each component with a single hexadecimal digit For exam ple h 339933 and h 393 both specify the same greenish gray Like for other colors an uppercase H means that the line is thick Style s stairs is supported only by the plot dimpulse dstep dlsim and dinitial functions It is equivalent to a zero order hold i e two points are linked with a horizontal segment followed by a vertical segment Style f fill fills the shape instead of drawing its contour Exactly how the shape is filled depends on the underlying graphics architecture if the contour intersects itself there may be holes Style a adds an arrow at the end of lines drawn by plot and style A adds arrows to the beginning and the end The arrow size depends only on the default character size neither on the line length nor on the plot scale Its color and thickness are the same as the line s Many graphical commands accept data for more than one line If the style string contains several sequences of styles the f
92. reached See also base64encode base64encode Encode data using base64 Syntax strt base64encode strb 300 LMEPPC User Manual 1999 2008 Calerga Sarl Description base64encode strb encodes the contents of string strb which rep resents binary data The result contains only characters A Z a z 0 9 and it is suitable for transmission or storage on media which accept only text Each character of encoded data represents 6 bits of binary data i e one needs four characters for three bytes The six bits represent 64 different values encoded with the characters A to Z a to z 0 to 9 and in this order When the binary data have a length which is not a multiple of 3 encoded data are padded with one or two characters to have a multiple of 4 Base64 encoding is an Internet standard described in RFC 1521 Example s base64encode char 10 S AAECAWQFBgcICQo double base64decode s 1 2 3 4 5 6 7 8 9 10 See also base64decode char Convert an array to a character array string Syntax char A char sl s2 S S Description char A converts the elements of matrix A to characters resulting in a string of the same size Characters are stored in unsigned 16 bit words The shape of A is preserved Even if most functions ignore the string shape you can force a row vector with char A
93. real array of any size and dimension The default value of mu is 255 See also ulawcompress alawexpand 5 9 wav wav is a library which adds to LME functions for encoding and decoding WAV files WAV files contain digital sound The wav library supports un compressed 8 bit and 16 bit monophonic and polyphonic WAV files It can also encode and decode WAV data in memory without files The following statement makes available functions defined in wav use wav wavread WAV decoding Syntax use wav samples samplerate nbits wavread filename samples samplerate nbits wavread filename n samples samplerate nbits wavread filename n1 n2 samples samplerate nbits wavread data Description wavread filename reads the WAV file filename The result is a 2 d array where each row corresponds to a sample and each column to a channel Its class is the same as the native type of the WAV file i e int8 or int16 Libraries wav 551 wavread filename n where n is a scalar integer reads the first n samples of the file wavread filename n1 n2 where the second input argument is a vector of two integers reads samples from n1 to n2 the first sample corresponds to 1 Instead of a file name string the first input argument can be a vector of bytes of class int8 or uint8 which represents directly the contents of the WAV file In addition to the samples wavread can return the sample rate in Hz suc
94. result If a previous local variable with the same name exists it is deleted If the global variable does not exist it is created and initialized with the empty array Every access which follows the declaration in the same function or workspace uses the global variable Like global variables persistent variables are preserved between func tion calls but they cannot be shared between different functions They are declared with persistent They cannot be declared outside a function Different persistent functions can have the same name in different functions Examples Functions to reset and increment a counter function reset global counter counter Q function value increment global counter counter counter 1 value counter Here is how the counter can be used reset i increment i 1 j increment j 2 See also function LME Reference variables 57 matrixcol First index in a subscript expression Syntax A matrixcol function e C matrixcol obj i n Description In an expression used as a single subscript to access some elements of an array A expr matrixcol gives an array of the same size as A where each element is the column index For instance for a 2 by 3 matrix matrixcol gives the 2 by 3 matrix 1 1 1 2 2 2 In an expression used as the second of multiple subscripts to access some elements of an array A expr or A expr matrixcol gives a
95. scale equal plot x e y e plot x e y e 0 Array of vertex indices is modified to have closed triangles Triangles are displayed plot x t y t See also delaunayn N d Delaunay triangulation Syntax t delaunayn x t e delaunayn x Description delaunayn x calculates the Delaunay triangulation of points given by the rows of array x in a space of dimension size x 2 The result is an array with one more column Each row corresponds to a simplex values are row indices in x and give the vertices of each polyhedron The second output argument if requested is a logical vector with as many elements as rows in x elements are true if the corresponding point in x belongs to the convex hull of the set of points LME Reference triangulation 275 See also delaunay tsearchn voronoin griddata Data interpolation in 2 d plane Syntax vi vi griddata x y v xi yi griddata x y v xi yi method Description griddata x y v xi yi interpolates values at coordinates given by the corresponding elements of arrays xi and yi in a 2 dimension plane Original data are defined by corresponding elements of ar rays x y and v which must have the same size such that the value at coordinate x i y i is v i The result is an array with the same size as xi and yi where vi j is the value interpolated at xi j yi j All coordinates are real imaginary components are ignored Va
96. shal strb calculates the SHA1 digest of strb which represents bi nary data strb can be a string only the least significant byte of each character is considered or an array of bytes of class uint8 or int8 The result is a string of 40 hexadecimal digits It is believed to be hard to create the input to get a given digest or to create two inputs with the same digest LME Reference strings 307 shal fd calculates the SHA1 digest of the bytes read from file descriptor fd until the end of the file The file is left open SHA1 digest is an Internet standard described in RFC 3174 Example SHA1 digest of the three characters a b and c shal abc a9993e364706816aba3e25717850c26c9cd0d89d See also strcmp String comparison Syntax b strcmp sl1 s2 b strcmp sl1 s2 n Description strcmp s1 s2 is true if the strings s1 and s2 are equal i e same length and corresponding characters are equal strcmp s1 s2 n compares the strings up to the n th character Note that this function does not return the same result as the strcmp function of the standard C library Examples strcmp abc abc true strcmp abc def false strcmp abc abd 2 true strcemp abc abc 5 false See also 308 LMEPPC User Manual 1999 2008 Calerga Sarl strcmpi String comparison with ignoring letter case Syntax b strcmpi sl s2 b strcmpi sl1 s2 n Desc
97. simplex is shrinked around the vertex with minimum value It erations stop when the simplex is smaller than the tolerance or when the maximum number of iterations or function evaluations is reached then an error is thrown Examples Minimum of a sine near 2 displayed with 15 digits fprintf 15g n fminsearch sin 2 4 712388977408411 Maximum of xey xy 0 1x The function if defined as an anony mous function stored in variable fun fun x y x exp xX y 2 x y O 1 x 2 In Sysquake the contour plot can be displayed with the following com mands X Y meshgrid 0 0 02 3 0 0 02 3 contour feval fun X Y 0 3 0 3 0 1 0 05 0 5 The maximum is obtained by minimizing the opposite of the function rewritten to use as input a single variable in R 286 LMEPPC User Manual 1999 2008 Calerga Sarl mfun X X 1 exp X 1 X 2 2 X 1 X 2 1 X 1 2 fminsearch mfun 1 2 2 1444 0 3297 For the same function with a constraint x lt 1 the objective function can be modified to return co for inputs outside the feasible region note that we can start on the constraint boundary but starting from the infeasible region would probably fail mfunc X X 1 lt 1 X 1 exp X 1 X 2 2 X 1 X 2 O 1 X 1 2 inf fminsearch mfunc 1 2 1 0 7071 See also fzero Zero of a function Syntax x fzero fun x0 x fzero fun xlow xhigh
98. string double single int8 int16 LME Reference triangulation 273 int32 int64 uint8 uint16 uint32 or uint64 64 bit arrays are not supported on all platforms Examples zeros 2 3 000 000 zeros 2 0 0 0 0 zeros 1 5 uint16 1x5 uintl6 array 0000 0 See also 3 18 Triangulation Functions delaunay 2 d Delaunay triangulation Syntax t delaunay x y t e delaunay x y Description delaunay x y calculates the Delaunay triangulation of 2 d points given by arrays x and y Both arrays must have the same number of values m The result is an array of three columns Each row corre sponds to a triangle values are indices in x and y The second output argument if requested is a logical vector of size m by 1 elements are true if the corresponding point in x and y belongs to the convex hull of the set of points The Delaunay triangulation is a net of triangles which link all the starting points in such a way that no point is included in the circum scribed circle of any other triangle Triangles are as equilateral as possible 274 LMEPPC User Manual 1999 2008 Calerga Sarl Example Delaunay triangulation of 20 random points Xx rand 20 1 rand 20 1 t e delaunay x y With Sysquake graphical functions points belonging to the convex hull are displayed as crosses and interior points as circles clf
99. the global variable names info persistent displays the list of all persistent variables With an output argument info persistent gives the list of the persis tent variable names info libraries displays the list of all loaded libraries With an output argument info libraries gives the list of the library names info usedlibraries displays the list of libraries available in the current context With an output argument info usedlibraries gives the list of the names of these libraries info threads displays the ID of all threads With an output argu ment info threads gives a list of structures which describe each thread with the following fields id thread ID totaltime execution time in seconds Only the first character of the argument is meaningful info b is equivalent to info builtin LME Reference miscellaneous functions 97 Examples info LME 4 5 info b abs acos acosh etc info v ans 1x1 complex vars info v dumpvar vars struct name ans defined true struct name vars defined false See also inline Creation of inline function Syntax fun inline funstr fun inline expr fun inline expr argl fun inline funstr param fun inline expr argl paramstruct Description Inline function are LME objects which can be evaluated to give a result as a function of their input arguments Contrary to functio
100. the result Examples num2list 1 5 1 2 3 4 5 num2list 1 2 3 4 1 2 3 4 num2list 1 2 3 4 1 1 2 3 4 num2list 1 2 3 4 2 1 3 2 4 See also replist Replicate a list Syntax listout replist listin n Description replist listin n makes a new list by concatenating n copies of list listin LME Reference structures 327 Example replist 1 abc 3 1 abc 1 abc 1 abc See also 3 24 Structure Functions fieldnames List of fields of a structure Syntax fields fieldnames strct Description fieldnames strct returns the field names of structure strct as a list of strings Example fieldnames struct a 1 b 1 5 a b See also orderfields getfield Value of a field in a structure Syntax value getfield strct name 328 LMEPPC User Manual 1999 2008 Calerga Sarl Description getfield strct name gets the value of field name in structure strct It is an error if the field does not exist getfield s f gives the same value as s f getfield is especially useful when the field name is not fixed but is stored in a variable or is the result of an expression See also isfield Test for the existence of a field in a structure Syntax b isfield strct name Description isfield strct name is true if the structure strct has a field whose name is the string name fal
101. then normal execution is resumed dbstep y 1 1 25 1 5 1 75 2 Display breakpoint and clear it dbstatus stdlib linspace 0 dbclear LME Reference debugging commands 81 See also abstop dbstop Set a breakpoint Syntax dbstop fun dbstop fun line dbstop fun line Description dbstop funsets a breakpoint at the beginning of function fun dbstop fun line or dbstop fun line sets a breakpoint in function fun at line Line When LME executes a line where a breakpoint has been set it sus pends execution and returns to the command line interface The user can inspect or change variables executes expressions or other func tions continue execution with dbstep or dbcont or abort execution with dbquit Example use stdlib dbstop linspace dbstatus stdlib linspace 0 dbclear lLinspace See also dbtype Display source code with line numbers breakpoints and current exe cution point Syntax dbtype fun dbtype 82 LMEPPC User Manual 1999 2008 Calerga Sarl Description dbtype fun displays the source code of function fun with line num bers breakpoints and the position where execution is suspended if it is in fun Without argument dbtype displays the function which is suspended dbtype can be used at any time to check the source code of any function known to LME Example use stdlib dbstop linspace Linspace 1 2 5 lt lLinspace 8 gt if nargin lt 3 dbstep lt lLinspace 11
102. time and the end time Such an explicit time range is required when the response is not displayed in a plot where the x axis represents the time The optional arguments style and id have theirjusual meaning With output arguments dlsim gives the output and the time as column vectors or an array for the output of a multiple output state space model where each row represents a sample No display is produced LME Reference graphics for dynamical systems 427 disim 10 Figure 3 11 dlsim 1 poly 0 9 0 7 0 6j 0 7 0 6j u Example Simulation of a third order system with a rectangular input see Fig 3 11 u repmat ones 1 10 zeros 1 10 1 3 dlsim 1 poly 0 9 0 7 0 6j 0 7 0 6j u 1 rs See also dnichols Nichols diagram of a discrete time system Syntax dnichols numd dend dnichols numd dend w dnichols numd dend opt lt dnichols numd dend w opt dnichols style dnichols style id w dnichols 428 LMEPPC User Manual 1999 2008 Calerga Sarl mag phase dnichols mag phase w dnichols Description dnichols numd dend displays the Nichols diagram of the discrete time transfer function given by polynomials numd and dend In dis crete time the Nichols diagram is the locus of the complex values of the transfer function evaluated at e where w is a real number between 0 and 7 inclusive displayed in the phase magnitude plane Us
103. to half the sampling frequency Libraries filter 513 butter n w0 high gives a nth order digital highpass filter with a cutoff frequency of w0 relatively to half the sampling frequency butter n wl wh stop where the second input argument is a vector of two numbers gives a 2nth order digital bandstop filter with stopband between wl and wh relatively to half the sampling frequency With an additional input argument which is the string s butter gives an analog Butterworth filter Frequencies are given in rad s See also cheblap Chebyshev type 1 analog filter prototype Syntax use filter z p k cheblap n rp Description cheblap n rp calculates the zeros the poles and the gain of a Chebyshev type 1 analog filter of degree n with a cutoff angular fre quency of 1 rad s Ripples in the passband have a peak to peak mag nitude of rp dB See also cheb2ap Chebyshev type 2 analog filter prototype Syntax use filter z p k cheb2ap n rs 514 LMEPPC User Manual 1999 2008 Calerga Sarl Description cheb2ap n rs calculates the zeros the poles and the gain of a Chebyshev type 2 analog filter of degree n with a cutoff angular fre quency of 1 rad s Ripples in the stopband have a peak to peak mag nitude of rs dB See also chebyl1 Chebyshev type 1 filter Syntax use filter Z p k chebyl n w0 num den chebyl n w0 cheby1 n wl wh
104. to inv a b See also lti mrdivide lti times lti inv Iti mrdivide System right division Syntax use lti C a b C mrdivide a b Description a b is equivalent to axinv b See also t1i mldivide ilt1i times Lt1 1nv Iti mtimes System product Syntax use lti c axb c mtimes a b Libraries lti 533 Description axb connects the outputs of lti object b to the inputs of lti object a If a and b are transfer functions or matrices of transfer functions this is equivalent to a product of matrices See also lti series Iti norm H2 norm Syntax use lti h2 norm a Description norm a gives the H2 norm of the system a See also ss obsv Observability matrix Syntax use lti 0 obsv a Description obsv a gives the observability matrix of system a which is full rank if and only if a is observable See also ss ctrb 534 LMEPPC User Manual 1999 2008 Calerga Sarl Iti parallel Parallel connection Syntax use lti c parallel a b c parallel a b ina inb outa outb Description parallel a b connects lti objects a and b in such a way that the inputs of the result is applied to both a and b and the outputs of the result is their sum parallel a b ina inb outa outb specifies which inputs are shared between a and b and which outputs are summed The inputs of the result are partitioned as ua uab ub and the outputs as ya yab yb Input
105. type and size as the input Example igraycode graycode Q 7 01234567 See also islogical Test for a boolean object Syntax b islogical obj 344 LMEPPC User Manual 1999 2008 Calerga Sarl Description islogical obj is true if obj is a logical value and false otherwise The result is always a scalar even if obj is an array Logical values are obtained with comparison operators logical operators test functions and the function Logical Examples islogical eye 10 false islogical eye 10 true See also logical Transform a number into a boolean Syntax B logical A Description logical x converts array or number A to logical boolean type All nonzero elements of A are converted to true and zero elements to false Logical values are stored as 0 for false or 1 for true in unsigned 8 bit integers They differ from the uint8 type when they are used to select the elements of an array or list Examples a 1 3 a 1 0 1 Index out of range a 1 3 a logical 1 0 1 13 See also LME Reference logical functions 345 true Boolean constant true Syntax b true B true n B true nl1 n2 B true nl n2 Description The boolean constant true can be used to set the value of a variable It is equivalent to Logical 1 The constant 1 is equivalent in many cases indices to get or set the elements of an array are an important exception With
106. uniformly to one of the discrete color entries O to the first row and 1 to the last row With an input argument colormap clut sets the colormap to clut With an output argument colormap returns the current col ormap LME Reference base graphics 385 See also contour Level curves Syntax contour z contour z xmin xmax ymin ymax contour z xmin xmax ymin ymax levels contour z xmin xmax ymin ymax levels style Description contour z plots seven contour lines corresponding to the surface whose samples at equidistant points 1 size z 2 in the x direction and 1 size z 1 on the y direction are given by z Contour lines are at equidistant levels With a second non empty argument xmin xmax ymin ymax the samples are at equidistant points between xmin and xmax in the x direction and between ymin and ymax in the y direction The optional third argument levels if non empty gives the num ber of contour lines if it is a scalar or the levels themselves if it is a vector The optional fourth argument is the style of each line from the minimum to the maximum level styles are recycled if necessary The default style is kbrmgcy When the style is f for a filled region the corresponding level is filled on the side with a lower value of z If the style argument is the single character f all levels are filled with the default colors Regions with a value of z smaller than the lowest level ar
107. url soapreadcall str method fun ns namespace pstruct x 3 1416 y true url See also soapreadresponse soapwritecall soapreadresponse Decode a SOAP call response Extensions Web Services 587 Syntax fault value fault value soapreadresponse fd soapreadresponse str Description soapreadresponse fd where fd is a file descriptor reads a com plete SOAP response and decodes it In case of success it returns true in the first output argument and the decoded response value in the second output argument In case of failure it returns false and the fault structure which contains the fields faultcode error code as a string and faultstring error message as a string soapreadresponse str decodes its string argument which must be a whole SOAP response Examples str soapwriteresponse fun namespace 123 fault value soapreadresponse str fault false value 123 strf soapwritefault 12int32 No power fault value soapreadresponse strf fault true value faultcode 712 faultstring No power See also soapreadcall soapwritefault soapwritecall Encode a SOAP call request Syntax soapwritecall fd server url action method ns params soapwritecall server url action method ns params str soapwritecall server url action method ns params 588 LMEPPC User Manual 1999 2008 Calerga Sarl Description soapwritec
108. uses the specified conversion method method is one of LME Reference dynamical systems 347 zoh or z zero order hold default foh or f first order hold tustin or t Tustin bilinear transformation matched or m Matched zeros poles and gain The input and output arguments numc denc numd and dend can also be matrices in that case the conversion is applied separately on each row with the same sampling period Ts c2dm Ac Bc Cc Dc Ts method performs the conversion from continuous time state space model Ac Bc Cc Dc to discrete time state space model Ad Bd Cd Dd defined by dx ae A x t B u t y t C x t Dcu t and x k 1 Agx k Bgu k y k Cax k Dau k Method matched is not supported for state space models Examples numd dend c2dm 1 1 1 0 1 numd 0 0952 dend 1 0 9048 numd dend c2dm 1 1 1 0 1 foh numd 0 0484 dend 1 0 9048 numd dend c2dm 1 1 1 0 1 tustin numd 0 0476 0 0476 dend 1 0 9048 See also 348 LMEPPC User Manual 1999 2008 Calerga Sarl d2cm Discrete to continuous time conversion Syntax numc denc d2cm numd dend Ts denc d2cm numd dend Ts numc denc d2cm numd dend Ts method denc d2cm numd dend Ts method Description numc denc d2cm numd dend Ts method converts the discrete time transfer function numd dend with sampling period Ts to a contin
109. values When its first input argument is a structure imageset adds or changes fields which correspond to the name value pairs which fol low Here is the list of permissible options Name Default Meaning Type PNG PNG or JPG JPEG Quality 80 JPEG quality O worst 100 best Progressive false true to permit progressive decoding 566 LMEPPC User Manual 1999 2008 Calerga Sarl Examples Default options imageset Type png Quality 80 Progressive false Writing the contents of array A into a small low quality JPEG file fd fopen A jpg w imagewrite fd A imageset Type JPG Quality 20 fclose fd See also imagewrite imagewrite Write an image file Syntax imagewrite fd A imagewrite fd A options Description imagewrite fd A writes array A to a PNG file specified by file de scriptor fd Image A is an array whose first dimension is the image height and second dimension the image width Grayscale images have their third dimension equal to 1 i e they are plain matrices Color images have a third dimension equal to 3 fist plane is the red com ponent second plane the green component and third plane the blue component In both cases value range is 0 for black to 1 for maximum intensity Values outside this range are clipped imagewrite fd A options uses structure options to specify im age file options Options are usually created with functi
110. why the conditional expression in filterfun is less than or equal to and not less than Then the event occurs and integration continues from t 1 with u 0 Non integrated state For the last example we will consider a system made of an integrator and a relay with hysteresis in a loop Let y 1 be the output of the integrator and y 2 the output of the relay Only y 1 is integrated 296 LMEPPC User Manual 1999 2008 Calerga Sarl Relay with hysteresis 1 An event occurs when the integrator is larger or smaller than the hys teresis value y 1 y 2 isTerminal false direction sign y 2 When the event occurs a new value is computed for the 2nd state yn y 2 To integrate this the following functions are defined function yp relayfun t y yp y 2 function v te d relayevents t y v y 1 y 2 te false d sign y 2 function yn r yn y 2 elayonevent t y i The initial state is 0 1 O for the integrator and 1 for the output of the relay State is integrated during 5 s see Fig 3 4 with t y ode45 relayfun 0 5 0 1 odeset Events relayevents OnEvent relayonevent plot t y LME Reference non linear numerical functions 297 See also optimset Options for minimization and zero finding Syntax options optimset options optimset namel valuel options optimset optionsO namel valuel Descri
111. x fzero options x fzero options Description fzero fun finds numerically a zero of function fun fun is either specified by its name or given as an anonymous or inline function or a function reference It has at least one input argument x and it returns one output argument also a real number fzero finds the value x such that fun x 0 up to some tolerance Second argument tells where to search it can be either a starting point or a pair of values xLow and xhigh which must bracket the zero such that fun xlow and fun xhigh have opposite sign The optional third argument may contain options It is either the empty array for the default options or the result of optimset Additional input arguments of fzero are given as additional input arguments to the function specified by fun They permit to parame terize the function LME Reference non linear numerical functions 287 Examples Zero of a sine near 3 displayed with 15 digits fprintf 15g n fzero sin 3 3 141592653589793 To find the solution of e c x between 0 and 100 with c 10 a function f whose zero gives the desired solution is written function y f x c y exp x c sqrt x Then fsolve is used with the value of c passed as an additional argu ment x fzero f 0 100 10 x 2 4479 f x 10 1 9984e 15 An anonymous function can be used to avoid passing 10 as an ad ditional argument which can be error pr
112. y is equivalent to x gt y It can be used to redefine this op erator for objects Example 2 3 4 gt 2 4 2 TFT See also operator operator operator lt operator lt operator gt 136 LMEPPC User Manual 1999 2008 Calerga Sarl Operator Not Syntax b not b Description b is false logical 0 if b is different from 0 or false and true otherwise If b is an array the operation is performed on each element not b is equivalent to b It can be used to redefine this operator for objects Examples true false 1 0 3 false FTFT See also pitomp Operator amp And Syntax b1 amp b2 and b1 b2 Description b1 amp b2 performs the logical AND operation between the corresponding elements of b1 and b2 the result is true logical 1 if both operands are different from false or 0 and false logical 0 otherwise and b1 b2 is equivalent to b1 amp b2 It can be used to redefine this operator for objects LME Reference operators 137 Example false false true true amp false true false true FFFT See also operator 6 Operator amp And with lazy evaluation Syntax b1 amp amp b2 Description b1 amp amp b2 is b1 if b1 is false and b2 otherwise Like with if and while statements b1 is true if it is a nonempty array with only non zero elements b2 is evaluated only if b1 is true b1 amp amp b2 amp amp amp amp bn returns the
113. y f p x a b deal p y a x b 2 3 See also inmem List of functions loaded in memory Syntax inmem list inmem Description inmem displays the list of user defined functions loaded in memory with the library where they are defined With an output argument inmem gives a list of structures which describe each user defined function loaded in memory with the following fields library library name class class name for functions name function name 100 LMEPPC User Manual 1999 2008 Calerga Sarl See also isglobal Test for the existence of a global variable Syntax b isglobal str Description isglobal str returns true if the string str is the name of a global variable defined as such in the current context See also iskeyword Test for a keyword name Syntax b iskeyword str list iskeyword Description iskeyword str returns true if the string str is a reserved keyword which cannot be used as a function or variable name or false other wise Keywords include if and global but not the name of built in functions like sin or i Without input argument iskeyword gives the list of all keywords Examples iskeyword otherwise true iskeyword break case catch continue else elseif end endfunction for function global if LME Reference miscellaneous functions 101 otherwise persiste
114. y i end The optional second output argument is set to the final state of the filter Examples filter 1 2 1 2 3 ones 1 10 1 1 2 41 11 22 8 47 121 5 6 5 6 5 6 5 p 0 8 filter 1 p 1 p u p u 1 low pass with matching initial state 5 5 2 5 16 5 328 5 2624 5 4099 5 3279 u See also funm Matrix function Syntax Y funm X fun Y err funm X fun Description funm X fun returns the matrix function of square matrix X specified by function fun fun takes a scalar input argument and gives a scalar output It is either specified by its name or given as an inline function or a function reference With a second output argument err funm also returns an estimate of the relative error LME Reference linear algebra 213 Examples funm 1 2 3 4 sin 0 4656 0 1484 0 2226 0 6882 X 1 2 3 4 funm X inline 1 x 2 x 0 25 0 75 1 125 1 375 eye 2 X 2 eye 2 X 0 25 0 75 1 125 1 375 See also ifft Inverse Fast Fourier Transform Syntax f ifft F f ifft F n f ifft F n dim Description ifft returns the inverse Discrete Fourier Transform inverse DFT Up to the sign and a scaling factor the inverse DFT and the DFT are the same operation for a vector ifft d conj fft d length d ifft has the same syntax as fft Examples ft 1 2 3 4 See also 214 LMEPPC User Manual 1999 2008 Calerga Sarl ifft2 Inverse 2 d F
115. years is applied back to the past before its introduction Negative years are permitted the year 0 does exist The julian date is the number of days since the reference point January 1st 4713 B C Julian calendar at noon The fractional part corresponds to the fraction of day after noon a fraction of 0 25 for instance is 18 00 or 6 P M The julian date is used by astronomers with GMT but using a local time zone is fine as long as an absolute time is not required cal2julian Calendar to julian date conversion Syntax jd cal2julian datetime jd cal2julian year month day jd cal2julian year month day hour minute second Description cal2julian datetime converts the calendar date and time to the julian date Input arguments can be a vector of 3 components year month and day or 6 components date and hour minute and sec onds or scalar values provided separately The result of clock can be used directly Example Number of days between October 4 1967 and April 18 2005 cal2julian 2005 4 18 cal2julian 1967 10 4 14624 See also julian2cal julian2cal Julian date to calendar conversion 374 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax datetime julian2cal jd year month day hour minute second julian2cal jd Description julian2cal jd converts the julian date to calendar date and time With a single output the result is given a a row vector of 6 values for the year
116. 0 _x0 _y0 _id and _ix such that they correspond to the nearest element if it is close enough to the mouse coordinates Second the ar gument _id is set to the ID value so that the mousedown mousedrag and mouseup handlers can identify the different objects the user can manipulate In applications without live interactivity such as Sysquake Remote the graphic ID argument is accepted for compatibility reasons but ignored Scale Before any figure can be drawn on the screen the scale or equiv alently the portion of the plane which is represented on the screen must be determined The scale depends on the kind of graphics and consequently is specified in the draw handler but can be changed by the user with the zoom and shift commands What the user specifies has always the priority If he or she has not specified a new scale the scale command found in the draw handler is used scale xMin xMax yMin yMax If scale is not used or if some of the limits are NaN not an number a default scale is given by the plot commands themselves If used the scale command should always be executed before any plot command because several of them use the scale to calculate traces only over the visible range or to adjust the density of the calculated points of the traces If you need to know the limits of the displayed area in your draw handler use scale to get them right after setting the default scale so that you take into account the z
117. 0 delay after character output in seconds Handshake false hardware handshake StopBits 2 number of stop bits 1 1 5 or 2 TextMode false text mode Timeout 1 timeout in seconds Output operations wait for the specified delay after each character this can be useful with slow devices without handshake When text mode is set input CR and CR LF sequences are con verted to LF Output CR and LF are not converted Depending on the platform operations which use the timeout value such as input can be interrupted with the platform dependent abort key s typically Escape or Control C or are limited to 10 seconds Example serialdevset BPS 19200 Handshake false StopBits 2 TextMode false Timeout 1 See also serialaevopen jserilatdevname Chapter 5 Libraries Libraries are collections of functions which complement the set of built in functions and operators of LME To use them type or add at the beginning of the libraries which rely on them a use command such as use stdlib bench bench implements a benchmark which can be used to com pare the performance of LME on different platforms bitfield bitfield implements constructors and methods for bit fields binary numbers Standard operators are redefined to en able the use of amp and for bitwise operations and subscripts for bit extraction and assignment classes classes implements constructors and methods for poly nomial and rational functions With them you
118. 002 eee ee 27 3 2 Function Call 0 000 000 00005 28 3 3 LibrarieS 02 666 ce ee e e a 30 3 4 TYPES babe ek ee lee Remy Bite aa ow i Bale a 30 3 5 Input and Output 0 0000 37 3 6 Error Messages 2 200000 e eee eee 38 3 7 List of Commands Functions and Operators 43 3 8 Variable Assignment and Subscripting 53 3 9 Programming Constructs 0000005 60 3 10 Debugging Commands 00 0000 76 S211 Profilen inc 2 aia aa oa ot aca Soe Aa ae ee ee AS 83 3 12 Miscellaneous Functions 86 eee ee ee ee ee ee ee 110 3 14 Operators 0 00000 eee ee 113 4 LMEPPC User Manual 1999 2008 Calerga 3 15 Mathematical Functions 000005 3 17 Array Functions 3 18 Triangulation Functions 3 19 Integer Functions 3 20 Non Linear Numerical Functions 3 21 String Functions 00000002 ee eee 3 22 QuatermiOms o e sbe koe he ae bh We A ala Reed ao AS 3 23 LISE FUNCTIONS secs e a hdd ee oe BGO dw Sal a are 3 24 Structure Functions 0 00000 e eens 3 25 Object Functions 3 26 Logical Functions 3 27 Dynamical System Functions 3 28 Input Output Functions 3 29 File System Functions 3 30 Time Functions 3 31 Date Conversion Functions 0005 3 32 Graphics 3 33 Remarks on graphics 3 34 Base Graphical Functions 3 35 3D Graphics 3 37 Surface shading 3 38 Functions
119. 1 3 5 nan 2 3 5 max 1 3 5 nan 2 23 5 2 See also min mean Arithmetic mean of a vector Syntax x mean v v mean M v mean M dim Description mean v returns the arithmetic mean of the elements of vector v mean M returns a row vector whose elements are the means of the LME Reference linear algebra 223 corresponding columns of matrix M mean M dim returns the mean of matrix M along dimension dim the result is a row vector if dim is 1 or a column vector if dim is 2 Examples mean 1 5 7 5 mean 1 5 7 5 mean 1 2 3 5 6 7 345 mean 1 2 3 5 6 7 1 345 mean 1 2 3 5 6 7 2 2 6 See also min Minimum value of a vector or of two arguments Syntax x min v v ind min v v fiy dim v ind min M dim M3 SCE Description min v returns the largest number of vector v NaN s are ignored The optional second smallest argument is the index of the minimum in v if several elements have the same minimum value only the first one is obtained The argument type can be double single or integer of any size min M operates on the columns of the matrix M and returns a row vector min M dim operates along dimension dim 1 for columns 2 for rows min M1 M2 returns a matrix whose elements are the minimum be tween the corresponding elements of the matrices M1 and M2 M1 and 224 LMEPPC User Manual 1999 2008 Calerga Sarl M2 must have the same size
120. 16 See also uint8 and related functions intmin Smallest integer Syntax i intmin i intmin type Description Without input argument intmin gives the smallest signed 32 bit inte ger intmin type gives the largest integer of the type specified by string type which can be uint8 uint16 uint32 uint64 int8 int16 int32 or int64 64 bit integers are not sup ported on all platforms The result has the corresponding integer type Examples intmin 2147483648int32 intmin uint16 Ouint16 282 LMEPPC User Manual 1999 2008 Calerga Sarl See also uint8 and related functions map2int Mapping of a real interval to an integer type Syntax B B B map2int A map2int A vmin vmax map2int A vmin vmax type Description map2int A vmin vmax converts number or array A to 8 bit unsigned integers Values between vmin and vmax in A are mapped linearly to values 0 to 255 With a single input argument the default input interval is O to 1 map2int A vmin vmax type converts A to the specified type which can be any integer type given as a string uint8 uint16 uint32 uint64 int8 int16 int32 or int64 64 bit integers are not supported on all platforms The input interval is mapped to its full range In all cases input values outside the interval are clipped to the minimum or maximum values Examp
121. 18 See also prod 238 LMEPPC User Manual 1999 2008 Calerga Sarl svd Singular value decomposition Syntax s svd M U S V svd M U S V svd M false Description The singular value decomposition U S V svd M decomposes the m by n matrix M such that M UxS V where S is an m by n diagonal matrix with decreasing positive diagonal elements the singular values of M Uis an m by m unitary matrix and V is an n by n unitary matrix The number of non zero diagonal elements of S up to rounding errors gives the rank of M When M is rectangular in expression UxS V some columns of U or V are multiplied by rows or columns of zeros in S respectively U S V svd M false produces U S and V where these columns or rows are discarded relationship M U S V still holds Size of A Size of U Size ofS Size of V mbyn m lt n mbym m by m n by m mbyn m gt n m by n n by n n by n svd M true produces the same result as svd M With one output argument s svd M returns the vector of sin gular values s diag S The singular values of M can also be computed with s sqrt eig M M but svd is faster and more robust Examples U S V svd 1 2 3 4 U _ 0 4046 0 9145 0 9145 0 4046 S 5 465 0 0 0 366 V 0 576 0 8174 0 8174 0 576 U S V 12 3 4 LME Reference linear algebra 239 svd 1 2 1 2 3 1623 3 4697e 19 See also trace Trace of a matrix Syntax tr trace
122. 1999 2008 Calerga Sarl numel 2 vwxyz 2 See also ones Array of ones Syntax A ones n A ones nl1 n2 A ones nl n2 A ones type Description ones builds an array whose elements are 1 The size of the array is specified by one integer for a square matrix or several integers either as separate arguments or in a vector for an array of any size An additional input argument can be used to specify the type of the result It must be the string double single int8 int16 int32 int64 uint8 uint16 uint32 or uint64 64 bit arrays are not supported on all platforms Example ones 2 3 111 111 ones 2 int32 2x2 int32 array 11 11 See also permute Permutation of the dimensions of an array LME Reference arrays 259 Syntax B permute A perm Description permute A perm returns an array with the same elements as A but where dimensions are permuted according to the vector of dimensions perm It is a generalization of the matrix transpose operator perm must contain integers from 1 to n dimension i in A becomes dimen sion perm i in the result Examples size permute rand 3 4 5 2 3 1 453 See also rand Uniformly distributed random number Syntax x rand M rand n M rand nl n2 M rand nl n2 rand seed s Description rand builds a scalar pse
123. 2 0 2 4 2 208 LMEPPC User Manual 1999 2008 Calerga Sarl See also eig Eigenvalues and eigenvectors of a matrix Syntax e eig M V D eig M Description eig M returns the vector of eigenvalues of the square matrix M V D eig M returns a diagonal matrix D of eigenvalues and a matrix V whose columns are the corresponding eigenvectors They are such that M V VD Examples eig 1 2 3 4 0 3723 5 3723 V D eig 1 2 2 1 V 0 7071 0 7071 0 7071 0 7071 D 1 0 03 1 2 2 1 V 0 7071 2 1213 0 7071 2 1213 V xD 0 7071 2 1213 0 7071 2 1213 See also expm Exponential of a square matrix LME Reference linear algebra 209 Syntax M2 expm M1 Description expm M is the exponential of the square matrix M which is usually different from the element wise exponential of M given by exp Examples expm 1 1 1 1 4 1945 3 1945 3 1945 4 1945 exp 1 1 1 1 2 7183 2 7183 2 7183 2 7183 See also fft Fast Fourier Transform Syntax F fft f F fft f n F fft f n dim Description fft f returns the discrete Fourier transform DFT of the vector f or the DFT s of each columns of the array f With a second argument n the n first values are used if n is larger than the length of the data zeros are added for padding An optional argument dim gives the dimension along which the DFT is performed it is 1 for calculating the DFT of the columns of f
124. 2x2x2 array 1 5 6 7 8 2 2 4 w See also fliplr Flip an array or a list around its vertical axis Syntax A2 fliplr A1 list2 fliplr list1 Description fliplr A1 gives an array A2 which has the same size as Al but where all columns are placed in reverse order fliplr list1 gives a list List2 which has the same length as list1 but where all top level elements are placed in reverse order Elements themselves are left unchanged Examples fliplr 1 2 3 4 2 1 43 fliptr 1 x 1 2 3 1 2 3 x 1 See also flipud flipdim flipud Flip an array upside down LME Reference arrays 247 Syntax A2 flipud A1 Description flipud A1 gives an array A2 which has the same size as Al but where all lines are placed in reverse order Example flipud 1 2 3 4 3 4 1 2 See also ind2sub Conversion from single index to row column subscripts Syntax i j ind2sub size ind Description ind2sub size ind gives the subscripts of the element which would be retrieved from an array whose size is specified by size by the single index ind size must be either a scalar for square matrices or a vector of two elements or more for arrays ind can be an array the result is calculated separately for each element and has the same size Example M 3 6 8 9 M 3 8 i j ind2sub size M 3 p Fi N ie M i j 8 248 LMEPPC User Manual 19
125. 99 2008 Calerga Sarl See also jsub2ind size interpn Interpolation Syntax Vi interpn xl xn V xil Xin Vi interpn xl xn V xil xin method Description interpn x1 xn V xil xin interpolates data in a space of n dimensions Input data are defined by array V where element V i j Corresponds to coordinates x1 i x2 j etc Interpolation is performed for each coordinates defined by arrays xil xi2 etc which must all have the same size the result is an array of the same size Length of vectors x1 x2 must match the size of V along the corresponding dimension Vectors x1 x2 must be sorted mono tonically increasing or decreasing but they do not have to be spaced uniformly Interpolated points outside the input volume are set to nan Input and output data can be complex Imaginary parts of coordinates are ignored The default interpolation method is multilinear An additional input argument can be provided to specify it with a string only the first character is considered Argument Meaning 0 or nearest nearest value r lt lower coordinates gt higher coordinates 1 or linear multilinear Method lt takes the sample where each coordinate has its in dex as large as possible lower or equal to the interpolated value and smaller than the last coordinate Method gt takes the sample where each coordinate has its index greater
126. Bc Cc Dc LME Reference graphics for dynamical systems 421 bodephase Ac Bc Cc Dc w bodephase Ac Bc Cc Dc opt bodephase Ac Bc Cc Dc w opt bodephase style bodephase style id phase w bodephase Description bodephase numc denc plots the phase of the frequency response of the continuous time transfer function numc denc The range of fre quencies is selected automatically or can be specified in an optional argument w a vector of frequencies Further options Such as time delay can be provided in a structure opt created with responseset fields Delay and Range are utilized The optional arguments style and id have their usual meaning bodemag Ac Bc Cc Dc plots the phase of the frequency response YQw JU jw of the continuous time state space model Ac Bc Cc Dc defined as jwX jw AcX jW BCUGw YUGw C XUjw D U Ujw With output arguments bodephase gives the phase and the frequency as column vectors No display is produced Example Green plot for arg 1 s 2s 3s 4 with s jw see Fig 3 10 bodephase 1 1 2 3 4 g See also bodemag dbodephase dbodemag Magnitude Bode diagram for a discrete time system Syntax dbodemag numd dend Ts dbodemag numd dend Ts w dbodemag numd dend Ts opt 422 LMEPPC User Manual 1999 2008 Calerga Sarl scale loglin bodephase 1 1 2 3 4 Figure 3 10 scale loglin bodephase 1
127. Calerga 2 LME for Pocket PC 071208 User Manual 2 LMEPPC User Manual 1999 2008 Calerga Sarl Copyright 1999 2008 Calerga Sarl No part of this publication may be reproduced transmitted or stored in any form or by any means including electronic mechanical recording or oth erwise without the express written permission of Calerga Sarl The information provided in this manual is for reference and information use only and Calerga assumes no responsibility or liability for any inaccura cies or errors that may appear in this documentation Sysquake LME Calerga the Calerga logo and icons are copyrighted and are protected under the Swiss and international laws Copying this software for any reason beyond archival purposes is a violation of copyright and viola tors may be subject to civil and criminal penalties Sysquake LME and Calerga are trademarks of Calerga Sarl All other trademarks are the property of their respective owners LME for Pocket PC User Manual December 2007 Yves Piguet Calerga Sarl Lausanne Switzerland Most of the material in LME Pocket PC User Manual has first been written as a set of XHTML files with lots of cross reference links Since X HTML is not very well suited for printing it has been converted to TEX with the help of a home made conversion utility Additional XML tags have been used to benefit from BEX features e g raster images have been replaced with EPS images equations have been co
128. Example num den ss2tf 1 1 1 0 num 1 de e Il n 1 See also tf2ss Conversion from transfer function to state space Syntax A B C D tf2ss num den LME Reference input output 353 Description tf2ss num den returns the state space representation of the trans fer function num den which is given as two polynomials The transfer function must be causal i e num must not have more columns than den Systems with several outputs are specified by a num having one row per output the denominator den must be the same for all the outputs tf2ss applies to continuous time systems Laplace transform as well as to discrete time systems z transform or delta transform Example A B C D tf2ss 2 5 2 3 8 A 1 5 4 10 B 1 0 C 12 5 D 0 See also 3 28 Input Output Functions bwrite Store data in an array of bytes Syntax bwrite data bwrite data precision S S Description bwrite data stores the contents of the matrix data into an array of class uint8 The second parameter is the precision whose meaning is the same as for fread Its default value is uint8 354 LMEPPC User Manual 1999 2008 Calerga Sarl Examples bwrite 12345 uint32 1l 1x4 uint8 array 57 48 0 0 bwrite 12345 uint32 b 1x4 uint8 array 0 0 48 57 See also clc Clear the text window or panel Syntax clc clc fd Description clc clear console clears the content
129. Example gammainc 2 1 5 0 7385 See also gammalin Logarithm of gamma function Syntax y gammaln x 170 LMEPPC User Manual 1999 2008 Calerga Sarl Description gammaln x gives the logarithm of the gamma function of x Argument and result are real imaginary part is discarded gammaln does not rely on the computation of the gamma function to avoid overflows for large numbers Examples gammaln 1000 5905 2204 gamma 1000 inf See also gammainc betaln gcd Greatest common divisor Syntax q gcd a b Description gcd a b gives the greatest common divisor of integer numbers a and b Example gcd 72 56 8 See also goldenratio Golden ratio constant LME Reference mathematical functions 171 Syntax x goldenratio Description goldenratio is the golden ration v5 1 2 up to the precision of its floating point representation Example goldenratio 1 6180 See also hypot Hypotenuse Syntax c hypot a b Description hypot a b gives the square root of the square of a and b or of their absolute value if they are complex The result is always real hypot avoids overflow when the result itself does not overflow Examples hypot 3 4 5 hypot 1 2 3 4j inf 5 5 099 5 3852 5 831 inf See also 172 LMEPPC User Manual 1999 2008 Calerga Sarl ij Imaginary unit Syntax i j 1 23e4i 1 23e4j Description i or j are the im
130. F See also isnumeric Test for a numeric object Syntax b isnumeric x Description isnumeric x is true if the input argument is numeric real or complex scalar vector or array and false otherwise Examples isnumeric pi true isnumeric abc false 178 LMEPPC User Manual 1999 2008 Calerga Sarl See also isscalar Test for a scalar number Syntax b isscalar x Description isscalar x is true if the input argument is scalar real or complex number of any floating point or integer type character or logical value and false otherwise Examples isscalar 2 true isscalar 1 2 5 false See also isnumeric isvector size isvector Test for a vector Syntax b isvector x Description isvector x is true if the input argument is a row or column vec tor real or complex 2 dimension array of any floating point or inte ger type character or logical value with one dimension equal to 1 or empty array and false otherwise LME Reference mathematical functions 179 Examples isvector 1 2 3 true isvector 1 2 true isvector 7 true isvector 1 2 3 4 false See also tength Icm Least common multiple Syntax q lcm a b Description lcm a b gives the least common multiple of integer numbers a and b Example lcm 72 56 504 See also gcd log Natural base e logarithm Syntax y log x 180 LMEPPC User Manu
131. L beginning with http or only the absolute path in the second case the server address and port come from argument opt method is the XML RPC method name as a string opt is a structure which contains the options it is typically created with xmlrpccallset or can be the Extensions Web Services 591 empty array for the default options The remaining input arguments are sent to the server as parameters of the XML RPC call Examples The following call requests the current time and date with a complete URL it assumes that the computer is connected to the Internet and that the service is available url http time xmlrpc com RPC2 dateTime xmlrpccall url currentTime getCurrentTime dateTime 2005 1 20 17 32 47 The server address and the server port if it was not the default value of 80 can also be specified in the options then the URL contains only the absolute path server xmlrpccallset Server time xmlrpc com dateTime xmlrpccall RPC2 currentTime getCurrentTime server dateTime 2005 1 20 17 32 47 See also xmlrpccallset xmIirpccallset Options for XML RPC call Syntax options xmlrpccallset options xmlrpccallset namel valuel options xmlrpccallset options0O namel valuel Description xmlrpccallset namel valuel creates the option argument used by xmlrpccall including the server and port Options are specified with name value pai
132. M Description trace M returns the trace of the matrix M i e the sum of its diagonal elements Example trace 1 2 3 4 5 See also var Variance of a set of values Syntax s2 var A s2 var A p s2 var A p dim 240 LMEPPC User Manual 1999 2008 Calerga Sarl Description var A gives the variance of the columns of array A or of the row vector A The variance is normalized with the number of observations minus 1 or by the number of observations if a second argument is true The dimension along which var proceeds may be specified with a third argument See also 3 17 Array Functions cat Array concatenation Syntax cat dim Al A2 Description cat dim A1 A2 concatenates arrays Al A2 etc along dimen sion dim Other dimensions must match cat is a generalization of the comma and the semicolon inside brackets Examples cat 2 1 2 3 4 5 6 7 8 1 2 5 6 3 4 7 8 cat 3 1 2 3 4 5 6 7 8 2x2x2 array w See also operator 1 LME Reference arrays 241 cell Cell array of empty arrays Syntax C cell n C cell nl1 n2 C cell nl1 n2 Description cell builds a cell array whose elements are empty arrays The size of the cell array is specified by one integer for a square array or several integers either as separate arguments or in a vector for a cell array of any size Example cell 2 3 2x3 cell array See also operator
133. Number of output arguments Syntax n n nargout nargout fun 104 LMEPPC User Manual 1999 2008 Calerga Sarl Description A function may be called with between O and the number of out put arguments listed in the function definition The function can use nargout to check whether some output arguments are not used so that it can avoid computing them or do something else With one argument nargout fun returns the maximum number of output arguments a function can provide fun may be the name of a built in or user function a function reference or an inline function Functions with a variable number of output arguments such as feval give 1 Example A function which prints nicely its result when it is not assigned or used in an expression function y multiplyByTwo x if nargout gt 0 y 2 X else fprintf The double of f is f n x 2 x end Maximum number of output arguments of svd nargout svd 3 See also nargin varargout function rethrow Throw an error described by a structure Syntax rethrow s Description rethrow s throws an error described by structure s which contains the same fields as the output of Lasterror rethrow is typically used in the catch part of a try catch construct to propagate further an error but it can also be used to initiate an error like error LME Reference miscellaneous functions 105 Example The error whose identifier is LME i
134. Octal number ooo 000 16 bit UTF 16 uhhhh unicode UTF 16 code For octal and hexadecimal representations up to 3 octal or 2 hex adecimal digits are decoded the first non octal or non hexadecimal digit marks the end of the sequence The null character can conve niently be encoded with its octal representation 0 provided it is not followed by octal digits it should be written 000 in that case It is an error when another character is found after the backslash Single ticks can be represented either by a backslash followed by a single tick or by two single ticks Depending on the application and the operating system strings can contain directly Unicode characters encoded as UTF 8 or MBCS multi byte character sequences 16 bit characters encoded with uhhhh escape sequences are always accepted and handled correctly by all built in LME functions low level input output to files and devices which are byte oriented is an exception explicit UTF 8 conversion should be performed if necessary Lists and cell arrays Lists are ordered sets of other elements They may be made of any type including lists Literal lists are enclosed in braces elements are separated with commas 1 3 6 2 9 abc 1 xx Lists can be empty List s purpose is to collect any kind of data which can be assigned to variables or passed as arguments to functions Cell arrays are arrays whose elements or cells contain data of any type T
135. PPC User Manual 1999 2008 Calerga Sarl sandbox try fd fopen etc passwd end Security violation fopen See also sandboxtrust eval sandboxtrust Escape the sandbox restrictions Syntax sandboxtrust fun Description sandboxtrust fun sets a flag associated with function fun so that fun is executed without restriction even when called from a sandbox All functions called directly or indirectly from a trusted function are executed without restriction except if a nested call to sandbox is per formed Argument fun can be a function reference or the name of a function as a string the function must be a user function not a built in one The purpose of sandboxtrust is to give back some of the capabili ties of unrestricted code to code executed in a sandbox For instance if unsecure code must be able to read the contents of a specific file a trusted function should be written for that It is very important for the trusted function to check carefully its arguments such as file paths or URL Example Function which reads the contents of file data txt function data readFile fd fopen data txt data fread fd inf char fclose fd Execution of unsecure code which may read this file sandboxtrust readFile sandbox d readFile LME Reference operators 113 See also sandbox 3 14 Operators Operators are special functions with a syntax which
136. Sarl See also chol Cholesky decomposition Syntax M2 chol M1 Description If a square matrix M1 is symmetric or hermitian and positive definite it can be decomposed into the following product M MSM2 where M2 is an upper triangular matrix The Cholesky decomposi tion can be seen as a kind of square root The part of M1 below the main diagonal is not used because M1 is assumed to be symmetric or hermitian An error occurs if M1 is not positive definite Example chol 5 3 3 8 Wux On I Il co w 2361 1 3416 2 4900 See also cond Condition number of a matrix Syntax x cond M LME Reference linear algebra 199 Description cond M returns the condition number of matrix M i e the ratio of its largest singular value divided by the smallest one or infinity for singu lar matrices The larger the condition number the more ill conditioned the inversion of the matrix Examples cond 1 0 0 1 1 cond 1 1 1 1 le 3 4002 0008 See also conv Convolution or polynomial multiplication Syntax v conv vl1 v2 M conv M1 M2 M conv M1 M2 dim Description conv vl v2 convolves the vectors v1 and v2 giving a vector whose length is length v1 length v2 1 The result is a row vector if both arguments are row vectors and a column vector if both arguments are column vectors Otherwise arguments are considered as matrices conv M1 M2 convolves the
137. Stats false Option refine 293 ode45 is typically able to use large time steps to achieve the requested tolerance When plotting the output however interpolating it with straight lines produces visual artifacts This is why ode45 inserts 3 interpolated points for each calculated point based on the fifth order approximation calculated for the integration Refine is 4 by default In the following code curves with and without interpolation are com pared see Fig 3 2 Note that the numbers of evaluations of the func tion being integrated are the same mu 1 fun t y y 2 mux 1 y 1 2 y 2 y 1 294 LMEPPC User Manual 1999 2008 Calerga Sarl t y ode45 fun 0 5 2 0 odeset Refine 1 Stats true Number of function evaluations 289 Successful steps 42 Failed steps error too large 6 size y 43 2 ti yi ode45 fun 0 5 2 0 odeset Stats true Number of function evaluations 289 Successful steps 42 Failed steps error too large 6 size yi 169 2 plot ti yi g plot t y State based events For simulating a ball bouncing on the ground an event is generated every time the ball hits the ground and its speed is changed instan taneously Let y 1 be the height of the ball above the ground and y 2 its speed SI units are used The state space model is y y 2 9 81 An event occurs when the ball hits the ground value y 1 is
138. Syntax y sin x Description sin x gives the sine of x which is complex if x is complex Example sin 2 0 9093 See also sinc Sinc LME Reference mathematical functions 191 Syntax y sinc x Description Sinc x gives the sinc of x i e Sin pi x pi x if x 0 or 1 if x 0 The result is complex if x is complex Example sinc 1 5 0 2122 See also single Conversion to single precision numbers Syntax B single A Description single A converts number or array A to single precision A can be any kind of numeric value real complex or integer or a character or logical array Single literal numbers can be entered as a floating point number with the single suffix Examples single pi 3 1416single Single AB 1x2 single array 65 66 3 7e4single 37000single 192 LMEPPC User Manual 1999 2008 Calerga Sarl See also and related functions Logical sinh Hyperbolic sine Syntax y sinh x Description sinh x gives the hyperbolic sine of x which is complex if x is com plex Example sinh 2 3 6269 See also sqrt Square root Syntax r sqrt z Description sqrt z gives the square root of z which is complex if z is not real positive Examples sqrt 4 2 sqrt 1 4 9 3 4j 1 2 3j 2 1j LME Reference mathematical functions 193 See also swapbytes Conversion between big endian and little endian representation Syn
139. User Manual 1999 2008 Calerga Sarl plotpoly x y z color uses color instead of z to set the filling color of each polygon color is always a real double array or scalar whose elements are between 0 and 1 How it is interpreted depends on its size A scalar defines the color of all polygons it is mapped to the color map A vector of three elements defines the RGB color of all polygons row vector if there are 3 vertices to avoid ambiguity A vector with as many elements as x y and z defines the color of each vertex column vector if there are 3 vertices to avoid ambiguity Polygons have the mean value of all their vertices which is mapped to the color map An array with as many columns as elements in x y and z defines the RGB color of each vertex Polygons have the mean value of all their vertices plotpoly vis uses string vis to specify which side of the sur face is visible f for front only b for back only or fb or bf for both sides The front side is defined as the one where vertices have an anticlockwise orientation The default is f plotpoly vis style uses string style to specify the style of edges plotpoly id specifies the used for interactivity in Sysquake See also sensor3 Make graphical element sensitivive to 3D interactive displacement Syntax sensor3 type param id sensor3 type param typeAlt paramAlt id LME Reference 3D graphics 417
140. YUw C XUw D U Ujw The range of frequencies is selected automatically or can be specified in an optional argument w a vector of frequencies Further options can be provided in a structure opt created with responseset field Range is utilized The optional arguments style and id have their usual meaning Sigma is the equivalent of bodemag for multiple input systems For single input systems it produces the same plot With output arguments sigma gives the singular values and the frequency as column vectors No display is produced See also podephase step Step response plot of a continuous time linear system Syntax step numc denc step numc denc opt step Ac Bc Cc Dc step Ac Bc Cc Dc opt step style step style id y t step 452 LMEPPC User Manual 1999 2008 Calerga Sarl step 1 1 4 0 2 Figure 3 24 step 1 1 2 3 4 Description step numc denc plots the step response of the continuous time transfer function numc denc Further options can be provided in a structure opt created with responseset fields Delay and Range are utilized The optional argu ments style and id have their usual meaning step Ac Bc Cc Dc plots the step response of the continuous time state space model Ac Bc Cc Dc defined as dx a Acx t Bcu t y t C _x t D u t where u is a unit step The state space model must have a scalar input and may have a scalar or vector output With output a
141. a 1 5 99 a 9 erel 2309 5600 Extraction and assignment of elements in a list 1 2 7 3 abc magic 3 x al 12 51 2 7 3 x a 2 5 ab cde a 1 ab abc 8 1 6 3 5 7 4 9 2 cde a 2 5 3 9 a 1 3 9 abc 8 1 6 3 5 7 4 9 2 3 9 Removing elements in a list and have the same effect here a 4 a 1 3 9 abc 3 9 a 1 3 a 3 91 13 9 Replacing NaN with empty arrays in a cell array abc nan 2 false C cellfun x any isnan x C See also Operator endl Operator Brackets Syntax matrix_elements 118 LMEPPC User Manual 1999 2008 Calerga Sarl Description A pair of brackets is used to define a 2 d array given by its elements or by submatrices The operator or spaces is used to separate elements on the same row and the operator or newline is used to separate rows Since the space is considered as a separator when it is in the direct scope of brackets it should not be used at the top level of expressions as long as this rule is observed each element can be given by an expression Inside brackets commas and semicolons are interpreted as calls to horzcat and vertcat Brackets themselves have no other effect than changing the meaning of commas semicolons spaces and new lines the expression 1 for instance is strictly equivalent to
142. a long enough time period because of round off errors But in most cases this is not a problem Example Exact simulation of the output of a continuous time system whose in put comes from a zero order hold converter see Fig 3 16 unstable system continuous time transfer function num 1 den 1 1 sampling at Ts 1 too slow only for illustration Ts 1 numd dend c2dm num den Ts Stabilizing proportional controller 436 LMEPPC User Manual 1999 2008 Calerga Sarl scale 0 5 hstep 1 0 5 1 1 1 5 Figure 3 16 scale 0 5 hstep 1 1 0 5 1 1 1 5 kp 1 5 transfer function between ref signal and input conv kp dend addpol conv kp numd dend continuous time output for a ref signal step scale 0 10 hstep b a Ts num den discrete time output exact dstep conv b numd conv a dend Ts b a o See also impulse Impulse response plot of a continuous time linear system Syntax impulse numc denc impulse numc denc opt impulse Ac Bc Cc Dc impulse Ac Bc Cc Dc opt impulse style LME Reference graphics for dynamical systems 437 impulse style id y t impulse Description impulse numc denc plots the impulse response of the continuous time transfer function numc denc Further options can be provided in a structure opt created with responseset fields Delay and Range are utilized The
143. a separate line or set of marks row or column vectors are replicated to match the size of matrix arguments if required plot3 1id specifies the ID used for interactivity in Sysquake LME Reference 3D graphics 415 See also fLine3 plotpoly plot plotpoly Plot polygons in 3D space Syntax plotpoly x y z ind plotpoly x y z strip plotpoly x y z fan plotpoly x y z color ind plotpoly x y z color strip see a y z color fan plotpoly vis plotpoly vis style plotpoly vis style id Description plotpoly x y z ind plots polygons whose vertices are given by vectors x y and z Rows of argument ind contain the indices of each polygon in arrays x y and z Vertices can be shared by several poly gons Color of each polygon is mapped linearly from the z coordinate of the center of gravity of its vertices to the color map Each poly gon can be concave but must be planar and must not self intersect different polygons may intersect plotpoly x y z strip plots a strip of triangles Triangles are made of three consecutive vertices their indices could be defined by the following array ind_strip in Ordering is such that triangles on the same side of the strip have the same orientation plotpoly x y z fan plots triangles which share the first ver tex and form a fan Their indices could be defined by the following array ind_fan 416 LMEPPC
144. aginary unit i e the pure imaginary number whose square is 1 i and j are equivalent Used as a suffix appended without space to a number i or j mark an imaginary number They must follow the fractional part and the exponent if any for single precision numbers they must precede the single suffix To obtain a complex number i you can write either i or 1i or j or 1j The second way is safer because variables i and j are often used as indices and would hide the meaning of the built in functions The expression 11 is always interpreted as an imaginary constant number Imaginary numbers are displayed with i or j depending on the op tion set with the format command Examples i 1j format i 2i 2i 2single 5jsingle 2 5i single See also icdf Inverse cumulative distribution function LME Reference mathematical functions 173 Syntax X X X icdf distribution p icdf distribution p al icdf distribution p al a2 Description icdf distribution p calculates the value of x such that cdf distribution x is p The distribution is specified with the first argument a string case is ignored t and T are equivalent Additional arguments must be provided for some distributions The distributions are given in the table below Default values for the parameters when mentioned mean that the parameter may be omitted Distribution Name Parameters Beta beta aandb x chi2 deg of freedom v Y gamma
145. ails with the Grid menu scale equal 2 2 2 2 zgrid plotoption fullgrid plotroots 1 1 5 0 8 3 34 Base Graphical Functions activeregion Region associated with an ID Syntax activeregion xmin xmax ymin ymax id activeregion X Y id 380 LMEPPC User Manual 1999 2008 Calerga Sarl Description The command activeregion defines invisible regions with an ID for interactive manipulations in Sysquake Contrary to most other graph ical objects a hit is detected when the mouse is inside the region not close like with points and lines activeregion xmin xmax ymin ymax id defines a rectangular shape activeregion X Y id defines a polygonal shape The start and end points do not have to be the same the shape is closed automati cally Example Rectangular button If an ID was given to plot without activeregion a hit would be detected when the mouse is close to any of the four cor ners with activeregion a hit is detected when the mouse is inside the rectangle plot 50 70 70 50 50 10 10 30 30 10 activeregion 50 70 10 30 1 See also area Area plot Syntax area y area x y area x y y0 area style area style id Description With column vector arguments area x y displays the area between the horizontal axis y 0 and the points given by x and y When the second argument is an array with as many rows as elements in x area x Y displays the cont
146. al 1999 2008 Calerga Sarl Description log x gives the natural logarithm of x It is the inverse of exp The result is complex if x is not real positive Example log 1 0 1 10 1 2j 0 3 1416j inf 0 2 3026 0 8047 1 1071j See also log10 Decimal logarithm Syntax y logl10 x Description log10 x gives the decimal logarithm of x defined by log10 x log x log 10 The result is complex if x is not real positive Example 1og10 1 0 1 10 1 2j 0 1 3644j inf 0 1 0 3495 0 4808j See also loglp Logarithm of x plus one Syntax y loglp x LME Reference mathematical functions 181 Description logip x is log 1 x with improved precision for small x Example loglp le 15 le 15 log 1 le 15 1 1102e 15 See also log2 Base 2 logarithm Syntax y log2 x Description log2 x gives the base 2 logarithm of x defined as log2 x log x log 2 The result is complex if x is not real positive Example log2 1 2 1024 2000 5 0 1 10 10 9658 2 3219 4 5324j See also mod Modulo Syntax m mod x y 182 LMEPPC User Manual 1999 2008 Calerga Sarl Description mod x y gives the modulo of x divided by y i e a number m between O and y such that x q y m with integer q Imaginary parts if they exist are ignored Examples mod 10 7 3 mod 10 7 4 mod 10 7 4 mod 10 7 3 See also rem nan Not a Number Syntax nan NaN nan n na
147. al of gain for which the closed loop system remains stable the phase margin psi al ways positive if it exists which defines the symmetric range of phases which can be added to the open loop system while keeping the closed loop system stable the critical frequency associated to the gain mar gins where the open loop frequency response intersects the real axis around 1 and the cross over frequency associated to the phase mar gin where the open loop frequency response has a unit magnitude If the Nyquist diagram does not cross the unit circle psi and wx are empty Examples Stable closed loop Nyquist inside unit circle gm psi wc wx dmargin 0 005 poly 0 9 0 9 gm 2 38 psi wc 0 0 4510 wx Stable closed loop Nyquist crosses unit circle 350 LMEPPC User Manual 1999 2008 Calerga Sarl gm psi wc wx dmargin 0 05 poly 0 9 0 9 gm 0 2 3 8 psi 0 7105 we 0 0 4510 wx 0 2112 Unstable closed loop gm psi wc wx dmargin 1 poly 0 9 0 9 gm psi we wx Caveats Contrary to many functions dmargin cannot be used with several transfer functions simultaneously because not all of them may cor respond simultaneously to either stable or unstable closed loop sys tems See also margin Robustness margins of a continuous time system Syntax gm psi wc wx margin num den Description The open loop continuous time transfer function is gi
148. algebra 219 inprog c A b xlb xub Check that the solution is feasible and bounded all isfinite x true logm Matrix logarithm Syntax Y logm X Y err Logm X Description logm X returns the matrix logarithm of X the inverse of the matrix exponential X must be square The matrix logarithm does not always exist With a second output argument err Logm also returns an estimate of the relative error norm expm lLogm X X norm X Example logm 1 2 3 4 lt lt ll 0 3504 2 3911j 0 9294 1 0938j 1 394 1 6406j 1 0436 0 7505j expm Y 1 5 5511e 16j 2 7 7716e 16j 3 8 3267e 16j 4 See also lu LU decomposition 220 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax L U P lu A L2 U lu A Y lu A Description With three output arguments Lu A computes the LU decomposition of matrix A with partial pivoting i e a lower triangular matrix L an up per triangular matrix U and a permutation matrix P such that P A L U If Ain an m by n mytrix L is m by min m n U is min m n by n and P is m by m A can be rank deficient With two output arguments Lu A permutes the lower triangular matrix and gives L2 P L such that A L2x U With a single output argument lu gives Y L U eye n Example X 1 2 3 4 5 6 7 8 8 L U P lu X L 1 0 0 0 143 1 0 0 571 0 5 1 U ree 7 8 8 0 0 857 1 857 0 0 0 5 P 001 10 0 010 P X L U ans 000 000 000
149. all fd server url action method ns params writes to file descriptor fd a complete SOAP call including the HTTP header If fd is missing the call is written to standard output file descriptor 1 since the output contains carriage return characters it may not be displayed correctly on all platforms The server argument is a string which contains the server name and optionally a colon and the server port number url is a string which contains the absolute path without the protocol server and port part action is a string which contains the SOAP action or is empty if no action is required for the service method contains the method name sent to the server ns is its XML name space param if present is a structure which contains the parameters of the SOAP call With an output argument soapwritecall returns the call as a string without any output Example param struct x pi y true soapwritecall server com action fun ns param POST HTTP 1 1 User Agent LME 4 5 Host server com Content Type text xml charset utf 8 Content Length 495 SOAPAction action lt xml version 1 0 gt lt SOAP ENV Envelope SOAP ENV encodingStyle http schemas xmlsoap org soap encoding xmLns SOAP ENC http schemas xmlsoap org soap encoding xmlns SOAP ENV http schemas xmlsoap org soap envelope xmlins xsd http www w3 org 1999 XMLSchema xmlins xsi http www w3 org 1999 XMLSchema
150. ally shorter than it argument str String str can be reconstructed with inflate using only strc deflate and inflate process any sequence of bytes 8 bit words their input argument can be any array However their shape and their type are lost the result of inflate is always a row vector of characters and their elements are restored modulo 256 Depending on the data compression rates of 2 or more are typi cal Sequences without redundancy such as random numbers or the result of deflate can produce a result slightly larger than the initial sequence Example str repmat abcd ef 1 1000 Llength str 8000 strc deflate str Llength strc 43 str repmat abcd ef 1 1000 strc deflate str str2 inflate strc str str2 true To compress objects which are not sequence of bytes you can use dumpvar and str2obj to convert them to and from a textual represen tation A repmat 600 2 2 A 600 600 600 600 inflate deflate A 1x4 uint8 array 88 88 88 88 str dumpvar A str2obj deflate inflate str 600 600 600 600 See also Extensions data compression 563 inflate Uncompress the result of deflate Syntax str inflate strc Description inflate strc uncompresses strc to undo the effect of compress The output is always a character string with one row whose characters are coded on one byte See also deflate zread Read deflated data and uncompress them Syn
151. ame length as c Example use stdlib hankel 1 3 3 1 2 8 3 4 5 4 5 6 5 6 7 See also diag hist Histogram 470 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax use stdlib N X hist Y N X hist Y m N X hist Y m dim N hist Y X N hist Y X dim Description hist Y gives the number of elements of vector Y in 10 equally spaced intervals A second input argument may be used to specify the number of intervals The center of the intervals may be obtained in a second output argument If Y is an array histograms are computed along the dimension spec ified by a third argument or the first non singleton dimension the re sult N has the same size except along that dimension When the second argument is a vector it specifies the centers of the intervals Example use stdlib N X hist logspace 1 5 N 45 21 14 11 9 X 1 9 3 7 5 5 7 3 9 1 ifftshift Shift DC frequency of FFT from center to beginning of spectrum Syntax use stdlib Y ifftshift X Description ifftshift X shifts halves of vector 1 d or matrix 2 d X to move the DC component from the center It should be used before ifft or ifft2 It reverses the effect of fftshift Libraries stdlib See also isprime Prime number test Syntax use stdlib b isprime n Description 471 isprime n returns true if n is a prime number or false otherwise If n is a matrix the test is applied
152. ame size as M1 whose ele ments M2 i j are the product of all the elements M1 k j with k lt i cumprod M1 dim operates along the dimension dim column wise if dim is 1 row wise if dim is 2 Examples cumprod 1 2 3 4 5 6 1 2 3 4 10 18 cumprod 1 2 3 4 5 6 2 12 6 4 20 120 See also prod cumsum LME Reference linear algebra 203 cumsum Cumulative sums Syntax M2 cumsum M1 M2 cumsum M1 dim Description cumsum M1 returns a matrix M2 of the same size as M1 whose ele ments M2 i j are the sum of all the elements M1 k j with k lt i cumsum M1 dim operates along the dimension dim column wise if dim is 1 row wise if dim is 2 Examples cumsum 1 2 3 4 5 6 123 579 cumsum 1 2 3 4 5 6 2 13 6 49 15 See also dare Discrete time algebraic Riccati equation Syntax X L K dare A B Q X L K dare A B Q R Description dare A B Q calculates the stable solution X of the following discrete time algebraic Riccati equation X A XA A XB B XB 1 1B XA Q All matrices are real Q and X are symmetric 204 LMEPPC User Manual 1999 2008 Calerga Sarl With four input arguments dare A B Q R with R real symmetric solves the following Riccati equation X A XA A XB B XB R 1B XA Q With two or three output arguments X L K dare also re turns the gain matrix K defined as K B XB R B XA and the column vector of closed loop ei
153. ammatic interface the objects Two OOP languages in common use today are C and Java The exact definition of OOP varies from person to person Here is what it means when it relates to LME Data encapsulation Objects contain data but the data cannot be accessed directly from the outside All accesses are performed via special functions called methods What links a particular method to a particular object is a class Class are identified with a name When an object is created its class name is specified The names of methods able to act on objects of a particular class are prefixed with the class name followed with two colons Objects are special structures whose contents are accessible only to its methods Function and operator overloading Methods may have the same name as regular functions When LME has to call a function it first checks the type of the input arguments If one of them is an object the corresponding method is called rather than the function defined for non object arguments A method which has the same name as a function or another method is said to overload it User functions as well as built in ones can be LME Reference 37 overloaded Operators which have a function name for instance x y can also be written plus x y can also be overloaded Special functions called object constructors have the same name as the class and create new objects They are also methods of the class even if their input arguments are not
154. an observation where n quantities were measured nancov data Q is the same as nancov data nancov data 1 returns the m by m covariance matrix of the n by m matrix data which contains the whole population NaN values are ignored See also Libraries stat 485 nanmean Mean after discarding NaNs Syntax use stat y nanmean A y nanmean A dim Description nanmean v returns the arithmetic mean of the elements of vector v nanmean A returns a row vector whose elements are the means of the corresponding columns of array A nanmean A dim returns the mean of array A along dimension dim the result is a row vector if dim is 1 or a column vector if dim is 2 In all cases NaN values are ignored Examples use stat nanmean 1 2 nan nan 6 7 147 nanmean 1 2 nan nan 6 7 2 1 5 6 5 nanmean nan nan nan See also nanmedian Median after discarding NaNs Syntax use stat y nanmedian A y nanmedian A dim 486 LMEPPC User Manual 1999 2008 Calerga Sarl Description nanmedian v gives the median of vector v i e the value x such that half of the elements of v are smaller and half of the elements are larger NaN values are ignored nanmedian A gives a row vector which contains the median of the columns of A With a second argument nanmedian A dim operates along dimension dim See also nanstd Standard deviation after discarding NaNs Syntax use stat y nanstd A y nanstd A p y
155. and optionally the diagonal scaling matrix T such that T A T B Example A 1 2e6 3e 6 4 T B balance A T 16384 0 0 3 125e 2 B 1 3 8147 1 5729 4 See also care Continuous time algebraic Riccati equation Syntax X L K care A B Q X L K care A B Q R X L K care A B Q R S X L care A S Q true LME Reference linear algebra 197 Description care A B Q calculates the stable solution X of the following continuous time algebraic Riccati equation A X XA XBB X Q 0 All matrices are real Q and X are symmetric With four input arguments care A B Q R with R real symmetric solves the following Riccati equation A X XA XBR 1B X Q 0 With five input arguments care A B Q R S solves the following equation A X XA S XB R71 S B X Q 0 With two or three output arguments X L K care also re turns the gain matrix K defined as K R 1B x and the column vector of closed loop eigenvalues L eig A BK care A S Q true with up to two output arguments is equivalent to care A B Q or care A B Q false with S B B Example A 4 2 1 2 B 0 1 c 2 1 Q C C R 5 X L K care A B Q R X 1 07 3 5169 3 5169 23 2415 L 4 3488 2 2995 K 0 7034 4 6483 A X Xx x A Xx x BS Rx B X Q 1 7319e 14 1 1369e 13 8 5265e 14 6 2528e 13 198 LMEPPC User Manual 1999 2008 Calerga
156. anges the sign of the imaginary part of the complex num ber z Example conj 1 2j 3 5j 4 0 1 2 3 5j 40 156 LMEPPC User Manual 1999 2008 Calerga Sarl See also cos Cosine Syntax y cos x Description cos x gives the cosine of x which is complex if x is complex Example cos 1 2j 1 2 0327 3 0519j See also cosh Hyperbolic cosine Syntax y cosh x Description cos x gives the hyperbolic cosine of x which is complex if x is com plex Example cosh 0 1 2j 1 0 6421 1 0686j LME Reference mathematical functions 157 See also cos cot Cotangent Syntax y cot x Description cot x gives the cotangent of x which is complex if x is See also acot coth Hyperbolic cotangent Syntax y coth x Description coth x gives the hyperbolic cotangent of x which is complex if x is See also tanh csc Cosecant Syntax y csc x 158 LMEPPC User Manual 1999 2008 Calerga Sarl Description csc x gives the cosecant of x which is complex if x is See also acsc csch Hyperbolic cosecant Syntax y csch x Description csch x gives the hyperbolic cosecant of x which is complex if x is See also diln Dilogarithm Syntax y diln x Description diln x gives the dilogarithm or Spence s integral of x Argument and result are real imaginary part is discarded The dilogarithm is define
157. are of type double so is the result and the operation is performed on 32 bits Examples bitand 1 3 1 bitand 1 6 1 1031010 bitand 7uint8 1234int16 2int16 LME Reference logical functions 337 See also bitany Check whether any of the corresponding bits is true Syntax v bitany A bitany A dim bitany v vV b Description bitany A performs a bitwise OR on the elements of the columns of array A or the elements of a vector If a second argument dim is provided the operation is performed along that dimension A can be a double or an integer array For double arrays bitany uses the 32 least significant bits Examples bitany 5 3 7 bitany Quint8 6uint8 3uint8 6uint8 2 2x1 uint8 array 6 7 See also bitcmp Bit complement bitwise NOT Syntax b bitcmp i b bitcmp a n 338 LMEPPC User Manual 1999 2008 Calerga Sarl Description bitcmp i gives the 1 complement bitwise NOT of the integer i bitcmp a n where a is an integer or a double gives the 1 complement of the n least significant bits The result has the same type as a The inputs can be scalar arrays of the same size or a scalar and an array If a is of type double so is the result and the operation is performed on at most 32 bits Examples bitcmp 1 4 14 bitcmp 0 1 8 13 7 15 31 63 127 255 bitcmp Ouint8 luint8 255uint8 1x3 uint8 array 255 254 0 See also bitget Bit extraction
158. aring NaN not a number to any number yields false including to NaN If x and or y is an array the comparison is performed element wise and the result has the same size eq x y is equivalent to x y It can be used to redefine this oper ator for objects Example 1 true 1 1 eps false 1 1 eps 2 true inf inf true nan nan false LME Reference operators 131 1 2 3 1 3 3 TFT See also operator gt operator gt opera Operator Object equality Syntax a same a b Description a bis true if ais the same as b and false otherwise a and b must have exactly the same internal representation to be considered as equal with IEEE floating point numbers nan nan is true and 0 0 is false Contrary to the equality operator returns a single boolean even if its operands are arrays same a b is equivalent to a b Example 1 5 1 5 true 1 5 1 5 TTTTT 1 2 3 4 5 false 1 2 3 4 5 Incompatible size nan nan true nan nan false See also 132 LMEPPC User Manual 1999 2008 Calerga Sarl Operator Inequality Syntax xX y ne x y Description x y is true if x is not equal to y and false otherwise Comparing NaN not a number to any number yields true including to NaN If x and or y is an array the comparison is performed element wise and the result has the same size ne x y is eq
159. art from each pole and end to each zero or to a real or complex point at infinity The locus is symmetric with respect to the real axis because the coefficients of the characteristic polynomial are real By definition closed loop poles for the current gain i e the roots of num den are on the root locus and move on it when the gain change rlocus plots only the root locus not the particular val ues of the roots for the current gain a null gain or an infinite gain If necessary these values should be plotted with plot roots The part of the root locus which is calculated and drawn depends on the scale If no scale has been set before explicitly with scale or implicitly with plotroots or plot the default scale is set such that the zeros of num and den are visible As with other plots the id is used for interactive manipulation Manipulating a root locus means changing the gain of the controller which keeps the locus at the same place but makes the closed loop poles move on it Other changes are done by dragging the open loop poles and zeros which are plotted by plotroots To change the gain you must also plot the current closed loop poles with the plotroots 448 LMEPPC User Manual 1999 2008 Calerga Sarl rlocus 2 0 Oo O 2 4 2 0 Figure 3 22 Example of rlocus function and use the same ID so that the initial click identifies the nearest closed loop pole and the mouse drag makes Sysquake use the root locus to cal
160. as a pure quaternion a xi yj zk giving point a also as a pure quaternion then b q a q and a q b q The rotation can also be seen as changing coordinates from body to absolute where the body s attitude is given by pitch roll and yaw In order to have the usual meaning of pitch roll and yaw the x axis must be aligned with the direction of motion the y axis with the lateral direction and the z axis with the vertical direction with the usual sign conventions for cross products Two common choices are x pointing forward y to the left and z upward or x forward y to the right and z downward If input arguments are arrays of compatible size same size or scalar the result is a quaternion array of the same size conversion from angles to quaternion is performed independently on corresponding elements Example Conversion of two vectors from aircraft coordinates x axis forward y axis to the left z axis upward to earth coordinates x directed to the north y to the west z to the zenith In aircraft coordinates vectors are 2 0 0 propeller position and 0 5 0 left wing tip The air craft attitude has a pitch of 10 degrees upward i e 10 degrees with the choice of axis and null roll and yaw a l rpy2q 0 10 pi 180 0 q 0 9962 0 0872j q x quaternion 2 0 0 q 1 96961 0 3473k q quaternion 0 5 0 q 5j See also q2rpy 3 23 List Functions apply Function evaluation with arguments in lis
161. as a scalar number or a string which is converted by datevec The result has the following format jj mmm yyyy HH MM SS where jj is the two digit day mmm the beginning of the month name yyyy the four digit year HH the two digit hour MM the two digit minute and SS the two digit second The format can be specified with a second input argument When datestr scans the format string it replaces the following sequences of characters and keeps the other ones unchanged Libraries date 553 Sequence Replaced with dd day 2 digits ddd day of week 3 char HH hour 2 digits 01 12 or 00 23 MM minute 2 digits mm month 2 digits mmm month 3 char PM AM or PM QQ quarter Q1 to Q4 SS second 2 digits yy year 2 digits yyyy year 4 digits If the sequence PM is found the hour is between 1 and 12 other wise between 0 and 23 Examples use date datestr clock 18 Apr 2005 16 21 55 datestr clock ddd mm dd yyyy HH MM PM Mon 04 18 2005 04 23 PM See also julian2cal datevec String to date and time conversion Syntax use date datetime datevec str Description datevec str converts the string str representing the date and or the time to a row vector of 6 elements for the year month day hour minute and second The following formats are recognized 554 LMEPPC User Manual 1999 2008 Calerga Sarl Example Value 20050418T162603 ISO 8601 date and time 2005 04 18 year month and
162. ast Fourier Transform Syntax f ifft2 F f ifft2 F size f ifft2 F nr nc f ifft2 F n Description ifft2 returns the inverse 2 d Discrete Fourier Transform inverse DFT along dimensions 1 and 2 With two or three input arguments ifft2 resizes the two first di mensions by cropping or by padding with zeros ifft2 F nr nc re sizes first dimension to nr rows and second dimension to nc columns In ifft2 F size the new size is given as a two element vector nr nc ifft2 F n is equivalent to ifft2 F n n If the first argument is an array with more than two dimensions ifft2 performs the inverse 2 d DFT along dimensions 1 and 2 sepa rately for each plane along remaining dimensions ifftn performs an inverse DFT along each dimension Up to the sign and a scaling factor the inverse 2 d DFT and the 2 d DFT are the same operation ifft2 has the same syntax as See also ifftn Inverse n dimension Fast Fourier Transform Syntax f ifftn F f ifftn F size Description ifftn F returns the inverse n dimension Discrete Fourier Transform of array F inverse DFT along each dimension of F With two input arguments ifftn F size resizes F by cropping or by padding F with zeros LME Reference linear algebra 215 Up to the sign and a scaling factor the inverse n dimension DFT and the n dimension DFT are the same operation ifftn has the same syntax as fftn See also hess Hessenberg reduction Syntax
163. ay be used with ratio ob jects with results analog to the corresponding functions of LME eq mldivide gt ge mpower gt gt mrdivide inv mtimes lt le ne lt lt plus max uminus min uplus minus Examples use ratio r ratio 2 3 r 2 3 q 5 r 1 q 7 3 See also ratio disp ratio double ratio char ratio char Display a ratio object Syntax use ratio char r Description char r converts ratio r to a character string See also ratio disp 502 LMEPPC User Manual 1999 2008 Calerga Sarl ratio disp Display a ratio object Syntax use ratio disp r Description disp r displays ratio r with the same format as char It is also ex ecuted implicitly when LME displays the ratio result of an expression which does not end with a semicolon See also disp ratio double Convert a ratio object to a floating point number Syntax use ratio x double r Description double r converts ratio r to a floating point number of class double Example use ratio r ratio 2 3 double r 0 6666 See also ratio ratio Libraries bitfield 503 5 5 bitfield Library bitfield implements the constructor and methods of class bitfield for bit fields binary numbers Basic arithmetic operators and functions are overloaded to support expressions with the same syntax as for numbers and matrices Contrary to integer numbers bitfield objects have a l
164. b le a b a b ldivide a b a lt b lt a b a b mpower a b a gt b ge a b a b power a b a gt b gt a b a not a b eq a b a uminus a a b ne a b a uplus a a b same a b a ctranspose a a unsame a b a transpose a a b plus a b Operator which do not have a corresponding function are amp amp and because unlike functions they do not always evaluate all of their operands Operator Parenthesis Syntax expr v v index v index1 index2 v index v index v select v selectl select2 v Description A pair of parenthesis can be used to change the order of evaluation The subexpression it encloses is evaluated as a whole and used as if it was a single object Parenthesis serve also to indicate a list of input or output parameters see the description of the function keyword The last use of parenthesis is for specifying some elements of an array or list variable Arrays In LME any numerical object is considered as an array of two dimensions or more Therefore at least two indices are required LME Reference operators 115 to specify a single element the first index specifies the row the sec ond the column and so on In some circumstances however it is sometimes convenient to consider an array as a vector be it a column vector a row vector or even a matrix whose elements are indexed row wise For this way of handling arrays a single index is spec
165. be replaced with the use of In this case the size of the variable is expanded when required padding elements are O for numeric arrays and empty ar rays for cell arrays and lists 54 LMEPPC User Manual 1999 2008 Calerga Sarl See also beginning First index of an array Syntax v beginning A beginning function e C beginning obj i n Description In an expression used as an index to access some elements of an array beginning gives the index of the first element line or column depending of the context It is always 1 for native arrays beginning can be overloaded for objects of used defined classes Its definition should be have a header equivalent to function e C beginning obj i n where C is the name of the class obj is the object to be indexed i is the position of the index expression where beginning is used and n is the total number of index expressions See also Operator 0 operator 1 end Last index of an array Syntax v end A end function e C end obj i n Description In an expression used as an index to access some elements of an ar ray end gives the index of the last element line or column depending of the context LME Reference variables 55 end can be overloaded for objects of used defined classes Its definition should be have a header equivalent to function e C end obj i n where C is the name of the class obj is the object to be
166. by Events There can be multiple streams of events which are checked independently and are identified by a positive integer for Events or a negative integer for EventTime For instance for a ball which bounces between several walls the inter section between each wall and the ball trajectory would be a different event stream For events which occur at regular times EventTime is an n by two matrix for each row the first column gives the time step ts and the second column gives the offset to Non repeating events are specified with an infinite time step ts Events occur at time t to k ts where k is an integer When event time is varying EventTime is a function which can be defined as function eventTime eventtimefun t y where t is the current time y the current state and the ellipsis stand for additional arguments passed to ode The function returns a col umn vector whose elements are the times where the next event oc curs In both cases each row corresponds to a different event stream For events which are based on the state the value of a function which depends on the time and the states is checked the event occurs when its sign changes Events is a function which can be defined as function value isterminal direction eventsfun t y Input arguments are the same as for EventTime Output arguments are column vectors where each element i corresponds to an event stream An event occurs when value i cross
167. c tion With more arguments warning uses the first argument as a format string and displays remaining arguments accordingly like fprintf Example warning Doesn t converge See also which Library where a function is defined 110 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax fullname which name Description which name returns an indication of where function name is defined If name is a user function or a method prefixed with its class and two colons the result is name prefixed with the library name and a slash If name is a built in function it is prefixed with builtin If itis a variable it is prefixed with var If name is neither a function nor a variable which returns the empty string Examples which lLogspace stdlib logspace which polynom plus classes polynom plus which sin builtin sin X 2 which x var x See also 3 13 Sandbox Function sandbox Execute untrusted code in a secure environment Syntax sandbox str sandbox str varin varout sandbox str varout sandbox str varin LME Reference sandbox function 111 Description sandbox str executes the statements in string str Functions which might do harm if used improperly are disabled they include those related to the file system to devices and to the network Global and persistent variables are forbidden as well but local variables can be created The same restrictions apply to functions
168. client side of the XML RPC and SOAP protocols as well as low level functions which can also be used to implement the server side XML RPC and SOAP per mit web services i e calling a function on a remote server over the World Wide Web XML RPC is based on two standards XML eXtended Mark up Language used to encode the request to the server and its response to the client and HTTP HyperText Transfer Protocol the main communication protocol used by the World Wide Web In XML RPC RPC means Remote Procedure Call it is a mechanism used for decades to communicate between a client and a server on a network The advantages of XML RPC are that it is based on the same technolo gies as the Web and it is very simple Its drawbacks are that it is less efficient than a binary encoding and it is sometimes too simple and requires encoding of binary data which defeats its main advantage For instance strings are encoded in ASCII and supported types are much less rich than LME s SOAP is also a standard used for exchanging data encoded with XML It is more complicated than XML RPC and supports more types Function parameters are referenced by name while XML RPC uses an ordered list SOAP requests can be sent with different communica tion protocols the implementation described here uses only the most common one HTTP XML RPC In LME XML RPC makes calls to remote procedure similar to the use of feval The two main functions are xmlrpccall and xml
169. codebook as an initial guess for the codebook The result has the same length A third argument can be used to specify the tolerance used as the stopping criterion of the optimization loop The default is 1e 7 Example We start from a suboptimal partition and compute the distortion use sigenc partition codebook oly 0 1 2 0 5 0 5 2 548 LMEPPC User Manual 1999 2008 Calerga Sarl in 5 0 6 3 i out dist quantiz in partition codebook dist 2 1421 The partition is optimized with Lloyds and the same signal is quan tized again The distortion is reduced partition_opt codebook_opt lloyds in codebook partition_opt 2 9 0 5 1 3 codebook_opt 4 1 1 7 0 4 2 2 i out dist quantiz in partition_opt codebook_opt dist 1 0543 See also quantiz Table based signal quantization Syntax use sigenc i quantiz input partition i output distortion quantiz input partition codebook Description quantiz input partition quantizes signal input using partition as boundaries between different ranges Range from o to partition 1 corresponds to code 0 range from partition 1 to partition 2 corresponds to code 1 and so on input may be a real array of any size and dimension partition must be a sorted vector The output i is an array of codes with the same size and dimension as input quantiz input partition codebook uses codebook as a look up table to con
170. cription mesh x y z plots a mesh defined by 2 D arrays x y and z Ar guments x and y must have the same size as z or be vectors of size z 2 and size z 1 elements respectively If x and y are miss ing their default values are coordinates from 1 to size z 2 along x axis and from 1 to size z 1 along y axis Color is obtained by mapping the full range of z values to the color map mesh x y z color maps values of array color to the color map color must have the same size as z and contain values between 0 and 1 which are mapped to the color map mesh kind specifies which side of the mesh is visible kind is a string of 1 or 2 characters f if the front side is visible the side where increasing y are on the left of increasing x coordinates and b if the back side is visible Default is equivalent to fb mesh style specifies the line or symbol style of the mesh The default is to map z or color values to the color map mesh 1d specifies the ID used for interactivity in Sysquake See also plotpoly plot3 Generic 3D plot Syntax plot3 x y Z plot3 x y z style plot3 x y z style id Description The command plot3 displays 3D graphical data in the current figure The data are given as three vectors of coordinates x y and z De pending on the style the points are displayed as individual marks or are linked with lines If x y and z are matrices each row is considered as
171. ct struct fieldnamel valuel fieldname2 value2 Description struct builds a new structure Input arguments are used by pairs to create the fields for each pair the first argument is the field name provided as a string and the second one is the field value Example X X struct a 1 b 2 5 a 1 x b 2345 332 LMEPPC User Manual 1999 2008 Calerga Sarl See also 3 25 Object Functions class Object creation Syntax object class strct classname object class strct classname parentl str class object Description class strct classname makes an object of the specified class with the data of structure strct Object fields can be accessed only from methods of that class i e functions whose name is classname methodname Objects must be created by the class constructor classname classname class strct classname parent1 makes an object of the specified class which inherits fields and methods from one or several other object s parent1 Parent objects are inserted as additional fields in the object with the same name as the class Fields of parent objects cannot be directly accessed by the new object s methods only by the parent s methods class object gives the class of object as a string The table below gives the name of native types Class Native type double real complex or logical scalar or array char character or character arra
172. ction of the upper triangular part of a matrix Description tril M extracts the upper triangular part of a matrix the result is a matrix of the same size where all the elements below the main di agonal are set to zero A second argument can be used to specify another diagonal 0 is the main diagonal positive values are above and negative values below Examples M M magic 3 ct s QOooroooar AWO I il D Ee ee ae NN OS NNO rt rp m ONO See also tril diag union Set union Syntax c union a b c ia ib union a b LME Reference arrays 271 Description union a b gives the union of sets a and b i e it gives the set of members of sets a or b or both Sets are any type of numerical char acter or logical arrays or lists or cell arrays of character strings Mul tiple elements of input arguments are considered as single members the result is always sorted and has unique elements The optional second and third output arguments are vectors of in dices such that if c ia ib union a b then elements of c are the elements of a ia or b ib the intersection of a ia and b ib is empty Example a a bc bbb de b z bc aa bbb c ia ib union a b c a aa bbb bc de z ia 1324 ib 31 a ia a bbb bc de b ib aa z Set exclusive or can
173. ctions to create special matrices The zeros ones rand and randn functions create matrices full of zeros ones random num bers uniformly distributed between 0 and 1 and random numbers nor mally distributed with a mean of 0 and a standard deviation of 1 re spectively The eye function creates an identity matrix i e a matrix with ones on the main diagonal and zeros elsewhere All of these func tions can take one scalar argument n to create a square n by n matrix or two arguments m and n to create an m by n matrix Tutorial 17 ans 0 1386 0 9274 0 3912 0 8219 gt randn 2 ans 0 2931 1 2931 2 3011 0 9841 gt eye 3 ans 10 01 0 0 gt eye ans 0 1 0 0 1 2 3 Ors 0 0 You can use most scalar functions with matrices functions are applied to each element gt sin 1 2 ans 0 8415 0 9093 There are also functions which are specific to matrices For example det calculates the determinant of a square matrix gt det 1 2 5 3 ans 7 Arithmetic operations can also be applied to matrices with their usual mathematical behavior Additions and subtractions are performed on each element The multiplication symbol x is used for the product of two matrices or a scalar and a matrix gt 1 2 3 4 2 7 ans 16 34 18 LMEPPC User Manual 1999 2008 Calerga Sarl The division symbol denotes the multiplication by the inverse of the right argument which must be a square matri
174. culate the change of gain which can be retrieved in _q see the example below Examples Root locus of s 3s 2 s 2s 35 4 with open loop poles and zeros added with plotroots see Fig 3 22 num 1 3 2 den 1 2 3 4 scale equal 4 1 2 2 sgrid rlocus num den plotroots num plotroots den 0 x The second example shows how rlocus can be used interactively in Sysquake figure Root Locus draw myPlotRLocus num den mousedrag num myDragRLocus num _q function LME Reference graphics for dynamical systems 449 function myPlotRLocus num den scale equal 3 1 2 2 rlocus num den 1 plotroots addpol num den 1 function num myDragRLocus num q if isempty q cancel else num q num end Caveat The Laguerre algorithm is used for fast evaluation roots and plotroots are based on eig and have a better accuracy but their evaluation for a single polynomial is typically 10 times slower The price to pay is a suboptimal precision for multiple roots and or high order polynomials See also sgrid Relative damping and natural frequency grid for the poles of a continuous time system Syntax sgrid sgrid style sgrid damping freq sgrid damping freq style Description With no or one argument sgrid plots a grid of lines with constant relative damping and natural frequencies in the complex plane of s
175. current context so that they may be called by the functions or statements which follow Using a library does not make available functions defined in its sublibraries however libraries may be used multiple times in each context where their functions are referenced All use statements are parsed before execution begins They may be placed anywhere in the code typically before the first function They cannot be skipped by placing them after an if statement Like wise try catch cannot be used to catch errors useifexists should be used if the absence of the library is to be ignored See also useifexists Import libraries if they exist LME Reference programming constructs 75 Syntax useifexists lib useifexists libl lib2 Description useifexists has the same syntax and effect as use except that li braries which are not found are ignored without error See also while Loop controlled by a boolean expression Syntax while expr sl end Description The statements between the while statement and the corresponding end are executed repeatedly as long as the expression of the while statement yields true nonempty and all elements different from 0 and false If a break statement is executed in the scope of the while loop i e not in an enclosed loop the loop is terminated If a continue statement is executed in the scope of the while loop statements following continue are ignored and a new loop is per fo
176. d new elements are set to 0 for numeric arrays false for logical arrays the nul character for character array and the empty array for cell arrays Lists In LME lists have one dimension thus a single index is re quired Be it with a single index or a vector of indices indexed el ements are grouped in a list New elements also provided in a list can be assigned to indexed elements if the list to be assigned has a single element the element is assigned to every indexed element of the variable Cell arrays cell arrays are subscripted like other arrays The re sult or the right hand side of an assignment is also a cell array or a list for the syntax v select lists are to cell arrays what column vectors are to non cell arrays To create a single logical array for se lecting some elements function cellfun may be useful To remove 116 LMEPPC User Manual 1999 2008 Calerga Sarl cells the right hand side of the assignment can be the empty list or the empty array Examples Ordering evaluation 1 2 3 9 Extracting a single element a row and a column 1 2 3 4 5 6 a a 2 3 Extracting a sub array with contiguous rows and non contiguous columns a 1 2 1 3 1 2 13 46 Array elements as a vector a 3 5 o mBW Ww AUBWNEe Selections of elements where a logical expression is true a a gt 5 5 6 a sum a 1 gt 6 23 5 6 LME Reference operators 117 Assignment
177. d Ts plots the step response of the discrete time state space model Ad Bd Cd Dd defined as x k 1 Agx k Bgu t y k Cgx k Dau k where u k is a unit step The state space model must have a scalar input and may have a scalar or vector output With output arguments dstep gives the output and the time as column vectors No display is produced Example Step response of a discrete time third order system see Fig 3 13 dstep 1 poly 0 9 0 7 0 6j 0 7 0 6j 1 g 432 LMEPPC User Manual 1999 2008 Calerga Sarl dstep 1 poly 0 9 0 7 0 6j 0 7 0 6j 0 2 s Figure 3 13 dstep 1 poly 9 7 6j 7 6j 0 2 s See also erlocus Root locus of a polynomial with coefficients bounded by an ellipsoid Syntax erlocus C0 P erlocus C0 P sizes colors Description erlocus displays the set of the roots of all the polynomial whose coef ficients are bounded by an ellipsoid defined by CO and P The polyno mials are defined as CO 0 dC where dCxinv P dC lt 1 If sizes and colors are provided sizes must be a vector of n val ues and colors an n by 3 matrix whose columns correspond respec tively to the red green and blue components The locus correspond ing to dCxinv P dC lt sizes i 2 is displayed with colors i The vector sizes must be sorted from the smallest to the largest ellip soid The default values are sizes 0 1 0 5 1 2 and colors LME Reference graph
178. d as x log t dinco gl Hi 1 t 1 Example diln 0 2 0 7 10 1 0748 0 3261 3 9507 LME Reference mathematical functions 159 double Conversion to double precision numbers Syntax B double A Description double A converts number or array A to double precision A can be any kind of numeric value real complex or integer or a character or logical array To keep the integer type of logical and character arrays the unitary operator should be used instead Examples double uint8 3 3 double AB 65 66 islogical double 1 gt 2 false See also and related functions SingTel cast operator setstr char logical ellipam Jacobi elliptic amplitude Syntax phi phi ellipam u m ellipam u m tol Description ellipam u m gives the Jacobi elliptic amplitude phi Parameter m must be in 0 1 The Jacobi elliptic amplitude is the inverse of the Jacobi integral of the first kind such that u F g m ellipam u m tol uses tolerance tol the default tolerance is eps 160 LMEPPC User Manual 1999 2008 Calerga Sarl Example phi ellipam 2 7 0 6 u llipf phi 0 6 N Il See also ettip ettiri ellipe Jacobi elliptic integral of the second kind Syntax u ellipe phi m Description ellipe phi m gives the Jacobi elliptic integral of the second kind defined as o E g m V1 msin tdt 0 Complete elliptic integrals of first and second
179. d to the vectors The absolute value of a complex number also called its magnitude is the length of the vector gt abs 3 4j ans 5 gt sqrt 3 2 4 2 ans 5 The argument of a complex number is the angle between the x axis real axis and the vector counterclockwise It is calculated by the angle function gt angle 2 3j ans 0 9828 The last function specific to complex numbers we will mention here is conj which calculates the conjugate of a complex number The con jugate is simply the original number where the sign of the imaginary part is changed gt conj 2 3j ans 2 3j Real numbers are also complex numbers with a null imaginary part hence gt abs 3 ans 16 LMEPPC User Manual 1999 2008 Calerga Sarl gt conj 3 ans gt angle 3 ans gt angle 3 ans 3 1416 2 3 Vectors and Matrices LME manipulates vectors and matrices as easily as scalars To define a matrix enclose its contents in square brackets and use commas to separate elements on the same row and semicolons to separate the rows themselves gt 1 2 5 3 ans 12 5 3 Column vectors are matrices with one column and row vectors are matrices with one row You can also use the colon operator to build a row vector by specifying the start and end values and optionally the step value Note that the end value is included only if the range is a multiple of the step Negative steps are allowed There are fun
180. d write binary mode create new file a read write binary mode seek to end are read only text mode seek to beginning wt read write text mode create new file at read write text mode seek to end Examples Reading a whole text file into a string fd fopen file txt rt str fread fd inf char fclose fd Reading a whole text file line by line fd fopen file txt rt while feof fd str fgets fd end fclose fd Writing a matrix to a CSV comma separated values text file M magic 5 fd fopen file txt wt for i 1 size M 1 for j 1 size M 2 1 fprintf fd g M i j end fprintf fd g n M i end end fclose fd Reading 5 bytes at offset 3 in a binary file giving an 5 by 1 array of unsigned 8 bit integers LME Reference time functions fd fopen file bin fseek fd 3 data fread fd 5 uint8 fclose fd See also 3 30 Time Functions clock Current date and time Syntax t clock Description 371 clock returns a 1x6 row vector containing the year four digits the month the day the hour the minute and the second of the current date and time All numbers are integers except for the seconds which are fractional The absolute precision is plus or minus one second with respect to the computer s clock the relative precision is plus or minus 1 microsecond on a Macintosh
181. database Syntax n sqlite_last_insert_rowid c Description sqlite_last_insert_rowid c gives the last row inserted by the INSERT command with sqlite_exec SQLite call sqlite3_last_insert_rowid See also sqlite_exec sqlite_changes sqlite_open Open an SQLite database Extensions SQLite 573 Syntax c sqlite_open filename sqlite_open filename options Description sqlite_open filename opens the database in the specified file If the file does not exist a new database is created The result is an identifier which should be used in all other SQLite calls The database is closed with sqlite_close sqlite_open filename options specifies options in the second input argument which is usually the result of sqlite_set Example c sqlite_open test sqlite C Il rows sqlite_exec c select from person sqlite_close c SQLite calls sqlite_open See also sqlite_close sqlite_set sqlite_set Options for SQLite Syntax options sqlite_set options sqlite_set namel valuel options sqlite_set options0 namel valuel Description sqlite_set namel valuel creates the option argument used by sqlite_open Options are specified with name value pairs where the name is a string which must match exactly the names in the table below Case is significant Options which are not specified have a 574 LMEPPC User Manual 1999 2008 Calerga Sarl
182. de b z bc aa bbb c ia ib intersect a b C bbb bc ia 3 2 ib 42 a ia bbb bc b ib bbb bc Set exclusive or can also be computed as the union of a and b minus the intersection of a and b setdiff union a b intersect a b a aa de z See also ipermute Inverse permutation of the dimensions of an array Syntax B ipermute A perm Description ipermute A perm returns an array with the same elements as A but where dimensions are permuted according to the vector of dimensions perm It performs the inverse permutation of permute perm must con tain integers from 1 to n dimension perm i in A becomes dimension i in the result Examples size permute rand 3 4 5 2 3 1 534 LME Reference arrays 251 See also isempty Test for empty matrices or empty lists Syntax b b isempty M isempty list Description isempty obj gives true if obj is the empty array the empty string or the empty list and false otherwise Examples isempty T true isempty 0 false isempty true isempty true isempty false See also iscell Test for cell arrays Syntax b iscell X Description iscell X gives true if X is a cell array or a list and false otherwise 252 LMEPPC User Manual 1999 2008 Calerga Sarl Examples iscell 1 2
183. ded according to the format string The format string follows the same rules as sscanf The optional second output argument is set to the number of ele ments decoded successfully may be different than the length of the first argument if decoding strings Example Read a number from a file fopen and fclose are not available in all LME applications fd fopen test txt rt fscanf fd f 2 3 fclose fd See also sscanf fseek Change the current read or write position in a file Syntax status fseek fd position status fseek fd position mode Description fseek fd position mode changes the position in an open file where the next input output commands will read or write data The first ar gument fd is the file descriptor returned by fopen or similar functions fopen is not available in all LME applications The second argument is the new position The third argument mode specifies how the posi tion is used b absolute position from the beginning of the file c relative position from the current position e offset from the end of the file must be lt 0 The default value is b Only the first character is checked so beginning is a valid alternative for b fseek returns 0 if success ful or 1 if the position is outside the limits of the file contents 362 LMEPPC User Manual 1999 2008 Calerga Sarl See also ftell Get the current read or write position in a file Syntax
184. default value The result is a structure whose 600 LMEPPC User Manual 1999 2008 Calerga Sarl fields correspond to each option Without any input argument serialdevset creates a structure with all the default settings Note that serialdevopen also interprets the lack of an option argument or the empty array as a request to use the default values When its first input argument is a structure serialdevset adds or changes fields which correspond to the name value pairs which follow Here is the list of permissible options Name Default Meaning BPS 19200 bit per seconds Delay 0 delay after character output in seconds Handshake false hardware handshake StopBits 2 number of stop bits 1 1 5 or 2 TextMode false text mode Timeout 1 timeout in seconds Output operations wait for the specified delay after each character this can be useful with slow devices without handshake When text mode is set input CR and CR LF sequences are con verted to LF Output CR and LF are not converted Depending on the platform operations which use the timeout value such as input can be interrupted with the platform dependent abort key s typically Escape or Control C or are limited to 10 seconds Example serialdevset BPS 19200 Handshake false StopBits 2 TextMode false Timeout 1 See also serialdevopen serialdevname 6 14 Audio output This section describes functions which play sounds audioplay Play audio samples Ext
185. default value The result is a structure whose fields correspond to each option Without any input argument sqlite_set creates a structure with all the default options Note that sqlite_open also interprets the lack of an option argument or the empty array as a request to use the default values When its first input argument is a structure sqlite_set adds or changes fields which correspond to the name value pairs which follow Here is the list of permissible options empty arrays mean auto matic Name Default Meaning ExecResultClass list row type Llist or struct ExecResultNumeric true conversion of numeric columns to double SQLite is usually typeless If ExecResultNumeric is true columns are converted to numbers of class double unless they contain a non numeric value or the type name used during declaration contains BLOB CHAR CLOB or TEXT This is the same convention as what SQLite uses itself for example when sorting rows NULL values are always represented as the double empty array Examples Default options sqlite_set ExecResultClass list ExecResultNumeric true See also sqlite_version Get the version of SQLite Syntax str sqlite_version Description sqlite_version gives the version of SQLite compiled in the exten sion as a string No database is required Extensions sockets 575 SQLite call sqlite3_version 6 9 Sockets Socket functions enable communica
186. des the contents of uint8 or int8 array b which represents Unicode characters encoded with UTF 8 Each Unicode character corresponds to one two or three bytes of UTF 8 code The result is a standard character array with a single row Invalid codes for example when the beginning of the decoded data does not correspond to a character boundary are ignored See also utf8encode Encode a string of Unicode characters using UTF 8 Syntax b utf8encode str 312 LMEPPC User Manual 1999 2008 Calerga Sarl Description utf8encode b encodes the contents of character array str using UTF 8 Each Unicode character in str corresponds to one two or three bytes of UTF 8 code The result is an array of unsigned 8 bit integers If the input string does not contain Unicode characters the output is invalid Example b utf8encode abc 200 2000 20000 b 1x10 uint8 array 97 98 99 195 136 223 144 228 184 160 str utf8decode b str 1x6 uint16 array 97 98 99 200 2000 20000 See also 3 22 Quaternions Quaternion functions support scalar and arrays of quaternions Basic arithmetic operators and functions are overloaded to support expres sions with the same syntax as for numbers and matrices Quaternions are numbers similar to complex numbers but with four components instead of two The unit imaginary parts are named i j and k A quaternion can be written w ix jy kz The following relationships hold j k i
187. dlib phi theta r cart2sph 1 2 3 phi 1 1071 theta 0 9303 r 3 7417 See also pol2cart circshift Shift the elements of a matrix in a circular way Syntax use stdlib B circshift A shift_vert B circshift A shift_vert shift_hor Description circshift A sv shifts the rows of matrix A downward by sv rows The sv bottom rows of the input matrix become the sv top rows of the output matrix sv may be negative to go the other way around circshift A sv sh shifts the rows of matrix A downward by sv rows and its columns to the right by sh columns The sv bottom rows of the input matrix become the sv top rows of the output matrix and the sh rightmost columns become the sh leftmost columns See also blkdiag Block diagonal matrix Libraries stdlib 465 Syntax use stdlib X blkdiag Bl B2 Description blkdiag B1 B2 creates a block diagonal matrix with matrix blocks B1 B2 etc Its input arguments do not need to be square Example use stdlib blkdiag 1 2 3 4 5 1 2 3 4 See also compan Companion matrix Syntax use stdlib X compan pol Description compan pol gives the companion matrix of polynomial pol a square matrix whose eigenvalues are the roots of pol Example use stdlib compan 2 3 4 5 1 5 2 0 2 5 1 0 0 0 0 0 0 0 1 0 0 0 466 LMEPPC User Manual 1999 2008 Calerga Sarl See also corrcoef Correlation coefficients
188. dlib median v median M median M dim S oO lt lt XCC ou ul Description median v gives the median of vector v i e the value x such that half of the elements of v are smaller and half of the elements are larger median M gives a row vector which contains the median of the columns of M With a second argument median M dim operates along dimension dim Example use stdlib median 1 2 5 6 inf 5 474 LMEPPC User Manual 1999 2008 Calerga Sarl See also perms Array of permutations Syntax use stdlib M perms v Description perm v gives an array whose rows are all the possible permutations of vector v Example use stdlib perms 1 3 RPNrRN WW NrPWWRN WWNRNF See also sort pol2cart Polar to Cartesian coordinates transform Syntax use stdlib x y pol2cart phi r x y Z pol2cart phi r z Libraries stdlib 475 Description x y pol2cart phi r transforms polar coordinates phi and r to Cartesian coordinates x and y such that x rcos and x rsin x y z pol2cart phi r z transforms cylindrical coordinates to Cartesian coordinates leaving z unchanged Example use stdlib x y pol2cart 1 2 x 1 0806 y 1 6829 See also polyfit Polynomial fit Syntax use stdlib pol polyfit x y n Description polyfit x y n calculates the polynomial given as a vector of de scending power coefficients of order n wh
189. e Syntax line3 A b line3 A b style line3 A b style id Description line3 displays one or several straight line s in the 3D space Each line is defined by two equations of the form a x a2y a3z b The first argument of line3 is a matrix which contains the coefficients a in the first column az in the second column and a3 in the third column two rows define a different line The second argument is a column vector which contains the coefficients b If one of these arguments has two rows and the other has several pairs the same rows are reused multiple times The optional third and fourth arguments are the same as for all graphical commands LME Reference 3D graphics Example Vertical line at x 5 y 6 Lline3 1 0 0 1 5 6 See also material Surface reflexion properties Syntax material p Description 413 material p sets the reflexion properties of the Blinn Phong model of following surfaces drawn with surf and plotpoly Argument p is a scalar or a vector of two real values between 0 and 1 The first or only element ka is the weight of ambiant light the second element kd is the weight of diffuse light reflected from all light sources See also mesh Plot a mesh in 3D space Syntax mesh x y Z mesh z mesh x y z color mesh z color mesh kind mesh kind style mesh kind style id 414 LMEPPC User Manual 1999 2008 Calerga Sarl Des
190. e The default is to map z or color values to the color map for the surface cells and not to draw cell bounds mesh 1d specifies the ID used for interactivity in Sysquake See also 3 39 Graphical Functions for Dynamical Systems Graphical commands described in this section are related to automatic control They display the time responses and frequency responses of linear time invariant systems defined by transfer functions or state space models in continuous time Laplace transform or discrete time z transform Some of these functions can return results in output arguments instead of displaying them These values depend not only on the input LME Reference graphics for dynamical systems 419 arguments but also on the current scale of the figure For instance the set of frequencies where the response of the system is evaluated for the Nyquist diagram is optimized in the visible area Option Range of responseset can be used when this behavior is not suitable such as for phase portraits using lsim Output can be used for uncommon display purposes such as special styles labels or export Evaluation or simulation functions not related to graphics like polyval ode45 or filter are better suited to other usages bodemag Magnitude Bode diagram of a continuous time system Syntax bodemag numc denc bodemag numc denc w bodemag numc denc opt bodemag numc denc w opt bodemag Ac Bc Cc Dc bodemag Ac
191. e kind of bar plot The following values are recognized grouped Columns of y are grouped horizontally default stacked Columns of y are stacked vertically interval Bars defined with min and max val 382 LMEPPC User Manual 1999 2008 Calerga Sarl bar 2 4 3 6 bar 2 4 3 6 3 5 4 1 5 5 ol ll 2 4 2 4 bar 1 4 magic 4 stacked 2 4 3 1 5 6 4 6 interval mna BE 6 ne a C F 20 4 ee er 4 ou i Ly _ l l 2 4 2 4 Figure 3 5 Example of bar with different options With interval intervals are defined by two consecutive rows of y which must have an even number of rows The optional arguments style and id have their usual meaning bar uses default colors when argument style is missing Examples Simple bar plot see Fig 3 5 bar 2 4 3 6 3 5 4 1 Stacked bar plot bar 1 4 magic 4 stacked Interval plot bar 1 4 2 4 3 1 5 6 4 6 interval See also barh Horizontal bar plot LME Reference base graphics 383 Syntax barh x barh y x barh y x w barh kind barh kind style barh id Description barh plots a bar plot with horizontal bars Please see bar for a de scription of its behavior and arguments Examples Simple horizontal bar plot barh 2 4 3 6 3 5 4 1 Stacked horizontal bar plot barh 1 4 magic 4 stacked Horizontal interval plot barh 1 4 2 4 3 1 5 6 4 6
192. e left trans parent an explicit lower level should be specified to fill the whole rectangle Examples A function is evaluated over a grid of two variables x and y and is drawn with contour see Fig 3 6 meshgrid 2 0 40 10 xp x 0 2 2 y 0 3 2 exp x 0 5 2 y 0 1 2 0 1 x scale equal contour z 1 1 1 1 x y z e 386 LMEPPC User Manual 1999 2008 Calerga Sarl contour Figure 3 6 Example of contour Filled contours 2 0 80 20 repmat u 81 1 x exp x 0 2 2 y 0 3 2 exp x 0 5 2 y 0 1 2 0 1 x 0 5 x sin y levels 1 0 2 1 scale equal contour z 1 1 1 1 levels f NX KC See also fontset Options for fonts Syntax options fontset options fontset namel valuel options fontset options0 namel valuel LME Reference base graphics 387 Description fontset namel valuel creates the font description used by text Options are specified with name value pairs where the name is a string which must match exactly the names in the table below Case is significant Options which are not specified have a default value The result is a structure whose fields correspond to each option Without any input argument fontset creates a structure with all the default options When its first input argument is a structure fontset adds or changes fields which correspond to the name valu
193. e lti var end 526 LMEPPC User Manual 1999 2008 Calerga Sarl Description In an expression used as an index between parenthesis end gives the last valid value for that index It is size var 1 or size var 2 Example Time response when the last input is a step use lti P ss 1 2 3 4 1 0 0 1 3 5 P1 P end continuous time LTI state space system A 1 2 3 4 B step P1 See also Uti beginning lti subsasgn lti subsref Iti evalfr Frequency value Syntax use lti y evalfr a x Description evalfr a x evaluates system a at complex value or values x If x is a vector of values results are stacked along the third dimension Libraries lti 527 Example use lti sys tf 1 1 2 3 tf 2 1 2 3 4 evalfr sys 0 1j 3j ans 1x2x4 array 1 0 3333 0 5 2 0 25 0 25j 0 5 0 5j 3 5 8824e 2 0 2353 0 4 0 2j 4 8 3333e 2 8 3333e 2j 5 3846e 2 6 9231e 2j See also polyval ss ctrb Controllability matrix Syntax use lti C crtb a Description ctrb a gives the controllability matrix of system a which is full rank if and only if a is controllable See also SS ODSV Iti dcgain Steady state gain Syntax use lti g dcgain a 528 LMEPPC User Manual 1999 2008 Calerga Sarl Description dcgain a gives the steady state gain of system a See also Uti inorm Iti feedback Feedback co
194. e of the function or oper ator involved Here stdlib is the library name primes is the function name and 164 is the line number in the file which contains the library If the function where the error occurs is called itself by another func tion the whole chain of calls is displayed here primes was called by factor at line 174 in library stdlib Here is the list of errors which can occur For some of them LME attempts to solve the problem itself e g by allocating more memory for the task Stack overflow Too complex expression or too many nested func tion calls Data stack overflow Too large objects on the stack in expres sions or in nested function calls Variable overflow Not enough space to store the contents of a variable LME Reference 39 Code overflow Not enough memory for compiling the program Not enough memory Not enough memory for an operation out side the LME core Algorithm does not converge A numerical algorithm does not converge to a solution or does not converge quickly enough This usually means that the input arguments have invalid values or are ill conditioned Incompatible size Size of the arguments of an operator or a func tion do not agree together Bad size Size of the arguments of a function are invalid Non vector array A row or column vector was expected but a more general array was found Not a column vector A column vector was expected but a more general array was found Not
195. e pairs which follow Here is the list of permissible options empty arrays mean auto matic Name Default Meaning Font fad font name Size 10 character size in points Bold false true for bold font Italic false true for italic font Underline false true for underline characters Color 0 0 0 text color The default font is used if the font name is not recognized The color is specified as an empty array black a scalar gray or a 3 element vector RGB of class double O black 1 maximum brightness or uint8 O black 255 maximum brightness Examples Default font fontset Font Size 10 Bold false Italic false Underline false Color real 1x3 See also text fplot Function plot 388 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax fplot fun fplot fun limits fplot fun limits style fplot fun limits style id fplot fun limits style id pl p2 Description Command fplot fun limits plots function fun specified by its name as a string a function reference or an inline function The function is plotted for x between Limit 1 and Limit 2 the default limits are 5 5 The optional third and fourth arguments are the same as for all graphical commands Remaining input arguments of fplot if any are given as additional input arguments to function fun They permit to parameterize the function For example fplot fun 0 10 1 2 5 calls fun as y fun x
196. e shading Surface and mesh colors add information to the image helping the viewer in interpreting it Colors specified by the style argument also accepted by 2D graphical commands are used unchanged Colors specified by a single component value RGB colors or implicit are pro cessed differently whether Lightangle and or material have been executed or not In the first case colors depend directly on the col ors specified or the default value in the second case the Blinn Phong reflection model is used with flat shading In both cases single color values are mapped to colors using the current color map set with colormap Commands which accept a color argument are mesh surf and plotpoly Direct colors If neither Lightangle nor material has been executed colors depend only on the color argument provided with x y and z coordinates If the this argument is missing color is obtained by mapping linearly the z coordinates to the full range of the current color map Blinn Phong reflection model In the Blinn Phong reflexion model the color of a surface depends on the intrinsic object color the surface reflexion properties and the relative positions of the surface the viewer and light sources 3 38 Functions camdolly Move view position and target Syntax camdolly d 406 LMEPPC User Manual 1999 2008 Calerga Sarl Description camdolly d translates the camera by 3x1 or 1x3 vector d moving the target and the view
197. e specified options which are typically built with audiorecordset Example samples audiorecord 1 audioplay samples See also audiorecordset audioplay audiorecordset Options for audio Syntax options audiorecordset options audiorecordset namel valuel options audiorecordset options0 namel valuel Description audiorecordset namel valuel creates the option argument used by audiorecord Options are specified with name value pairs where the name is a string which must match exactly the names in the table below Case is significant Options which are not specified have a default value The result is a structure whose fields correspond to each option Without any input argument audiorecordset creates a structure with all the default options Note that audiorecord also interprets the lack of an option argument or the empty array asa request to use the default values 604 LMEPPC User Manual 1999 2008 Calerga Sarl When its first input argument is a structure audiorecordset adds or changes fields which correspond to the name value pairs which fol low Here is the list of permissible options Name Default Meaning SampleRate 44100 sample rate in Hz Stereo true true for stereo false for mono Default values may be different on platforms with limited audio ca pabilities Examples Default options audiorecordset SampleRate 44100 Stereo true Record in mono samples audioreco
198. e two main ad vantages of SQLite with respect to larger relational database systems there is no need to install any additional software or to have access to a remote database and the database file can be archived and re stored extremely easily On the other hand it lacks concurrent access stored procedures etc Its SQL compatibility permits the developer to port easily applications to other databases should it be necessary This documentation assumes you have a basic knowledge of SQL Even if you do not the examples should help you to get started For more informations about SQLite please visit the Web site http www sqlite org The creator of SQLite D Richard Hipp is gratefully acknowledged The following functions are defined Function Purpose sqlite_changes Number of affected rows in the last command sqlite_close Close an SQLite database sqlite_exec Execute an SQL query sqlite_last_insert_rowid Index of tha last row inserted sqlite_open Open an SQLite database sqlite_set Options for sqlite_open sqlite_version Get the version of SQLite 6 7 Compiling the extension The extension is installed with Sysquake or LME and ready to use but it is also provided as source code If you want you can check on the Web if there is a more recent version of SQLite and compile the extension again with it The steps below show the simplest way to do it Check your development tools Make sure you have the devel opment tools required fo
199. e user whatever the setting is Bit Meaning 0 log x 2 tick on x axis 3 grid for x axis 4 labels on x axis 6 log y 7 dB y 8 tick on y axis 9 grid for y axis 10 labels on y axis 12 same scale on both axis 13 minimum grid 14 maximum grid scale lock locks the scale as if the user had done it by hand It fixes only the initial value the user may change it back afterwards The scale is usually limited to a range of 1e 6 for linear scales and a ratio of 1e 6 for logarithmic scales This avoids numerical problems such as when a logarithmic scale is chosen and the data contain the value 0 In some rare cases a large scale may be required The lock option is used to push the limits from 1e 6 to 1e 24 for both linear and logarithmic scales A second argument must be provided scale lock xmin xmax ymin ymax The command must be used in a draw handler or from the command line interface To add other options use a separate scale command scale logdb scale lock le 5 1e8 le 9 1e9 The scale is locked and the user may not unlock it In the example above note also that a single string argument can be written without quote and parenthesis if it contains only letters and digits With an output argument scale returns the current scale as a vec tor xmin xmax ymin ymax If the scale is not fixed the vector is empty If only the horizontal scale is set the vector is xmin xmax During a mouse drag
200. e values in the table below Perm Description ol es read only w read write r r mmap filename n type perm offset specified the offset of the part being memory mapped in the file The following functions are overloaded to accept the type of ob jects returned by mmap beginning disp end Length subsasgn and subsref Example Bytes 0 3999 of file test are mapped in memory as 32 bit signed integers They are multiplied by two mmap test 1000 int32 w m m 999 2 x m 0 999 Extensions data compression 561 unmap m See also munmap Unmap a memory mapped file Syntax munmap m Description munmap m unmaps a file which has been mapped with mmap Its argu ment is the object given by mmap See also 6 3 Data Compression This section describes functions which compress and uncompress se quences of bytes such as text Often these sequences present redun dancy which can be removed to produce a shorter sequence while still being able to revert to the initial one The ZLib extension is based on zlib by J L Gailly and M Adler whose work is gratefully acknowledged To preserve their terminology com pression is performed with function deflate and uncompression with inflate deflate Compress a sequence of bytes Syntax strc deflate str 562 LMEPPC User Manual 1999 2008 Calerga Sarl Description deflate str produces a string strc which is usu
201. ed by if or while because these statements consider an array to be true if all its elements are nonzero Examples all 1 2 3 2 false all 1 2 3 gt 0 true LME Reference logical functions 335 See also any Check whether any element is true Syntax v any A any A dim any v v b Description any A performs a logical OR on the elements of the columns of array A or the elements of a vector If a second argument dim is provided the operation is performed along that dimension Examples any 1 2 3 2 true any 1 2 3 gt 5 false See also bitall Check whether all the corresponding bits are true Syntax v bitall A v bitall A dim b bitall v 336 LMEPPC User Manual 1999 2008 Calerga Sarl Description bitall A performs a bitwise AND on the elements of the columns of array A or the elements of a vector If a second argument dim is provided the operation is performed along that dimension A can be a double or an integer array For double arrays bitall uses the 32 least significant bits Examples bitall 5 3 1 bitall 7uint8 6uint8 3uint8 6uint8 2 2x1 uint8 array 6 2 See also bitany jall bitand bitand Bitwise AND Syntax c bitand a b Description Each bit of the result is the binary AND of the corresponding bits of the inputs The inputs can be scalar arrays of the same size or a scalar and an array If the input arguments
202. ee also switch catch Error recovery See also try continue Continue loop from beginning Syntax continue Description When a continue statement is executed in the scope of a loop con struct while repeat or for statements following continue are ig nored and a new loop is performed if the loop termination criterion is not fulfilled 62 LMEPPC User Manual 1999 2008 Calerga Sarl The loop must be in the same function as continue It is an error to execute continue outside any loop See also define Definition of a constant Syntax define c expr define c expr Description define c expr assign permanently expression expr to c It is equiv alent to function y c y expr Since c does not have any input argument the expression is usually constant A semicolon may follow the definition but it does not have any effect define must be the first element of the line spaces and comments are skipped Examples define e exp 1 define g 9 81 define c 299792458 define G 6 672659e 11 See also unction for Loop controlled by a variable which takes successively the value of the elements of a vector or a list LME Reference programming constructs Syntax for v vect sl end for v list s1 end Description 63 The statements between the for statement and the corresponding end are executed repeatedly with the control variable v taking succes siv
203. efault 580 LMEPPC User Manual 1999 2008 Calerga Sarl Example socketset ListenQueue 5 Proto tcp TextMode true Timeout 30 See also socketnew socketservernew socketsetopt socketsetopt Settings change for sockets Syntax socketsetopt fd namel valuel socketsetopt fd options Description socketsetopt fd namel valuel changes the options for the socket identified by fd Options are specified by pairs of name and value They are the same as those valid with socketset However only TextMode and Timeout have an effect other ones are ig nored socketsetopt fd options takes as second argument a structure of options created with socketset See also socketset socketnew socketservernew 6 10 Launch URL This section describes a function which requests the default WWW browser to open a URL The intended use of Launchurl is the display of local or Web based documentation You can add menu entries to your SQ files to help your users point to updates or send e mail Extensions download URL 581 launchurl Launch a URL in the default browser Syntax status Launchurl url Description Launchurl asks the current browser to launch a URL given as a String Exactly what launching a URL means depends on the URL protocol i e the part before the colon and on the program which processes it If the URL cannot be processed the status is set to false otherwise it is t
204. efines how numbers are displayed Line width The default line width can be set to 1 or 2 pixels In graphics commands an uppercase color letter in the style argu ment increases the width to 2 or 3 pixels respectively Font The default font used in figures can be set The font used by text can be changed with fontset currently the option Font can be serif sansserif or monospace and Size Italic and Underline are ignored 1 6 Libraries LME for Pocket PC does not implement its own text editor Functions are stored in library files To make their editing easier library files end with lml txt double suffix Tapping their icon in File Explorer should open them with the standard application used for editing text files typically Pocket Word the txt suffix is hidden When you create a new library make sure you add a lml txt suffix and save it as text only When you transfer libraries from a desktop application for instance Sysquake you should also add this suffix if you want to edit 12 LMEPPC User Manual 1999 2008 Calerga Sarl it on the Pocket PC device LME also finds library files with a simple Lml suffix but you cannot edit them as easily LME finds libraries in the directory Lib in the same directory as LME exe If you want to store libraries in other places you should add directories with the Options dialog or the command path see above Chapter 2 LME Tutorial The remainder of this chapter i
205. ely every column of vect or every element of list List Typically vect is a row vector defined with the You can change the value of the control variable in the loop how ever next time the loop is repeated that value is discarded and the next column of vect is fetched Examples for i 1 3 i end i 1 si 2 i 3 for i 1 3 i end i 1 2 3 for i 1 2 5 end i i 5 for i 1 3 break end i i 1 for el 1 abc 2 5 el end el 1 el abc el 2 5 64 LMEPPC User Manual 1999 2008 Calerga Sarl See also variable assignment function endfunction Definition of a function operator or method Syntax function f statements function f x1 x2 statements function f x1 x2 expr2 statements function y f x1 x2 statements function yl y2 f x1 x2 statements function class method statements function statements endfunction Description New functions can be written to extend the capabilities of LME They begin with a line containing the keyword function followed by the list of output arguments if any the function name and the list of input arguments between parenthesis if any The output arguments must be enclosed between parenthesis or square brackets if they are several One or more variable can be shared in the list of input and output arguments When the execution of the function terminates ei
206. ength between 1 and 32 and are displayed in binary The following statement makes available functions defined in bitfield use bitfield bitfield beginning First bit position in a bitfield Syntax use bitfield a beginning Description In the index expression of a bitfield beginning is the position of the least significant bit i e 0 See also bitfield bitfield Bitfield object constructor Syntax use bitfield a bitfield a bitfield n a bitfield n wordlength 504 LMEPPC User Manual 1999 2008 Calerga Sarl Description bitfield n wordlength creates a bitfield object initialized with the wordlength least significant bits of the nonnegative integer number n The default value of wordlength is 32 if n is a double an int32 or a uint32 number 16 is n is an int16 or uint16 number or 8 if n is an int8 or uint8 number Without argument bitfield gives a bit field of 32 bits 0 Like any integer number in LME n may be written in base 2 8 10 or 16 0b1100 014 12 and Oxc all represent the same number The following operators and functions may be used with bitfield arguments with results analog to the corresponding functions of LME Logical functions operate bitwise amp and not eq or minus plus mldivide uminus mrdivide uplus mtimes xor ne Indexes into bit fields are non negative integers 0 represents the least significant bit and wordlength 1 the most sig
207. ensions audio output 601 Syntax audioplay samples audioplay samples options Description audioplay samples plays the audio samples in array samples at a sample rate of 44 1 kHz Each column of samples is a channel i e samples is a column vector for monophonic sound and a two column array for stereophonic sound and each row is a sample Samples are stored as double or single numbers between 1 and 1 int8 numbers between 128 and 127 or int16 numbers between 32768 and 32767 audioplay samples options uses the specified options which are typically built with audioset Examples A monophonic bell like sound of two seconds with a frequency of 740 Hz and a damping time constant of 0 5 second t 0 88200 44100 samples sin 2 pix740 t exp t 0 5 audioplay samples Some white noise which oscillates 5 times between left and right t 0 44099 44100 noise 0 1 randn length t 1 left cos 2 pi t noise right sin 2 pi t noise opt audioset Repeat 5 audioplay left right opt See also audioset audioset Options for audio Syntax options audioset options audioset namel valuel options audioset optionsO namel valuel 602 LMEPPC User Manual 1999 2008 Calerga Sarl Description audioset namel valuel creates the option argument used by audioplay Options are specified with name value pairs where the name is a str
208. ensions of array A which is at least 2 Scalars row and column vectors and matrices have 2 dimen sions Examples ndims magic 3 2 ndims rand 3 4 5 3 See also nnz Number of nonzero elements Syntax n nnz A Description nnz A returns the number of nonzero elements of array A See also find num2cell Conversion from numeric array to cell array Syntax C num2cell A C num2cell A dims LME Reference arrays 257 Description num2cell A creates a cell array the same size as numeric array A The value of each cell is the corresponding elements of A num2cell A dims cuts array A along dimensions dims and creates a cell array with the result Dimensions of cell array are the same as dimensions of A for dimensions not in dims and 1 for dimensions in dims dimensions of cells are the same as dimensions of A for dimen sions in dims and 1 for dimensions not in dims Argument A can be a numerical array of any dimension and class a logical array or a char array Examples num2cell 1 2 3 4 1 2 3 4 num2cell 1 2 3 4 1 1 3 2 4 num2cell 1 2 3 4 2 1 2 3 4 See also numel Number of elements of an array Syntax n numel A Description numel A gives the number of elements of array A It is equivalent to prod size A Examples numel 1 5 5 numel ones 2 3 6 numel 1 1 6 abc 4 258 LMEPPC User Manual
209. ents like a 2 f 3 2 5 3 are accepted The syntax v expr permits to specify the field name dynamically at run time as the result of evaluating expression expr LME Reference operators 121 v f is equivalent to v f This syntax is more elegant than functions getfield and setfield Examples N 2 hello 2 string 1 s f tow e wma real 1x2 string Q See also Operator getfieldjsetfietd Operator Addition Syntax xX y M1 M2 M xX plus x y Description With two operands both operands are added together If both operands are matrices with a size different from 1 by 1 their size must be equal the addition is performed element wise If one operand is a scalar it is added to each element of the other operand With one operand no operation is performed except that the result is converted to a number if it was a string or a logical value like with all mathematical operators and functions For strings each character is replaced with its numerical encoding The prefix is actually a synonym of double 122 LMEPPC User Manual 1999 2008 Calerga Sarl plus x y is equivalent to x y and uplus x to x They can be used to redefine these operators for objects Example 2 3 5 1 2 3 5 47 3 4 2 5 6 See also Operator Subtraction or negation Syntax X y M1 M2 M x minus x y X M uminus x Description With two operands the second ope
210. ep sgrid dinitial impulse sigma dlsim initial step dnichols lsim zgrid dnyquist ngrid Date and time cal2julian julian2cal toc clock tic Threads semaphoredelete semaphoreunlock threadset semaphorelock threadkill threads leep semaphorenew threadnew LME Reference variables 53 Extensions loaded on demand exteval extload extunload LME for Pocket PC functions lmepath path 3 8 Variable Assignment and Subscripting Variable assignment Assignment to a variable or to some elements of a matrix variable Syntax var expr varl var2 function Description var expr assigns the result of the expression expr to the variable var When the expression is a naked function call varl var2 function assigns the value of the output arguments of the function to the different variables Usually providing less variables than the function can provide just discards the superfluous output arguments however the function can also choose to perform in a different way an example of such a function is size which returns the number of rows and the number of columns of a matrix either as two numbers if there are two output arguments or as a 1 by 2 vector if there is a single output argument Providing more variables than what the function can provide is an error Variables can store any kind of contents dynamically the size and type can change from assignment to assignment A subpart of a matrix variable can
211. eport with a special for mat specified by the string format This string is similar to the format argument of sprintf it is reused for each line of the profiled func tion Its characters are output literally except for sequences which begin with a percent character whose meaning is given in the table below Char Meaning single l line number t cumulative time p percentage of the total time S source code of the line Like with sprintf precision numbers may be inserted between the percent sign and the letter for instance 8 3t displays the cumula tive time in a column of 8 characters with a fractional part of 3 digits The percentage is displayed only if it is greater than 1 otherwise it is replaced together with the percent character which may follow it with spaces The default format is 41 9 3t 6 1p s n Example We shall profile function Logspace from library stdlib the source code of this function has been revised since the profiling was done use stdlib profile logspace x logspace 1 10 profile report 13 0 000 function r logspace x1 x2 n 14 0 000 15 0 000 14 8 if nargin lt 3 16 0 000 5 8 n 100 17 0 000 2 2 end 18 0 000 77 1 r exp log x1 log x2 x1 O0 n 1 n 1 86 LMEPPC User Manual 1999 2008 Calerga Sarl While the times spent for all lines are smaller than half a millisecond the resolution is fine enough to permit relative timing of each line The
212. equest Syntax fd socketaccept fds Description socketaccept fds accepts a new connection requested by a client to the server queue created with socketservernew Its argument fds is the file descriptor returned by socketservernew Once a connection has been opened the file descriptor fd can be used with functions such as fread fwrite fscanf and fprintf The connection is closed with fclose Extensions sockets 577 See also socketconnect fgetl fgets fprintf socketconnect Change UDP connection Syntax socketconnect fd hostname port Description socketconnect fd hostname port changes the remote host and port of the UDP connection specified by fd An attempt to use socketconnect on a TCP connection throws an error See also socketnew socketnew Create a new connection to a server Syntax fd socketnew hostname port options fd socketnew hostname port Description socketnew hostname port creates a new TCP connection to the specified hostname and port and returns a file descriptor fd The third argument of socketnew hostname port options is a structure which contains configuration settings It is set with socketset Once a connection has been opened the file descriptor fd can be used with functions such as fread fwrite fscanf and fprintf The connection is closed with fclose 578 LMEPPC User Manual 1999 2008 Calerga Sarl Example fd socketnew www somewebserver c
213. era around the view direction The projection is such that the up vector is in a plane which is vertical in the 2D projection Changing it makes the projection rotate around the image of the target View angle The view angle defines the part of the 3D space which is projected onto the image window in perspective projections It is zero in orthographic mode All of these parameters can be set automatically Here is how the whole projection and scaling process is performed Scale data separately along each direction according to daspect Find bounding box of all displayed data or use limits set with scale Find radius of circumscribed sphere of bounding box If the target point is automatic set it to the center of the bound ing box otherwise use position set with camtarget If the view point is automatic set it to direction 3 2 1 at infinity in orthographic mode or in that direction with respect to the target point at a distance such that the view angle of the circumscribed sphere is about 6 degrees otherwise use position set with campos If the up vector is automatic set it to 0 0 1 vertical pointing upward otherwise use position set with camup Compute the corresponding homogeneous matrix transform LME Reference 3D graphics 405 Set the base scaling factor so that the circumscribed sphere fits the display area Apply an additional zoom factor which depends on camva and camzoom 3 37 Surfac
214. erator gt operator gt Operator gt Greater than Syntax x gt y gt x y Description x gt y is true if x is greater than y and false otherwise Comparing NaN not a number to any number yields false including to NaN If x and or y is an array the comparison is performed element wise and the result has the same size gt x y is equivalent to x gt y It can be used to redefine this oper ator for objects Example 2 3 4 gt 2 4 2 FFT See also operator operator operator lt operator lt operator gt Operator lt Less or equal to Syntax LME Reference operators 135 Description x lt y is true if x is less than or equal to y and false otherwise Comparing NaN not a number to any number yields false including to NaN If x and or y is an array the comparison is performed element wise and the result has the same size le x y is equivalent to x lt y It can be used to redefine this op erator for objects Example 2 3 4 lt 2 4 2 TTF See also operator operator operator lt operator gt operator gt Operator gt Greater or equal to Syntax x gt y ge x y Description x gt y is true if x is greater than or equal to y and false otherwise Comparing NaN not a number to any number yields false including to NaN If x and or y is an array the comparison is performed element wise and the result has the same size ge x
215. eros poles and gain if there are three output arguments or as numerator and denominator coefficient vectors if there are two output arguments ellip n w0 where w0 is a scalar gives a nth order digital low pass filter with a cutoff frequency of w0 relatively to half the sampling frequency ellip n wl wh where the second input argument is a vector of two numbers gives a 2nth order digital bandpass filter with passband between wl and wh relatively to half the sampling frequency ellip n w0 high gives a nth order digital highpass filter with a cutoff frequency of w0 relatively to half the sampling frequency ellip n wl wh stop where the second input argument is a vector of two numbers gives a 2nth order digital bandstop filter with stopband between wl and wh relatively to half the sampling frequency With an additional input argument which is the string s ellip gives an analog elliptic filter Frequencies are given in rad s See also ellipap Elliptic analog filter prototype Syntax use filter z p k ellipap n rp rs Libraries filter 517 Description ellipap n rp rs calculates the zeros the poles and the gain of an elliptic analog filter of degree n with a cutoff angular frequency of 1 rad s Ripples have a peak to peak magnitude of rp dB in the passband and of rs dB in the stopband See also Ip2bp Lowpass prototype to bandpass filter conversion Syntax use filter z
216. erpolation 1 5649 1 571 2 Inverse quadratic interpolation 1 571 1 5708 1 5649 Inverse quadratic interpolation 1 5708 1 5708 1 571 Inverse quadratic interpolation 1 5708 1 5708 1 571 ans 1 5708 See also quad Numerical integration Syntax y quad fun a b y quad fun a b tol y quad fun a b tol trace y quad fun a b tol trace Description quad fun a b integrates numerically function fun between a and b fun is either specified by its name or given as an anonymous or inline function or a function reference The optional fourth argument is the requested relative tolerance of the result It is either a positive real scalar number or the empty ma trix or missing argument for the default value which is sqrt eps The optional fifth argument if true or nonzero makes quad displays information at each step Additional input arguments of quad are given as additional input arguments to function fun They permit to parameterize the function LME Reference strings 299 Example 2 te dt 0 quad t txexp t 0 2 0 5940 See also 3 21 String Functions base64decode Decode base64 encoded data Syntax strb base64decode strt Description base64decode strt decodes the contents of string strt which rep resents data encoded with base64 Characters which are not A Z a 2 0 9 e or are ignored Decoding stops at the end of the string or when is
217. es equal Same linear scale for x and y axis Typically used for representation of the complex plane such as the roots of a poly nomial or a Nyquist diagram For 3D graphics same effect as daspect 1 1 1 lLock See below Linlin Linear scale for both axis lLinlog Linear scale for the x axis and logarithmic scale for the y axis loglin Logarithmic scale for the x axis and linear scale for the y axis Loglog Logarithmic scale for both axis lindb Linear scale for the x axis and dB scale for the y axis logdb Logarithmic scale for the x axis and dB scale for the y axis Lindb logdb Linear scale for the x axis and dB scale for the y axis The user can choose a logarithmic scale for the x axis anda logarithmic or linear scale for the y axis This last setting shows how to enable the options the user can choose in Sysquake The setting and the enabled options are separated by a dash if a simple setting is specified the enabled options are assumed 400 LMEPPC User Manual 1999 2008 Calerga Sarl to be the same Enabling dB always permits the user to choose a loga rithmic or linear scale and enabling a logarithmic scale always permits to choose a linear scale The equal option cannot be combined with anything else When the properties are specified with one or two integer numbers each bit corresponds to a property Only the properties in bold in the table below can be set by th
218. es functions 5 1 stdlib stdlib is a library which extends the native LME functions in the fol lowing areas creation of matrices blkdiag compan hankel linspace logspace toeplitz geometry cart2sph cart2pol pol2cart sph2cart subspace functions on integers factor isprime primes statistics corrcoef median perms data processing circshift cumtrapz fftshift filter2 hist ifftshift polyfit polyvalm trapz other isreal sortrows The following statement makes available functions defined in stdlib use stdlib cart2pol Cartesian to polar coordinates transform Libraries stdlib 463 Syntax use stdlib phi r cart2pol x y phi r z cart2pol x y z Description phi r cart2pol x y transforms Cartesian coordinates x and y to polar coordinates phi and r such that x r cos and x rsin phi r z cart2pol x y z transform Cartesian coordinates to cylindrical coordinates leaving z unchanged Example use stdlib phi r cart2pol 1 2 phi 1 1071 r 2 2361 See also polzcart cart2sph Cartesian to spherical coordinates transform Syntax use stdlib phi theta r cart2sph x y zZ Description phi theta r cart2sph x y z transforms Cartesian coordinates x y and z to polar coordinates phi theta and r such that x rcos g cos 9 y rsin g cos 9 and z rsin 9 464 LMEPPC User Manual 1999 2008 Calerga Sarl Example use st
219. es zero in either direction if direction i 0 from negative to nonnegative if direction i gt 0 or from positive to nonpositive if direction i lt 0 The event terminates integration if isterminal i is true The Events function is evaluated for each state obtained by integration 292 LMEPPC User Manual 1999 2008 Calerga Sarl intermediate time steps obtained by interpolation when Refine is larger than 1 are not considered When an event occurs the integration time step is reset to the initial value and new events are disabled during the next integration step to avoid shattering MaxStep should be used if events are missed when the result of Events is not monotonous between events When an event occurs function OnEvent is called if it exists It can be defined as function yn onevent t y i where i identifies the event stream positive for events produced by Events or negative for events produced by EventTime and the out put yn is the new value of the state immediately after the event The primary goal of odex functions is to integrate states However there are systems where some states are constant between events and are changed only when an event occurs For instance in a relay with hysteresis the output is constant except when the input over shoots some value In the general case ni states are integrated and n ni states are kept constant between events The total number of states n is given by the length of the
220. expr args paramstruct is a simplified way to create an inline function when the code consists of a single expression args is the list of arguments which must be supplied when the inline function is called paramstruct is a structure whose fields define fixed param eters Anonymous functions are an alternative often easier way of creat ing inline functions The result is the same Since inline is a normal function it must be used in contexts where fixed parameters cannot be created as separate variables Examples A simple expression evaluated at x 1 and x 2 fun inline cos x exp x y feval fun 2 5 6319e 2 feval fun 5 1 9113e 3 lt Il A function of x and y fun inline exp x 2 y 2 x y A function with two output arguments the string is broken in three lines to have a nice program layout a mean v b prod v 1 length v 1 am gm feval fun 1 10 fun inline function a b f v LME Reference miscellaneous functions 99 am 5 5 gm 4 5287 Simple expression with fixed parameter a fun inline cos axx x struct a 2 feval fun 3 0 9602 An equivalent function where the source code of a complete function is provided fun inline function y f a x y cos a x 2 feval fun 3 0 9602 A function with two fixed parameters a and b whose values are pro vided in a list inline function
221. f an assignment does not contain a variable a structure field a list element or the part of an array which can be assigned to Bad variable in a for loop The left part of the assignment of a for loop is not a variable LME Reference 43 Source code not found The source code of a function is not avail able File not found fopen does not find the file specified Bad file ID I O function with a file descriptor which neither is stan dard nor corresponds to an open file or device Cannot write to file Attempt to write to a read only file Bad seek Seek out of range or attempted on a stream file Too many open files Attempt to open too many files End of file Attempt to read data past the end of a file Timeout Input or output did not succeed before a too large amount of time elapsed No more OS memory The operating system cannot allocate more memory Bad context Call of a function when it should not application dependent Not supported The feature is not supported at least in the current version 3 7 List of Commands Functions and Op erators Programming keywords break error repeat case for rethrow catch function return clear global Switch continue if try define otherwise until endfunction persistent use else private useifexists elseif public while 44 LMEPPC User Manual 1999 2008 Calerga Sarl Programming operators and functions assert fun2str nargout Variable assignment help sandbox Operat
222. feedback 528 impulse inv 528 isct 529 isdt 529 isempty isproper issiso 530 lsim 542 minreal 531 minus 531 mldivide 531 mrdivide 532 mtimes 532 nichols 542 norm 533 nyquist parallel plus repmat 535 series 535 size ssdata 536 step 543 MAR subsref tfdata 538 uminus 539 uplus 539 class polynom diff 494 disp double feval 495 inline 495 int 494 ee subst class ratfun den 498 diff 498 disp feval 499 inline 499 num 497 Index rat fun 496 class ratio char A double ratio 500 class ss augstate 523 ctrb 527 initial 541 obsv 533 ss 520 class tf tf 521 540 cle clear clock 371 colon color colormap compan conp E cond 198 conj HES continue 61 contour 385 contour3 410 conv conv2 200 agg as cos cosh cot coth 157 cov cross csc csch ce e 114 cumprod cumsum 203 cumt rapz 466 d2cm dare 5 dash pattern EEF ga 201 z H wn Sy wE 607 daspect datestr 552 datevec 553 dbclear 76 dbcont dbhalt 77 dbodemag dbedenh vas 3 dbquit dbstack 7 doton Ga 89 deblank BOT 301 deconv 204 def ine 62 deflate delaunay delaunayn det 205 diag diff diln 158 dimpulse dinitial disp dlsim dlyap dmargin 349 dnichols dnyquist 428 dot 207 double
223. forms the opposite of dpcmenco See also dpcmenco Differential pulse code modulation encoding Syntax use Sigenc i dpcmenco input codebook partition predictor Description dpcmenco input codebook partition predictor quantizes the signal in vector input with differential pulse code modulation It predicts the future response with the finite impulse response filter given by polynomial predictor and it quantizes the residual error 546 LMEPPC User Manual 1999 2008 Calerga Sarl with codebook and partition like quantiz The output i is an array of codes with the same size and dimension as input The prediction y k for sample k s degpredictor y k gt predictor yq k i i 1 where yg k is the quantized reconstructed signal The predictor must be strictly causal predictor must be zero To encode the difference between in k and yq k 1 predictor 0 1 Note that there is no drift between the reconstructed signal and the input contrary to the case where the input is differentiated quantized and integrated Example use sigenc t 0 0 1 10 x Sin t codebook 1 01 1 partition 0 01 09 predictor 0 1 i dpcmenco x codebook partition predictor y dpcmdeco i codebook predictor See also dpcmopt Differential pulse code modulation decoding Syntax use sigenc predictor codebook partition dpcmopt in order n predictor codebook partition dpcm
224. fs Conversion is performed with the bilinear transormation Z 1 Zc 2fs 1l Z 2fs If the analog transfer function has less zeros than poles additional digital zeros are added at 1 to avoid a delay With three input arguments bilinear numc denc fs uses the coefficients of the numerators and denominators instead of their ze ros poles and gain 512 LMEPPC User Manual 1999 2008 Calerga Sarl buttap Butterworth analog filter prototype Syntax use filter z p k buttap n Description buttap n calculates the zeros the poles and the gain of a Butter worth analog filter of degree n with a cutoff angular frequency of 1 rad s See also butter Butterworth filter Syntax use filter z k butter n w0 num den butter n w0 butter n wl wh butter n w0 high butter n wl wh stop butter s Description butter calculates a Butterworth filter The result is given as zeros poles and gain if there are three output arguments or as numera tor and denominator coefficient vectors if there are two output argu ments butter n w0 where w0 is a scalar gives a nth order digital low pass filter with a cutoff frequency of w0 relatively to half the sampling frequency butter n wl wh where the second input argument is a vector of two numbers gives a 2nth order digital bandpass filter with pass band between wl and wh relatively
225. function header does not correspond to any code and is not timed To improve the accuracy of the timing we repeat the execution 10000 times for i 1 10000 x logspace 1 10 end profile report 13 0 000 14 0 000 15 0 055 16 0 057 17 0 047 18 0 458 ANLO WON WO X X X amp function r logspace x1 x2 n if nargin lt 3 n 100 end r exp log x1 log x2 x1 0 n 1 n 1 Finally here is a report with a different format the first column is the percentage as an integer a space and the percent sign followed by spaces and the source code profile report 3 0p s n function r logspace x1 x2 n 9 if nargin lt 3 9 n 100 8 end 74 r exp log x1 log x2 x1 O n 1 n 1 See also tic toc sprintf 3 12 Miscellaneous Functions This section describes functions related to programming function ar guments error processing evaluation memory assert Check that an assertion is true Syntax assert expr assert expr str assert expr format argl arg2 assert expr identifier format argl arg2 LME Reference miscellaneous functions 87 Description assert expr checks that expr is true and throws an error otherwise Expression expr is considered to be true if it is a non empty array whose elements are all non zero With more input arguments assert checks that expr is true and throws the error specified by remaining arguments otherw
226. genvalues L eig A BK Example 4 2 1 2 0 1 2 1 ee DOOWD gt Y x lt X oul uo ou tl C 5 L K dare A B Q R 2327 9552 1047 113 1047 113 496 0624 L 0 2315 0 431 K 9 3492 2 1995 X A X A A X B B X xB R B X A Q 1 0332e 9 4 6384e 10 4 8931le 10 2 2101e 10 See also Care deconv Deconvolution or polynomial division Syntax q deconv a b q r deconv a b LME Reference linear algebra 205 Description q r deconv a b divides the polynomial a by the polynomial b re sulting in the quotient q and the remainder r All polynomials are given as vectors of coefficients highest power first The degree of the remainder is strictly smaller than the degree of b deconv is the inverse of conv a addpol conv b q r Examples q r deconv 1 2 3 4 5 1 3 2 q 1 14 r 6 3 addpol conv q 1 3 2 r 12345 See also det Determinant of a square matrix Syntax d det M Description det M is the determinant of the square matrix M which is O up to the rounding errors if M is singular The function rank is a numerically more robust test for singularity Examples det 1 2 3 4 2 det 1 2 1 2 0 See also poly 206 LMEPPC User Manual 1999 2008 Calerga Sarl diff Differences Syntax dm diff A dm diff A n dm diff A n dim dm diff A dim Description diff A calculates the differences
227. gives the output and the time as column vectors No display is produced Example Response of a continuous time system whose initial state is 5 3 see Fig 3 17 initial 0 3 0 1 0 8 0 4 2 3 1 3 2 1 2 1 5 3 See also dinitial impulse responseset Isim Time response plot of a continuous time linear system with piece wise linear input Syntax lsim numc denc u t lsim numc denc u t opt lsim Ac Bc Cc Dc u t lsim Ac Bc Cc Dc u t opt lsim Ac Bc Cc Dc u t x0 tsim Ac Bc Cc Dc u t x0 opt style LME Reference graphics for dynamical systems 439 initial 10m Figure 3 17 Example of initial lsim style id y t lsim Description Llsim numc denc u t plots the time response of the continuous time transfer function numd dend The input is piece wise linear it is de fined by points in real vectors t and u which must have the same length Input before t 1 and after t end is 0 The input used for the simulation is interpolated to have a smooth response lsim Ac Bc Cc Dc u t plots the time response of the continuous time state space model Ac Bc Cc Dc defined as dx a Acx t B u t y t C x t D u t r where the system input at time sample t i is u i For single input systems u can also be a row vector lsim Ac Bc Cc Dc u t x0 starts with initial state x0 at time t 0 The length of x0 must match the number of states The
228. gmas with unknown names are ignored Name Arguments Effect line n Set the current line number to n pragma line 120 sets the current line number as reported by er ror messages or used by the debugger or profiler to 120 This can be useful when the LME source code has been generated by process ing another file and line numbers displayed in error messages should refer to the original file 3 2 Function Call Functions are fragments of code which can use input arguments as parameters and produce output arguments as results They can be built in LME built in functions loaded from optional extensions or defined with LME statements user functions A function call is the action of executing a function maybe with input and or output arguments LME supports different syntaxes LME Reference 29 fun fun fun inl fun inl in2 outl fun out1 out2 fun out1 out2 fun out1 out2 fun Input arguments are enclosed between parenthesis They are passed to the called function by value which means that they cannot be mod ified by the called function When a function is called without any input argument parenthesis may be omitted Output arguments are assigned to variables or part of variables structure field list element or array element A single output argu ment is specified on the left on an equal character Several output arguments must be enclosed between parenthesis or square brackets a
229. grees Example Hall chart grid with a Nyquist diagram see Fig 3 15 scale equal 1 5 1 5 1 5 1 5 hgrid nyquist 20 poly 1 2 1j 2 1j LME Reference graphics for dynamical systems 435 See also plotoption hstep Step response plot of a discrete time transfer function followed by a continuous time transfer function Syntax hstep numd dend Ts numc denc hstep numd dend Ts numc denc style hstep numd dend Ts numc denc style id Description A step is filtered first by numd dend a discrete time transfer function with sampling period Ts the resulting signal is converted to continuous time with a zero order hold and filtered by the continuous time transfer function numc denc Most discrete time controllers are used with a zero order hold and a continuous time system hstep can be used to display the simu lated output of the system when a step is applied somewhere in the loop e g as a reference signal or a disturbance The transfer func tion numd dend should correspond to the transfer function between the step and the system input the transfer function numc denc should be the model of the system Note that the simulation is performed in open loop If an unsta ble system is stabilized with a discrete time feedback controller all closed loop transfer functions are stable however the simulation with hstep which uses the unstable model of the system may diverge if it is run over
230. gument function magicsum n magc magic n sum_of_each_line sum magc 2 sum_of_each_column sum magc 1 When you call this function add an argument gt magicsum 2 magc 13 42 sum_of_each_line 4 6 sum_of_each_column 55 Tutorial 23 Note that since there is no 2 by 2 magic square magic 2 gives some thing else Finally let us define a function which returns the sum of each line and the sum of each column function sum_of_each_line sum_of_each_column magicSum n magc magic n sum_of_each_line sum magc 2 sum_of_each_column sum magc 1 Since we can obtain the result by other means we have added semi colons after each statement to suppress any output Note the upper case S in the function name for LME this function is different from the previous one To retrieve the results use the same syntax gt sl sc magicSum 3 15 15 15 You do not have to retrieve all the output arguments To get only the first one just type gt sl magicSum 3 Sl 15 15 15 When you retrieve only one output argument you can use it directly in an expression gt magicSum 3 3 ans 18 18 18 One of the important benefits of defining function is that the variables have a limited scope Using a variable inside the function does not make it available from the outside thus you can use common names such as x and y without worrying about whether they are used in some other part of
231. h as 8000 for phone quality speech or 44100 for CD quality music and the number of bits per sample and channel See also Wwavwrite wavwrite WAV encoding Syntax use wav wavwrite samples samplerate nbits filename data wavwrite samples samplerate nbits data wavwrite samples samplerate Description wavwrite samples samplerate nbits filename writes a WAV file filename with samples in array samples sample rate samplerate in Hz and nbits bits per sample and channel Rows of samples corre sponds to samples and columns to channels nbits can be 8 or 16 With 2 or 3 input arguments wavwrite returns the contents of the WAV file as a vector of class uint8 The default word size is 16 bits per sample and channel Example use wav sr 44100 t O sr sr s Sin 2 pi 740 x t wavwrite map2int s 1 1 int16 sr 16 beep wav 552 LMEPPC User Manual 1999 2008 Calerga Sarl See also Wwavread 5 10 date date is a library which adds to LME functions to convert date and time between numbers and strings The following statement makes available functions defined in date use date datestr Date to string conversion use date str datestr datetime str datestr date format Description datestr datetime converts the date and time to a string The input argument can be a vector of 3 to 6 elements for the year month day hour minute and second a julian date
232. he left part of an assign ment 42 LMEPPC User Manual 1999 2008 Calerga Sarl Unbounded language construct if while for switch or try without end Unexpected end The end statement does not match an if Switch while for or catch block case or otherwise without switch The case or otherwise statement is not inside a switch block catch without try The catch statement does not match a try block break or continue not in a loop The break or continue statement is not inside a while or for block Variable name reused Same variable used twice as input or as output argument Too many user functions Not enough memory for that many user functions Attempt to redefine a function A function with the same name already exists Can t find function definition Cannot find a function definition during compilation Unexpected end of expression Missing right parenthesis or square bracket Unexpected statement Expression expected but a statement is found e g if Null name Name without any character when given as a string in functions like feval and struct Name too long More than 32 characters in a variable or function name Unexpected function header A function header keyword func tion has been found in an invalid place for example in the argu ment of eval Function header expected A function header was expected but not found Bad variable in the left part of an assignment The left part o
233. he programming language of Sysquake compiled in a simple application for Windows Mobile ARM based hand held devices It has been tested on a Dell Axim X30 device but should also run on other Axim and HP iPaq devices LME for Pocket PC is a technology preview Its user interface is basic and there is support only for static graphics not for interac tive graphics It is based on LME a Matlab compatible programming language aimed at numerical computing used in Sysquake and other products of Calerga since 1997 You should install it only if you want to bring Matlab compatibility in your pocket There is no expiration date We do not guarantee that LME for Pocket PC will be a supported product in the long term but we intend to continue providing solutions for Pocket PC based on LME in the future LME for Pocket PC is neither Sysquake nor LyME It has neither the interactive graphics of Sysquake nor its SQ file support which makes developing user interfaces so easy It has not the simple yet efficient user interface of LyME with its integrated text editor It is more a first step in the direction of a full Sysquake on Pocket PC it supports files input output and extensions like Sysquake Its graphical capa bilities are borrowed from Sysquake Remote i e it is fully compatible with Sysquake without the interactivity Some of the most powerful extensions have been ported audio input output web services with XML RPC and SOAP and TCP IP sockets
234. he response is written to standard output file descriptor 1 since the output contains carriage return characters it may not be dis played correctly on all platforms The method argument is the method name as a string ns is the XML name space and value is the result of the call 590 LMEPPC User Manual 1999 2008 Calerga Sarl With an output argument soapwriteresponse returns the response as a String without any output Example SOapwriteresponse fun namespace 123 HTTP 1 1 200 OK Connection close Server LME 4 5 Content Length 484 Content Type text xml lt xml version 1 0 gt lt SOAP ENV Envelope SOAP ENV encodingStyle http schemas xmlsoap org soap encoding xmLns SOAP ENC http schemas xmlsoap org soap encoding xmlns SOAP ENV http schemas xmlsoap org soap envelope xmlins xsd http www w3 org 1999 XMLSchema xmlins xsi http www w3 org 1999 XMLSchema instance gt lt SOAP ENV Body gt lt m funResponse xmlns m namespace gt lt Result xsi type xsd double gt 123 lt Result gt lt m funResponse gt lt SOAP ENV Body gt lt SOAP ENV Envelope gt See also soapwriteca soapreadaresponse SOapreadCa xmirpccall Perform an XML RPC remote procedure call Syntax response xmlrpccall url method opt params Description xmlrpccall url method opt params calls a remote procedure us ing the XML RPC protocol url a string is either the complete UR
235. he rows or columns as a vector of indices Example use stdlib sortrows 3 1 2 2 2 1 2 1 2 2 1 2 2 2 1 3 1 2 See also sort sph2cart Spherical to Cartesian coordinates transform Syntax use stdlib x y Z sph2cart phi theta r 478 LMEPPC User Manual 1999 2008 Calerga Sarl Description x y z sph2cart phi theta r transforms polar coordinates phi theta and r to Cartesian coordinates x y and z such that x rcos g cos 9 y rsin g cos 9 and z rsin 9 Example use stdlib x y z sph2cart 1 2 3 x 0 6745 1 0505 Zz 2 7279 See also subspace Angle between two subspaces Syntax use stdlib theta subspace A B Description subspace A B gives the angle between the two subspaces spanned by the columns of A and B Examples Angle between two vectors in R 2 use stdlib a 3 2 b 1 5 subspace a b 0 7854 Angle between the vector 1 1 1 and the plane spanned by 2 5 3 and 7 1 0 in R 3 Libraries stdlib subspace 1 1 1 2 7 5 1 3 0 0 2226 toeplitz Toeplitz matrix Syntax use stdlib X toeplitz c r X toeplitz c Description 479 toeplitz c r creates a Toeplitz matrix whose first column contains the elements of vector c and whose first row contains the elements of vector r A Toeplitz matrix is a matrix whose diagonals have the same value In case of conflict the first element of r is ignored With one argumen
236. her level interface to design filters of these different types In addition to the filter parameters degree bandpass and band stop ripples one can specify the kind of filter lowpass highpass 510 LMEPPC User Manual 1999 2008 Calerga Sarl bandpass or bandstop and the cutoff frequency or frequencies The result can be an analog or a digital filter given as a rational transfer function or as zeros poles and gain lp2lp lp2hp lp2bp and lp2bs which convert analog lowpass filters respectively to lowpass highpass bandpass and bandstop with specified cutoff frequency or frequencies Transfer functions are expressed as the coefficient vectors of their nu merator num and denominator den in decreasing powers of s Laplace transform for analog filters or z z transform for digital filters or as the zeros z poles p and gain k besselap Bessel analog filter prototype Syntax use filter z p k besselap n Description besselap n calculates the zeros the poles and the gain of a Bessel analog filter of degree n with a cutoff angular frequency of 1 rad s See also besself Bessel filter Syntax use filter Zz k besself n w0 num den besself n w0 besself n wl wh besself n w0 high besself n wl wh stop as d besself 7 7S Libraries filter 511 Description besself calculates a Bessel filter The result i
237. here each element is the norm of the corresponding element of q See also quaternion abs qslerp Quaternion spherical linear interpolation Syntax q qslerp ql q2 t Description qslerp q1 q2 t performs spherical linear interpolation between quaternions ql and q2 The result is on the smallest great circle arc defined by normalized q1 and q2 for values of real number t between 0 and 1 If q1 or q2 is O the result is NaN If they are opposite the great circle arc going through 1 or 1i is picked If input arguments are arrays of compatible size same size or scalar the result is a quaternion array of the same size conversion 320 LMEPPC User Manual 1999 2008 Calerga Sarl from angles to quaternion is performed independently on corresponding elements Example q qslerp 1 rpy2q 0 1 1 5 0 0 33 0 66 1 roll pitch yaw q2rpy q roll 0 0000 0 1843 0 2272 0 0000 pitch 0 0000 0 3081 0 6636 1 0000 yaw 0 0000 0 4261 0 8605 1 5000 See also rpy2q q2rpy quaternion Quaternion creation Syntax quaternion quaternion w quaternion c quaternion x y Z quaternion w x Yy Z quaternion w v OGO DDD tod woud uu Description With a real argument quaternion x creates a quaternion object whose real part is w and imaginary parts are 0 With a complex argument quaternion c creates the quaternion object real c iximag c With four real arguments quaternion w
238. hey differ from lists only by having more than one dimension LME Reference 35 Most functions which expect lists also accept cell arrays functions which expect cell arrays treat lists of n elements as 1 by n cell arrays To create a cell array with 2 dimensions cells are written between braces where rows are separated with semicolons and row elements with commas 1 abc 27 true Since the use of braces without semicolon produces a list there is no direct way to create a cell array with a single row or an empty cell array Most of the time this is not a problem since lists are accepted where cell arrays are expected To force the creation of a cell array the reshape function can be used reshape ab cde 1 2 Structures Like lists and cell arrays structures are sets of data of any type While list elements are ordered but unnamed structure elements called fields have a name which is used to access them There are two ways to make structures with the struct function or by setting each field in an assignment s f refers to the value of the field named f in the structure s Usually s is the name of a variable but unless it is in the left part of an assignment it can be any expression a struct name Sysquake os Windows Mac OS X Linux b x 200 b y 280 b radius 90 c s b With the assignments above a os 3 is Linux and c s radius
239. hout output argument redirect displays the current redirection for the specified file descrip tor 1 or 2 or for both of them Note that the redirection itself may alter where the result is displayed With an output argument redirect returns a 1 by 2 row vector if the file descriptor is specified or a 2 by 2 matrix otherwise The first column contains the target file descriptor and the second column 1 for copy mode and 0 for pure redirection mode Examples Create a new file diary txt and copy to it both standard output and error fd fopen diary txt w redirect 1 fd true redirect 2 fd true Stop copying standard output and error and close file redirect 1 1 redirect 2 2 fclose fd Redirect standard error to standard output and get the redirection state 364 LMEPPC User Manual 1999 2008 Calerga Sarl redirect 2 1 redirect stdout fd 1 gt fd 1 stderr fd 2 gt fd 1 redirect 2 stderr fd 2 gt fd 1 R redirect R er il 0 0 R redirect 2 R 10 sprintf Formatted conversion of objects into a string Syntax s sprintf format a b Description sprintf converts its arguments to a string The first parameter is the format string All the characters are copied verbatim to the out put string except for the control sequences which all begin with the character They have the form fn dt where f is zero one or more of the following flags
240. i initial a x0 initial a x0 Description initial a x0 plots the time response of state space system a with initial state xO and null input See also lti impulse lt1 step Iti lsim Time response Syntax use lti lsim a u t lsim a u t Description lsim a u t plots the time response of system a For continuous time systems The input is piece wise linear it is defined by points in real vectors t and u which must have the same length Input before t 1 and after t end is 0 For discrete time systems u is sampled at the rate given by the system and t is ignored or can be omitted See also Lti step Lti initial Iti nichols Nichols plot Syntax use lti nichols a nichols a Libraries lti 543 Description nichols a plots the Nichols diagram of system a See also lti nyquist lti bodemag lti bodephase Iti nyquist Nyquist plot Syntax use lti nyquist a nyquist a Description nyquist a plots the Nyquist diagram of system a See also ti nichols lt1i bodemag lt1i bodephase Iti step Step response Syntax use lti step a step a Description step a plots the step response of system a See also lti impulse Uti initial 544 LMEPPC User Manual 1999 2008 Calerga Sarl 5 8 sigenc Sigenc is a library which adds to LME functions for encoding and de coding scalar sig
241. iable provided it is a list i e complicated assignments like a 2 f 3 2 5 3 are accepted In an assignment when the index or indices are larger than the list or cell array size the variable is expanded with empty arrays In the list of the input arguments of a function call v is replaced with its elements v may be a list variable or the result of an expres sion Examples 1 abc 3 5 7 1 x 1 string real 2x2 xX 120 LMEPPC User Manual 1999 2008 Calerga Sarl x 3 35 7 1 x 2 2 3j x 1 2 3j real 2x2 x 3 2 x 1 2 3j list x end 1 123 x 1 24 3j list 123 C 1 false ab magic 3 2x2 cell array C 2 1 ab a 1 3 5 fprintf sd a 99 1345 99 See also operator TT operator U Operator dot Structure field access Syntax v field v field expr Description A dot is used to access a field in a structure In v field v is the name of a variable which contains a structure and field is the name of the field In expressions v field gives the value of the field it is an error if it does not exist As the target of an assignment the value of the field is replaced if it exists or a new field is added otherwise if v itself is not defined a structure is created from scratch v itself may be an element or a field in a larger variable provided it is a structure or does not exists in an assignment i e complicated assignm
242. iable defined else where The first time a global variable is defined its value is set to the empty matrix In our case there is no need to initialized it to another value Here is how these functions can be used Tutorial 25 gt queueput 1 gt queueget ans 1 gt queueput 123 gt queueput 2 3j gt queueget ans 123 gt queueget ans 2 3j To observe the value of QUEUE from the command line interface QUEUE must be declared global there If a local variable already exists it is discarded gt global QUEUE gt QUEUE QUEUE gt queueput 25 gt queueput 17 gt QUEUE QUEUE 17 25 Chapter 3 LME Reference This chapter describes LME Lightweight Matrix Engine the inter preter for numerical computing used by Sysquake 3 1 Program format Statements An LME program or a code fragment typed at a command line is com posed of statements A statement can be either a simple expression a variable assignment or a programming construct Statements are separated by commas semicolons or end of lines The end of line has the same meaning as a comma unless the line ends with a semicolon When simple expressions and assignments are followed by a comma or an end of line the result is displayed to the standard output when they are followed by a semicolon no output is produced What follows programming constructs does not matter When typed at the command line the result of simp
243. iable is retrieved in an expression like A f LME executes subsref A s where s is a structure with two fields s type which is and s subs which is the name of the field f in this case While the primary purpose of subsref is to permit the use of sub scripts with objects a built in implementation of subsref is provided for arrays when s type is for lists when s type is and for structures when s typeis Examples A 1 2 3 4 subsref A struct type subs 1 12 See also Operator operator subsasgn beginning 3 9 Programming Constructs Programming constructs are the backbone of any LME program Ex cept for the variable assignment all of them use reserved keywords which may not be used to name variables or functions In addition to the constructs described below the following keyword is reserved for future use goto break Terminate loop immediately Syntax break LME Reference programming constructs 61 Description When a break statement is executed in the scope of a loop construct while repeat or for the loop is terminated Execution continues at the statement which follows end Only the innermost loop where break is located is terminated The loop must be in the same function as break It is an error to execute break outside any loop See also case Conditional execution of statements depending on a number or a string S
244. ich best fits the points given by vectors x and y The least square algorithm is used Example use stdlib pol polyfit 1 5 2 1 4 5 2 3 pol 0 6667 5 5714 12 7619 9 8000 polyval pol 1 5 1 9429 1 2286 3 6571 5 2286 1 9429 476 LMEPPC User Manual 1999 2008 Calerga Sarl polyvalm Value of a polynomial with square matrix argument Syntax use stdlib Y polyvalm pol X Description polyvalm pol X evaluates the polynomial given by the coefficients pol in descending power order with a square matrix argument Example use stdlib polyvalm 1 2 8 2 1 0 1 16 5 0 11 See also primes List of primes Syntax use stdlib v primes n Description primes n gives a row vector which contains the primes up to n Example use stdlib primes 20 2 3 5 71113 17 19 Libraries stdlib 477 See also sortrows Sort matrix rows Syntax use stdlib S index sortrows M S index sortrows M sel S index sortrows M sel dim Description sortrows M sort the rows of matrix M The sort order is based on the first column of M then on the second one for rows with the same value in the first column and so on sortrows M sel use the columns specified in sel for comparing the rows of M A third argument dim can be used to specify the dimen sion of the sort 1 for sorting the rows or 2 for sorting the columns The second output argument of sortrows gives the new order of t
245. ics for dynamical systems 433 erlocus Figure 3 14 erlocus poly 8 7 6 7 6j eye 3 0 0 0 0 0 1 0 4 0 4 1 0 8 0 8 0 8 i e black dark blue light blue and light gray Warning depending on the size of the figure in pixels and the speed of the computer the computation may be slow several sec onds The number of sizes does not have a big impact Example Roots of the polynomial z 0 8 z 0 7 0 6 z 0 7 0 6 where the coefficients in R have an uncertainty bounded by a unit sphere see Fig 3 14 scale equal 2 2 2 2 erlocus poly 0 8 0 7 0 6j 0 7 0 6j eye 3 zgrid See also plotroots hgrid Hall chart grid 434 LMEPPC User Manual 1999 2008 Calerga Sarl Figure 3 15 scale equal 2 2 2 2 hgrid Syntax hgrid hgrid style Description hgrid plots a Hall chart in the complex plane of the Nyquist diagram The Hall chart represents circles which correspond to the same mag nitude or phase of the closed loop frequency response The optional argument specifies the style The whole grid is displayed only if the user selects it in the Grid menu or after the command plotoption fullgrid By default only the unit circle and the real axis are displayed The whole grid is made of the circles corresponding to a closed loop magnitude of 0 2 0 5 0 8 1 1 0 8 2 and 5 and to a closed loop phase of plus or minus O 10 20 30 45 60 and 75 de
246. ide of the library private function d discr a b c d b2 4xarxcC public function r roots2 p a p 1 b p 2 c p 3 d discr a b c 5 b sqrt d b sqrt d 2 a See also public Mark the beginning of a sequence of public function definitions in a library Syntax public 70 LMEPPC User Manual 1999 2008 Calerga Sarl Description In a library functions which are defined after the public keyword are public public may not be placed in the same line of source code as any other command comments are possible though In a library functions are either public or private Private functions can only be called from the same library while public functions can also be called from contexts where the library has been imported with a use command Functions are public by default the public keyword is not required at the beginning of the library See also private function repeat Loop controlled by a boolean expression Syntax repeat sl until expr Description The statements between the repeat statement and the corresponding until are executed repeatedly at least once until the expression of the until statement yields true nonempty and all elements different from 0 and false Example v repeat v v sum v 1 until v end gt 100 V 1 2 4 8 16 32 64 128 See also LME Reference programming constructs return Early return from a function Sy
247. ified The first valid value of an index is always 1 The array whose ele ments are extracted is usually a variable but can be any expression an expression like 1 2 3 4 1 2 is valid and gives the 2nd element of the first row i e 3 In all indexing operations several indices can be specified simulta neously to extract more than one element along a dimension A single colon means all the elements along the corresponding dimension Instead of indices the elements to be extracted can be selected by the true values in a logical array of the same size as the variable the result is a column vector or in a logical vector of the same size as the corresponding dimension Calculating a boolean expression based on the variable itself used as a whole is the easiest way to get a logical array Variable indexing can be used in an expression or in the left hand side of an assignment In this latter case the right hand size can be one of the following An array of the same size as the extracted elements A scalar which is assigned to each selected element of the vari able An empty matrix which means that the selected elements should be deleted Only whole rows or columns or hyper planes for arrays of more dimensions can be deleted i e a 2 5 and b 3 6 8 if b is a row or column vector are legal while c 2 3 is not When indices are larger than the dimensions of the variable the vari able is expande
248. ified with name value pairs where 290 LMEPPC User Manual 1999 2008 Calerga Sarl the name is a string which must match exactly the names in the table below Case is significant Options which are not specified have a de fault value The result is a structure whose fields correspond to each option Without any input argument odeset creates a structure with all the default options Note that ode23 and ode45 also interpret the lack of an option argument or the empty array as a request to use the default values When its first input argument is a structure odeset adds or changes fields which correspond to the name value pairs which follow Here is the list of permissible options empty arrays mean auto matic Name Default Meaning AbsTol le 6 maximum absolute error Events none state based event function EventTime none time based event function InitialStep 10 MinStep initial time step MaxStep time range 10 maximum time step MinStep time range le6 minimum time step NormControl false error control on state norm OnEvent none event function OutputFcn none output function PreArg list of prepended input arguments Refine 1 4 for ode45 refinement factor RelTol le 3 maximum relative error Stats false statistics display Time steps and output Several options control how the time step is tuned during the numeri cal integration Error is calculated separately on each element of y if NormC
249. iles in memory which can be read and written like regular arrays Data compression Windows Mac Unix Support for com pressing and uncompressing data using ZLib Image Input Output Windows Mac Unix Support for reading and writing arrays as PNG or JPEG image files MAT file Windows Mac Unix Support for reading and writing MAT files native MATLAB binary files 456 LMEPPC User Manual 1999 2008 Calerga Sarl Databases ODBC Windows Connection to a relational database using ODBC MySQL Windows Mac OS X Unix Connection to a MySQL re lational database locally or on a remote server SQLite Windows Mac OS X Unix SQLite an embedded rela tional database in single files also using SQL as its query language Operating system Socket Windows Mac Unix TCP IP communication with servers or clients on the same computer on a local network or on the Internet Launch URL Windows Mac Unix Opening of documents ina World Wide Web browser Download URL Windows Mac Linux Download of documents from the World Wide Web Open Script Architecture Mac Communication with other ap plications Power Management Windows Mac Functions related to power management System Log Mac OS X Unix Output to system log Shell Windows Mac OS X Unix Shell related functions Signal Mac OS X Unix Support for signals POSIX functions kill and signal Web Services Windows Mac OS X Unix Web Services stan
250. imensions so that all dimensions match For instance three arguments of size 3x1x2 1x5 and 1x1 are replicated into arrays of size 3x5x2 Output arguments are assigned to Y1 Y2 etc Function fun is specified by either by its name as a string a function reference or an inline function Example fevalx plus 1 5 10 10 30 11 12 13 14 15 21 22 23 24 25 31 32 33 34 35 See also fun2str Name of a function given by reference or source code of an inline function Syntax str str fun2str funref fun2str inlinefun Description fun2str funref gives the name of the function whose reference is funref fun2str inlinefun gives the source code of the inline function inlinefun LME Reference miscellaneous functions 95 Examples fun2str sin sin fun2str inline x 2 y x y function y f x y y x 2xy See also info Information about LME Syntax info info builtin info functions info methods info variables info global info persistent info libraries info usedlibraries info threads str info list info kind Description info displays the language version With an output argument the language version is given as a string info builtin displays the list of built in functions with their mod ule name modules are subsets of built in functions A letter u is displayed after each untrusted function functions which cannot be ex ecuted in the sandbox With an outp
251. in many cases indices to getlor set the elements of an array are an important exception With input arguments false builds a logical array whose elements are false The size of the array is specified by one integer for a square matrix or several integers either as separate arguments or in a vec tor for an array of any size Examples false false islogical false true false 2 3 FFF FFF See also graycode Conversion to Gray code Syntax g graycode n Description graycode n converts the integer number n to Gray code The argu ment n can be an integer number of class double converted to an unsigned integer or any integer type If it is an array conversion is performed on each element The result has the same type and size as the input Gray code is an encoding which maps each integer of s bits to another integer of s bits such that two consecutive codes i e graycode n and graycode n 1 for any n have only one bit which differs LME Reference logical functions Example graycode Q 7 01326754 See also igraycode Conversion from Gray code Syntax n igraycode g Description 343 igraycode n converts the Gray code g to the corresponding integer It is the inverse of graycode The argument n can be an integer num ber of class double converted to an unsigned integer or any integer type If it is an array conversion is performed on each element The result has the same
252. indexed i is the position of the index expression where end is used n is the total number of index expressions Examples Last 2 elements of a vector a a end 1 end 1 5 45 Assignment to the last element of a vector a end 99 a 123499 Extension of a vector a end 1 100 a 12 3 4 99 100 See also Operator foperator length global persistent Declaration of global or persistent variables Syntax global x y persistent xy Description By default all variables are local and created the first time they are assigned to Local variables can be accessed only from the body of the function where they are defined but not by any other function even the ones they call They are deleted when the function exits If the function is called recursively i e if it calls itself directly or indirectly distinct variables are defined for each call Similarly local variables 56 LMEPPC User Manual 1999 2008 Calerga Sarl defined in the workspace using the command line interface cannot be referred to in functions On the other hand global variables can be accessed by multiple functions and continue to exist even after the function which cre ated them exits Global variables must be declared with global in each functions which uses them They can also be declared in the workspace There exists only a single variable for each different name Declaring a global variable has the following
253. ing which must match exactly the names in the table below Case is significant Options which are not specified have a default value The result is a structure whose fields correspond to each option Without any input argument audioset creates a structure with all the default options Note that audioplay also interprets the lack of an option argument or the empty array as a request to use the default values When its first input argument is a structure audioset adds or changes fields which correspond to the name value pairs which fol low Here is the list of permissible options Name Default Meaning Repeat 1 number of repetitions SampleRate 44100 sample rate in Hz Default values may be different on platforms with limited audio ca pabilities Example Default options audioset Repeat 1 SampleRate 44100 See also 6 15 Audio Input This section describes functions which record sounds Currently these functions are available on Windows and Mac OS X audiorecord Record audio samples Extensions audio input 603 Syntax samples audiorecord t samples audiorecord t options Description audiorecord t records audio samples for t seconds and returns them in an array of single numbers On computers which support them the default sample rate is 44 1 kHz and the default number of channels is 2 stereo The result has 2 columns one per channel and as many rows as samples audiorecord t options uses th
254. initial state vector y0 and the number of integrated states ni is given by the size of the output of the integrated function Function OnEvent can produce a vector of size n to replace all the states of size n ni to replace the non integrated states or empty to replace no state this can be used to display re sults or to store them in a file for instance Event times are computed after an integration step has been ac cepted If an event occurs before the end of the integration step the step is shortened event information is stored in the output arguments of ode te ie and ye and the OnEvent function is called The output arguments t and y of ode contain two rows with the same time and the state right before the event and right after it The time step used for integration is not modified by events Additional arguments PreArg is a list of additional input arguments for all functions called during integration they are placed before normal arguments For ex ample if its value is 1 abc the integrated function is called with fun 1 abc t y the output function as outfun 1 abc tn yn and so on Examples Default options odeset AbsTol 1le 6 LME Reference non linear numerical functions Figure 3 2 Van der Pol equation with Refine set to 1 and 4 Events EventTime InitialStep MaxStep MinStep NormControl false OnEvent OutputFecn PreArg Refine RelTol le 3
255. input arguments true builds a logical array whose elements are true The size of the array is specified by one integer for a square matrix or several integers either as separate arguments or in a vec tor for an array of any size Examples true true islogical true true true 2 TT TT See also xor Exclusive or Syntax b3 xor b1 b2 346 LMEPPC User Manual 1999 2008 Calerga Sarl Description xor b1 b2 performs the exclusive or operation between the corre sponding elements of b1 and b2 b1 and b2 must have the same size or one of them must be a scalar Examples xor false false true true false true false true FTTF xor pi 8 false See also 3 27 Dynamical System Functions This section describes functions related to linear time invariant dy namical systems c2dm Continuous to discrete time conversion Syntax numd dend c2dm numc denc Ts dend c2dm numc denc Ts numd dend c2dm numc denc Ts method dend c2dm numc denc Ts method Ad Bd Cd Dd c2dm Ac Bc Cc Dc Ts method Description numd dend c2dm numc denc Ts converts the continuous time transfer function numc denc to a discrete time transfer function numd dend with sampling period Ts The continuous time transfer function is given by two polynomials in s and the discrete time transfer function is given by two polynomials in z all as vectors of coefficients with highest powers first c2dm numc denc Ts method
256. inputs u to one or more outputs y The mapping is defined as a state space model or as a matrix of transfer functions either in continuous time or in discrete time Methods are provided to create combine and analyze LTI objects Graphical methods are based on the corresponding graphical func tions the numerator and denominator coefficient vectors or the state space matrices are replaced with an LTI object They accept the same optional arguments such as a character string for the style 520 LMEPPC User Manual 1999 2008 Calerga Sarl The following statement makes available functions defined in lti use lti Ss SS LTI state space constructor Syntax Uti v wv v wW wn tou i i i i wn wn u a a a a a a Description ss A B C D creates an LTI object which represents the continuous time state space model t A x Cx t t Bu t Du ss A B C D Ts creates an LTI object which represents the discrete time state space model with sampling period Ts x k 1 y k In both cases if D is O it is resized to match the size of B and C if neces sary An additional argument var may be used to specify the variable of the Laplace s default or p or z transform z default or q ss A B C D b where b is an LTI object creates a state space model of the same kind continuous discrete time sampling time and variable as b ss b converts the LTI object b to a state space
257. inv 216 ipermute 250 isa iscell 251 ischar 802 isdigit isempty 251 isfield 328 isfinite 175 isfloat 175 SNE OOA 609 isglobal Tsor eparl isinteger iskeyword 100 isletter 303 islist 324 islogical 343 ismember isnan 177 isnumeric 177 isobject 333 isprime isquaternion 315 isreal 471 isscalar 178 isspace 304 isstruct 328 isvector 1 8 join julian2cal kron 216 kurtosis 21 7 Label 390 lasterr 101 lasterror 101 Launchurl 581 Lem 179 ldivide 114 te 114 legend Lesern Zea library constants 555 date filter 509 lti 519 ratio 500 Soe aaa stat 480 stdlib 462 wav 550 Lightangle 412 Line 392 Line3 412 610 LMEPPC User Manual 1999 2008 Calerga Sarl linprog Linspace 472 list 34 List2num 324 Lloyds LME 2 7 command syntax 29 comments 28 error messages file descriptor function call input output libraries program format 27 statements types variable assignment ea 472 LongInt Longint 558 lower 304 lp2bp lp2bs lp2hp lp2lp lsim 4 Ut 214 ma lu 2 tyap 220 220 mad 483 ma Se map map2int 282 margin 350 material matfiledecode matfileencode matrixcol 57 mat rixrow 57 max 221 md5 mean 222 median 473 mesh 413 meshgrid methods 333 min 223 minus 114 mldivide 114 mmap
258. iple prime factors are repeated 468 LMEPPC User Manual 1999 2008 Calerga Sarl Example use stdlib factor 350 2 5 5 7 See also fftshift Shift DC frequency of FFT from beginning to center of spectrum Syntax use stdlib Y fftshift X Description fftshift X shifts halves of vector 1 d or matrix 2 d X to move the DC component to the center It should be used after fft or fft2 See also filter2 Digital 2 d filtering of data Syntax use stdlib Y filter2 F X Y filter2 F X shape Description filter2 F X filters matrix X with kernel F with a 2 d correlation The result has the same size as X An optional third argument is passed to conv2 to specify another method to handle the borders Libraries stdlib 469 filter2 and conv2 have three differences arguments F and X are permuted filtering is performed with a correlation instead of a con volution i e the kernel is rotated by 180 degrees and the default method for handling the borders is same instead of full See also filter conv2 hankel Hankel matrix Syntax use stdlib X hankel c r Description hankel c r creates a Hankel matrix whose first column contains the elements of vector c and whose last row contains the elements of vector r A Hankel matrix is a matrix whose antidiagonals have the same value In case of conflict the first element of r is ignored The default value of r is a zero vector the s
259. iption cheby2 calculates a Chebyshev type 2 filter The result is given as zeros poles and gain if there are three output arguments or as nu merator and denominator coefficient vectors if there are two output arguments cheby2 n w0 where w0 is a scalar gives a nth order digital low pass filter with a cutoff frequency of w0 relatively to half the sampling frequency cheby2 n wl wh where the second input argument is a vector of two numbers gives a 2nth order digital bandpass filter with pass band between wl and wh relatively to half the sampling frequency cheby2 n w0 high gives a nth order digital highpass filter with a cutoff frequency of w0 relatively to half the sampling frequency cheby2 n wl wh stop where the second input argument is a vector of two numbers gives a 2nth order digital bandstop filter with stopband between wl and wh relatively to half the sampling frequency With an additional input argument which is the string s cheby2 gives an analog Chebyshev type 2 filter Frequencies are given in rad s See also ellip Elliptic filter 516 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax use filter z k ellip n w0 num den ellip n w0 ellip n wl wh ellip n w0 high ellip n wl wh stop ellip s Description ellip calculates a elliptic filter or Cauer filter The result is given as z
260. irst line bor rows its style from the first sequence the second line from the second sequence and so on If there are not enough styles they are recycled A sequence is one or two style specifications one of them for the color and the other one for the dash pattern or the symbol shape in any or der Sequences of two specifications are used if possible Commas may be used to remove ambiguity Here are some examples plot 0 1 0 1 0 1 1 1 2 2 3 3 k r The first line from 0 1 to 1 1 is black and dashed the second line from 0 2 to 1 2 is red and dash dot and the third line from 0 3 to 1 3 is black and dashed again plot 0 1 0 1 0 1 1 1 2 2 3 3 rbk The first line is red the second line is blue and the third line is black plot 0 1 0 1 0 1 1 1 2 2 3 3 br The first and third lines are blue and dashed and the second line is red and solid plot 0 1 0 1 0 1 1 1 2 2 3 3 H cccccc The first and third lines are dotted and the second line is gray solid and thick 378 LMEPPC User Manual 1999 2008 Calerga Sarl Graphic ID The second optional argument is the graphic ID It has two purposes First it specifies that the graphic element can be manipulated by the user When the user clicks in a figure Sysquake scans all the curves which have a non negative graphic ID the default value of all com mands is 1 making the graphical object impossible to grasp and sets z
261. is 90 Function references Function references are equivalent to the name of a function together with the context in which they are created Their main use is as argu ment to other functions They are obtained with operator 36 LMEPPC User Manual 1999 2008 Calerga Sarl Inline and anonymous functions Inline and anonymous functions encapsulate executable code They differ only in the way they are created inline functions are made with function inline while anonymous functions have special syntax and semantics where the values of variables in the current context can be captured implicitly without being listed as argument Their main use is aS argument to other functions Sets Sets are represented with numerical arrays of any type integer real or complex double or single character or logical or lists or cell ar rays of strings Members correspond to an element of the array or list All set related functions accept sets with multiple values which are always reduced to unique values with function unique They imple ment membership test union intersection difference and exclusive or Numerical sets can be mixed the result has the same type as when mixing numerical types in array concatenation Numerical sets and list or cell arrays os strings cannot be mixed Objects Objects are the basis of Object Oriented Programming OOP an ap proach of programming which puts the emphasis on encapsulated data with a known progr
262. is discarded The error function is defined as 2 fx oe erf0 a e dt 0 Example erf 1 0 8427 See also erfc Complementary error function Syntax y erfc x LME Reference mathematical functions 165 Description erfc x gives the complementary error function of x Argument and result are real imaginary part is discarded The complementary error function is defined as fc x 1 erf x dt ertTc x 1 ern x e VT Jx Example erfc 1 0 1573 See also erfinv Inverse error function Syntax x erfinv y Description erfinv y gives the value x such that y erf x Argument and result are real imaginary part is discarded y must be in the range 1 1 values outside this range give nan Example y erf 0 8 0 7421 erfinv y 0 8 See also 166 LMEPPC User Manual 1999 2008 Calerga Sarl exp Exponential Syntax y exp x Description exp x is the exponential of x i e 2 7182818284590446 x Example exp 0 1 0 5j pil 1 2 7183 1j See also expm1 Exponential minus one Syntax y expm1 x Description expm1 x is exp x 1 with improved precision for small x Example expm1 le 15 le 15 exp le 15 1 1 1102e 15 See also LME Reference mathematical functions 167 factorial Factorial Syntax y factorial n Description factorial n gives the factorial n of nonnegative integer n If the input argument is
263. is equivalent to inv M1 M2 mldivide x y is equivalent to x y It can be used to redefine this operator for objects Examples 3 9 3 1 2 3 4 2 6 2 4 10 NZ ON 5 See also Operator Scalar left division Syntax M1 M2 M1 x ldivide x y LME Reference operators 127 Description The second operand is divided by the first operand If both operands are matrices with a size different from 1 by 1 their size must be equal the division is performed element wise If one operand is a scalar it is repeated to match the size of the other operand ldivide x y is equivalent to x y It can be used to redefine this operator for objects Example 1 2 3 10 11 12 10 5 5 4 See also Operator Matrix power Syntax x y M k x 7M mpower x y Description x y calculates x to the y power provided that either both operands are scalar the first operand is a square matrix and the second operand is an integer or the first operand is a scalar and the second operand is a square matrix Other cases yield an error mpower x y is equivalent to x y It can be used to redefine this operator for objects 128 Examples 2 3 8 1 2 3 4 2 7 10 15 22 2 1 2 3 4 10 4827 14 1519 21 2278 31 7106 See also Operator Scalar power Syntax M1 M2 x M M x power x y Description LMEPPC User Manual 1999 2008 Calerga Sarl
264. is of the columns of array A or of the row vector A The dimension along which kurtosis proceeds may be specified with a second argument The kurtosis measures how much values are far away from the mean It is 3 for a normal distribution and positive for a distribution which has more values far away from the mean Example kurtosis rand 1 10000 1 8055 See also linprog Linear programming 218 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax x linprog c A b x linprog c A b xlb xub Description Linprog c A b solves the following linear programming problem mincx s t Ax lt b The optimum x is either finite infinite if there is no bounded solution or not a number if there is no feasible solution Additional arguments may be used to constrain x between lower and upper bounds linprog c A b xlb xub solves the following lin ear programming problem mincx s t Ax lt b X 2 Xib X lt Xub If xub is missing there is no upper bound xlb and xub may have less elements than x or contain inf or inf corresponding elements have no lower and or upper bounds Examples Maximize 3x 2y subject to x y lt 9 3x y lt 18 x lt 7 and y lt 6 c 3 2 A 1 1 3 1 1 0 0 1 b 9 18 7 6 x linprog c A b x 4 5 4 5 A more efficient way to solve the problem with bounds on variables c 3 2 A 1 1 3 1 b 9 18 xlb LME Reference linear
265. ise These arguments are the same as those expected by function error When the intermediate code is optimized assert can be ignored It should be used only to produce errors at an early stage or as a de bugging aid not to trigger the try catch mechanism The expression should not have side effects The most common use of assert is to check the validity of input arguments Example function y fact n assert length n 1 amp amp isreal n amp amp n round n LME nonIntArg y prod 1 n See also error warning try builtin Built in function evaluation Syntax argoutl builtin fun arginl Description y1l y2 builtin fun x1 x2 evaluates the built in func tion fun with input arguments x1 x2 etc Output arguments are as signed to yl y2 etc Function fun is specified by its name as a String builtin is useful to execute a built in function which has been re defined Example Here is the definition of operator plus so that it can be used with character strings to concatenate them 88 LMEPPC User Manual 1999 2008 Calerga Sarl function r plus a b if ischar a amp amp ischar b r a b else r builtin plus a b end The original meaning of plus for numbers is preserved 1 2 3 ab cdef abcdef See also eva clear Discard the contents of a variable Syntax clear clear vl v2 clear functions Descriptio
266. it the state ment should be followed by a semicolon randn n randn n1 n2 and randn n1 n2 return an n by n square matrix or an array of arbitrary size whose elements are pseudo random numbers chosen from a normal distribution Examples randn 1 5927 randn 1 3 0 7856 0 6489 0 8141 randn seed Q LME Reference arrays 261 randn 1 5927 See also rand repmat Replicate an array Syntax A2 repmat Al n A2 repmat Al m n A2 repmat Al nl Description repmat creates an array with multiple copies of its first argument It can be seen as an extended version of ones where 1 is replaced by an arbitrary array The number of copies is m in the vertical direction and n in the horizontal direction The type of the first argument number character or logical value is preserved With a vector as second argu ment the array can be replicated along more than two dimensions Examples repmat 1 2 3 4 1 2 1212 3434 repmat abc 3 abcabcabc abcabcabc abcabcabc See also reshape Rearrange the elements of an array to change its shape 262 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax A2 reshape A1 A2 reshape Al nl n2 A2 reshape Al nl n2 Description reshape Al1 gives a column vector with all the elements of array Al which is read row wise If Al is a variable reshape Al1 is the same as Al reshape Al n1 n2 or reshape A
267. its loose spacing fixed format with 0 or 4 digits exponential format with 4 digits engineering format with 4 digits general format with up to 4 digits fixed format with 0 or 15 digits exponential format with 15 digits engineering format with 15 digits general format with up to 15 digits signed decimal integer signed decimal integer unsigned decimal integer hexadecimal integer octal integer binary integer fixed format with 2 digits for currencies orl for nonzero space for zero symbol i to represent the imaginary unit symbol j to represent the imaginary unit empty lines to improve readability no empty line Format for numbers for imaginary unit symbol and for spacing is set separately Format displays compactly numeric and boolean arrays positive numbers and complex numbers with a positive real part are displayed as negative numbers or complex numbers with a negative real part as pure imaginary nonzero numbers as I and zeros aS spaces The default format is format short g format j and format compact See also fprintf Formatted output Syntax fprintf fd format a b fprintf format a b LME Reference input output 359 Description fprintf format a b converts its arguments to a string and writes it to the standard output fprintf fd format a b spec ifies the output file descriptor See sprintf for a description of the conversion process Example fprintf
268. ix A i e a unitary matrix U and a square matrix T the Schur matrix such that A U T U If Ais complex the Schur matrix is upper triangular and its diagonal contains the eigenvalues of A if A is real the Schur matrix is real upper triangular except that there may be 2 by 2 blocks on the main diagonal which correspond to the complex eigenvalues of A To force a complex Schur factorization with an upper triangular matrix T schur is given a second input argument c or complex Example U T schur 1 2 3 4 U 0 8246 0 5658 0 5658 0 8246 T 0 3723 1 0 5 3723 eig 1 2 3 4 ans 0 3723 5 3723 LME Reference linear algebra 235 T schur 1 0 0 0 1 2 0 3 1 T 1 0 0 0 1 2 0 3 1 T schur 1 0 0 0 1 2 0 3 1 c T 1 0 0 0 1 2 4495j 1 0 0 1 2 4495j See also skewness Skewness of a set of values Syntax skewness A skewness A dim S S Description skewness A gives the skewness of the columns of array A or of the row vector A The dimension along which skewness proceeds may be specified with a second argument The skewness measures how asymmetric a distribution is It is 0 for a symmetric distribution and positive for a distribution which has more values much larger than the mean Example skewness randn 1 10000 2 2 6833 See also sqrtm Matrix square root 236 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax Y sqrtm X Y err sqrt
269. jk 1 It follows that the product of two quaternions is not commutative for instance ij k but ji k Quaternions are convenient to represent arbitrary rotations in the 3d space They are more compact than matrices and are easier to normalize This makes them suitable to simulation and control of me chanical systems and vehicles such as flight simulators and robotics Functions below are specific to quaternions LME Reference Quaternions 313 Function isquaternion q2mat q2rpy q2str qimag qinv qnorm qslerp quaternion rpy2q Purpose test for quaternion type conversion to rotation matrix conversion to attitude angles conversion to string imaginary parts element wise inverse scalar norm spherical linear interpolation quaternion creation conversion from attitude angles Operators below accept quaternions as arguments Function ctranspose eq horzcat ldivide ne minus mldivide mrdivide mtimes plus rdivide times transpose uminus uplus vertcat Operator Purpose LA l ll ba wi conjugate transpose element wise equality horizontal array concatenation left division element wise inequality difference matrix left division matrix right division matrix multiplication addition division multiplication transpose unary minus unary plus vertical array concatenation Most of these operators work as expected like with complex scalars and matrices Multiplication and left righ
270. l ues v and vi can be real or complex The result for coordinates outside the convex hull defined by x and y is NaN griddata is based on Delaunay triangulation The interpolation method used in each triangle is linear by default or can be specified with an additional input argument a string Argument Meaning 0 or nearest nearest value 1 or linear linear See also griddatan Data interpolation in N d space Syntax vi griddatan x v xi vi griddatan x v xi method 276 LMEPPC User Manual 1999 2008 Calerga Sarl Description griddatan x v xi interpolates values at coordinates given by the p rows of p by n array xi in an n dimension space Original data are defined by m by n array x and m by 1 column vector v such that the value at coordinate x i is v i The result is a p by 1 column vector vi where vi j is the value interpolated at xi j Coordinates x and xi are real imaginary components are ignored Values v and vi can be real or complex The result for coordinates outside the convex hull defined by x is NaN griddatan is based on Delaunay triangulation The interpolation method used in each simplex is linear by default or can be specified with an additional input argument a string Argument Meaning 0 or nearest nearest value 1 or linear linear See also de launayn tsearcnn griddata jinterpn tsearch Search of points in triangles Syntax ix tsea
271. l nl n2 changes the dimensions of array A1 so that the result has m rows and n columns Al must have nl n2 elements read line wise both Al and the result have the same elements When dimensions are given as separate elements one of them can be replaced with the empty array it is replaced by the value such that the number of elements of the result matches the size of input array Example reshape 1 2 3 10 20 30 3 2 1 2 3 10 20 30 reshape 1 12 3 123 4 5 6 7 8 9 10 11 12 See also operator rot90 Array rotation Syntax A2 rot90 A1 A2 rot90 Al k LME Reference arrays 263 Description rot90 A1 rotates array Al 90 degrees counter clockwise the top left element of Al becomes the bottom left element of A2 If Al is an array with more than two dimensions each plane corresponding to the first two dimensions is rotated In rot90 A1 k the second argument is the number of times the array is rotated 90 degrees counter clockwise With k 2 the array is rotated by 180 degrees with k 3 ork 1 the array is rotated by 90 degrees clockwise Examples rot90 1 2 3 4 5 6 3 6 25 14 rot90 1 2 3 4 5 6 1 rot90 1 2 3 4 5 6 1 654 Ww setdiff Set difference Syntax c setdiff a b c ia setdiff a b Description setdiff a b gives the difference between sets a and b i e the set of members of set a which do not belong to b Sets are any type of n
272. lar frequency Option NegFreq is used in Nyquist and Nichols diagrams continuous time or discrete time when true the response is computed for negative frequencies instead of positive frequencies Option Range should take into account the sampling period for discrete time commands where it is specified Examples Default options responseset Delay 0 NegFreq false Nyquist diagram of e 5 s 1 nyquist 1 1 1 responseset Delay 1 Complete Nyquist diagram of 1 s 2s 2s 1 with dashed line for negative frequencies LME Reference graphics for dynamical systems 447 nyquist 2 1 2 2 1 nyquist 2 1 2 2 1 responseset NegFreq true See also bodemag bodephase dbodemag dbodephase dnichols nyquist sigma step rlocus Root locus Syntax rlocus num den rlocus num den style rlocus num den style id Description The root locus is the locus of the roots of the denominator of the closed loop transfer function characteristic polynomial of the system whose open loop transfer function is num den when the gain is be tween 0 and inclusive The characteristic polynomial is num k den with k gt 0 rlocus requires a causal system with real coefficients i e Length den gt Length num Note that the rlocus is defined the same way in the domain of the Laplace transform the z transform and the delta transform The root locus is made of length den 1 branches which st
273. lative time of execution for each line in fun Function execution Each execution of the function adds to the profile data Since the relative execution times are usually what is really interesting you may want to execute the function several times to reduce fluctuations due to rounding errors Time spent outside the function such as the time you spend typing the com mands at the command line interface is not included Profile report profile report displays a report for the function being profiled The default format is a listing of all lines with the line number the cumulative time spent for the line in seconds its percentage with respect to the time spent in the whole function and the source code of the line You can continue executing the function and creating new reports times are cumulative but see profile reset and profile off below LME Reference profiler 85 End profile done releases the data structures set up with profile fun Other options are available profile off suspends profiling and profile on resumes it When profiling is suspended calls to the pro filed function are not taken into account profile reset resets all the times and resumes profiling if it was suspended profile function fun is equivalent to profile fun but it may also be used to profile functions with the same name as one of the op tions which have a special meaning for profile like report or done profile report format produces a r
274. le expressions is assigned to the variable ans this makes easy reusing intermediate results in successive expressions Continuation characters A statement can span over several lines provided all the lines but the last one end with three dots For example 1 2 is equivalent to 1 2 After the three dots the remaining of the line as well as empty lines and lines which contain only spaces are ig nored 28 LMEPPC User Manual 1999 2008 Calerga Sarl Comments Unless when it is part of a string enclosed between single ticks a single percent character or two slash characters mark the beginning of a comment which continues until the end of the line and is ignored by LME Comments must follow continuation characters if any a 2 comment at the end of a line X25 another comment comment spanning the whole line b comment after the continuation characters a a 3 no need to put spaces before the percent sign S percent characters in a string Comments may also be enclosed between and in that case they can span several lines Pragmas Pragmas are directives for LME compiler They can be placed at the same location as LME statements i e in separate lines or between semicolons or commas They have the following syntax pragma name arguments where name is the pragma name and arguments are additional data whose meaning depends on the pragma Currently only one pragma is defined Pra
275. lement of the input argument and the result has the same size Example isfinite 0 1 nan inf TTFF See also isfloat Test for a floating point object Syntax b isfloat x Description isfloat x is true if the input argument is a floating point type dou ble or single and false otherwise Examples isfloat 2 true isfloat 2int32 false See also isnumeric isinteger 176 LMEPPC User Manual 1999 2008 Calerga Sarl isinf Test for infinity Syntax b isinf x Description isinf x is true if the input argument is infinite neither finite nor nan and false otherwise The result is performed on each element of the input argument and the result has the same size Example isinf 0 1 nan inf FF FT See also isinteger Test for an integer object Syntax b isinteger x Description isinteger x is true if the input argument is an integer type includ ing char and logical and false otherwise Examples isinteger 2int16 true isinteger false true isinteger abc true isinteger 3 false LME Reference mathematical functions See also 1snumeric isfloat isnan Test for Not a Number Syntax b isnan x Description 177 isnan x is true if the input argument is nan not a number and false otherwise The result is performed on each element of the input argument and the result has the same size Example isnan 0 1 nan inf FFT
276. les map2int 0 2 0 2 1 2 1x5 uint8 array 0 51 102 153 204 255 255 map2int 1 3 7 10 uint16 1x3 uint16 array 6553 19660 45875 map2int 1 3 7 0 10 int16 1x3 int16 array 26214 13107 13107 See also and related functions LME Reference non linear numerical functions 283 3 20 Non Linear Numerical Functions fminbnd Minimum of a function Syntax x y fminbnd fun x0 x y fminbnd fun xlow xhigh x y fminbnd options x y fminbnd options x y didConverge fminbnd Description fminbnd fun finds numerically a local minimum of function fun fun is either specified by its name or given as an anonymous or inline function or a function reference It has at least one input argument x and it returns one output argument also a real number fminbnd finds the value x such that fun x is minimized Second argument tells where to search it can be either a starting point or a pair of values which must bracket the minimum The optional third argument may contain options It is either the empty array for default options or the result of optimset Remaining input arguments of fminbnd if any are given as addi tional input arguments to function fun They permit to parameterize the function For example fminbnd fun x0 2 5 calls fun as fun x 2 5 and minimizes its value with respect to x The first output argument of fminbnd is the value of x at
277. lines if it is a scalar or the levels themselves if it is a vector The optional fourth argument is the style of each line from the minimum to the maximum level styles are recycled if necessary The default style is kbrmgcy See also daspect Scale ratios along x y and Z axis Syntax daspect rx ry rz daspect R daspect Description daspect R specifies the scale ratios along x y and z axis Argument R is a vector of 3 elements rx ry and rz Coordinates in the 3D space are divided by rx along the x axis and so on before the projection is performed For example a box whose size is 2 5 3 would be displayed as a cube with daspect 2 5 3 daspect sets the scale ratios so that the bounding box of 3D elements is displayed as a cube With an output argument R daspect gives the current scale ratios as a vector of 3 elements See also 412 LMEPPC User Manual 1999 2008 Calerga Sarl lightangle Set light sources in 3D world Syntax Llightangle lightangle az el Description Lightangle az el set lighting source s at infinity with asimuth az and elevation el both in radians With missing input argument the default azimuth is 4 and the default elevation is 1 If az and el are vectors they must have the same size except if one of them is a scalar then it is replicated as needed Lightangle sets multiple light sources See also material line3 Plot straight lines in 3D spac
278. long second dimension as if they were placed inside brackets and separated with commas Element sizes must be compatible LME Reference lists 325 Example List2num 1 2 3j 4 6 1 2 3j 4 5 6 See also operator T map Function evaluation for each element of a list Syntax listoutl map fun listinl Description map fun listinl evaluates function fun successively for each corresponding elements of the remaining arguments which must be lists or cell arrays It returns the result s of the evaluation as list s or cell array s with the same size as inputs Input lists which contain a single element are repeated to match other arguments if necessary fun is the name of a function as a string a function reference or an inline function Examples map max 2 6 4 7 1 1 100 6 7 100 map inline x 10 3 7 16 13 17 26 nr nc map size 1 abc 4 7 3 4 nr 1 1 2 nc 1 3 2 map size 1 abc 4 7 3 4 S 1 1 1 3 2 2 map disp hello lme hello lme map atan2 1 2 3 0 4636 0 3218 S 326 LMEPPC User Manual 1999 2008 Calerga Sarl See also num2list Conversion from array to list Syntax list num2list A list num2list A dim Description num2list A creates a list with the elements of non cell array A num2list A dim cuts array A along dimension dim and creates a list with
279. losed loop systems See also ss2tf Conversion from state space to transfer function Syntax num den ss2tf A B C D den ss2tf A B C D num den ss2tf A B C D iu den ss2tf A B C D iu 352 LMEPPC User Manual 1999 2008 Calerga Sarl Description A continuous time linear time invariant system can be represented by the state space model Ax t Bu t Cx t Du t dx a y t where x t is the state u t the input y t the output and ABCD four constant matrices which characterize the model If it is a single input single output system it can also be represented by its trans fer function num den num den ss2tf A B C D converts the model from state space to transfer function If the state space model has multiple outputs num is a matrix whose lines correspond to each output the denominator is the same for all outputs If the state space model has multiple inputs a fifth input argument is required and spec ifies which one to consider For a sampled time model exactly the same function can be used The derivative is replaced by a forward shift and the variable s of the Laplace transform is replaced by the variable z of the z transform But as long as coefficients are concerned the conversion is the same The degree of the denominator is equal to the number of states i e the size of A The degree of the numerator is equal to the number of states if D is not null and one less if D is null
280. lse other wise Strings can have more than one line Examples ischar abc true ischar 0 false ischar false ischar true LME Reference strings 303 ischar abc def true See also isdigit Test for decimal digit characters Syntax b isdigit s Description For each character of string s isdigit s is true if it is a digit 0 to 9 and false otherwise Examples isdigit al23bAB12 FTTTFFFTTFF See also isletter Test for letter characters Syntax b isletter s Description For each character of string s isletter s is true if it is a letter and false otherwise Letters with diacritical signs are not considered as letters 304 LMEPPC User Manual 1999 2008 Calerga Sarl Examples isletter a TTTTF See also isspace Test for space characters Syntax b isspace s Description For each character of string s isspace s is true if it is a space a tabulator a carriage return or a line feed and false otherwise Example isspace a tb c nd 01031010 See also lower Convert all uppercase letters to lowercase Syntax s2 lower s1 Description lower s1 converts all the uppercase letters of string s1 to lowercase Currently only ASCII letters without diacritic are converted LME Reference strings 305 Example Lower abcABC123 abcabc123 See also md5 Calculate MD5 diges
281. m 0 vV1l msin t T 2 Em V1 msin tdt 0 Parameter m must be in 0 1 ellipke m tol uses tolerance tol the default tolerance is eps LME Reference mathematical functions 163 Example K K E ellipke 0 3 1 7139 E 1 4454 See also ellip eps Difference between 1 and the smallest number x such that x gt 1 Syntax e e e eps eps x eps type Description Because of the floating point encoding of real numbers the absolute precision depends on the magnitude of the numbers The relative precision is characterized by the number given by eps which is the smallest double positive number such that 1 eps can be distinguished from 1 eps x gives the smallest number e such that x e has the same sign as x and can be distinguished from x It takes into account whether x is a double or a single number If x is an array the re sult has the same size each element corresponds to an element of the input eps single gives the smallest single positive number e such that 1single e can be distinguished from lsingle eps double gives the same value as eps without input argument Examples eps 2 2204e 16 1 eps 1 2 2204e 16 eps 2 1 1102e 16 164 LMEPPC User Manual 1999 2008 Calerga Sarl 1 eps 2 1 0 See also erf Error function Syntax y erf x Description erf x gives the error function of x Argument and result are real imaginary part
282. m X Description sqrtm X returns the matrix square root of X such that sqrtm X 2 X X must be square The matrix square root does not always exist With a second output argument err sqrtm also returns an estimate of the relative error norm sqrtm X 2 X norm X Example Y sqrtm 1 2 3 4 Y 0 5537 0 4644 0 807 0 2124 1 2104 0 3186j 1 7641 0 1458 Y 2 1 2 3 4 See also std Standard deviation Syntax lt lt lt XK xX nou ot ou wn ct a s3s3 lt lt Description std v gives the standard deviation of vector v normalized by length v 1 With a second argument std v p normalizes by length v 1 if pis true or by Length v if p is false std M gives a row vector which contains the standard deviation of the columns of M With a third argument std M p dim operates along dimension dim LME Reference linear algebra Example std 1 2 5 6 10 12 4 3359 See also sum Sum of the elements of a vector Syntax x V V sum v sum M sum M dim Description 237 sum v returns the sum of the elements of vector v sum M returns a row vector whose elements are the sums of the corresponding columns of matrix M sum M dim returns the sum of matrix M along dimension dim the result is a row vector if dim is 1 or a column vector if dim is 2 Examples sum 1 5 15 sum 1 5 15 sum 1 2 3 5 6 7 6 8 10 sum 1 2 3 5 6 7 1 6 8 10 sum 1 2 3 5 6 7 2 6
283. ments sensor3 type param typeALt paramALt id specifies an alternative constraint surface used when the modifier key is held down Examples simple XY plane phi theta without modifier R with modifier with plane and ignored 2nd param See also surf Plot a surface defined by a grid in 3D space 418 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax surf x y zZ surf z surf x y z color surf z color surf vis surf vis style surf vis style id Description surf x y z plots a surface defined by 2 D arrays x y and z Ar guments x and y must have the same size as z or be vectors of size z 2 and size z 1 elements respectively If x and y are miss ing their default values are coordinates from 1 to size z 2 along x axis and from 1 to size z 1 along y axis Color of each surface cell is obtained by mapping the average z values to the color map surf x y zZ color maps values of array color to the color map color must have the same size as z and contain values between 0 and 1 surf Vvis specifies which side of the surface is visible vis is a string of 1 or 2 characters f if the front side is visible the side where increasing y are on the left of increasing x coordinates and b if the back side is visible Default is equivalent to fb surf style specifies the line or symbol style of the mesh between surface cells or the fill style of the surfac
284. metric used to calculate the distance is the eu clidean distance but it can be specified with a second argument 488 LMEPPC User Manual 1999 2008 Calerga Sarl euclid euclidean distance seuclid standardized euclidean distance mahal Mahalanobis distance cityblock sum of absolute values minkowski Minkowski metric with parameter p The standardized euclidean distance is the euclidean distance after each column of M has been divided by its standard deviation The Minkowski metric is based on the p norm of vector differences Examples use stat pdist 1 3 121 squareform pdist 1 3 012 101 210 squareform pdist 1 2 6 3 1 7 6 1 2 0 2 4495 6 4807 2 4495 0 5 831 6 4807 5 831 0 See also squareform prctile Percentile Syntax use stat m prctile A prc m prctile A prc dim Description prctile A prc gives the smallest values larger than prc percent of the elements of each column of array A or of the row vector A The dimension along which prctile proceeds may be specified with a third argument Libraries stat Example prctile rand 1 1000 90 0 8966 See also range Mean absolute deviation Syntax use stat m range A m range A dim Description 489 range A gives the differences between the maximum and minimum values of the columns of array A or of the row vector A The dimension along which range proceeds may be specified with a second argu
285. mple use classes p polynom 3 0 1 4 2 fun inline p fun lt inline function gt dumpvar fun fun fun inline function y f x y polyval 3 0 1 4 2 x See also polynom polynom polynom feval polynom feval Evaluate a polynom object 496 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax use classes y feval a x Description feval a x evaluates polynomial a for the value of x If x is a vector or a matrix the evaluation is performed separately on each element and the result has the same size as x Example use classes p polynom 3 0 1 4 2 y feval p 1 5 y 2 46 242 770 1882 See also polynom polynom polynom inline feval ratfun ratfun Ratfun object constructor Syntax use classes a ratfun a ratfun coefnum a ratfun coefnum coefden Description ratfun coefnum coefden creates a ratfun object initialized with the coefficients in vectors coefnum and coefden given in descending pow ers of the variable Without argument ratfun returns a ratfun object initialized to 0 If omitted coefden defaults to 1 The following operators and functions may be used with ratfun ar guments with results analog to the corresponding functions of LME Libraries classes 497 inv mtimes minus plus mldivide uminus mpower uplus mrdivide Example use classes r ratfun 3 0 1 4 2 2 5 0 1 r 3x 4 x 2 4x 2 2x
286. n 188 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax r rem x y Description rem x y gives the remainder of x divided by y i e a number r be tween 0 and sign x abs y such that x q y r with integer q Imaginary parts if they exist are ignored Examples rem 10 7 3 rem 10 7 3 rem 10 7 3 rem 10 7 3 See also round Rounding to the nearest integer Syntax y round x Description round x gives the integer nearest to x If the argument is a complex number the real and imaginary parts are handled separately Examples round 2 3 2 round 2 6 3 round 2 3 2 LME Reference mathematical functions 189 See also Floor ceil sign Sign of a real number or direction of a complex number Syntax s sign x z2 sign z1 Description With a real argument sign x is 1 if x gt 0 0 if x 0 or 1 if x lt 0 With a complex argument sign z1 is a complex value with the same phase as Z1 and whose magnitude is 1 Examples sign 2 1 sign 1 1j 0 7071 0 7071j sign 0 5 01 See also sec Secant Syntax y sec x Description sec x gives the secant of x which is complex if x is 190 LMEPPC User Manual 1999 2008 Calerga Sarl See also asec cos sech Hyperbolic secant Syntax y sech x Description acot x gives the hyperbolic secant of x which is complex if x is See also jasech seci cosh sin Sine
287. n Without argument clear discards the contents of all the local variables including input arguments With string input arguments clear vl v2 discards the contents of the enumerated variables Note that the variables are specified by strings clear is a normal function which evaluates its arguments if they are enclosed between parenthesis You can also omit parenthesis and quotes and use clear is usually not necessary because local variables are auto matically discarded when the function returns It may be useful if a large variable is used only at the beginning of a function or at the command line interface clear functions or clear f removes the definition of all func tions It can be used only from the command line interface not in a function LME Reference miscellaneous functions 89 Examples In the example below clear b evaluates its argument and clears the variable whose name is a clear b without parenthesis and quotes does not evaluate it the argument is the literal string b a 2 b a clear a Undefined variable b a clear b b Undefined variable b b Fad a See also variable assignment deal Copy input arguments to output arguments Syntax v1 v2 deal e vl v2 deal el e2 Description With a single input argument deal provides a copy of it to all its output arguments With multiple input arguments deal provides them as output arguments
288. n a structure opt created with responseset field Range is utilized The optional arguments style and id have their usual meaning dimpulse Ad Bd Cd Dd Ts plots the impulse response of the discrete time state space model Ad Bd Cd Dd defined as x k 1 y k where u k is a unit discrete impulse The state space model must have a scalar input and may have a scalar or vector output With output arguments dimpulse gives the output and the time as column vectors No display is produced Adx k Bgu t Cgx k Dgu k LME Reference graphics for dynamical systems 425 Example dimpulse 1 poly 0 9 0 7 0 6j 0 7 0 6j 1 r See also dinitial Time response plot of a discrete time linear state space model with initial conditions Syntax dinitial Ad Bd Cd Dd Ts x0 dinitial Ad Bd Cd Dd Ts x0 opt dinitial style dinitial style id y t dinitial Description dinitial Ad Bd Cd Dd Ts x0 plots the output s of the discrete time state space model Ad Bd Cd Dd with null input and initial state x0 The model is defined as x kK 1 Agx k Bgu t y k Cax k Dqu k where u k is null Sampling period is Ts The state space model may have a scalar or vector output The simulation time range can be provided in a structure opt cre ated with responseset It is a vector of two elements the start time and the end time Such an explicit time range is required when the resp
289. n be inserted before s d x o i f e or g it limits the number of characters to be decoded In the input string spaces and tabulators are skipped before decoding s d x 0 i f e or g The format string is recycled as many times as necessary to de code the whole input string The decoding is interrupted if a mismatch occurs The optional second output argument is set to the number of ele ments decoded successfully may be different than the length of the first argument if decoding strings The optional third output argument 368 LMEPPC User Manual 1999 2008 Calerga Sarl is set to the number of characters which were consumed in the input string Examples sscanf f 2 3 f f 2 3 sscanf 12a34x778 d c 12 97 34 120 778 sscanf abc def abcdef sscanf abc def abc def sscanf 12 34 d d 34 sscanf 0275a0ff 2x 2 117 160 255 S c See also swrite Store data in a string Syntax swrite data swrite data precision S S Description swrite fd data stores the contents of the matrix data in a string The third parameter is the precision whose meaning is the same as for fread Its default value is uint8 LME Reference file system 369 Examples swrite 65 68 ABCD double swrite 1 2 int16 1020 double swrite 1 2 int16 b 0102 See also 3 29 File System Functions
290. n n1 n2 nan n1 n2 nan type x x XXX X tod i id ouweou Description NaN Not a Number is the result of the primitive floating point func tions or operators called with invalid arguments For example 0 0 inf inf and O inf all result in NaN When used in an expression NaN propagates to the result All comparisons involving NaN result in false except for comparing NaN with any number for inequality which re sults in true Contrary to built in functions usually found in the underlying oper ating system many functions which would result in NaNs give complex numbers when called with arguments in a certain range LME Reference mathematical functions 183 With integer non negative arguments nan creates arrays whose elements are NaN Arguments are interpreted the same way as zeros and ones The last argument of nan can be a string to specify the type of the result double for double precision default or single for single precision Examples nan nan Oxnan nan nan nan false nan nan true log 1 0 3 1416j See also nchoosek Binomial coefficient Syntax b nchoosek n k Description nchoosek n k gives the number of combinations of n objects taken k ata time Both n and k must be nonnegative integers with k lt n Examples nchoosek 10 4 210 nchoosek 10 6 210 184 LMEPPC User Manual 1999 2008 Calerga Sarl See also factorial pdf Probability den
291. nals It implements quantization DPCM differential pulse code modulation and companders used in telephony The following statement makes available functions defined in sigenc use sigenc alawcompress A law compressor Syntax use sigenc output alawcompress input output alawcompress input a Description alawcompress input a compresses signal input with A law method using parameter a The signal is assumed to be in 1 1 values out side this range are clipped input can be a real array of any size and dimension The default value of a is 87 6 The compressor and its inverse the expander are static nonlin ear filters used to improve the signal noise ratio of quantized signals The compressor should be used before quantization or on a signal represented with a higher precision See also alawexpand u Lawcompress alawexpand A law expander Syntax use sigenc output alawexpand input output alawexpand input a Libraries sigenc 545 Description alawexpand input a expands signal input with A law method using parameter a input can be a real array of any size and dimension The default value of a is 87 6 See also atlawcompress juLawexpand dpcmdeco Differential pulse code modulation decoding Syntax use sigenc output dpcmdeco i codebook predictor Description dpcmdeco i codebook predictor reconstructs a signal encoded with differential pulse code modulation It per
292. nates Syntax X Y meshgrid x y X Y meshgrid x Description meshgrid x y produces two arrays of x and y coordinates suitable for the evaluation of a function of two variables The input argument x is copied to the rows of the first output argument and the input argument y is copied to the columns of the second output argument so that both arrays have the same size meshgrid x is equivalent to meshgrid x x Example X X lt l meshgrid 1 5 2 4 N Ul NN Ww w w D AUN ul 0 4636 0 7854 0 9828 1 1071 0 3218 0 5880 0 7854 0 9273 0 2450 0 4636 0 6435 0 7854 LME Reference arrays 255 See also ndgrid Arrays of N dimension coordinates Syntax X1 Xn ndgrid xl xn X1 Xn ndgrid x Description ndgrid x1 xn produces n arrays of n dimensions Array i is obtained by reshaping input argument i as a vector along dimension i and replicating it along all other dimensions to match the length of other input vectors All output arguments have the same size With one input argument ndgrid reuses it to match the number of output arguments Y X ndgrid y x is equivalent to X Y meshgrid x y Example X1 X2 ndgrid 1 3 X1 1 1 1 2 2 2 3 3 3 X2 1 2 3 1 2 3 1 2 3 See also ndims Number of dimensions of an array Syntax n ndims A 256 LMEPPC User Manual 1999 2008 Calerga Sarl Description ndims A returns the number of dim
293. ndexOutOfRange is handled by catch other errors are not try catch err lasterror if err identifier LME indexOutOfRange else rethrow err end end See also tasterror Ery error str2fun Function reference Syntax funref str2fun str Description str2fun funref gives a function reference to the function whose name is given in string str It has the same effect as operator which is preferred when the function name is fixed Examples str2fun sin sin sin sin a cos str2fun a cos See also 106 LMEPPC User Manual 1999 2008 Calerga Sarl str2obj Convert to an object its string representation Syntax obj str2obj str Description str2obj str evaluates string str and gives its result It has the in verse effect as dumpvar with one argument It differs from eval by restricting the syntax it accepts to literal values and to the basic con structs for creating complex numbers arrays lists structures objects and other built in types Examples str2obj 1 2j 1 2j str dumpvar 1 abc 1 100 str abc 1 100 str2obj str 1 abc real 1x100 eval str 1 abc real 1x100 str2obj sin 2 Bad argument str2obj eval sin 2 0 9093 See also varargin Remaining input arguments Syntax function fun varargin l varargin LME Reference miscellaneous func
294. nds only if a condition holds true gt if 2 lt 3 ok else amazing end ans ok 2 8 Functions LME permits you to extend its set of functions with your own This is convenient not only when you want to perform the same computation on different values but also to make you code clearer by dividing the whole task in smaller blocks and giving names to them To define a 22 LMEPPC User Manual 1999 2008 Calerga Sarl new function you have to write its code in a file you cannot do it from the command line In Sysquake put them in a function block Functions begin with a header which specifies its name its input arguments parameters which are provided by the calling expression and its output arguments result of the function The input and out put arguments are optional The function header is followed by the code which is executed when the function is called This code can use arguments like any other variables We will first define a function without any argument which just displays a magic square the sum of each line and the sum of each column function magicsum3 magic_3 magic 3 sum_of_each_line sum magic_3 2 sum_of_each_column sum magic_3 1 You can call the function just by typing its name in the command line gt magicsum3 magic_3 816 357 492 sum_of_each_line sum_of_each_column 15 15 15 This function is limited to a single size For more generality let us add an input ar
295. necessarily objects Inheritance A class subclass may extend the data and methods of another class base class or parent It is said to inherit from the parent In LME objects from a subclass contain in a special field an object of the parent class the field name has the same name as the parent class If LME does not find a method for an object it tries to find one for its parent great parent etc if any An object can also inherit from several parents Here is an example of the use of polynom objects which as can be guessed from their name contain polynomials Statement use classes imports the definitions of methods for class polynom and oth ers use classes p polynom 1 5 0 1 p x 3 5x 241 p2 3 p polynom 1 0 a l X 6 10x 54 25x 44 2x 34 13xX 2415x4 1 3 5 Input and Output LME identifies channels for input and output with non negative integer numbers called file descriptors File descriptors correspond to files devices such as serial port network connections etc They are used as input argument by most functions related to input and output such as fprintf for formatted data output or fgets for reading a line of text Note that the description below applies to most LME applications For some of them files command prompts or standard input are ir relevant or disabled and standard output does not always correspond to the screen At least four file descriptors are predefined Value Input
296. nificant bit Unlike arrays bits are not selected with logical arrays but with other bit fields where ones represent the bits to be selected for example a 0b1011 selects bits 0 1 and 3 This is consistent with the way bitfield find is defined Examples use bitfield a bitfield 123 16 a 0b0000000001111011 b a o 0b1111111110000100 b a gt 5 o 0b0000001001100111 See also bitfield disp bitfield double bitfield disp Display a bitfield object Libraries bitfield 505 Syntax use bitfield disp a Description disp a displays bitfield a It is also executed implicitly when LME displays the bitfield result of an expression which does not end with a semicolon See also bitfield double Convert a bitfield object to a double number Syntax use bitfield n double a Description double a converts bitfield a to double number Example use bitfield a bitfield 123 16 double a 123 See also bitfield end Last bit position in a bitfield 506 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax use bitfield a end Description In the index expression of a bitfield end is the position of the most significant bit i e 1 less than the word length See also bitfield bitfield bitfield beginning bitfield find Find the ones in a bitfield Syntax use bitfield ix find a Description find a finds the bits equal to 1 in bitfield a
297. nnection Syntax use lti c feedback a b c feedback a b sign c feedback a b ina outa c feedback a b ina outa sign Description feedback a b connects all the outputs of lti object a to all its inputs via the negative feedback Lti object b feedback a b sign applies positive feedback with weight sign the default value of sign is 1 feedback a b ina outa specifies which inputs and outputs of a to use for feedback The inputs and outputs of the result always cor respond to the ones of a See also Lti connect Iti inv System inverse Syntax use lti b inv a Description inv a gives the inverse of system a Libraries lti 529 See also ti mldivide lti mrdivide isct Test for a continous time LTI Syntax use lti b isct a Description isct a is true if system a is continuous time or static and false oth erwise See also isdt Test for a discrete time LTI Syntax use lti b isdt a Description isdt a is true if system a is discrete time or static and false other wise See also isct Iti isempty Test for an LTI without input output 530 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax use lti b isempty a Description isempty a is true if system a has no input and or no output and false otherwise See also Lti sizel lti issiso Iti isproper Test for a proper causal LTI Syntax use lti b isproper a Descri
298. ns Note that soapcall also interpret the lack of an option argument or the empty array as a request to use the default values When its first input argument is a structure soapcallset adds or changes fields which correspond to the name value pairs which follow Here is the list of permissible options Name Default Meaning Server ot server name or IP address Port 80 port number Timeout 10 maximum time in seconds Debug false true to display data If the server is an empty string it is replaced with localhost The Debug field is not included in the default options when set it causes the display of the request and responses Example Default options soapcallset Server 7 Port 80 Timeout 10 586 LMEPPC User Manual 1999 2008 Calerga Sarl See also soapca soapreadcall Decode a SOAP call request Syntax method namespace pstruct url method namespace pstruct url soapreadcall fd soapreadcall str Description soapreadcall fd where fd is a file descriptor reads a complete SOAP call decodes it and returns the result in four output arguments the method name and namespace as strings a structure which con tains the parameters and the URL as a string soapreadcall str decodes its string argument which must be a whole SOAP call Example param struct x pi y true str soapwritecall fun namespace param method ns pstruct
299. ns declared with the function keyword inline functions can be assigned to vari ables passed as arguments and built dynamically Evaluating them with feval is faster than using eval with a string because they are compiled only once to an intermediate code They can also be used as the argument of functions such as fzero and fmin inline funstr returns an inline function whose source code is funstr Input argument funstr follows the same syntax as a plain function The function name is ignored 98 LMEPPC User Manual 1999 2008 Calerga Sarl inline expr returns an inline function with one implicit input ar gument and one result The input argument expr is a string which evaluates to the result The implicit input argument of the inline func tion is asymbol made of a single lower case letter different from i and j such as x or t which is found in expr If several such symbols are found the one closer to x in alphabetical order is picked inline expr argl returns an inline function with one re sult and the specified arguments arg1 etc These arguments are also given as strings Inline functions also accept an additional input argument which cor respond to fixed parameters provided when the function is executed inline funstr param where funstr is a string which contains the source code of a function stores param together with the function When the function is called param is prepended to the list of input arguments inline
300. nsions you can also develop your own Extensions are stored in the directory LMEExt itself located at the same place as LME exe To disable all extensions you can switch off the Load extensions option Introduction 11 Hide messages Extensions usually display a short status message when they are loaded at LME startup When Hide messages is switched on no message is displayed Path of libraries Libraries contain additional functions written in the LME programming language see below The Path of li braries option specifies where LME looks for library files Direc tories are separated with semicolons For example if you store your own libraries in My Documents LMELib you could add this directory to the default path Program Files Calerga Lib My Documents LMELib The path of libraries can also be set with the LME function path Startup commands Startup commands are LME commands ex ecuted every time the application is launched For instance if you often use functions from libraries such as stdlib for function which extend the built in functions of LME or stat for advanced functions related to statistics you can add use statements as startup commands to make them always available use stdlib stat Startup commands can also be used to define variables They are executed after the file Imestartup txt if it exists see above Format Format specified in the Options dialog are an alternative to the LME function format It d
301. nstructor using zeros and poles Syntax use lti a zpk z p k a zpk zeroslist poleslist gainlist a zpk TS a zpk TS var a zpk b a zpk b Description zpk creates transfer function LTI systems like tf tf Instead of using transfer function coefficients as input it accepts a vector of zeros a vector of poles and a gain for a simple input simple output SISO system or lists of sublists of zeros poles and gains for multiple input multiple output MIMO systems Examples use lti sd zpk 0 3 0 8 0 5j 0 8 0 5j 10 0 1 sd discrete time transfer function Ts 0 1 10z 3 z 2 1 6z 0 89 See also Iti bodemag Magnitude of the Bode plot Syntax use lti bodemag a bodemag a Description bodemag a plots the magnitude of the Bode diagram of system a Libraries lti 541 See also ti nichols lt1 nyquist Iti bodephase Phase of the Bode plot Syntax use lti bodephase a bodephase a Description bodephase a plots the magnitude of the Bode diagram of system a See also ti bodemag lti nichols Tti nyquist Iti impulse Impulse response Syntax use lti impulse a impulse a Description impulse a plots the impulse response of system a See also Lti step lti tanita l Iti initial Time response with initial conditions 542 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax use lt
302. nt private public repeat return switch try until use useifexists while See also lasterr Last error message Syntax msg lasterr msg identifier lasterr Description lasterr returns a string which describes the last error With two out put arguments it also gives the error identifier It can be used in the catch part of the try construct Example Xx 2 x 3 Index out of range msg identifier lasterr msg Index out of range identifier LME indexOutOfRange See also Tasterror Ery error lasterror Last error structure Syntax s lasterror 102 LMEPPC User Manual 1999 2008 Calerga Sarl Description Lasterror returns a structure which describes the last error It con tains the following fields identifier string short tag which identifies the error message string error message The structure can be used as argument to rethrow in the catch part of a try catch construct to propagate the error further Example Index out of range lasterror message Index out of range identifier LME indexOut0OfRange See also nargin Number of input arguments Syntax n n nargin nargin fun Description Calling a function with less arguments than what the function expects is permitted In this case the trailing variables are not defined The function may use the nargin function to know how many arguments
303. nt sread abc data 97 98 99 count 3 data count sread abcdef 2 2 data 97 98 99 100 count 4 data count sread abcd inf 3 data 97 98 99 count 3 See also fread LME Reference input output 367 sscanf Decoding of formatted numbers Syntax r sscanf str format r count scanf str format r count nchar scanf str format Description Numbers characters and strings are extracted from the first argu ment Exactly what is extracted is controlled by the second argument which can contain the following elements Substring in format Meaning single character string integer number in decimal unsigned integer number in hexadecimal unsigned integer number in octal integer number floating point number x ann H X X X X X g X X X amp e floating point number g floating point number other character exact match i recognizes an optional sign followed by a decimal number an hexadecimal number prefixed with 0x or 0X a binary number prefixed with Ob or OB or an octal number prefixed with 0 The decoded elements are accumulated in the output argument either as a column vector if the format string contains d 0 x i f e or g or a string if the format string contains only c s or literal values If a star is inserted after the percent character the value is decoded and discarded A width as one or more decimal characters ca
304. nt uint32 uint8s uint64 LME Reference Set functions 47 intersect setdiff union ismember setxor unique Constants eps intmax pi false intmin realmax i j realmin inf nan true Arithmetic functions 7 Al 2k cumprod cumsum diff kron mod prod rem sum Trigonometric and hyperbolic functions acos asinh acosh atan acot atan2 acoth atanh acsc cos acsch cosh asec cot asech coth asin CSC csch sec sech sin sinh tan tanh 48 LMEPPC User Manual 1999 2008 Calerga Sarl Other scalar math functions abs angle beta betainc betaln cdf conj diln ellipam ellipe ellipf ellipj ellipke erf erfc erfinv exp expml factorial gamma gammainc gammaln gcd hypot imag lcm log log10 loglp log2 nchoosek pdf real reallog realpow realsqrt sign sinc sqrt Type conversion functions cast ceil complex double fix floor round single swapbytes typecast Matrix math functions r r balance care chol cond conv2 dare det dlyap eig expm fft funm hess ifft inv linprog logm lu lyap norm null orth pinv qr rank schur sqrtm svd trace 49 LME Reference Geometry functions cross dot Statistic functions cov mean skewness kurtosis min std max moment var Polynomial math functions addpol filter polyint conv poly polyval deconv polyder roots Triangulation functions delaunay griddatan voronoi delaunayn tsearch vo
305. ntax return Description 71 return stops the execution of the current function and returns to the calling function The current value of the output arguments if any is returned return can be used in any control structure such as if or try or at the top level Example function dispFactTable n display the table of factorials from 1 to n if n return nothing to display end fwrite i i n for i 1 n fwrite 2d 3d n i prod 1 i end See also unction switch Conditional execution of statements depending on a number or a string Syntax switch expr case el sl case e2 e3 s23 case e4 e5 s45 72 otherwise so end switch string case strl sl case str2 s2 case str3 str4 s34 otherwise so end Description LMEPPC User Manual 1999 2008 Calerga S rl The expression of the switch statement is evaluated If it yields a number it is compared successively to the result of the expressions of the case statements until it matches one then the statements which follow the case are executed until the next case otherwise or end If the case expression yields a vector or a list a match occurs if the switch expression is equal to any of the elements of the case expres sion If no match is found but otherwise is present the statements following otherwise are executed If the switch expression yields a string a match occurs only in case of
306. ntax y atan x Description atan x gives the arc tangent of x which is complex if x is complex Example atan 1 0 7854 See also 150 LMEPPC User Manual 1999 2008 Calerga Sarl atan2 Direction of a point given by its Cartesian coordinates Syntax phi atan2 y x Description atan2 y x gives the direction of a point given by its Cartesian coor dinates x and y Imaginary component of complex numbers is ignored atan2 y x is equivalent to atan y x if x gt 0 Examples atan2 1 1 0 7854 atan2 1 1 2 3562 atan2 0 0 0 See also atanh Inverse hyperbolic tangent Syntax y atanh x Description atan x gives the inverse hyperbolic tangent of x which is complex if x is complex or if abs x gt 1 Examples atanh 0 5 0 5493 atanh 2 0 5493 1 5708j LME Reference mathematical functions 151 See also beta Beta function Syntax y beta z w Description beta z w gives the beta function of z and w Arguments and result are real imaginary part is discarded The beta function is defined as 1 B z w i t tdt 0 Example beta 1 2 0 5 See also betainc Incomplete beta function Syntax y betainc x z w Description betainc x z w gives the incomplete beta function of x z and w Arguments and result are real imaginary part is discarded x must be between 0 and 1 The incomplete beta function is defined as 1 B z w x I z
307. ntroduces LME TM Lightweight Matrix Engine the interpreter for numerical computing used by Sysquake and shows you how to perform basic computations It supposes you can type commands to a command line interface You are invited to type the examples as you read this tutorial and to experiment on your own For a more systematic description of LME please consult the LME Reference chapter In the examples below we assume that LME displays a prompt gt This is not the case for all applications You should never type it your self Enter what follows the prompt on the same line hit the Return key or tap the Eval or Execute button and observe the result 2 1 Simple operations LME interprets what you type at the command prompt and displays the result unless you end the command with a semicolon Simple ex pressions follow the syntactic rules of many programming languages gt 2 3 4 ans 14 gt 2 3 4 ans 2 75 As you can see the evaluation order follows the usual rules which state that the multiplication denoted with a star and division slash have a higher priority than the addition and subtraction You can change this order with parenthesis gt 24 3 4 ans 20 14 LMEPPC User Manual 1999 2008 Calerga Sarl The result of expressions is automatically assigned to variable ans more about variables later which you can reuse in the next expres sion gt 3xans ans 60 Power is represented by the symb
308. nverted from text to real mathematic notation and a table of contents and an index have been added The same method has been used to create the material for the help command Thanks to the make utility the whole process is completely automatic This system has proved to be very flexible to maintain three useful formats in parallel two for on line help and one for high quality printing World Wide Web http www calerga com E mail sysquake calerga com Mail alerga Sar Av de la Chabli re 35 1004 Lausanne Switzerland Typesetting 2008 1 4 Contents 7 1 1 LMEInstallation 0 0 00 cee es 8 1 2 Userinterface 0 000002 ee eee ee 8 1 3 Code fragments soc s seu se 5 eee ae eed de eee es 9 1 4 First Steps oea naie Beales G a MGS PER eG eee 9 1 5 User preferences 2 0 00 a 10 1 6 Libraries a suc ea hee ae a GA Ae RRR EA 11 2_LME Tutorial 13 2 1 Simple operations 000 00002 13 2 2 Complex Numbers 000 0000s 14 2 3 Vectors and Matrices 00 005 16 2 4 Polynomials 2 000000 eee eee 19 2 9 SUrNGS 2 280 ee ce ee ee eee Pew eee eee Pe 20 2 6 Variables ss sae i eed aes Pe de eRe ee eR 20 2 7 Loops and Conditional Execution 21 2 8 FUNCUIONS si ea a oe ee ta we Pee we ie ee ia 21 2 9 Local and Global Variables 05 24 27 3 1 Programformat 000
309. obustness of the estimate with re spect to the choice of the observations Example use stat D rand 1000 1 bootstrp 5 std D 0 2938 0 2878 0 2793 0 2859 0 2844 geomean Geometric mean of a set of values Syntax use stat m geomean A m geomean A dim Description geomean A gives the geometric mean of the columns of array A or of the row vector A The dimension along which geomean proceeds may be specified with a second argument The geometric mean of vector v of length n is defined as vv Example use stat geomean 1 10 4 5287 mean 1 10 5 5 exp mean log 1 10 4 5287 See also 482 LMEPPC User Manual 1999 2008 Calerga Sarl harmmean Harmonic mean of a set of values Syntax use stat m harmmean A m harmmean A dim Description harmmean A gives the harmonic mean of the columns of array A or of the row vector A The dimension along which harmmean proceeds may be specified with a second argument The inverse of the harmonic mean is the arithmetic mean of the inverse of the observations Example use stat harmmean 1 10 3 4142 mean 1 10 5 5 See also geomean iqr Interquartile range Syntax use stat m iqr A m iqr A dim Description iqr A gives the interquartile range of the columns of array A or of the row vector A The dimension along which igr proceeds may be specified with a second argument Libraries stat 483 The interquar
310. od M returns a row vector whose elements are the products of the corre sponding columns of matrix M prod M dim returns the product of matrix M along dimension dim the result is a row vector if dim is 1 or a column vector if dim is 2 Examples prod 1 5 120 prod 1 5 120 prod 1 2 3 5 6 7 5 12 21 prod 1 2 3 5 6 7 1 5 12 21 prod 1 2 3 5 6 7 2 6 210 See also qr QR decomposition Syntax Q R E qr A Q R qr A Qe Re e qr A false Qe Re qr A false 232 LMEPPC User Manual 1999 2008 Calerga Sarl Description With three output arguments qr A computes the QR decomposition of matrix A with column pivoting i e a square unitary matrix Q and an upper triangular matrix R such that A E Q R With two output argu ments qr A computes the QR decomposition without pivoting such that A Q R With a second input argument with the value false if A has m rows and n columns with m gt n qr produces an m by n Q and an n by n R Bottom rows of zeros of R and the corresponding columns of Q are discarded With column pivoting the third output argument e is a permutation vector A e Q R Example Q R qr 1 2 3 4 5 6 0 169 0 8971 0 4082 0 5071 0 276 0 8165 0 8452 0 345 0 4082 R 5 9161 7 4374 0 0 8281 0 0 Q R qr 1 2 3 4 5 6 false Q 0 169 0 8971 0 5071 0 276 0 8452 0 345 R 5 9161 7 4374 0 0 8281 See also rank Rank of a matrix Syn
311. oe ee scalefactor 401 schur sec 189 sech 190 sensor3 416 serialdevname 457 598 AEA E EE serialdevset 459 599 set 36 setdiff setfield setstr 306 setxor 264 sgrid 449 shal 306 sigma sign sin 190 sinc 190 single sinh size skewness 235 soapcall soapcallset 585 soapreadcall soapreadresponse 586 soapwritecall soapwritefault soapwriteresponse E socketconnect 5 socketnew 577 socketservernew 578 socketset 579 socketsetopt 580 sort 266 sortrows 477 sph2cart 4 sprintf 364 sqlite_changes sqlite_close 5 1 sqlite_exec sqlite_last_insert_rowid 57 sqlite_open sqlite_set 5 3 sqlite_version 5 4 sqrt 192 sqrtm 235 squarefo a 489 squeeze 267 sread 36 ss2tf 351 sscanf 36 nee 77 std 2 step 4 str2fun 105 str2obj 1 NJI ON 5 a o gt EEM st teh BOE strtok 309 strtrim struct Index structure style style parameter sub2ind subsasgn subspace 4 78 subsref sum 237 surf 417 svd 238 swapbytes switch 71 swrite 368 symbol shape tan 193 tanh 194 text 402 tf2ss B52 Bee thick line 3 thin ue BE tic B71 times 114 title 403 toc 72 toeplitz 479 trace transpose trapz ikek trimmean 490 triu 270 true 345 try 73 tsearch 2 tsearchn 277 typecast uint16 uint32 2 uin
312. ol gt 25 ans 32 LME has many mathematical functions Trigonometric functions as sume that angles are expressed in radians and sqrt denotes the square root gt sin pi 4 sqrt 2 ans 1 2 2 Complex Numbers In many computer languages the square root is defined only for non negative arguments However it is extremely useful to extend the set of numbers to remove this limitation One defines i such that i 1 and applies all the usual algebraic rules For instance 1 V i and 4 V4 1 2i Complex numbers of the form a bi are the sum of a real part a and an imaginary part b It should be mentioned that i the symbol used by mathematicians is called j by engineers LME accepts both symbols as input but it always writes it j You can use it like any function or stick an i or j after a number gt 2 3 j ans 2 3j gt 3j 2 ans 2 3j Many functions accept complex numbers as argument and return a complex result when the input requires it even if it is real gt sqrt 2 ans 04 1 4142i gt exp 3 2j Tutorial 15 ans 8 3585 18 2637j gt log 8 3585 18 2637j ans 3 2j To get the real or imaginary part of a complex number use the func tions real or imag respectively gt real 2 3j ans 2 gt imag 2 3j ans 3 Complex numbers can be seen as vectors in a plane Then addition and subtraction of complex numbers correspond to the same opera tions applie
313. om 80 socketset TextMode true fprintf fd GET s HTTP 1 0 n n reply fgets fd reply HTTP 1 1 200 OK fclose fd See also socketset socketconnect fwrite fgetl fgets fprintf socketservernew Create a new server queue for accepting connections from clients Syntax fds socketservernew port options fds socketservernew port Description socketservernew hostname port creates a new TCP or UDP socket for accepting incoming connections Connections from clients are ac cepted with socketaccept which must provide as input argument the file descriptor returned by socketservernew Using multiple threads multiple connections can be accepted on the same port using multiple socketaccept for one socketservernew The second argument of socketservernew port options is a structure which contains configuration settings It is set with socketset Options are inherited by the connections established with socketaccept On platforms where administrator authorizations are enforced only an administrator account root account can listen to a port below 1024 Only one server can listen to the same port To stop listening to new connections the socket is closed with fclose The file descriptor returned by socketservernew can be used only with socketaccept and fclose Example fds socketservernew 8080 fd socketaccept fds Extensions sockets 579 request fscanf fd GET s fp
314. om file descriptor fd and returns it as an array whose first dimension is the image height and second dimension the image width Grayscale images give a third dimension equal to 1 i e plain matrices Color images give a third dimension equal to 3 fist plane is the red component second plane the green component and third plane the blue component In both cases value range is 0 for black to 1 for maximum intensity Extensions image files 565 The file descriptor is usually obtained by opening a file with fopen in binary mode text mode with end of line translation would produce garbage or cause a decoding error Example fd fopen image png r im imageread fd fclose fd See also imagewrite imageset Options for image output Syntax options imageset options imageset namel valuel options imageset options0O namel valuel Description imageset namel valuel creates the option argument used by imagewrite Options are specified with name value pairs where the name is a string which must match exactly the names in the table below Case is significant Options which are not specified have a default value The result is a structure whose fields correspond to each option Without any input argument imageset creates a structure with all the default options Note that imagewrite also interpret the lack of an option argument or the empty array as a request to use the default
315. on from quaternion to string Syntax str q2str q Description q2str q converts quaternion q to its string representation with the same format as disp See also quaternion format qimag Quaternion imaginary parts Syntax b qimag q 318 LMEPPC User Manual 1999 2008 Calerga Sarl Description qimag q gives the imaginary parts of quaternion q as a quaternion i e the same quaternion where the real part is set to zero real q gives the real part of quaternion q as a double number Example q quaternion 1 2 3 4 q 1 2i 3j 4k real q 1 qimag q 2i 3j 4k See also quaternion qinv Quaternion element wise inverse Syntax b qinv q Description qinv q gives the inverse of quaternion q If its input argument is a quaternion array the result is an quaternion array of the same size whose elements are the inverse of the corresponding elements of the input The inverse of a normalized quaternion is its conjugate Example q quaternion 0 4 0 1 0 2 0 2 0 4 0 1i 0 2j 0 2k p qinv q p 1 6 0 4i 0 8j 0 8k abs q 0 5 LME Reference Quaternions 319 abs p 2 See also quaternion qnorm conj qnorm Quaternion scalar norm Syntax n qnorm q Description qnorm q gives the norm of quaternion q i e the sum of squares of its components or the square of its absolute value If q is an array of quaternions qnorm gives a double array of the same size w
316. on imageset they include the file type The file descriptor is usually obtained by opening a file with fopen in binary mode text mode with end of line translation would produce a corrupted image file Extensions MAT files 567 Example Write the image contained in the matrix im to a file image png using the default options fd fopen image png w imagewrite fd im fclose fd Write the same image as a JPEG file fd fopen image jpg w imagewrite fd im imageset Type JPEG fclose fd See also imageset imageread 6 5 MAT files matfiledecode Decode the contents of a MATLAB MAT file Syntax var var var matfiledecode fd mat filedecode data matfiledecode ignoreErr Description matfiledecode fd reads data from file descriptor fd until the end of the file The data must be the contents of a MATLAB compatible MAT file They are made of 8 bit bytes no text conversion must take place The result is a structure whose fields have the name and the contents of the variables saved in the MAT file Instead of a file descriptor the data can be provided directly as the argument In that case the argument data must be an array which can be read from the actual file with f readlor obtained from a network connection Only arrays are supported scalar matrices arrays of more than two dimensions real or complex numerical logical or char A second in
317. on onto the line _nb is the index of the line in A and b and _ix is empty Examples Vertical line at x 5 line 1 0 5 Draggable horizontal lines at y 2 and y 3 line 0 1 2 3 b 1 See also LME Reference base graphics 393 pcolor Pseudocolor plot Syntax pcolor C pcolor X Y C pcolor style pcolor style id Description Command pcolor C displays a pseudocolor plot i e a rectangular array where the color of each cell corresponds to the value of elements of 2 D array C These values are real numbers between 0 and 1 The color used by pcolor depends on the current color map the default is a grayscale from black 0 to white 1 pcolor X Y C displays the plot on a grid whose vertex coordi nates are given by arrays X and Y Arrays X X and C must all have the same size With an additional string input argument pcolor style specifies the style of the lines drawn between the cells The following argument if it exists is the ID used for interactivity During interactive manipulation the index obtained with _ix corre sponds to the corner of the patch under the mouse with the smallest index Example use colormaps n 11 x y meshgrid 1 n phi pi 8 X x cos phi y sin phi Y x sin phi y cos phi C magic n n 2 pcolor X Y C k colormap blue2yellow2redcm plotoption noframe See also 394 LMEPPC User Manual 1999 2008 Calerga Sarl
318. one since a dummy empty option arguments has to be inserted zero x f x 10 0 100 See also ode23 ode45 Ordinary differential equation integration Syntax ode23 fun t0 tend yO ode23 fun t0 tend y0 options ode23 fun t0 tend y0 options ode45 fun t0 tend yO ode45 fun t0 tend y0 options ode45 fun t0 tend y0 options oo ct et et et et lt lt lt M lt tou on uo ue a 288 LMEPPC User Manual 1999 2008 Calerga Sarl Description ode23 fun tQ tend y0 and ode45 fun t0 tend yO integrate numerically an ordinary differential equation ODE Both functions are based on a Runge Kutta algorithm with adaptive time step ode23 is low order and ode45 high order In most cases for non stiff equations ode45 is the best method The function to be integrated is either spec ified by its name or given as an anonymous or inline function or a function reference It should have at least two input arguments and exactly one output argument function yp f t y The function calculates the derivative yp of the state vector y at time t Integration is performed over the time range specified by the sec ond argument t0 tend starting from the initial state y0 It may stop before reaching tend if the integration step cannot be reduced enough to obtain the required tolerance If the function is continuous you can try to reduce MinStep in the options argument see below The
319. onse is not displayed in a plot where the x axis represents the time The optional arguments style and id have their usual meaning With output arguments dinitial gives the output and the time as column vectors No display is produced See also 426 LMEPPC User Manual 1999 2008 Calerga Sarl disim Time response plot of a discrete time linear system with arbitrary in put Syntax dlsim numd dend u Ts dlsim Ad Bd Cd Dd u Ts dlsim Ad Bd Cd Dd u Ts x0 dlsim opt dlsim style dlsim style id dlsim opt style nes opt style id y t dlsim Description dlsim numd dend u Ts plots the time response of the discrete time transfer function numd dend with sampling period Ts The input is given in real vector u where the element i corresponds to time i 1 Ts Input samples before 0 and after Length u 1 are 0 dlsim Ad Bd Cd Dd u Ts plots the time response of the discrete time state space model Ad Bd Cd Dd defined as x k 1 Agx k Bgu t y k Cax k Dau k where the system input at time sample k is u k For single input systems u can also be a row vector dlsim Ad Bd Cd Dd u Ts x0 starts with initial state x0 at time t 0 The length of x0 must match the number of states The default initial state is the zero vector The simulation time range can be provided in a structure opt cre ated with responseset It is a vector of two elements the start
320. onseset namel valuel 446 LMEPPC User Manual 1999 2008 Calerga Sarl options responseset options0 namel valuel Description responseset namel valuel creates the option argument used by functions which display frequency and time responses such as nyquist and step Options are specified with name value pairs where the name is a string which must match exactly the names in the table below Case is significant Options which are not specified have a de fault value The result is a structure whose fields correspond to each option Without any input argument responseset creates a structure with all the default options Note that functions such as nyquist and step also interpret the lack of an option argument as a request to use the default values Contrary to other functions which accept options in structures such as ode45 empty array cannot be used it would be interpreted incorrectly as a numerical argument When its first input argument is a structure responseset adds or changes fields which correspond to the name value pairs which follow Here is the list of permissible options Name Default Meaning Delay 0 time delay NegFreq false negative frequencies Range time or frequency range tOnly false samples for specified time only lsim Option Delay is used only by continuous time frequency response and time response functions for frequency responses it subtracts a phase of delay w where w is the angu
321. ontrol is false or on norm y if it is true time steps are chosen so that it remains under AbsTol or RelTol times the state whichever is larger If this cannot be achieved for instance if the system is stiff and requires an integration step smaller than MinStep integration is aborted Refine specifies how many points are added to the result for each integration step When it is larger than 1 additional points are interpolated which is much faster than reducing MaxStep The output function OutputFcn if defined is called after each step It is a function name in a string a function reference or an anonymous or inline function which can be defined as function stop outfun tn yn LME Reference non linear numerical functions 291 where tn is the time of the new samples yn their values and stop a logical value which is false to continue integrating or true to stop The number of new samples is given by the value of Refine when multiple values are provided tn is a row vector and yn is a matrix whose columns are the corresponding states The output function can be used for incremental plots for animations or for managing large amounts of output data without storing them in variables Events Events are additional time steps at controlled time to change instan taneously the states and to base the termination condition on the states Time instants where events occur are either given explicitly by EventTime or implicitly
322. oolean expressions to select some ele ments of an array matrixrow can be overloaded for objects of used defined classes Its definition should be have a header equivalent to function e C matrixrow obj i n where C is the name of the class obj is the object to be indexed i is the position of the index expression where matrixrow is used and n is the total number of index expressions See also beginning end subsasgn Assignment to a part of an array list or structure Syntax A subsasgn A s B Description When an assignment is made to a subscripted part of an object in a statement like A s1 s2 B LME executes A subsasgn A s B where subsasgn is a method of the class of variable A and s is a struc ture with two fields s type which is and s subs which is the list of subscripts sl s2 If a subscript is the colon character which stands for all elements along the corresponding dimensions it is represented with the string in s subs LME Reference variables 59 When an assignment is made to a subscripted part of an object in a statement like A s B LME executes A subsasgn A s B where subsasgn is a method of the class of variable A and s is a structure with two fields s type which is and s subs which is the list containing the single subscript s When an assignment is made to the field of an object in a statement like A f B LME executes A subsasgn A s B where s is a s
323. oom and shift specified by the user scale optString defXMin defXMax defYMin defYMax sc scale xMin sc 1 xMax sc 2 yMin sc 3 yMax sc 4 LME Reference base graphics 379 Grids In addition to the scale ticks displayed along the bounding frame grids can be added to give visual clues and make easier the interpretation of graphics X and Y grids are vertical or horizontal lines displayed in the figure background They can be switched on and off by the user in the Grid menu or switched on by programs with the plotoption command they are set off by default In the example below both X and Y grids are switched on plotoption xgrid plotoption ygrid plot rand 1 10 Commands which display grids for special kind of graphics are also available Command Intended use hgrid nyquist dnyquist ngrid nichols dnichols sgrid plotroots rlocus continuous time zgrid plotroots rlocus discrete time They can be used without argument to let the user choose the level of details none means the command does not produce any out put basic is the default value and gives a simple non obstructive hint a single line or a circle and full gives more details To change by program the default level of details basic pLlotoption is used In the example below the grid for the complex plane of the z transform is displayed with full details Once the figure is displayed the user is free to reduce the level of det
324. opt in order codebook0 predictor codebook partition dpcmopt in predictor predictor codebook partition dpcmopt tol predictor dpcmopt in order lActually there may be a drift if the arithmetic units used for encoding and decoding do not produce exactly the same results Libraries sigenc 547 Description dpcmopt in order n gives the optimal predictor of order order codebook of size n and partition to encode the signal in vector in with differential pulse code modulation The result can be used with dpcmenco to encode signals with similar properties If the second input argument is a vector it is used as the predictor and not optimized further its first element must be zero If the third input argument is a vector it is used as an initial guess for the codebook which has the same length An optional fourth input argument provides the tolerance the default is le 7 If only the predictor is required only the input and the predictor order must be supplied as input arguments See also Uoyds lloyds Optimal quantization Syntax use sigenc partition codebook partition codebook partition codebook lloyds input n lloyds input codebook0 lloyds tol Description Lloyds input n computes the optimal partition and codebook for quantizing signal input with n codes using the Lloyds algorithm If the second input argument is a vector Lloyds input codebook uses
325. optimum The second output argument if it exists is the value of fun x at op timum The third output argument if it exists is set to true if fminbnd has converged to an optimum or to false if it has not in that case other output arguments are set to the best value obtained With one or two output arguments fminbnd throws an error if it does not con verge Examples Minimum of a sine near 2 displayed with 15 digits fprintf 15g n fminbnd sin 2 4 712389014989218 To find the minimum of ce sinx between 1 and 10 with c 0 1 the expression is written as an inline function stored in variable fun 284 LMEPPC User Manual 1999 2008 Calerga Sarl fun inline c exp x sin x x c Then fminbnd is used with the value of c passed as an additional argument xX fminbnd fun 1 10 0 1 x 1 2239 With an anonymous function this becomes wg x cxexp x sin x fminbnd fun 1 10 1 ll I c fun x x Il 2239 Attempt to find the minimum of an unbounded function x y didConverge fminbnd exp 10 x inf y 0 didConverge false See also fminsearch Minimum of a function in R n Syntax x fminsearch fun x0 x fminsearch options x fminsearch options x y didConverge fminsearch Description fminsearch fun x0 finds numerically a local minimum of func tion fun fun is either specified by i
326. optional argu ments style and id have their usual meaning impulse Ac Bc Cc Dc plots the impulse response of the continuous time state space model Ac Bc Cc Dc defined as Acx t Bcu t Cex t Decu t x8 dt y t where u is a Dirac impulse The state space model must have a scalar input and may have a scalar or vector output With output arguments impulse gives the output and the time as column vectors No display is produced Example impulse 1 1 4 m See also initial Time response plot for a continuous time state space model with initial conditions Syntax initial Ac Bc Cc Dc x0 initial Ac Bc Cc Dc x0 opt initial style initial style id y t initial 438 LMEPPC User Manual 1999 2008 Calerga Sarl Description initial Ac Bc Cc Dc x plots the output s of the continuous time state space model Ac Bc Cc Dc with null input and initial state x0 The model is defined as dx Ee Acx t Bcu t y t Ccex t Dc u t where u t is null The state space model may have a scalar or vector output The simulation time range can be provided in a structure opt cre ated with responseset It is a vector of two elements the start time and the end time Such an explicit time range is required when the response is not displayed in a plot where the x axis represents the time The optional arguments style and id have theirjusual meaning With output arguments initial
327. optional fourth argument may contain options It is either the empty array for the default options or the result of odeset the use of a vector of option values is deprecated Additional input arguments of ode45 are given as additional input arguments to the function specified by fun They permit to parame terize the ODE Example Let us integrate the following ordinary differential equation Van Der Pol equation parameterized by p x u 1 x x x Let y x and y2 x their derivatives are y2 u 1 yi y2 y yi y5 and can be computed by the following function function yp f t y mu yp y 2 mu 1 y 1 2 y 2 y 1 The following ode45 call integrates the Van Der Pol equation from 0 to 10 with the default options starting from x 0 2 and x 0 0 with u 1 see Fig 3 1 LME Reference non linear numerical functions 289 Van der Pol equation mu 1 Figure 3 1 Van der Pol equation with u 1 integrated with ode45 t y ode45 f 0 10 2 0 1 The plot command expects traces along the second dimension con sequently the result of ode45 should be transposed plot t y See also odeset Options for ordinary differential equation integration Syntax options odeset options odeset namel valuel options odeset optionsO namel valuel Description odeset namel valuel creates the option argument used by ode23 and ode45 Options are spec
328. or info sandboxtrust Operator inline str2fun builtin inmem str2obj deal isglobal subsasgn dumpvar iskeyword subsref eval lasterr variables exist lasterror which feval lookfor fevalx nargin Debugging dbclear dbstack dbtype dbcont dbstatus echo dbhatt dbstep profile dbquit dbstop Arrays ind2sub ones interpn permute ipermute rand iscell randn beginning isempty repmat cat length reshape cell magic rot90 cellfun matrixcol size diag matrixrow sort end meshgrid squeeze eye ndgrid sub2ind find ndims tril flipdim nnz triu fliplr num2cell unique flipud numel zeros LME Reference 45 Strings base64decode isspace strcmpi base64encode length strmatch char lower strtok deblank md5 strtrim findstr setstr upper ischar shal utf8decode isdigit sprintf utf8encode isempty sscanf isletter strcmp Lists islist num2List apply length replist join list2num isempty map Structures fieldnames isstruct setfield getfield orderfields struct isfield rmfield Objects class isobject isa methods 46 LMEPPC User Manual 1999 2008 Calerga Sarl Logical operators Logical functions all any false find ischar isdigit isempty Bitwise functions bitall bitand bitany bitcmp Integer functions int8 int16 int32 isfinite isnumeric isfloat isscalar isinf isspace isinteger isvector isletter logical islogical true isnan xor bitget bitxor bitor graycode bitset igraycode bitshift int64 uint16 map2i
329. or unique output argument When the function is called with more output arguments than what can be obtained from the other argu ments remaining ones are extracted from the list varargout In the body of the function varargout is a normal variable Its value can be set globally with the brace notation or element by element with varargout i nargout may be used to know how many output arguments to produce Example Here is a function which differentiates a vector of values as many times as there are output arguments function varargout multidiff v for i 1 nargout v diff v varargout i v end In the call below 1 3 7 2 5 3 1 8 is differentiated four times v1 v2 v3 v4 multidiff 1 3 7 2 5 3 1 8 vl 2 4 5 3 2 2 7 v2 2 9 8 5 0 9 v3 11 17 13 5 9 v4 28 30 18 4 See also nargout varargin function variables Contents of the variables as a structure Syntax v variables LME Reference miscellaneous functions 109 Description variables returns a structure whose fields contain the variables de fined in the current context Example 3 125 variables a 3 b real 1x5 ow See also into warning Write a warning to the standard error channel Syntax warning msg warning format argl arg2 Description warning msg displays the string msg It should be used to notify the user about potential problems not as a general purpose display fun
330. ort the rows of a matrix with respect to one of its columns as shown in the last example below Order of consecutive identical elements is preserved If a second numeric argument dim is provided the sort is performed along dimension dim columns if dim is 1 rows if 2 etc An additional argument can specify the ordering direction It must be the string ascending or a for ascending order or descending or d for descending order In both cases NaNs are moved to the end sort list sorts the elements of a list which must be strings Cell arrays are sorted like lists not column wise like numeric arrays The LME Reference arrays 267 second output argument is a row vector The direction can be specified with a second input argument Examples sort 3 6 2 3 9 1 2 1223369 sort 2 5 3 nan 4 2 6 1 1 2 1 1 6 4 2 nan 5 3 sort 2 5 3 nan 4 2 6 1 1 d 6 5 3 2 4 2 nan 1 1 sort def abcd abc abc abcd def To sort the rows of an array after the first column one can obtain the permutation vector by sorting the first column and use it as subscripts on the array rows Algorithm Shell sort See also squeeze Suppression of singleton dimensions of an array 268 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax B squeeze A Description squeeze A returns an array with the same elements as A but where dimensions equal to 1 are rem
331. orthonormal basis for the null space of m by n matrix A Z has n rank A columns which are the last right singular values of A that is those corresponding to the negligible singular values Example null 1 2 3 1 2 4 1 2 5 0 8944 0 4472 8 0581le 17 See also orth Orthogonalization Syntax Q orth A Description orth A returns a matrix Q whose columns are an orthonormal basis for the range of those of matrix A Q has rank A columns which are the first left singular vectors of A that is those corresponding to the largest singular values Example orth 1 2 3 1 2 4 1 2 5 0 4609 0 788 0 5704 8 9369e 2 0 6798 0 6092 See also LME Reference linear algebra 227 pinv Pseudo inverse of a matrix Syntax M2 M2 inv M1 inv M1 e TT Description pinv M1 returns the pseudo inverse of matrix M For a nonsingular square matrix the pseudo inverse is the same as the inverse For an arbitrary matrix possibly nonsquare the pseudo inverse M2 has the following properties size M2 size M1 M1 M2 M1 M1 M2 M1 M2 M2 and the norm of M2 is minimum To pseudo inverse is based on the singular value decomposition where only the singular values larger than some small threshold are considered This threshold can be specified with an optional second argument If M1 is a full rank matrix with more rows than columns pinv returns the least square solution pinv M1 xy M1 M1 M1 xy
332. oved The result has at least 2 dimen sions row and column vectors keep their dimensions Examples size squeeze rand 1 2 3 1 4 234 size squeeze 1 5 15 See also sub2ind Conversion from row column subscripts to single index Syntax ind sub2ind size i j Description sub2ind size i j gives the single index which can be used to re trieve the element corresponding to the i th row and the j th column of an array whose size is specified by size size must be either a scalar for square matrices or a vector of two elements or more for other arrays If i and j are arrays they must have the same size the result is calculated separately for each element and has the same size Example M 3 6 8 9 M 2 1 8 sub2ind size M 2 1 7 LME Reference arrays M 3 8 See also tril Extraction of the lower triangular part of a matrix Syntax tril M L L tril M k Description 269 tril M extracts the lower triangular part of a matrix the result is a matrix of the same size where all the elements above the main di agonal are set to zero A second argument can be used to specify another diagonal O is the main diagonal positive values are above and negative values below Examples magic 3 BWOrFRWOrRWO ll I ct ct 3 5 OUrPRAOUG OUP N OO N UND m NN O See also triu diag 270 LMEPPC User Manual 1999 2008 Calerga Sarl triu Extra
333. p If x2 x1 and step are orthogonal it is attempted to produce an infinite number of elements which will obviously trigger an out of memory error This is similar to having a null step in the real case Note that the default step value is always 1 for consistency with real values Choosing for instance sign x2 x1 would have made the 142 LMEPPC User Manual 1999 2008 Calerga Sarl generation of lists of indices more difficult Hence for a vector of purely imaginary numbers always specify a step colon x1 x2 is equivalent to x1 x2 and colon x1 step x2 to x1 step x2 It can be used to redefine this operator for objects The colon character is also used to separate the alternatives of a conditional expression b x y Example 2 D u 2 WW w D ul w TNMNASENWWNUNY ro o ul m D N w N 0 1j 10j 1j 2j 3j 4j 5j 6j 7j 8j 9j 10j 1 1 1j 5 4j 1 2 1j 3 2j 4 3j 5 4j 0 1 1j 5 O 1 1j 2 2j 3 3j 4 4j 5 5j See also Operator Function reference or anonymous function Syntax fun arguments expression Description fun gives a reference to function fun which can be used wherever an inline function can Its main use is as the argument of functions like feval or quad but it may also be stored in lists cell arrays or LME Reference operators 143 structures A reference cannot be cast to a double unlike characters or logical values nor can it be stored in an array Anonymous functions
334. plot Generic plot Syntax plot y plot x y plot style plot style id Description The command plot displays graphical data in the current figure The data are given as two vectors of coordinates x and y If x is omitted its default value is 1 size y 2 Depending on the style the points are displayed as individual marks or are linked with lines The stairs style s can be used to link two successive points with a horizontal line followed by a vertical line If x and y are matrices each row is considered as a separate line or set of marks if only one of them is a matrix the other one a row or column vector is replicated to match the size of the other argument The optional fourth argument is an identification number which is used for interactive manipulation It should be equal or larger than 1 If present and a mousedown mousedrag and or mouseup handler exists the position of the mouse where the click occurs is mapped to the closest graphical element which has been displayed with an ID for the command plot the closest point is considered lines linking the points are ignored If such a point is found at a small distance the built in variables _x0 _y0 and _z0 are set to the position of the point before it is moved the variable _id is set to the ID as defined by the command plot the variable _nb is set to the number of the row and the variable _ix is set to the index of the column of the matrix x and y
335. point by the same amount See also ampan camorbit amva ol o camorbit Camera orbit around target Syntax camorbit dphi dtheta Description camorbit dphi dtheta rotates the camera around the target point by angle dphi around the up vector and by angle dtheta around the vector pointing to the right of the projection plane Both angles are given in radians A positive value of dphi makes the camera move to the right and a positive value of dtheta makes the camera move down See also camdo tty campan camzoom campan Tilt and pan camera Syntax campan dphi dtheta LME Reference 3D graphics 407 Description campan dphi dtheta pans the camera by angle dphi and tilts it by angle dtheta Both angles are in radians More precisely the target point is changed so that the vector from view point to target is rotated by angle dphi around the up vector then by angle dtheta around a right vector a vector which is horizontal in view coordinates See also CandoUly camorbit campos Camera position Syntax campos p campos auto campos manual p campos Description campos p sets the view position to p p is a 3D vector campos auto sets the view position to automatic mode so that it follows the target campos manual sets the view position to manual mode With an output argument campos gives the current view position See also camdolly camorbit campan CcamZoom camproj
336. polynomial ratio N D as N1 D1 Input and output ar guments are polynomial coefficients Examples Derivative of x 2x2 5x 2 polyder 1 2 5 2 345 Derivative of x 2x2 5x 2 2x 3 N D polyder 1 2 5 2 2 31 N 4 13 12 11 D 4 12 9 See also polyint Integral of a polynomial Syntax pol2 polyint pol1 pol2 polyint poll c Description polyint pol1 returns the polynomial which is the integral of the polynomial pol1 whose zero order coefficient is 0 Both polynomi als are given as vectors of their coefficients highest power first The result is a row vector A second input argument can be used to specify the integration constant 230 LMEPPC User Manual 1999 2008 Calerga Sarl Example Y polyint 1 2 3 4 5 Y 0 2 0 5 1 2 5 0 y polyder Y 1 2 3 4 5 Y polyint 1 2 3 4 5 10 Y 0 2 0 5 1 2 5 10 See also polyval Numerical value of a polynomial evaluated at some point Syntax y polyval pol x Description polyval pol x evaluates the polynomial pol at x which can be a scalar or a matrix of arbitrary size The result has the same size as x Examples polyval 1 3 8 2 18 polyval 1 2 1 5 34567 See also prod Product of the elements of a vector LME Reference linear algebra Syntax x prod v v prod M v prod M dim Description prod v returns the product of the elements of vector v 231 pr
337. pond to the internal storage ordering and can be used to access the elements with a single subscript With two output arguments find M returns two vectors contain ing the subscripts row in the first output argument column in the second output argument of the nonzero elements of 2 dim array M To obtain subscripts for an array of higher dimension you can convert the single output argument of find to subscripts with ind2sub With three output arguments find M returns in addition the nonzero values themselves in the third output argument With a second input argument n find limits the maximum number of elements found It searches forward by default with a third input argument dir find gives the n first nonzero values if dir is first or f and the n last nonzero values if dir is last or UL LME Reference arrays 245 Examples ix find 1 2 0 0 3 6 1x 1 4 s1 s2 find 1 2 0 0 3 6 sl 1 2 s2 1 2 s1 s2 x find 1 2 0 0 3 6 sl 1 2 s2 2 6 rand 3 riworeil nw 0 5599 0 3074 0 5275 0 3309 0 8077 0 3666 0 7981 0 6424 0 6023 find A gt 0 7 2 last 7 5 See also flipdim Flip an array along any dimension Syntax B flipdim A dim Description flipdim A dim gives an array which has the same size as A but where indices of dimension dim are reversed 246 LMEPPC User Manual 1999 2008 Calerga Sarl Examples flipdim cat 3 1 2 3 4 5 6 7 8 3
338. port 459 Once a connection has been opened the file descriptor fd can be used with functions such as fread fwrite fscanf and fprintf The connection is closed with fclose Example fd serialdevopen serialdevname 1 serialdevset BPS 19200 TextMode true Timeout 2 fprintf fd L d 2 n 1 reply fgetl fd fclose fd serialdevname FFLUSh getl fgets serialdevset Configuration settings for serial port Syntax options serialdevset options serialdevset namel valuel options serialdevset options0 namel valuel Description serialdevset namel valuel creates the option argument used by serialdevopen Options are specified with name value pairs where the name is a string which must match exactly the names in the table below Case is significant Options which are not specified have a default value The result is a structure whose fields correspond to each option Without any input argument serialdevset creates a structure with all the default settings Note that serialdevopen also interprets the lack of an option argument or the empty array as a request to use the default values When its first input argument is a structure serialdevset adds or changes fields which correspond to the name value pairs which follow Here is the list of permissible options 460 LMEPPC User Manual 1999 2008 Calerga Sarl Name Default Meaning BPS 19200 bit per seconds Delay
339. ption isproper a is true if lti object a is causal or false otherwise An ss object is always causal A tf object is causal if all the transfer functions are proper i e if the degrees of the denominators are at least as large as the degrees of the numerators Iti issiso Test for a single input single output LTI Syntax use lti b issiso a Description issiso a is true if lti object a has one input and one output single input single output system or SISO or false otherwise Uti sizel lti isempty Libraries lti 531 Iti minreal Minimum realization Syntax use lti b minreal a b minreal a tol Description minreal a modifies lti object a in order to remove states which are not controllable and or not observable For tf objects identical zeros and poles are canceled out minreal a tol uses tolerance tol to decide whether to discard a state or a pair of pole zero Iti minus System difference Syntax use lti a b minus a b Description a b computes the system whose inputs are fed to both a and b and whose outputs are the difference between outputs of a and b Ifa and b are transfer functions or matrices of transfer functions this is equivalent to a difference of matrices See also lti parallel lti uminus Iti mldivide System left division 532 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax use lti c a b C mldivide a b Description a b is equivalent
340. ption optimset namel valuel creates the option argument used by fminbnd fminsearch and fzero Options are specified with name value pairs where the name is a string which must match exactly the names in the table below Case is significant Options which are not specified have a default value The result is a structure whose fields correspond to each option Without any input argument optimset creates a structure with all the default options Note that fminbnd fminsearch and fzero also interpret the lack of an option argument or the empty array as a request to use the default values When its first input argument is a structure optimset adds or changes fields which correspond to the name value pairs which fol low Here is the list of permissible options empty arrays mean auto matic Name Default Meaning Display false detailed display MaxFunEvals 1000 maximum number of evaluations MaxIter 500 maximum number of iterations TolXx maximum relative error The default value of TolX is eps for fzero and sqrt eps for fminbnd and fminsearch Examples Default options optimset Display false 298 LMEPPC User Manual 1999 2008 Calerga Sarl MaxFunEvals 1000 MaxIter 500 TolxX Display of the steps performed to find the zero of cosx between 1 and 2 fzero cos 1 2 optimset Display true Checking lower bound Checking upper bound Inverse quadratic interpolation 2 1 5649 1 Inverse quadratic int
341. put argument the main diagonal is extracted and returned as a column vector A second argument can be used to spec ify another diagonal Examples diag 1 3 10 0 2 00 Woo LME Reference arrays 3 D NNO Q OONO H A OWOo He UJ lt Q H Qa H yeo NUOV AUI looodoe g M 1 See also eye Identity matrix Syntax M eye n M eye m n M eye m n M eye type Description 243 eye builds a matrix whose diagonal elements are 1 and other elements 0 The size of the matrix is specified by one integer for a square ma trix or two integers either as two arguments or in a vector of two elements for a rectangular matrix An additional input argument can be used to specify the type of the result It must be the string double single int8 int16 int32 int64 uint8 uint16 uint32 or uint64 64 bit arrays are not supported on all platforms 244 LMEPPC User Manual 1999 2008 Calerga Sarl Examples eye 3 100 010 001 eye 2 3 100 010 eye 2 int8 2x2 int8 array 10 01 See also find Find the indices of the non null elements of an array Syntax ix find v s1 s2 find M s1 s2 x find M find n find n dir Description With one output argument find v returns a vector containing the indices of the nonzero elements of v v can be an array of any dimen sion the indices corres
342. put argument can be used to specify how to handle data of unsup ported types with false default value unsupported types cause an error with true they are ignored 568 LMEPPC User Manual 1999 2008 Calerga Sarl Example fd fopen data mat s matfiledecode fd fclose fd S S x real 1x1024 y real 1x1024 See also matfileencode matfileencode Encode the contents of a MATLAB MAT file Syntax matfileencode fd s matfileencode s Description matfileencode fd s writes the contents of structure s to file de scriptor fd as a MATLAB compatible MAT file Each field of s corre sponds to a separate variable in the MAT file With one argument matfileencode s writes to the standard output which should be un common since MAT files contain non printable bytes Only arrays are supported scalar matrices arrays of more than two dimensions real or complex numerical logical or char Examples s a 123 b abc S fd fopen data mat wb matfileencode fd s fclose fd Function variables can be used to save all variables v variables fd fopen var mat wb matfileencode fd v fclose fd Extensions SQLite 569 See also mat filedecode 6 6 SQLite This section describes functions which SQLite relational databases SQLite is a public domain relational database stored locally in a single file which uses SQL as its query language There ar
343. r See also camorbit camzoom camva View angle Syntax camva va va camva 410 LMEPPC User Manual 1999 2008 Calerga Sarl Description camva va sets the view angle to va which is expressed in degrees The projection mode is set to perspective The scale is adjusted so that the graphics have about the same size With an output argument camva gives the view angle in degrees which is O for an orthographic projection See also camdolly camorbit campan Camup Camzoom camzoom Zoom in or out Syntax camzoom f Description camzoom f scales the projection by a factor f The image grows if f is larger than one and shrinks if it is smaller See also contour3 Level curves in 3D space Syntax contour3 z contour3 z xmin xmax ymin ymax contour3 z xmin xmax ymin ymax levels contour3 z xmin xmax ymin ymax levels style LME Reference 3D graphics 411 Description contour3 z plots in 3D space seven contour lines corresponding to the surface whose samples at equidistant points 1 size z 2 in the x direction and 1 size z 1 on the y direction are given by z Contour lines are at equidistant levels With a second non empty argument xmin xmax ymin ymax the samples are at equidistant points between xmin and xmax in the x direction and between ymin and ymax in the y direction The optional third argument levels if non empty gives the num ber of contour
344. r T String Usually 1 by n char array but any shape of char arrays are also accepted by most functions Unless a conversion function is used explicitly numbers are repre sented by double or complex values Most mathematical functions ac cept as input any type of numerical value and convert them to double they return a real or complex value according to their mathematical definition Basic element wise arithmetic and comparison operators accept di rectly integer types element wise means the operators and the functions mod and rem as well as operators with a scalar multiplicand or divisor If their arguments do not have the same type 32 LMEPPC User Manual 1999 2008 Calerga Sarl they are converted to the size of the largest argument size in the fol lowing order double gt uint64 gt int64 gt uint32 gt int32 gt uint16 gt int16 gt uint8 gt int8 Functions which manipulate arrays such as reshape which changes their size or repmat which replicates them preserve their type To convert arrays to numerical char or logical arrays use func tions unary operator char or Logical respectively To convert the numerical types use functions double single or uint8 and similar functions Numbers Double and complex numbers are stored as floating point numbers whose finite accuracy depends on the number magnitude During computations round off errors can accumulate and lead to visible ar
345. r Transform LME Reference linear algebra 211 Syntax F fftn f F fftn f size Description fftn f returns the n dimension Discrete Fourier Transform of array f DFT along each dimension of f With two input arguments fftn f size resizes f by cropping or by padding f with zeros See also filter Digital filtering of data Syntax filter filter filter y xf f X0 X0 dim y b a u y b a u y b a u ilter Description filter b a u filters vector u with the digital filter whose coefficients are given by polynomials b and a The filtered data can also be an array filtered along the first non singleton dimension or along the dimension specified with a fifth input argument The fourth argu ment if provided and different than the empty matrix is a ma trix whose columns contain the initial state of the filter and have max length a length b 1 element Each column correspond to a signal along the dimension of filtering The result y which has the same size as the input can be computed with the following code if u is a vector a a a l if length a gt length b b b zeros 1 length a length b else a a zeros 1 length b length a end length x 212 LMEPPC User Manual 1999 2008 Calerga Sarl for i 1 length u y i b 1 u i x 1 for j 1 n 1 x j b j 1 u i x j 1 a j 1 y i end x n b n 1 u i a n 1
346. r compiling the extension Typically you need a C compiler chain like gcc You can get it as free software from GNU 570 LMEPPC User Manual 1999 2008 Calerga Sarl Get SQLite distribution Download the latest distribution from the site http www sqlite org Locate the required files To compile the extension you will need the following files LMESQLite c the main source code of the extension which defines new functions for LME LME_Ext h the header file for LME extensions which is pro vided with all LME applications which support extensions it is typically stored in a directory named ExtDevel Let extdevel be its path The source code of SQLite typically in the directory src of the SQLite distribution Compile the extension Create a new directory cd to it and run the Make file of the SQLite extension For example cd mkdir mysql build cd mysql_buid ext extpath sqlite sqlitepath make f extpath Makefile lme sqlite Install the extension For most LME applications just move or copy the extension sqlite so if you have used the command above to the directory where LME looks for extensions usually LMEExt For Sysquake Remote you also have to add the follow ing line to the configuration file of Apache please read Sysquake Remote documentation for more information SQRLoadExtension extpath sqlite so where extpath sqlite so is the absolute path of the extension Start or restart the LME applica
347. r function evaluated at e where w is a real number be tween 0 and r inclusive other definitions include the range between m and 27 which gives a symmetric diagram with respect to the real axis The range of frequencies is selected automatically between 0 and t or can be specified in an optional argument w a vector of normalized frequencies Further options can be provided in a structure opt created with responseset fields NegFreq and Range are utilized The optional ar guments style and id have theirjusual meaning With output arguments dnichols gives the real and imaginary parts of the frequency response and the frequency as column vectors No display is produced In Sysquake when the mouse is over a Nyquist diagram in addition to the complex value which can be retrieved with _z0 or _x0 and _y0 the normalized frequency is obtained in _q Example Nyquist diagram with the same scale along both x and y axis and a Hall chart grid reduced to a horizontal see Fig 3 12 scale equal hgrid dnyquist 3 poly 0 9 0 7 0 6j 0 7 0 6j See also dsigma Singular value plot for a discrete time state space model 430 LMEPPC User Manual 1999 2008 Calerga Sarl dnyquist 40P 20 Figure 3 12 dnyquist 3 poly 0 9 0 7 0 6j 0 7 0 6j Syntax dsigma Ad Bd Cd Dd Ts dsigma Ad Bd Cd Dd Ts w dsigma Ad Bd Cd Dd Ts opt dsigma Ad Bd Cd Dd Ts w opt dsigma style dsigma style id
348. ra 195 Example typecast luint32 uint8 1x4 uint8 array 0 0 Oo 1 typecast pi uint8 1x8 uint8 array 64 9 33 251 84 68 45 24 See also swapbytes 3 16 Linear Algebra addpol Addition of two polynomials Syntax p addpol p1 p2 Description addpol p1 p2 adds two polynomials p1 and p2 Each polynomial is given as a vector of coefficients with the highest power first e g x 2x 3 is represented by 1 2 3 Row vectors and column vectors are accepted as well as matrices made of row vectors or col umn vectors provided one matrix is not larger in one dimension and smaller in the other one addpol is equivalent to the plain addition when both arguments have the same size Examples addpol 1 2 3 2 5 148 addpol 10 addpol 124 457 1 2 3 2 5 subtraction 2 1 2 3 4 5 6 1 1 See also 196 LMEPPC User Manual 1999 2008 Calerga Sarl balance Diagonal similarity transform for balancing a matrix Syntax B balance A T B balance A Description balance A applies a diagonal similarity transform to the square ma trix A to make the rows and columns as close in norm as possible Balancing may reduce the 1 norm of the matrix and improves the accuracy of the computed eigenvalues and or eigenvectors To avoid round off errors balance scales A with powers of 2 balance returns the balanced matrix B which has the same eigen values and singular values as A
349. rand is subtracted from the first operand If both operands are matrices with a size different from 1 by 1 their size must be equal the subtraction is performed element wise If one operand is a scalar it is repeated to match the size of the other operand With one operand the sign of each element is changed minus x y is equivalent to x y and uminus x to x They can be used to redefine these operators for objects Example 2 3 1 1 2 3 5 LME Reference operators 123 2 3 3 4 2 12 2 2 3j 2 2 3j See also operator conj Operator Matrix multiplication Syntax xX Yy M1 x M2 M x mtimes x y Description xx y multiplies the operands together Operands can be scalars plain arithmetic product matrices matrix product or mixed scalar and matrix mtimes x y is equivalent to x y It can be used to redefine this operator for objects Example 2 3 6 1 2 3 4 3 5 See also prod Operator Scalar multiplication 124 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax xX y M1 M2 M x times x y Description x y is the element wise multiplication If both operands are matrices with a size different from 1 by 1 their size must be equal the mul tiplication is performed element wise If one operand is a scalar it multiplies each element of the other operand times x y is equivalent to x y It can be used to redefine this operator
350. rch x y t xi yi Description tsearch x y t xi yi searches in which triangle is located each point given by the corresponding elements of arrays xi and yi Corresponding elements of arrays x and y represent the vertices of the triangles and rows of array t represent their indices in x and y array t is usually the result of deLaunay Dimensions of x and y and of xi and yi must be equal The result is an array with the same size as Xi and yi where each element is the row index in t of the first triangle which contains the point or NaN if the point is outside all triangles i e outside the convex hull of points defined by x and y if t is a proper triangulation such as the one computed with delaunay LME Reference triangulation 277 Example Search for triangles containing points 0 0 and 0 1 corresponding to Delauny triangulation of 20 random points x randn 20 1 y randn 20 1 t delaunay x y xi 0 0 yi 0 1 ix tsearch x y t xi yi See also tsearchn delaunay vorono1 tsearchn Search of points in triangulation simplices Syntax ix tsearchn x t xi Description tsearchn x t xi searches in which simplex each point given by the rows of array xi is located Rows of array x represent the vertices of the simplices and rows of array t represent their indices in x array t is usually the result of deLaunayn Dimensions must match in a space of n dimensions x and xi have
351. rd 1 audiorecordset Stereo false See also audiorecord abs 144 acos acosh 145 acot 145 acoth 146 acsc 146 acsch 146 activeregion B79 addpol 195 alawcompress alawexpand all 334 and 114 m 147 asec 7 asech asin Us asinh eee a atan 149 atan2 atanh 150 aora Ee audiorecord audiorecordset 603 audioset 601 balance 196 bar 381 barh 382 base64decode base64encode beginning besselap ais Index besselLf 510 beta 151 betainc 151 betaln 152 bilinear 2 bitall bitand 336 a bitany 3 bitcmp bitget bitset bitshift bitxor 341 builtin 87 buttap butter bwrite 353 c2dm cal2julian camdolly camorbit 406 campan campos camproj camroll camtarget 408 camup 409 camva 409 camzoom 410 care 606 cart2pol cart2sph 463 case 61 cast cat 240 catch cdf 153 ceil 154 cell 24 cell array cellfun char 300 o gt m circle 383 circshift 464 class 332 class bitfield int16 506 int32 int8 506 uint16 508 uint32 508 uint8 508 class bitfield beginning bitfield nE double end 505 find 506 length sign class lti append 522 beginning bodemag bodephase c2d 524 connect 524 d2c 525 dcgain end LMEPPC User Manual 1999 2008 Calerga S rl evalfr 526
352. red If the variable is a state space model the result is equivalent the re sult remains a state space model For state space models changing all the inputs or all the outputs with the syntax var expr sys or var expr sys is much more efficient than specifying both sub scripts or a single index The syntax for field assignment var field value is defined for the following fields for state space models A B C and D matrices of the state space model for transfer functions num and den cell arrays of coefficients for both var string and Ts scalar or empty array for continuous time systems Field assignment must preserve the size of matrices and arrays The syntax with braces var i vaLue is not supported See also ti subsref operator subsasgn Iti subsref Extraction of a part of an LTI system 538 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax use lti var i j var ix var select var field b subsref a s Description The method subsref a permits the use of all kinds of extraction of a part of an LTI system If the variable is a matrix of transfer func tions subsref produces the expected result If the variable is a state space model the result is equivalent the result remains a state space model For state space models extracting all the inputs or all the outputs with the syntax var expr or var expr is much more efficient than specifying both subscripts or a single index
353. regions are in contact if and only if their initial points are linked in the corresponding Delaunay triangulation Example Voronoi tessalation of 20 random points x rand 20 1 y rand 20 1 v p voronoi x y These points are displayed as crosses with Sysquake graphical func tions The scale is fixed because Voronoi polygons can have vertices which are far away from the points clf scale equal 0 1 0 1 plot x y x Voronoi polygons are displayed in a loop skipping unbounded poly gons The first vertex is repeated to have closed polygons Since plot expects row vectors vertex coordinates are transposed LME Reference integers 279 for pl p if any pl 1 pl pl p1 1 plot v p1 1 v p1 2 end end See also voronoin delLaunay voronoin N d Voronoi tessalation Syntax v p voronoin x Description voronoin x calculates the Voronoi tessalation of the set of points given by the rows of arrays x in a space of dimension n size x 2 The first output argument v is an array of n columns which contains the coordinates of the vertices of the Voronoi cells one row per vertex The first row contains infinity and is used as a marker for unbounded Voronoi cells The second output argument p is a list of vectors of row indices in v each element describes the Voronoi cell corresponding to a point in x In each cell vertices are sorted by index See also 3
354. repmat a m n or repmat a m n repeats matrix a m times ver tically and n times horizontally 536 LMEPPC User Manual 1999 2008 Calerga Sarl See also Iti size Number of outputs and inputs Syntax use lti s size a nout nin size a n size a dim Description With one output argument size a gives the row vector nout nin where nout is the number of outputs of system a and nin its number of inputs With two output arguments size a returns these results separately as scalars size a 1 gives only the number of outputs and size a 2 only the number of inputs See also Uti isempty Lti issiso Iti ssdata Get state space matrices Syntax use lti A B C D ssdata a A B C D Ts ssdata a Description ssdata a where a is any kind of LTI object gives the four matrices of the state space model and optionally the sampling period or the empty array for continuous time systems Libraries lti 537 See also ti tfdata Iti subsasgn Assignment to a part of an LTI system Syntax use lti var i j a var ix a var select a var field value a subsasgn a s b Description The method subsasgn a permits the use of all kinds of assignments to a part of an LTI system If the variable is a matrix of transfer func tions subsasgn produces the expected result converting the right hand side of the assignment to a matrix of transfer function if requi
355. response xmlrpcreadca xml rpcreaaresponse xmIirpcwritedata Encode an XML RPC value Syntax xmlrpcwritedata fd val xmlrpcwritedata val str xmlrpcwritedata val Description xmLrpcwritedata fd val writes to file descriptor fd the value val encoded for XML RPC If fd is missing the value is written to standard output file descriptor 1 since the output contains carriage return characters it may not be displayed correctly on all platforms With an output argument xmlrpcwritedata returns the encoded value as a string without any output Example xmlrpcwritedata pi lt double gt 3 141592653589 lt double gt See also xmLlrpcwritecall xmlrpcwriteresponse xmIirpcwritefault Encode an XML RPC call response fault 596 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax xmlrpcwritefault fd faultCode faultString xmlrpcwritefault faultCode faultString str xmlrpcwritefault faultCode faultString Description xmlrpcwritefault fd faultCode faultString writes to file descriptor fd a complete XML RPC response fault including the HTTP header If fd is missing the response is written to standard output file descriptor 1 since the output contains carriage return characters it may not be displayed correctly on all platforms The faultCode argument is the numeric fault code and the faultString is the fault message With an output argument xmlrpcwritefault returns the response fault as a string withou
356. rguments step gives the output and the time as col umn vectors No display is produced Example Step response of the continuous time system 1 s 2s 3s5 4 see Fig 3 24 step 1 1 4 b LME Reference graphics for dynamical systems 453 scale equal 1 2 1 2 1 2 1 2 zgrid st HT Wy O a ST mm O SA SA sS T_T Uy KID O se xO SI NZ SS 5 a C CHH TH pee S TA Figure 3 25 scale equal 1 2 1 2 1 2 1 2 zgrid See also zgrid Relative damping and natural frequency grid for the poles of a discrete time system Syntax zgrid zgrid style zgrid damping freq zgrid damping freq style Description With no or one argument zgrid plots a grid of lines with constant relative damping and natural frequencies in the complex plane of z see Fig 3 25 The style argument has its usual meaning With two or three arguments zgrid plots only the lines for the specified values of damping and natural frequency The damping and the natural frequency w are defined the same way as for the sgrid function with the mapping z e a normalized sampling frequency 454 LMEPPC User Manual 1999 2008 Calerga Sarl is assumed With a damping the line z and its complex conjugate Z are generated by z e 1 1 6 u_ with O lt u lt Umax and Umax chosen such that the line has a positive imaginary part With a natural frequency w typically
357. rguments can simply be separated by spaces when they are en closed in brackets Parenthesis and square brackets are equivalent as far as LME is concerned parenthesis are preferred in LME code but square brackets are available for compatibility with third party appli cations In some cases a simpler syntax can be used when the function has only literal character strings as input arguments The following conditions must be satisfied No output argument Each input argument must be a literal string without any space tabulator comma or semicolon beginning with a letter a digit or one of minus slash dot colon or star containing at least one letter or digit In that case the following syntax is accepted left and right columns are equivalent fun strl fun str1 fun strl str2 fun stri str2 fun abc def fun abc def Arguments can also be quoted strings in that case they may con tain spaces tabulators commas semicolons and escape sequences beginning with a backslash see below for a description of the string data type Quoted and unquoted arguments can be mixed fun a bc n fun a bc n fun strl str 2 fun strl str 2 30 LMEPPC User Manual 1999 2008 Calerga Sarl This command syntax is especially useful for functions which accept well known options represented as strings such as format loose 3 3 Libraries Libraries are collec
358. ribution of each column of Y summed along each row When both the first and second arguments are ar rays of the same size area X Y displays independent area plots for corresponding columns of X and Y without summation LME Reference base graphics 381 With a single argument area y takes integers 1 2 n for the horizontal coordinates With a third argument area x y y0 displays the area between the horizontal line y y0 and values defined by y The optional arguments style and id have their usual meaning area uses default colors when argument style is missing Example area rand 20 10 See also bar Vertical bar plot Syntax bar y bar x y bar x y w bar kind bar kind style bar id Description bar x y plots the columns of y as vertical bars centered around the corresponding value in x If x is not specified its default value is l size y 2 bar x y w where w is scalar specifies the relative width of each bar with respect to the horizontal distance between the bars with values smaller than 1 bars are separated with a gap while with values larger than 1 bars overlap If wis a vector of two components w1 w2 wl corresponds to the relative width of each bar in a group columns of y and w2 to the relative width of each group Default values used if w is missing or is the empty matrix is 0 8 for both w1 and w2 bar kind where kind is a string specifies th
359. rintf fd Your request is s n request fclose fd fclose fds See also socketaccept socketset Configuration settings for sockets Syntax options socketset options socketset namel valuel options socketset options0O namel valuel Description socketset namel valuel creates the option argument used by socketnew and socketservernew Options are specified with name value pairs where the name is a string which must match exactly the names in the table below Case is significant Options which are not specified have a default value The result is a structure whose fields correspond to each option Without any input argument socketset creates a structure with all the default settings Note that socketnew also interprets the lack of an option argument or the empty array as a request to use the default values When its first input argument is a structure socketset adds or changes fields which correspond to the name value pairs which follow Here is the list of permissible options Name Default Meaning ListenQueue 5 queue size for incoming connections Proto tcp protocol tcp or udp TextMode true text mode Timeout 30 timeout in seconds When TextMode is true input CR and CR LF sequences are con verted to LF and output LF is converted to CR LF to follow the re quirements of many Internet protocols where lines are separated with CR LF Note that TextMode is true by d
360. ription realmax gives the largest positive real number in double precision realmin gives the smallest positive real number in double precision which can be represented in normalized form i e with full mantissa precision With integer non negative arguments realmax and realmin create arrays whose elements are all set to the respective value Arguments are interpreted the same way as zeros and ones The last argument of realmax and realmin can be a string to spec ify the type of the result double for double precision default or single for single precision Examples realmin 2 2251e 308 realmin single 1 1755e 38 realmax 1 7977e308 realmax single 3 4028e38single realmax eps realmax inf See also LME Reference mathematical functions 187 realpow Real power Syntax z realpow x y Description realpow x y gives the real value of x to the power y The imaginary parts of x and y are ignored The result is NaN if it is not defined for the input arguments If the arguments are arrays their size must match or one of them must be a scalar number the power is performed element wise See also realsqrt Real square root Syntax y realsqrt x Description realsqrt x gives the real square root of x The imaginary part of x is ignored The result is NaN if x is negative Example realsqrt 1 0 1 10 1 2j nan 0 1 3 1623 1 See also rem Remainder of a real divisio
361. ription strcmpi compares strings for equality ignoring letter case In every other respect it behaves like strcmp Examples strcmpi abc aBc true strcmpi Abc abd 2 true See also strmatch String match Syntax i i i strmatch str strMatrix strmatch str strList strmatch exact Description strmatch str strMatrix compares string str with each row of the character matrix strMatrix it returns the index of the first row whose beginning is equal to str or 0 if no match is found Case is significant strmatch str strList compares string str with each element of list strList which must be strings With a third argument which must be the string exact str must match the complete row or element of the second argument not only the beginning LME Reference strings 309 Examples strmatch abc axyz uabc abcd efgh E E ee uabc abcd efgh exact strmatch abe ABC any abcdefg ab abcd See also strtok Token search in string Syntax strtok str strtok str separators token remainder token remainder Description strtok str gives the first token in string str A token is defined as a substring delimited by separators or by the beginning or end of the string by default separators are spaces tabulators carriage returns and line feeds If no token is found i e if str is
362. ritecall Encode an XML RPC call request Syntax xmlrpcwritecall fd server url method params xmlrpcwritecall server url method params str xmlrpcwritecall server url method params Description xmlrpcwritecall fd server url method params writes to file descriptor fd a complete XML RPC call including the HTTP header If fd is missing the call is written to standard output file descriptor 1 since the output contains carriage return characters it may not be displayed correctly on all platforms The server argument is a string which contains the server name and optionally a colon and the server port number The url argument is a string which contains the absolute path without the protocol server and port part The method argument contains the method name sent to the server Remaining input arguments if any are sent as parameters With an output argument xmlrpcwritecall returns the call as a string without any output Example xmlrpcwritecall rpc remote com rpc getPressure lint32 POST rpc HTTP 1 0 User Agent LME 4 5 Host rpc remote com Content Type text xml Content Length 111 lt xml version 1 0 gt lt methodCall gt lt methodName gt getPressure lt methodName gt Extensions Web Services 595 lt params gt lt param gt lt value gt lt int gt 1 lt int gt lt value gt lt param gt lt params gt lt methodCall gt See also xmlrpcwrite
363. rmation in the Command window No further action is needed in order to use the new functions Note that the current release includes some extensions inside the EXE application itself You can also develop and add your own extensions as explained in the next chapter Here is the list of the extensions currently provided with LME for Pocket PC Mathematics Long integers Mac Windows Unix Arithmetic on arbitrary length integer numbers File input output and data compression Memory mapping Mac OS X Unix Mapping of files in memory which can be read and written like regular arrays Data compression Mac Windows Unix Support for com pressing and uncompressing data using ZLib Image Input Output Mac Windows Unix Support for reading and writing arrays as PNG or JPEG image files MAT file Mac Windows Unix Support for reading and writing MAT files native MATLAB binary files 558 LMEPPC User Manual 1999 2008 Calerga Sarl Operating system Download URL Mac Windows Linux Download of documents from the World Wide Web Launch URL Mac Windows Opening of documents in a World Wide Web browser Web Services Windows Mac OS X Unix Web Services stan dard remote procedure calls using XML RPC and SOAP Hardware support Audio playback Mac OS X Windows Linux Audio output Audio recording Mac OS X Windows Audio input 6 1 Long Integers This section describes functions which support long integer
364. rmed if the while statement yields true Example e l i 2 while true forever eNew 1 1 i i if abs e eNew lt 0 001 break end 76 LMEPPC User Manual 1999 2008 Calerga Sarl eNew 2 i 2 717 See also 3 10 Debugging Commands dbclear Remove a breakpoint Syntax dbclear fun dbclear fun line dbclear fun line dbclear Description dbclear fun removes all breakpoints in function fun dbclear fun line or dbclear fun line removes the breakpoint in function fun at line number Line Without argument dbclear removes all breakpoints See also dbstop dbcont Resume execution Syntax dbcont LME Reference debugging commands 77 Description When execution has been suspended by a breakpoint or dbhalt it can be resumed from the command line interface with dbcont See also dbhalt Suspend execution Syntax dbhalt Description In a function dbhalt suspends normal execution as if a breakpoint had been reached Commands dbstep dbcont and dbquit can then be used from the command line to resume or abort execution See also abstop dbquit Abort suspended execution Syntax dbquit Description When execution has been suspended by a breakpoint or dbhalt it can be aborted completely from the command line interface with dbquit See also dbstop dbhalt 78 LMEPPC User Manual 1999 2008 Calerga Sarl dbstack Chain of function calls Syntax
365. ronoin griddata tsearchn Quaternion operators 50 LMEPPC User Manual 1999 2008 Calerga Sarl Quaternion math functions abs q2mat real conj q2rpy rpy2q cos q2str sign cumsum qimag sin diff qinv sqrt exp qnorm sum log qslerp mean quaternion Quaternion other functions beginning fliplr permute cat flipud repmat char ipermute reshape disp isempty rot90 dumpvar isquaternion size double length squeeze end ndims subsasgn flipdim numel subsref Non linear numerical functions fminbnd ode23 optimset fminsearch ode45 quad fzero odeset Dynamical systems functions c2dm dmargin ss2tf d2cm margin tf2ss LME Reference Input output bwrite fgets clc format disp fprintf error fread fclose fscanf feof fseek fgetl ftell Files fopen 51 fwrite redirect sprintf sread sscanf swrite warning Graphical functions specific to LME for Pocket PC clf drawnow Basic graphics activeregion fplot polar area image quiver bar label scale barh legend scalefactor circle line subplot colormap pcolor text contour plot title fontset plotoption 52 LMEPPC User Manual 1999 2008 Calerga Sarl 3D graphics camdolly camup camorbit camva campan camzoom campos contour3 camproj daspect camroll Lightangle camtarget line3 material mesh plot3 plotpoly sensor3 surf Graphics for dynamical systems bodemag dsigma nichols bodephase dstep nyquist dbodemag erlocus plotroots dbodephase hgrid rlocus dimpulse hst
366. row vector of length size A 2 whose elements are the indices of each column It is equivalent to the range beginning end matrixcol is useful in boolean expressions to select some ele ments of an array matrixcol can be overloaded for objects of used defined classes Its definition should have a header equivalent to function e C matrixcol obj i n where C is the name of the class obj is the object to be indexed i is the position of the index expression where matrixcol is used and n is the total number of index expressions Example Set to 0 the NaN values which are not in the first column A 1 nan 5 nan 7 2 3 1 2 A matrixcol gt 1 amp isnan A 0 A 1 0 5 nan 7 2 3 1 2 See also matrixrow beginning matrixrow First index in a subscript expression 58 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax A matrixrow function e C matrixrow obj i n Description In an expression used as a single subscript to access some elements of an array A expr matrixrow gives an array of the same size as A where each element is the row index For instance for a 2 by 3 matrix matrixrow gives the 2 by 3 matrix 1 2 3 1 2 3 In an expression used as the first of multiple subscripts to access some elements of an array A expr matrixrow gives a row vec tor of length size A 1 whose elements are the indices of each row It is equivalent to the range beginning end matrixrow is useful in b
367. rpccallset Lower level functions which encode and decode calls and responses Extensions Web Services 583 while not necessary for standard calls can be used to understand ex actly how data are converted to implement the server or for special applications Procedure calls can contain parameters arguments and always return a single response These data have different types XML RPC converts them automatically as follows XML RPC LME i4 int32 scalar int int32 scalar boolean logical scalar string character 1 by n array double real double scalar dateTime iso8601 1 by 6 double array base64 1 by n uint8 array struct structure array list There is no difference between i4 and int In strings only the least significant byte is transmitted i e only ASCII characters between 0 and 127 are transmitted correctly Double values do not support an exponent a sufficient number of zeros are used instead The XML RPC standard does not support inf and NaN XML RPC functions do which should not do any harm In LME date and time are stored in a row vector which contains the year month day hour minute and second like the result of the function clock without time zone infor mation SOAP SOAP calls are very similar to XML RPC The main difference is that they use a single structure to represent the parameters The mem ber fields are used as parameter names The table below shows the mapping between SOAP types and LME type
368. rror mes sage and the computation is aborted With more arguments error use the first argument as a format string and displays remaining argu ments accordingly like fprintf In a try block error str throws a user error without displaying anything An error identifier may be added in front of other arguments It is a string made of at least two segments separated by semicolons Each segment has the same syntax as variable or function name i e it begins with a letter or an underscore and it continues with letters digits and underscores The identifier can be retrieved with Lasterr or Lasterror in the catch part of a try catch construct and helps to identify the error For errors thrown by LME built in functions the first segment is always LME Examples error Invalid argument Invalid argument o ground error robot hit The robot is going to hit s o The robot is going to hit ground 92 LMEPPC User Manual 1999 2008 Calerga Sarl lasterror message The robot is going to hit ground identifier robot hit See also eval Evaluate the contents of a string as an expression or statements Syntax x eval str_expression eval str_statement Description If eval has output argument s the input argument is evaluated as an expression whose result s is returned Without output arguments the input argument is evaluated as statement s eval can evaluate and assign to existing
369. rs where the name is a string which must match exactly the names in the table below Case is significant Options which are not specified have a default value The result is a structure whose fields correspond to each option Without any input argument xmlrpccallset creates a structure with all the default options Note that xmlrpccall also interpret the lack of an option 592 LMEPPC User Manual 1999 2008 Calerga Sarl argument or the empty array as a request to use the default values When its first input argument is a structure xmLrpccallset adds or changes fields which correspond to the name value pairs which follow Here is the list of permissible options Name Default Meaning Server oy server name or IP address Port 80 port number Timeout 10 maximum time in seconds Debug false true to display data If the server is an empty string it is replaced with localhost The Debug field is not included in the default options when set it causes the display of the request and responses Example Default options xmlrpccallset Server 7 Port 80 Timeout 10 See also xmlrpccall xmIirpcreadcall Decode an XML RPC call request Syntax method arglist url xmlrpcreadcall fd method arglist url xmlrpcreadcall str Description xmlrpcreadcall fd where fd is a file descriptor reads a complete XML RPC call decodes it and returns the result in three output argu ments the method name as a string a
370. rue which does not mean that a connection has been correctly established on the World Wide Web The current implementation uses the method openURL of the App Kit framework on the Macintosh and ShellExecute on Windows On Windows the URL must begin with http ftp gopher nntp news mailto or file On Linux the first application in the following list which is found in the current path is executed X11BROWSER BROWSER environment variables htmlview firefox mozilla netscape opera konqueror Launchurl always returns true Example if Launchurl http www calerga com dialog Cannot Launch http www calerga com end 6 11 Download URL This section describes a function which downloads data from the WWW urldownload Launch a URL in the default browser Syntax contents urldownload url 582 LMEPPC User Manual 1999 2008 Calerga Sarl Description urldownload url downloads data referenced by a URL The result is typically an HTML document or a data file such as an image Both input and output arguments are strings urldownload url query submits a query with the GET method and downloads the result The URL should use the HTTP or HTTPS protocol urldownload url query method query with the specified method get or post and downloads the result Example data urldownload http www w3 org 6 12 Web Services This section describes functions which implement the
371. rwise Examples isquaternion 2 false isquaternion quaternion 2 true 316 LMEPPC User Manual 1999 2008 Calerga Sarl See also quaternion isnumeric q2mat Conversion from quaternion to rotation matrix Syntax R q2mat q Description R q2mat q gives the 3x3 orthogonal matrix R corresponding to the rotation given by scalar quaternion q For a vector a x y z and its representation as a pure quaternion aq quaternion x y z the rotation can be performed with quaternion multiplication bq q aq q or matrix multiplication b Rxa Input argument q does not have to be normalized a quaternion cor responding to a given rotation is defined up to a multiplicative factor Example rpy2q 0 1 0 3 0 2 q2mat q R 0 9363 0 1688 0 3080 0 1898 0 9810 0 0954 0 2955 0 0954 0 9506 aq quaternion 1 2 3 qxaq q 5228i 2 0336j 2 7469k 1 2 3 a q R a R See also q2rpy rpy2q q2rpy Conversion from quaternion to attitude angles LME Reference Quaternions 317 Syntax pitch roll yaw q2rpy q Description q2rpy q gives the pitch roll and yaw angles corresponding to the rotation given by quaternion q It is the inverse of rpy2q All angles are given in radians If the input argument is a quaternion array the results are arrays of the same size conversion from quaternion to angles is performed independently on corresponding elements See also rpy2q q2str Conversi
372. s SOAP LME xsd int int32 scalar xsd boolean logical scalar xsd string character 1 by n array xsd double real double scalar xsd timelnstant 1 by 6 1 by 7 or 1 by 8 double array SOAP ENC base64 1 by n uint8 array structure structure SOAP ENC array list In LME time instants are stored as a row vector of 6 7 or 8 el ements which contains the year month day hour minute second time zone hour and time zone minute the time zone is optional Ar 584 LMEPPC User Manual 1999 2008 Calerga Sarl rays which are declared with a single type xsd int xsd boolean or xsd double are mapped to LME row vectors of the corresponding class The two main functions for performing a SOAP call are soapcall and soapcallset soapcall Perform a SOAP remote procedure call Syntax response soapcall url method ns action opt response soapcall url method ns action opt param Description soapcall url method ns action opt param calls a remote proce dure using the SOAP protocol url a string is either the complete URL beginning with http or only the absolute path in the second case the server address and port come from argument opt method is the SOAP method name as a string ns is its XML name space action is the SOAP action opt is a structure which contains the options it is typically created with soapcallset or can be the empty array for the default options param if present is a structure which contains
373. s ongint i e integer numbers with an arbitrary number of digits limited only by the memory available Some LME functions have been overloaded new definitions have been added and are used when at least one of their arguments is of type longint These functions are listed in the table below LME Operator Purpose abs absolute value char conversion to string disp display double conversion to floating point gcd greatest common divisor lcm least common multiple minus subtraction mldivide left division mpower power mrdivide right division mtimes multiplication plus addition rem remainder uminus negation uplus no operation longint Creation of a long integer Extensions memory mapping 559 ongint i ongint str Description Longint i creates a long integer from a native LME floating point number Longint str creates a long integer from a string of decimal digits Examples Longint 1234567890 1234567890 Longint 2 100 1267650600228229401496703205376 13th Mersenne prime Longint 2 521 1 6864797660130609714981900799081393217269 4353001433054093944634591855431833976560 5212255964066145455497729631139148085803 7121987999716643812574028291115057151 Number of decimal digits in the 27th Mersenne prime Length char longint 2 44497 1 13395 6 2 Memory Mapping This section describes functions which offer support for file memory mapping Once a file is mapped in memory
374. s given as zeros poles and gain if there are three output arguments or as numerator and denominator coefficient vectors if there are two output arguments besself n w where w0 is a scalar gives a nth order digital low pass filter with a cutoff frequency of w0 relatively to half the sampling frequency besself n wl wh where the second input argument is a vector of two numbers gives a 2nth order digital bandpass filter with pass band between wl and wh relatively to half the sampling frequency besself n w0 high gives a nth order digital highpass filter with a cutoff frequency of w0 relatively to half the sampling frequency besself n wl wh stop where the second input argument is a vector of two numbers gives a 2nth order digital bandstop filter with stopband between wl and wh relatively to half the sampling frequency With an additional input argument which is the string s besself gives an analog Bessel filter Frequencies are given in rad s See also bilinear Analog to digital conversion with bilinear transformation Syntax use filter zd pd kd bilinear zc pc kc fs numd dend bilinear numc denc fs Description bilinear zc pc kc fs converts the analog continuous time transfer function given by its zeros zc poles pc and gain kc to a digital discrete time transfer function given by its zeros poles and gain in the domain of the forward shift operator q The sampling frequency is
375. s of the command line window or panel clc fd clears the contents of the window or panel associated with file descriptor fd disp Simple display on the standard output Syntax disp obj Description disp obj displays the object obj Command format may be used to control how numbers are formatted Example disp hello hello LME Reference input output 355 See also format fprintt fclose Close a file Syntax fclose fd fclose all Description fclose fd closes the file descriptor fd which was obtained with functions such as fopen Then fd should not be used anymore fclose all closes all the open file descriptors feof Check end of file status Syntax b feof fd Description feof fd is false if more data can be read from file descriptor fd and true if the end of the file has been reached Example Count the number of lines and characters in a file fopen and fclose are not available in all LME applications fd fopen data txt lines 0 characters 0 while feof fd str fgets fd lines lines 1 characters characters length str end fclose fd 356 LMEPPC User Manual 1999 2008 Calerga Sarl See also ftell fflush Flush the input and output buffers Syntax fflush fd Description fflush fd discards all the data in the input buffer and forces data out of the output buffer when the device and their driver permits i
376. s uab are fed to inputs ina of a and inb of b inputs ua are fed to the remaining inputs of a and ub to the remaining inputs of b Similarly outputs yab are the sum of outputs outa of a and outputs outb of b and ya and yb are the remaining outputs of a and b respectively See also Lti series Iti plus System sum Syntax use lti c at b c plus a b Description a b computes the system whose inputs are fed to both a and b and whose outputs are the sum of the outputs of a and b If a and b are transfer functions or matrices of transfer functions this is equivalent to a sum of matrices Libraries lti 535 See also Lti parallel lti minus Iti series Series connection Syntax use lti c series a b C series a b outa inb Description series a b connects the outputs of lti object a to the inputs of lti object b series a b outa inb connects outputs outa of a to inputs inb of b Unconnected outputs of a and inputs of b are discarded See also ti mtimes lti paralle Iti repmat Replicate a system Syntax use lti b repmat a n b repmat a m n b repmat a m n Description repmat a n when ais a transfer function or a matrix of transfer func tions creates a new system described by a matrix of transfer functions where a is repeated n times horizontally and vertically If a is a state space system matrices B C and D are replicated to obtain the same effect
377. samples scrolling on the screen If you forget it interrupt the execution by pressing the selection button of your handheld snd audiorecord 1 The samples are stored as an array of two columns one for the left channel one for the right They can be played back audioplay snd There are probably simpler ways to record audio on a Pocket PC device But with LME you can manipulate the samples easily For instance you can play them backward by flipping the array upside down audioplay flipud snd To learn more about LME you can follow the LME tutorial 1 5 User preferences You can customize the way LME is working in the dialog displayed with the menu Tools gt Options Here is a description of the options Memory Amount of memory reserved for LME variables programs and data used for executing code Evaluate assert In LME programs the assert function can help in reporting errors during development If this option is off the eval uation of assert is skipped which can provide slightly improved performance Usually you should switch it on during development and off when using functions whose you trust the quality Load extensions Extensions are files which provide additional functions to LME Unlike functions written in the LME programming language extensions are compiled to native machine code so they are very fast and they have access to all the features of the operat ing system LME is provided with several exte
378. se otherwise Examples isfield struct a 1 3 x abc x true isfield struct a 1 3 x abc X false See also jusstruct struct isstruct Test for a structure object Syntax b isstruct obj LME Reference structures 329 Description isstruct obj is true if the object obj is a structure false otherwise Structures are lists whose at least one field has a name Examples isstruct struct a 123 true isstruct 1 2 x false a f 3 isstruct a true See also orderfields Reorders the fields of a structure Syntax strctout orderfields strctin strctout orderfields strctin structref strctout orderfields strctin names strctout orderfields strctin perm strctout perm orderfields Description With a single input argument orderfields strctin reorders struc ture fields by sorting them by field names With two input arguments orderfields reorders the fields of the first argument after the second argument Second argument can be a permutation vector containing integers from 1 to Llength strctin another structure with the same field names or a list of names In the last cases all the fields of the structure must be present in the second argument The first output argument is a structure with the same fields and the same value as the first input argument the only difference is the field order An op
379. second ampere The following statement makes available constants defined in constants use constants The following constants are defined 556 Name avogadro_number boltzmann_constant earth_mass earth_radius electron_charge electron_mass faraday_constant gravitational_constant gravity_acceleration hubble_constant ice_point induction_constant molar_gaz_constant molar_volume muon_mass neutron_mass plank_constant plank_constant_reduced plank_mass proton_mass solar_radius speed_of_light speed_of_sound stefan_boltzmann_constant vacuum_permittivity Value 6 0221367e23 1 380658e 23 5 97370e24 6 378140e6 1 60217733e 19 9 1093897e 31 9 6485309e4 6 672659e 11 9 80655 3 2e 18 273 15 1 256e 6 8 314510 22 41410e 3 1 8835327e 28 1 6749286e 27 6 6260755e 34 1 0545727e 34 2 17671e 8 1 6726231e 27 6 9599e8 299792458 340 29205 5 67051e 8 8 854187817e 12 LMEPPC User Manual 1999 2008 Calerga Sarl Unit 1 mole J K Vs Am J K mole m 3 mole kg kg Js Js kg kg m m s m s W m 2 K 4 As Vm Chapter 6 Extensions Extensions are additional functions usually developed in C or Fortran which extend the core functionality of LME Extensions are grouped in so called dynamically linked libraries DLL files At startup LME loads all extensions it finds in the folder LMEExt in the same location as the LME program file Each extension initializes itself and usually displays a line of info
380. sed loop frequency response The optional argument specifies the style The whole grid is displayed only if the user selects it in the Grid menu or after the command plotoption fullgrid By default only the lines corresponding to unit magnitude and to a phase equal to m 1 2k with integer k are displayed The whole grid is made of the lines corresponding to a closed loop magnitude of 12 6 3 0 3 6 and 12 dB 442 LMEPPC User Manual 1999 2008 Calerga Sarl Example ngrid nichols 7 1 3 See also plotoption nichols Nichols diagram of a continuous time system Syntax nichols numc denc nichols numc denc w nichols numc denc opt nichols numc denc w opt nichols style nichols style id w nichols mag phase nichols mag phase w nichols Description nichols numc denc displays the Nichols diagram of the continuous time transfer function given by polynomials numc and denc In con tinuous time the Nichols diagram is the locus of the complex val ues of the transfer function evaluated at jw where w is real posi tive displayed in the phase magnitude plane Usually the magnitude is displayed with a logarithmic or dB scale use scale lindb or scale Uinlog Lindb before nichols The range of frequencies is selected automatically or can be speci fied in an optional argument w a vector of frequencies Further options can be provided in a struct
381. see Fig 3 23 The style argument has its usual meaning With two or three arguments sgrid plots only the lines for the specified values of damping and natural frequency Let p and p be the complex conjugate roots of the polynomial s 2w s w where w is the natural frequency and lt 1 the damping The locus of roots 450 LMEPPC User Manual 1999 2008 Calerga Sarl scale equal 2 2 2 2 sgrid 2 Figure 3 23 scale equal 2 2 2 2 sgrid with a constant damping is generated by Imp y 1 Re p with Rep lt 0 The locus of roots with a constant natural frequency w is a circle of radius w The whole grid is displayed only if the user selects it in the Grid menu or after the command plotoption fullgrid By default only the imaginary axis the stability limit is displayed Example Typical use for poles or zeros displayed in the s plane scale equal sgrid plotroots pol See also plotoption sigma Singular value plot for a continuous time state space model LME Reference graphics for dynamical systems 451 Syntax sigma Ac Bc Cc Dc sigma Ac Bc Cc Dc w Sigma Ac Bc Cc Dc opt Sigma Ac Bc Cc Dc w opt sigma style sigma style id sv w Sigma Description Sigma Ac Bc Cc Dc plots the singular values of the frequency re sponse of the continuous time state space model Ac Bc Cc Dc de fined as jwX jw AcX jw BcU jw
382. shape q and scale A F f deg of freedom v and v2 lognormal logn mean 0 and st dev 1 normal norm mean 0 and st dev 1 Student s T t deg of freedom v uniform unif limits of the range 0 and 1 See also cdf pd imag Imaginary part of a complex number Syntax im imag z Description imag z is the imaginary part of the complex number z or 0 if z is real 174 LMEPPC User Manual 1999 2008 Calerga Sarl Examples imag 1 2 2 imag 1 0 See also inf Infinity Syntax x inf x Inf x inf n x inf nl1 n2 x inf nl1 n2 x inf type Description inf is the number which represents infinity Most mathematical func tions accept infinity as input argument and yield an infinite result if appropriate Infinity and minus infinity are two different quantities With integer non negative arguments inf creates arrays whose elements are infinity Arguments are interpreted the same way as zeros and ones The last argument of inf can be a string to specify the type of the result double for double precision default or single for single precision Examples 1 inf 0 inf inf See also LME Reference mathematical functions 175 isfinite Test for finiteness Syntax b isfinite x Description isfinite x is true if the input argument is a finite number neither infinite nor nan and false otherwise The result is performed on each e
383. signed 32 bit integer 2147483648 lt x lt 2147483647 int64 signed 64 bit integer 9 223372e18 lt x lt 9 223372e18 uint8 unsigned 8 bit integer 0 lt x lt 255 uchar unsigned 8 bit integer 0 lt x lt 255 uint16 unsigned 16 bit integer 0 lt x lt 65535 uint32 unsigned 32 bit integer 0 lt x lt 4294967295 uint64 unsigned 64 bit integer 0 lt x lt 18 446744e18 single 32 bit IEEE floating point double 64 bit IEEE floating point By default multibyte words are encoded with the least significant byte first little endian The characters b can be appended to spec ify that they are encoded with the most significant byte first big en dian for symmetry U is accepted and ignored By default the output is a double array To get an output which has the same type as what is specified by precision the character can be inserted at the beginning For instance uint8 reads bytes and stores them in an array of class uint8 int32 b reads signed 32 bit words and stores them in an array of class int32 after performing byte swapping if necessary and char reads bytes and stores them in a character row vector i e a plain string See also fscanf Reading of formatted numbers Syntax r fscanf fd format r count fscanf fd format LME Reference input output 361 Description A single line is read from a text file and numbers characters and strings are deco
384. sity function Syntax pdf distribution x pdf distribution x al pdf distribution x al a2 y y y Description pdf distribution x gives the probability of a density function The distribution is specified with the first argument a string case is ig nored t and T are equivalent Additional arguments must be pro vided for some distributions See cdf for the list of distributions See also cdf pi Constant Tr Syntax x pi Description pi is the number r up to the precision of its floating point represen tation Example exp 1j pi 1 LME Reference mathematical functions 185 See also real Real part of a complex number Syntax re real z Description real z is the real part of the complex number z or z if z is real Examples real 1 2j 1 real 1 1 See also reallog Real natural base e logarithm Syntax y reallog x Description reallog x gives the real natural logarithm of x It is the inverse of exp for real numbers The imaginary part of x is ignored The result is NaN if x is negative Example reallog 1 0 1 10 1 2j nan inf 0 2 3026 0 186 LMEPPC User Manual 1999 2008 Calerga Sarl See also realmax realmin Largest and smallest real numbers Syntax realmax realmax n realmax n1 n2 realmax nl1 n2 realmax type realmin realmin x x KK KK XK tou ud id ud oueou Desc
385. so dbstop dbtype dbstep Execute a line of instructions Syntax dbstep dbstep in dbstep out Description When normal execution is suspended after a breakpoint set with dbstop or the execution of function dbhalt dbstep issued from the command line executes the next line of the suspended function If the line is the last one of the function execution resumes in the calling function dbstep in has the same effect as dbstep except if a subfunction is called In this case execution is suspended at the beginning of the subfunction dbstep out resumes execution in the current function and sus pends it in the calling function 80 LMEPPC User Manual 1999 2008 Calerga Sarl Example Load library stdlib and put a breakpoint at the beginning of function linspace use stdlib dbstop linspace Start execution of function Linspace until the breakpoint is reached the next line to be executed is displayed v Linspace 1 2 5 lt lLinspace 8 gt if nargin lt 3 When the execution is suspended any function can be called Local variables of the function can be accessed and changed but no new variable can be created Here the list of variables and the value of x2 are displayed info v r not defined x1 1x1 x2 1x1 n 1x1 x2 X2 2 Display the stack of function calls dbstack stdlib linspace 8 Execute next line dbstep lt linspace 11 gt r xl x2 x1 x O n 1 n 1 Execute last line
386. sponding function e g 2int16 is the same as int16 2 except when the integer num ber cannot be represented with a double then the number is rounded to the nearest value which can be represented with a double Compare the expressions below Expression Value uint64 123456789012345678 123456789012345696 123456789012345678uint64 123456789012345678 Literal complex numbers are written as the sum or difference of a real number and an imaginary number Literal imaginary numbers are written as double numbers with an i or j suffix like 2i 3 7e5j or Oxffj Functions i and j can also be used when there are no variables of the same name but should be avoided for safety reasons The suffices for single and imaginary can be combined as isingle or jsingLe in this order only 2jsingle 3single 4isingle Command format is used to specify how numbers are displayed Strings Strings are stored as arrays usually row vectors of 16 bit unsigned numbers Literal strings are enclosed in single quotes Example of string The second string is empty For special characters the following es cape sequences are recognized 34 LMEPPC User Manual 1999 2008 Calerga Sarl Character Escape seq Character code Null 0 0 Bell a 7 Backspace b 8 Horizontal tab t 9 Line feed n 10 Vertical tab v 11 Form feed f 12 Carriage return r 13 Single tick V 39 Single tick two 39 Backslash 92 Hexadecimal number xhh hh
387. ss one of them is an empty matrix Outside brackets the comma is used to separate statements they loose any meaning between parenthesis and give a syntax error vertcat M1 M2 is equivalent to M1 M2 It can be used to rede fine this operator for objects Between braces the semicolon separates rows of cells Examples 1 2 1 2 1 5 3 2 4 5 1 12345 32451 LME Reference operators 141 abc def abc def See also operator operator Operator Range Syntax x1 x2 x1l step x2 colon x1 x2 colon x1 step x2 Description x1 x2 gives a row vector with the elements x1 x1 1 x1 2 etc until x2 The last element is equal to x2 only if x2 x1 is an integer and smaller otherwise If x2 lt x1 the result is an empty matrix x1 step x2 gives a row vector with the elements x1 x1 step x1 2 step etc until x2 The last element is equal to x2 only if x2 x1 step is an integer With fractional numbers rounding er rors may cause x2 to be discarded even if x2 x1 step is almost an integer If x2 sign step lt x1l sign step the result is an empty matrix If x1 or step is complex a complex vector is produced with the expected contents The following algorithm is used to generate each element z xl while real z x1 x2 x1 lt 1 add z to the vector z Z step end This algorithm is robust enough to stop even if x2 is not on the complex straight line defined by x1 and ste
388. ssing the Select hardware button when the command field is empty to see the command All fragments are stored in the XML file Imecodefragments xml To see or edit its contents you can use a text editor or open it in a browser which supports CSS2 style sheets 1 4 First steps Here are some commands you Can try 1 2 3 Simple expressions follow the standard syntax found in many comput ing languages if they are not followed by a semicolon the result is displayed To permit you to chain computations easily LME stores the anony mous result of expressions into the variable ans which you can reuse in the next expression ans sin pi 3 To keep multiple results you can assign them to other variables x 5 Operators and functions also support complex numbers and matrices This will compute the complex eigenvalues of a 2 by 2 matrix In addition to numerical results LME can display graphics fplot plots a function inline in the example below over some range fun inline x 0 3 2 7 exp 3 x 2 fplot fun 2 3 10 LMEPPC User Manual 1999 2008 Calerga Sarl To clear the figure use clf You can switch manually between graphics and text output with the View menu LME also supports audio input and output provided the hardware it runs on does We begin by recording one second of audio samples in an array Say something after you tap the Execute button The semicolon is important here we do not want to see 88100
389. sy isn t it Some control characters have a special representation For example the line feed used in LME as an end of line character is n gt Hello nWorld ans Hello World Strings are actually matrices of characters You can use commas and semicolons to build larger strings gt a bc de f ans abc def 2 6 Variables You can store the result of an expression into what is called a variable You can have as many variables as you want and the memory permits Each variable has a name to retrieve the value it contains You can change the value of a variable as often as you want gt a s 3s gt a 5 ans 8 gt a 4 gt a 5 ans 9 Note that a command terminated by a semicolon does not display its result To see the result remove the semicolon or use a comma if you have several commands on the same line Implicit assignment to variable ans is not performed when you assign to another variable or when you just display the contents of a variable Tutorial 21 gt a 3 a 3 gt a 7 b 3 2x gt x a a 7 b 17 2 7 Loops and Conditional Execution To repeat the execution of some commands you can use either a for end block or a while end block With for you use a variable as a counter gt for i 1 3 i end With while the commands are repeated as long as some expression is true gt i 1 while i lt 10 i 2 x i end i You can choose to execute some comma
390. t Syntax digest md5 strb digest md5 fd Description md5 strb calculates the MD5 digest of strb which represents binary data strb can be a string only the least significant byte of each character is considered or an array of bytes of class uint8 or ints The result is a string of 32 hexadecimal digits It is believed to be hard to create the input to get a given digest or to create two inputs with the same digest md5 fd calculates the MD5 digest of the bytes read from file de scriptor fd until the end of the file The file is left open MD5 digest is an Internet standard described in RFC 1321 Examples MD5 of the three characters a b and c md5 abc 900150983cd24fb0d6963f7d28e17Ff72 This can be compared to the result of the command tool md5 found on many unix systems echo n abc md5 900150983cd24fb0d6963f7d28e17F72 The following statements calculate the digest of the file somefile fd fopen somefile digest md5 fd fclose fd 306 LMEPPC User Manual 1999 2008 Calerga Sarl See also setstr Conversion of an array to a string Syntax str setstr A Description setstr A converts the elements of array A to characters resulting in a string of the same size Characters are stored in unsigned 16 bit words Example setstr 65 75 ABCDEFGHIJK See also shal Calculate SHA1 digest Syntax digest shal strb digest shal fd Description
391. t fflush can be useful to recover from errors fgetl Reading of a single line Syntax line fgetl fd line fgetl fd n Description A single line of at most n characters is read from a text file The end of line character is discarded Upon end of file fgetl gives an empty string See also fgets Reading of a single line Syntax line fgets fd line fgets fd n LME Reference input output 357 Description A single line of at most n characters is read from a text file Unless the end of file is encountered before the end of line always a single line feed is preserved Upon end of file fgets gives an empty string See also fgetl fscanf format Default output format Syntax format format short format short e format short eng format short g format long format long e format long eng format long g format int format int format int format int format int format int format bank format format i format j format loose format compact TOxXxSCE Description format changes the format used by command disp and for output produced with expressions which do not end with a semicolon The following arguments are recognized 358 Arguments none short short e short eng short g long long e long eng long g int int int int int int bank i j loose compact ToxKxca LMEPPC User Manual 1999 2008 Calerga Sarl Meaning fixed format with 0 or 4 dig
392. t toeplitz gives a symmetric square matrix Example use stdlib toeplitz 1 1 2 ENWASA 2 1 3 2 See also trapz Numerical integration with trapezoidal approximation Syntax use stdlib S trapz Y S trapz X Y S trapz X Y dim 480 LMEPPC User Manual 1999 2008 Calerga Sarl Description trapz Y calculates an approximation of the integral of a function given by the samples in Y with unit intervals The trapezoidal approxi mation is used If Y is an array integration is performed along the first non singleton dimension trapz X Y specifies the location of the samples A third argument may be used to specify along which dimension the integration is per formed Example use stdlib trapz 2 3 5 6 5 trapz 1 2 5 2 3 5 14 5 See also 5 2 stat stat is a library which adds to LME advanced statistical functions The following statement makes available functions defined in stat use stat bootstrp Bootstrap estimate Syntax use stat stats samples bootstrp n fun D1 Description bootstrp n fun D picks random observations from the rows of ma trix or column vector D to form n sets which have all the same size as D then it applies function fun a function name or reference or an inline function to each set and returns the results in the columns of stats Up to three different set of data can be provided Libraries stat 481 bootstrp gives an idea of the r
393. t and output arguments which can be retrieved by the called function with nargin and nargout respec tively The unused input arguments from nargin 1 to the last one are undefined unless a default value is provided in the function defi nition with the definition function f x y 2 y is 2 when f is called with a single input argument The unused output arguments from nargout 1 to the last one do not have to be set but may be To redefine an operator which is especially useful for object meth ods see below use the equivalent function such as plus for operator The complete list is given in the section about operators To define a method which is executed when one of the input argu ments is an object of class class or a child in the classes hierarchy add class before the method function name To call it use only the method name not the class name Examples Function with optional input and output arguments function Sum Prod calcSumAndProd x y if nargout 0 return nothing to be computed end if nargin make something to be computed x 0 end if nargin lt 1 sum of elements of x Sum sum x else sum of x and y Sum X y end if nargout also compute the product 66 LMEPPC User Manual 1999 2008 Calerga Sarl if nargin 1 product of elements of x Prod prod x else product of x and y Prod x y end end Two equivalent definitions function S area
394. t any output See also xml rpcwriteresponse xmlrpcreadresponse xmIirpcwriteresponse Encode an XML RPC call response Syntax xmlrpcwriteresponse fd value xml rpcwriteresponse value str xmlrpcwriteresponse value Description xmLrpcwriteresponse fd value writes to file descriptor fd a com plete XML RPC response including the HTTP header If fd is missing the response is written to standard output file descriptor 1 since the output contains carriage return characters it may not be displayed correctly on all platforms The value argument is the result of the call With an output argument xmlrpcwriteresponse returns the re sponse as a string without any output Extensions serial 597 Example xmlrpcwriteresponse 123 HTTP 1 1 200 OK Connection close Server LME 4 5 Content Length 123 Content Type text xml lt xml version 1 0 gt lt methodResponse gt lt params gt lt param gt lt double gt 123 lt double gt lt param gt lt params gt lt methodResponse gt See also xmLrpcwritecall xmlrpcreadresponse xmlrpcreadcall 6 13 Serial port Serial port functions enable communication with devices connected to the computer via an RS 232 interface Such devices include modems printers and many scientific instruments The operating system can also emulate RS 232 connections with other devices such as built in modems or USB Universal Serial Bus devices Functions described in
395. t division are not commuta tive Matrix operations are not supported operators and are defined as a convenience they are equivalent to and respectively and work only element wise with scalar arguments Mathematical functions below accept quaternions as arguments with arrays of quaternions they are applied to each element sepa rately 314 LMEPPC User Manual 1999 2008 Calerga Sarl Function Purpose abs absolute value conj conjugate cos cosine exp exponential log natural logarithm real real part sign quaternion sign normalization sin sine sqrt square root Functions below performs computations on arrays of quaternions Function Purpose cumsum cumulative sum diff differences double conversion to array of double mean arithmetic mean sum sum Functions below are related to array size Function Purpose beginning first subscript cat array concatenation end last subscript flipdim flip array fliplr flip left right flipud flip upside down ipermute dimension inverse permutation isempty test for empty array length length of vector ndims number of dimensions numel number of elements permute dimension permutation repmat array replication reshape array reshaping rot90 array rotation size array size squeeze remove singleton dimensions Finally functions below are related to output and assignment LME Reference Quaternions 315 Function Purpose disp display d
396. t scaled at all u and v give directly the absolute value of the vectors With a 6th or 4th string argument quiver style uses the specified style to draw the arrows Example Force field complex numbers are used to simplify computation scale equal z fevalx plus 5 0 5 5 1lj 5 0 5 5 z0 0 2 0 3j 1 20 sign z z0 max abs z z0 2 3 real z imag z real f imag f uiver x y u v f x y u v q See also scale Set the scale Syntax scale xmin xmax ymin ymax scale xmin xmax scale xmin xmax ymin ymax zmin zmax LME Reference base graphics 399 scale features scale features usersettablefeatures scale features xmin xmax ymin ymax scale features usersettablefeatures xmin xmax ymin ymax sc scale Description Without output argument the scale command which should be placed before any other graphical command sets the scale and scale options The last parameter contains the limits of the plot either for both x and y axis or only for the x axis in 2D graphics or for x y and z axis for 3D graphics The limits are used only if the user has not changed them by zooming The first parameter s specify some properties of the scale and which one can be changed by the user There are two ways to specify them with a string or with one or two integer numbers The recom mended way is with a string The list below enumerates the possible valu
397. t the ticks and labels are changed as if the graphical data had been scaled by the factor For 402 LMEPPC User Manual 1999 2008 Calerga Sarl instance you can plot data in radians the standard angle unit in LME and display ticks and labels in degrees by using a factor of 180 pi With an output argument scalefactor gives the current factors as a 2 elements vector Example Display the sine with a scale in degrees phi 0 0 01 2 pi plot phi sin phi scalefactor 180 pi 1 See also text Display text in a figure Syntax text x y string text x y string justification text font Description With three arguments text x y string displays a string centered at the specified position An optional fourth argument specifies how the string should be aligned with respect to the position x y Itisa string of one or two characters from the following set Char Alignment c Center may be omitted Left r Right t Top b Bottom For instance l means that the string is displayed to the right of the given position and is centered vertically and rt that the string is to the bottom left of the given position An optional trailing argument specifies the font size type face and color to use It is a structure which is typically created with fontset LME Reference 3D graphics 403 Examples A line is drawn between 1 1 and 1 1 with labels at both ends plot 1 1 1 1 te
398. t to the real axis The range of frequencies is selected automatically or can be speci fied in an optional argument w a vector of frequencies Further options can be provided in a structure opt created with responseset fields Delay NegFreq and Range are utilized The op tional arguments style and id have their usual meaning With output arguments nyquist gives the real and imaginary parts of the frequency response and the frequency as column vectors No display is produced In Sysquake when the mouse is over a Nyquist diagram in addition to the complex value which can be retrieved with _z0 or _x0 and _y0 the frequency is obtained in _q Example Nyquist diagram of a third order system see Fig 3 21 scale equal hgrid nyquist 20 poly 1 2 1j 2 1j See also plotroots Roots plot Syntax plotroots pol plotroots pol style plotroots pol style id LME Reference graphics for dynamical systems 445 scale equal nyquist 1 1 3 Figure 3 21 scale equal nyquist 1 1 2 3 Description plotroots pol displays the roots of the polynomial pol in the com plex plane If this argument is a matrix each line corresponds to a different polynomial The default style is crosses it can be changed with a second argument Example scale equal plotroots den x plotroots num o See also responseset Options for frequency responses Syntax options responseset options resp
399. t64 2 uint8 P a ress 549 ulawexpand uminus union 270 613 unique ones a uplus upper urldownload 581 use 74 useifexists 74 ut f8decode 311 ut f8encode 311 var bs varargin varargout eee vertcat 114 voronoi 278 voronoin wa sin goa wavread wavwrite 551 weekday which while 75 xmlrpccalt xmlrpccallset 591 xmlrpcreadcalt xml rpcreadresponse xmlrpcwritecall xmlrpcwritedata xmlrpcwritefault xmlrpcwriteresponse xor zeros 272 zgrid zread zscore 490 zwrite 564
400. tax Y swapbytes X Description swapbytes X swaps the bytes representing number X If X is an array each number is swapped separately The imaginary part if any is discarded X can be of any numerical type swapbytes is its own inverse for real numbers Example swapbytes luint32 16777216uint32 See also typecast cast tan Tangent Syntax y tan x Description tan x gives the tangent of x which is complex if x is complex Example tan 2 2 185 194 LMEPPC User Manual 1999 2008 Calerga Sarl See also atan tanh tanh Hyperbolic tangent Syntax y tanh x Description tanh x gives the hyperbolic tangent of x which is complex if x is complex Example tanh 2 0 964 See also atanh tan typecast Type conversion with same binary representation Syntax Y typecast X type Description typecast X type changes the numeric array X to the type given by string type which can be double single int8 or any other signed or unsigned integer type char or logical The binary representation in memory is preserved The imaginary part if any is discarded Depending on the conversion the number of elements is changed so that the array size in bytes in preserved The result is a row vector if X is a scalar or a row vector or a column vector otherwise The result depends on the computer architecture LME Reference linear algeb
401. tax zread fd n zread fd data nin data nin Description zread fd n reads up to n bytes from file descriptor fd uncom presses them using the inflate algorithm and returns the result as a row vector of type uint8 An optional second output argument is set to the number of bytes which have actually been read it is less than n if the end of file is reached With a single input argument zread fd reads data until the end of the file Note that you must read a whole segment of deflated data with one call Inflation is restarted every time zread is called See also 564 LMEPPC User Manual 1999 2008 Calerga Sarl zwrite Compress a sequence of bytes and write the result Syntax nout zwrite fd data Description zwrite fd data compresses the array data of type int8 or uint8 and writes the result to the file descriptor fd Note that you must write a whole segment of data with one call Deflation is restarted every time zwrite is called See also 6 4 Image Files This section describes functions which offer support for reading and writing image files Formats supported include PNG and JPEG Calerga gratefully acknowledges the following contributions PNG encoding and decoding are based on libpng and JPEG encoding and decoding are based on the work of the Independent JPEG Group imageread Read an image file Syntax A imageread fd Description imageread fd reads a PNG or JPEG file fr
402. tax x rank M x rank M e LME Reference linear algebra 233 Description rank M returns the rank of matrix M i e the number of lines or columns linearly independent To obtain it the singular values are computed and the number of values significantly larger than O is counted The value below which they are considered to be 0 can be specified with the optional second argument Examples rank 1 1 0 0 1 rank 1 1 0 1j 2 See also roots Roots of a polynomial Syntax r r r roots pol roots M roots M dim Description roots pol calculates the roots of the polynomial pol The polyno mial is given by the vector of its coefficients highest power first while the result is a column vector With a matrix as argument roots M calculates the roots of the polynomials corresponding to each column of M An optional second argument is used to specify in which dimension roots operates 1 for columns 2 for rows The roots of the i th polynomial are in the i th column of the result whatever the value of dim is Examples roots 1 0 1 1 1 roots 1 0 1 234 LMEPPC User Manual 1999 2008 Calerga Sarl 1 1 roots 1 1 0 5 1 6 1 2 1 3 roots 1 0 1 2 See also schur Schur factorization Syntax U T schur A T schur A U T schur A c T schur A c Description schur A computes the Schur factorization of square matr
403. te a ratfun object Syntax use classes y feval a x Description feval a x evaluates ratfun a for the value of x If x is a vector ora matrix the evaluation is performed separately on each element and the result has the same size as x 500 LMEPPC User Manual 1999 2008 Calerga Sarl Example use classes r ratfun 1 3 0 1 2 5 y feval r 1 5 0 7143 2 3333 5 0000 8 6923 13 4000 See also ratfun ratfun Teval 5 4 ratio Library ratio implements the constructors and methods of class ratio for rational numbers It is based on long integers so that the precision is limited only by available memory Basic arithmetic operators and functions are overloaded to support expressions with the same syntax as for numbers The following statement makes available functions defined in ratio use ratio ratio ratio Ratio object constructor Syntax use ratio r ratio r ratio n r ratio num den r ratio r Description ratio num den creates a rational fraction object whose value is num den Arguments num and den may be double integer numbers or longint Common factors are canceled out With one numeric input argument ratio n creates a rational fraction whose denominator is 1 Without input argument ratio creates a rational number whose value is 0 With one input argument which is already a ratio object ratio returns it without change Libraries ratio 501 The following operators and functions m
404. tep dbodemag erlocus dbodephase hgrid dimpulse hstep dinitial impulse dlsim initial dnichols lsim dnyquist ngrid Scaling and labels label plotoption Legend scale 3D contour3 plot3 line3 plotpoly mesh sensor3 3D scaling and lighting camdolly camroll camorbit camtarget campan camup campos camva camproj camzoom nyquist nyquist plotroots rlocus sgrid sigma step zgrid scalefactor title surf daspect Llightangle material 376 LMEPPC User Manual 1999 2008 Calerga Sarl 3 33 Remarks on graphics Most functions which produce the display of graphical data accept two optional arguments one to specify the style of lines and symbols and one to identify the graphical element for interactive manipulation Style The style defines the color the line dash pattern for continuous traces or the shape for discrete points of the data The possible values are given below Note that the color is ignored on some output devices such as black and white printers and the dash pattern is used only on high resolution devices such as printers or EPS output The color code is lowercase for thin lines and uppercase for thicker lines on devices which support it Color String black blue green cyan red magenta yellow white RGB RGB rrggbb rgb IIx Bsan0Qao R Dash Pattern String solid _ underscore dashed dotted i dash dot Shape String none invisible space point circle cross
405. terminal false direction 1 When the event occurs a new state is computed yn 0 damping xy 2 To integrate this the following functions are defined function yp ballfun t y damping yp y 2 9 81 function v te d ballevents t y damping v y 1 event when the height becomes negative te false do not terminate d 1 only for negative speeds function yn ballonevent t y i damping yn 0 damping y 2 Ball state is integrated during 5 s see Fig 3 3 with opt odeset Events ballevents OnEvent ballonevent t y ode45 ballfun 0 5 2 0 opt 1 plot t y LME Reference non linear numerical functions 295 Bouncing ball integrated with events Figure 3 3 Bouncing ball integrated with events Time events with discontinuous function If the function being integrated has discontinuities at known time in stants option EventTime can be used to insure an accurate switching time Consider a first order filter with input u t where u t O for t lt 1 and u t 1 fort gt 1 The following function is defined for the state derivative function yp filterfun t y yp y t lt 1 0 1 A single time event is generated at t 1 opt odeset EventTime inf 1 t y ode45 filterfun 0 5 0 opt plot t y Function filterfun is integrated in the normal way until t 1 inclu sive with u 0 This is
406. that each pixel has the same size otherwise the specified position is filled with the raster image You should use e when you want a better quality but do not add other elements in the figure Such as marks or lines and do not have interaction with the mouse Pixels on the screen are interpolated using the bilinear method if style is 1 and the bicubic method if style is 3 Examples Two ways to display a table of 10 by 10 random color cells see Fig 3 7 image rand 10 rand 10 rand 10 image rand 10 10 3 A ramp of gray shades image uint8 0 255 Operator and function meshgrid can be used to create the x and y coordinates used to display a function z x y as an image X Y meshgrid pi 0 1 pi Z cos X 2 Y 2 2 image Z 1 1 1 1 3 See also 390 LMEPPC User Manual 1999 2008 Calerga Sarl Figure 3 7 Example of image label Plot labels Syntax label label_x label label_x label_y Description label label_x label_y displays labels for the X and Y axis Its arguments are strings The label for the Y axis may be omitted Examples step 1 1 2 3 4 label t s y m With literal strings the may be more convenient label Re Im See also text legend LME Reference base graphics 391 Uniform random X Normal random Figure 3 8 Example of legend legend Plot legend Syntax legend str legend str s
407. the parameters of the SOAP call Example The following call requests a translation from english to french it as sumes that the computer is connected to the Internet and that the service is available url http services xmethods net perl soaplite cgi method BabelFish ns urn xmethodsBabelFish action urn xmethodsBabelFish BabelFish param struct param translationmode en_fr param sourcedata Hello Sysquake fr soapcall url method ns action param fr Bonjour Sysquake Note that since the server address is given in the URL the default op tions are sufficient The variable param is reset to an empty structure to make sure that no other parameter remains from a previous call Extensions Web Services 585 See also soapcallset soapcallset Options for SOAP call Syntax options soapcallset options soapcallset namel valuel options soapcallset optionsO namel valuel Description soapcallset namel valuel creates the option argument used by soapcall including the server and port Options are specified with name value pairs where the name is a string which must match exactly the names in the table below Case is significant Options which are not specified have a default value The result is a structure whose fields correspond to each option Without any input argument soapcallset creates a structure with all the default optio
408. this section include only those required for opening and configuring the connection They correspond to fopen for files Input output and control are done with the following generic functions Function Description fclose close the file fflush flush I O buffers fgetl read a line fgets read a line fprintf write formatted data fread read data fscanf read formatted data fwrite write data redirect redirect output Functions opendevice devicename closedevice and flushdevice are obsolete and may be removed in the future They 598 LMEPPC User Manual 1999 2008 Calerga Sarl are replaced with serialdevopen and serialdevset to specify configuration settings serialdevname fclose and fflush serialdevname Serial device name Syntax serialdevname n serialdevname name list Description serialdevname n returns the name of the n th serial device which can be opened by serialdevopen Argument n must be 1 or higher with other values such as those larger than the number of serial de vices available on your computer serialdevname returns the empty string Without input argument serialdevname gives the list of serial de vice names Examples On a Macintosh with internal modem serialdevname 1 Internal Modem Under Windows serialdevname 1 COM1 See also serialdevopen serialdevopen Open a serial port Syntax fd fd serialdevopen portname options serialdevopen portname Extensions
409. tifacts for example 2 sqrt 2 sqrt 2 which is mathematically 0 yields 4 4409e 16 Integers whose absolute value is smaller than 2 52 about 4 5e15 have an exact representation though Literal double numbers constant numbers given by their numerical value have an optional sign an integer part an optional fractional part following a dot and an optional exponent The exponent is the power of ten which multiplies the number it is made of the letter e or E followed by an optional sign and an integer number Numbers too large to be represented by the floating point format are changed to plus or minus infinity too small numbers are changed to 0 Here are some examples numbers on the same line are equivalent 123 123 123 123 00 12300e 2 2 5 25e 1 0 25e1 0 25e 1 0 0 0 0 le 99999 inf 1e999999 inf 1e999999 Literal integer numbers may also be expressed in hexadecimal with prefix Ox in octal with prefix 0 or in binary with prefix Ob The four literals below all represent 11 stored as double Oxb Literal integer numbers stored as integers and literal single numbers are followed by a suffix to specify their type such as 2int16 for the number 2 stored as a two byte signed number or 0x300uint32 for the LME Reference 33 number whose decimal representation is 768 stored as a four byte un signed number All the integer types are valid as well as single This syntax gives the same result as the call to the corre
410. tific notation same as g with an uppercase E same as g with as few characters as possible same as k with an uppercase E character string NDOARRTOQOCQ ZdMonNAoO XX EH A LL The flag forces octal numbers to begin with 0 nonzero hexadec imal numbers to begin with 0x and floating point numbers to always have a decimal point even if they do not have a fractional part Instead of decimal digits the width n and or the precision d can be replaced with character then one or two additional arguments or elements of an array are consumed and used as the width or preci sion Examples sprintf d 2f 2e 2E 2g pixones 1 5 3 3 14 3 14e0 3 14E0 3 14 sprintf 1k 0 001 0 11 111 1000 le 3 0 11 111 1e3 sprintf 8 3f 8 6S 8 6s pi abcdefgh abcdefgh 3 142 abcdef abcdef sprintf c_ a z a_b_c_d_e_f_g_h_i_j_k_l_m_n_o_p_q_r_s_t_u_v_w_x_y_z sprintf f 15 7 pi 3 1415927 sprintf 3d 3d 12 12345 012 12345 366 LMEPPC User Manual 1999 2008 Calerga Sarl Caveat Exotic formats unsupported See also sread Raw input from a string or an array of bytes Syntax a count sread str size precision a count sread str precision a count sread bytes Description sread str reads data from string str or array of class uint8 or int8 the same way as fread reads data from a file Examples data cou
411. tile range is the difference between the 75th per centile and the 25th percentile Example use stat iqr rand 1 1000 0 5158 See also mad Mean absolute deviation Syntax use stat m mad A m mad A dim Description mad A gives the mean absolute deviation of the columns of array A or of the row vector A The dimension along which mad proceeds may be specified with a second argument The mean absolute deviation is the mean of the absolute value of the deviation between each observation and the arithmetic mean Example use stat mad rand 1 1000 0 2446 See also nancorrcoef Correlation coefficients after discarding NaNs 484 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax use stat S nancorrcoef X S nancorrcoef X1 X2 Description nancorrcoef X calculates the correlation coefficients of the columns of the m by n matrix X NaN values are ignored The result is a square n by n matrix whose diagonal is 1 nancorrcoef X1 X2 calculates the correlation coefficients of X1 and X2 and returns a 2 by 2 matrix ignoring NaN values It is equiva lent to nancorrcoef X1 X2 See also nancov Covariance after discarding NaNs Syntax use stat M nancov data M nancov data 0 M nancov data 1 Description nancov data returns the best unbiased estimate m by m covariance matrix of the n by m matrix data for a normal distribution NaN values are ignored Each row of data is
412. tion To check that LME has loaded the extension successfully check the information line start ing with SQLite You can also try to evaluate sqlite_version which should display the version of SQLite 6 8 Functions sqlite_changes Number of affected rows in the last command Extensions SQLite 571 Syntax n sqlite_changes c Description sqlite_changes c gives the number of affected rows in the last UPDATE DELETE or INSERT command SQLite call sqlite3_changes See also sqlite_exec sqlite_last_insert_rowid sqlite_close Close an SQLite database Syntax sqlite_close c Description sqlite_close c closes the MYSQLite database identified by c SQLite call sqlite3_close See also sqlite_exec Execute an SQL query against an SQLite database Syntax sqlite_exec c query table sqlite_exec c query 572 LMEPPC User Manual 1999 2008 Calerga Sarl Description sqlite_exec c query executes a query given in SQL in a string against the SQLite database identified by c The number of modified rows can be obtained with sqlite_changes With an output argument sqlite_exec returns the resulting table as a list of rows Each row is given as a list of column values or as a structure as specified in the option argument of sqlite_open created with sqlite_set SQLite call sqlite3_exec See also sqlite_changes sqlite_last_insert_rowid Row ID of the last row inserted in a SQLite
413. tion with a server over TCP IP Ser vices which can be accessed via TCP IP include HTTP most common protocol for WWW documents and Web services SMTP for sending e mail POP for receiving mail and telnet Both TCP where the client and the server are connected and communicate with streams of bytes in both directions and UDP connectionless exchange of packets with out guarantee of transfer and order are supported Functions described in this section include only those required for opening and configuring the connection They correspond to fopen for files Input and output are done with the following generic functions Function Description fclose close the file fgetl read a line fgets read a line fprintf write formatted data fread read data fscanf read formatted data fwrite write data redirect redirect output fread does not block if there is not enough data it returns imme diately whatever is available in the input buffer gethostbyname Resolve host name Syntax ip gethostbyname host Description gethostbyname host gives the IP address of host in dot notation as a string 576 LMEPPC User Manual 1999 2008 Calerga Sarl Example gethostbyname localhost 127 0 0 1 See also gethostname Get name of current host Syntax str gethostname Description gethostname gives the name of the current host as a string See also gethostbyname socketaccept Accept a connection r
414. tional second output argument is set to the permu tation vector 330 LMEPPC User Manual 1999 2008 Calerga Sarl Examples s struct a 123 c 1 3 b 123 7 a 123 c real 1x3 b abcde t p orderfields s t a 123 b abcde c real 1x3 p 1 3 2 t orderfields s c b a t c real 1x3 b abcde a 123 See also fieldnames rmfield Deletion of a field in a structure Syntax strctout rmfield strctin name Description strctout rmfield strctin name makes a structure strctout with the same fields as strctin except for field named name which is re moved If field name does not exist strctout is the same as strctin Example x rmfield struct a 1 3 b abc a fieldnames x b LME Reference structures 331 See also struct set field get field orderfields setfield Assignment to a field in a structure Syntax strctout setfield strctin name value Description strctout setfield strctin name value makes a structure strctout with the same fields as strctin except that field named name is added if it does not exist yet and is set to value s setfield s f v has the same effect as s f v setfield is especially useful when the field name is not fixed but is stored in a variable or is the result of an expression See also struct Creation of a structure Syntax str
415. tions 107 Description varargin is a special variable which may be used to collect input ar guments In the function declaration it must be used as the last or unique input argument When the function is called with more argu ments than what can be assigned to the other arguments remaining ones are collected in a list and assigned to varargin In the body of the function varargin is a normal variable Its elements may be accessed with the brace notation varargin i nargin is always the total number of arguments passed to the function by the caller When the function is called with fewer arguments than what is de clared varargin is set to the empty list Example Here is a function which accepts any number of square matrices and builds a block diagonal matrix function M blockdiag varargin M for block varargin block takes the value of each input argument m n size block M end 1 end m end 1 end n block end In the call below varargin contains the list ones 3 2 ones 2 3 blockdiag ones 3 2 ones 2 3 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 2 2 0 0 0 0 2 2 0 0 0 0 0 0 3 See also varargout Remaining output arguments Syntax function varargout fun varargout 108 LMEPPC User Manual 1999 2008 Calerga Sarl Description varargout is a special variable which may be used to dispatch output arguments In the function declaration it must be used as the last
416. tions of user functions identified in LME by a name Typically they are stored in a file whose name is the library name with a Iml suffix for instance library stdlib is stored in file stdlib Iml Before a user function can be called its library must be loaded with the use statement use statements have an effect only in the context where they are placed i e ina library or the command line interface or a Sysquake SQ file this way different libraries may define functions with the same name provided they are not used in the same context In a library functions can be public or private Public functions may be called from any context which use the library while private functions are visible only from the library they are defined in 3 4 Types Numerical logical and character arrays The basic type of LME is the two dimensional array or matrix Scalar numbers and row or column vectors are special kinds of matrices Ar rays with more than two dimensions are also supported All elements have the same type which are described in the table below Two non numerical types exist for character arrays and logical boolean arrays Cell arrays which contain composite types are described in a section below Type Description double 64 bit IEEE number complex double Two 64 bit IEEE numbers single 32 bit IEEE number complex single Two 32 bit IEEE numbers uint32 32 bit unsigned integer int32 32 bit signed integer uint16 16 bit unsigned
417. to each element and the result is a matrix the same size Examples use stdlib isprime 7 true isprime 0 2 10 FTF See also primes factor isreal Test for a real number Syntax use stdlib b isreal x Description isreal x is true if x is a real scalar or a matrix whose entries are all real 472 LMEPPC User Manual 1999 2008 Calerga Sarl Examples use stdlib isreal 2 5 true isreal 2 3 2j false isreal exp pix 1j true See also 1snumeric isfloat 1sscalar linspace Sequence of linearly spaced elements Syntax use stdlib v linspace x1 x2 v linspace x1 x2 n Description linspace x1 x2 produces a row vector of 100 values spaced linearly from x1 and x2 inclusive With a third argument linspace x1 x2 n produces a row vector of n values Examples use stdlib linspace 1 10 1 0000 1 0909 1 1818 9 9091 10 0000 linspace 1 2 6 1 0 1 2 1 4 1 6 1 8 2 0 See also logspace Sequence of logarithmically spaced elements Libraries stdlib 473 Syntax use stdlib v logspace xl x2 v logspace xl x2 n Description logspace x1 x2 produces a row vector of 100 values spaced log arithmically from 10 x1 and 10 x2 inclusive With a third argument Logspace x1 x2 n produces a row vector of n values Example logspace 0 1 1 0000 1 0235 1 0476 9 5455 9 7701 10 0000 See also linspace operator median Median Syntax st
418. top of the screen lets you write commands with the LME syntax such as 1 2 or v 1 5 fft v Button Execute Tapping the Execute button makes LME interpret the contents of the input field You can interrupt computation by pressing the Scroll Down hardware button History To retrieve a previous command and display it in the com mand input tap the button with the lt sign To go forward in the list of commands tap the gt button You can edit the command before executing it Output The largest text field displays the result of commands You cannot write directly to it You can toggle between text output and graphics with the View menu or by pressing the Select hardware button when the command field is empty Menu Menus at the bottom of the screen let you change between text and graphics see the tree of code fragments see below change options and open the user manual in the default HTML browser usually Internet Explorer Introduction 9 If the operating system supports it you can rotate the screen the layout will be optimized for the new orientation 1 3 Code fragments To discover the power of LME you can execute small demonstrations called code fragments Code fragments are displayed as a tree with the menu Tools gt Code fragments To execute a fragment double tap its name The command itself and the result are displayed If the result is graphical you can switch to text mode with the menu View gt Text or simply by pre
419. tructure with two fields s type which is and s subs which is the name of the field f in this case While the primary purpose of subsasgn is to permit the use of sub scripts with objects a built in implementation of subsasgn is provided for arrays when s type is for lists when s type is a list and for structures when s typeis Examples A 1 2 3 4 subsasgn A struct type subs 1 999 999 999 3 4 subsasgn A struct type subs 1 2 4 See also subsref Reference to a part of an array list or structure Syntax B subsref A s Description When an object variable is subscripted in an expression like A s1 s2 LME evaluates subsref A s where subsref is a method of the class of variable A and s is a structure with two fields s type which is and s subs which is the list of subscripts s1 s2 If a subscript is the colon character which stands for all elements along the corresponding dimensions it is represented with the string in s subs 60 LMEPPC User Manual 1999 2008 Calerga Sarl When an object variable is subscripted in an expression like A s LME evaluates subsref A s where subsref is a method of the class of variable A and s is a structure with two fields s type which is and s subs which is the list containing the single subscript s When the field of an object var
420. true iscell 1 2 true islist 1 2 false See also ismember Test for set membership Syntax b ismember m s Description ismember m s tests if elements of array m are members of set s The result is a logical array the same size as m each element is true if the corresponding element of m is a member of s or false otherwise m must be a numerical array or a cell array matching type of set s Example S m b a bc bbb de d a x de a z ismember m s on i i 4m il TF TF See also length Length of a vector or a list LME Reference arrays 253 Syntax n n length v length list Description length v gives the length of vector v Length A gives the num ber of elements along the largest dimension of array A Length list gives the number of elements in a list Examples length 1 5 kama T E E T 1 6 abc Length 09 See also magic Magic square Syntax M magic n Description A magic square is a square array of size n by n which contains each integer between 1 and n2 and whose sum of each column and of each line is equal magic n returns magic square of size n by n There is no 2 by 2 magic square If the size is 2 the matrix 1 3 4 2 is returned instead 254 LMEPPC User Manual 1999 2008 Calerga Sarl Example magic 3 8 16 357 492 See also meshgrid Arrays of X Y coordi
421. ts LME Reference lists 323 Syntax listout apply fun listin listout apply fun listin nargout Description Listout apply fun listin evaluates function fun with input argu ments taken from the elements of list Listin Output arguments are grouped in list Listout Function fun is specified either by its name as a String or by an inline function The number of expected output arguments can be specified with an optional third input argument nargout Examples apply min 5 7 5 apply size magic 3 2 3 3 apply inline 2 x 3 y x y 5 10 40 See also join List concatenation Syntax list join ll 12 Description join 1l1 12 joins elements of lists l1 12 etc to make a larger list Examples join 1 a 2 5 4 2 xxx 1 a 2 3 4 5 14 2 Xxx 324 LMEPPC User Manual 1999 2008 Calerga Sarl See also islist Test for a list object Syntax b islist obj Description islist obj is true if the object obj is a list false otherwise Examples islist 1 2 x true islist true islist false ischar false See also isstruct isnumeric ischar is logical isempty list2num Conversion from list to numeric array Syntax A lList2num list Description List2num list takes the elements of List which must be numbers or arrays and concatenates them on a row a
422. ts name or given as an anonymous or inline function or a function reference It has at least one input argument x a real scalar vector or array and it returns one output LME Reference non linear numerical functions 285 argument a scalar real number fminsearch finds the value x such that fun x is minimized starting from point x0 The optional third input argument may contain options It is either the empty array for default options or the result of optimset Remaining input arguments of fminsearch if any are given as ad ditional input arguments to function fun They permit to parameterize the function For example fminsearch fun x0 2 5 calls fun as fun x 2 5 and minimizes its value with respect to x The first output argument of fminsearch is the value of x at opti mum The second output argument if it exists is the value of fun x at optimum The third output argument if it exists is set to true if fminsearch has converged to an optimum or to false if it has not in that case other output arguments are set to the best value obtained With one or two output arguments fminsearch throws an error if it does not converge Algorithm fminsearch implements the Nelder Mead simplex method It starts from a polyhedron centered around x0 the simplex Then at each it eration either vertex x_i with the maximum value fun x_i is moved to decrease it with a reflexion expansion a reflexion or a contraction or the
423. tyle Description legend str style displays legends for styles defined in string style In string str legends are separated by linefeed characters n Legends are displayed at the top right corner of the figure in a frame All styles are permitted symbols lines and filling They are recycled if more legends are defined in str With a single input argument Legend str uses the default style k Example Legend for two traces see Fig 3 8 plot 1 20 rand 1 20 randn 1 20 _x legend Uniform random nNormal random _x 392 LMEPPC User Manual 1999 2008 Calerga Sarl See also Label line Plot lines Syntax line A b line A b style line A b style id Description line displays one or several straight line s Each line is defined by an equation of the form a x azy b The first argument of Line is a matrix which contains the coefficients az in the first column and a2 in the second column each row corresponds to a different line The second argument is a column vector which contains the coefficients b If one of these arguments has one row and the other has several or none the same row is duplicated to match the other size In figures with a logarithmic scale only horizontal and vertical lines are allowed The optional third and fourth arguments are the same as for all graphical commands In mouse handlers _x0 and _y correspond to the projection of the mouse positi
424. u merical character or logical arrays or lists or cell arrays of character 264 LMEPPC User Manual 1999 2008 Calerga Sarl strings Multiple elements of input arguments are considered as single members the result is always sorted and has unique elements The optional second output argument is a vector of indices such that if c ia setdiff a b then cis a ia Example a a bc bbb de b z bc aa bbb c ia setdiff a b C a de ia 14 a ia a de See also setxor Set exclusive or Syntax c setxor a b c ia ib setxor a b Description setxor a b performs an exclusive or operation between sets a and b i e it gives the set of members of sets a and b which are not mem bers of the intersection of a and b Sets are any type of numerical character or logical arrays or lists or cell arrays of character strings Multiple elements of input arguments are considered as single mem bers the result is always sorted and has unique elements The optional second and third output arguments are vectors of indices such that if c ia ib setxor a b then c is the union of a ia and b ib LME Reference arrays 265 Example a a bc bbb de b z bc aa bbb c ia ib setxor a b C a aa de z ia 14 ib 31 union a ia b ib a aa
425. ually the magnitude is displayed with a logarithmic or dB scale use scale indb or scate Uinlog Uindb before dnichots The range of frequencies is selected automatically between 0 and t or can be specified in an optional argument w a vector of normalized frequencies Further options can be provided in a structure opt created with responseset fields NegFreq and Range are utilized The optional ar guments style and id have their usual meaning With output arguments dnichols gives the magnitude and phase of the frequency response and the frequency as column vectors No display is produced In Sysquake when the mouse is over a Nichols diagram in addition to the magnitude and phase which can be retrieved with _y0 and _x0 the normalized frequency is obtained in _q Example scale lindb ngrid dnichols 3 poly 0 9 0 7 0 6j 0 7 0 6j See also dnyquist Nyquist diagram of a discrete time system Syntax dnyquist numd dend dnyquist numd dend w dnyquist numd dend opt dnyquist numd dend w opt dnyquist style LME Reference graphics for dynamical systems 429 dnyquist style id w dnyquist re im dnyquist re im w dnyquist Description The Nyquist diagram of the discrete time transfer function given by polynomials numd and dend is displayed in the complex plane In dis crete time the Nyquist diagram is the locus of the complex values of the transfe
426. udo random number uniformly distributed be tween 0 and 1 The lower bound O may be reached but the upper bound 1 is never The current implementation is based on a scalar 64 bit seed which theoretically allows 2 64 different numbers This seed can be set with the arguments rand seed s where s is a scalar or a vector of two components rand seed s returns the empty array as output argument To discard it the statement should be followed by a semicolon rand n rand n1 n2 and rand nl1 n2 return an n by n square matrix or an array of arbitrary size whose elements are pseudo random numbers uniformly distributed between 0 and 1 260 LMEPPC User Manual 1999 2008 Calerga Sarl Examples rand 0 2361 rand 1 3 0 6679 0 8195 0 2786 rand seed 0 rand 0 2361 See also randn Normally distributed random number Syntax x randn M randn n M randn nl1 n2 M randn nl1 n2 randn seed s Description randn builds a scalar pseudo random number chosen from a normal distribution with zero mean and unit variance The current imple mentation is based on a scalar 64 bit seed which theoretically al lows 2 64 different numbers This seed can be set with the arguments randn seed s where s is a scalar or a vector of two components The seed is not the same as the seed of rand randn seed s re turns the empty array as output argument To discard
427. uivalent to x y It can be used to redefine this oper ator for objects Example 17 1 false inf inf false nan nan true 1 2 3 1 3 3 FTF See also operator gt operator gt joper Operator Object inequality Syntax a unsame a b LME Reference operators 133 Description a b is true if a is not the same as b and false otherwise a and b must have exactly the same internal representation to be considered as equal with IEEE numbers nan nan is false and 0 0 is true Contrary to the inequality operator returns a single boolean even if its operands are arrays unsame a b is equivalent to a b Example 1 5 1 5 false 1 5 1 5 FFFFF 1 2 3 4 5 true 1 2 3 4 5 Incompatible size nan nan false nan nan true See also operator lt joperator lt oper Operator lt Less than Syntax x lt y lt x y Description x lt y is true if x is less than y and false otherwise Comparing NaN not a number to any number yields false including to NaN If x and or y is an array the comparison is performed element wise and the result has the same size lt x y is equivalent to x lt y It can be used to redefine this oper ator for objects 134 LMEPPC User Manual 1999 2008 Calerga Sarl Example 2 3 4 lt 2 4 2 FTF See also operator operator operator lt op
428. umpvar conversion to string subsasgn assignment to subarrays or to quaternion parts subsref reference to subarrays or to quaternion parts Function imag is replaced with qimag which gives a quaternion with the real part set to zero because there are three imaginary compo nents instead of one with complex numbers Operators and functions which accept multiple arguments convert automatically double arrays to quaternions ignoring the imaginary part of complex numbers Conversion to numeric arrays with double adds a dimension for the real part and the three imaginary parts For example converting a scalar quaternion gives a 4 by 1 double column vector and converting a 2 by 2 quaternion array gives a 2 by 2 by 4 double array Real and imaginary components can be accessed with the field access notation q wis the real part of q q x q y and q z are its imaginary parts and q v is its imaginary parts as an array similar to the result of double but without the real part Compatibility note native functions for quaternions replace library quaternion which defined quaternion scalars and matrices It is much faster and supports arrays of more than two dimensions on the other hand matrix oriented functions are not supported anymore and the result of dumpvar is not directly compatible isquaternion Test for a quaternion Syntax b isquaternion q Description isquaternion q is true if the input argument is a quaternion and false othe
429. uous time transfer function numc denc The continuous time transfer function is given by two polynomials in s and the discrete time transfer function is given by two polynomials in z all as vectors of coefficients with highest powers first Method is tustinor t Tustin bilinear transformation default The input and output arguments numc denc numd and dend can also be matrices in that case the conversion is applied separately on each row with the same sampling period Ts d2cm Ad Bd Cd Dd Ts method performs the conversion from discrete time state space model Ad Bd Cd Dd to continuous time state space model Ac Bc Cc Dc defined by x kK 1 Agx k Bgu k y k Cgx k Dgu k and dx ae A x t B u t y t C x t D u t Example numd dend c2dm 1 1 1 5 t numd 0 7143 0 7143 dend 1 0 4286 LME Reference dynamical systems 349 numc denc d2cm numd dend numc 3 8858e 17 1 denc 11 See also dmargin Robustness margins of a discrete time system Syntax gm psi wc wx gm psi wc wx dmargin num den Ts dmargin num den Description The open loop discrete time transfer function is given by the two poly nomials num and den with sampling period Ts default value is 1 If the closed loop system with negative feedback is unstable all out put arguments are set to an empty matrix Otherwise dmargin calcu lates the gain margins gm which give the interv
430. ure opt created with responseset fields Delay NegFreq and Range are utilized The op tional arguments style and id have their usual meaning With output arguments nichols gives the phase and magnitude of the frequency response and the frequency as column vectors No display is produced In Sysquake when the mouse is over a Nichols diagram in addition to the magnitude and phase which can be retrieved with _y0 and _x0 the frequency is obtained in _q LME Reference graphics for dynamical systems 443 scale lindb nichols 1 1 4 Figure 3 20 scale lindb nichols 1 1 4 Example Nichols diagram of a third order system see Fig 3 20 scale lindb ngrid nichols 20 poly 1 2 1j 2 1j See also nyquist Nyquist diagram of a continuous time system Syntax nyquist numc denc nyquist numc denc w nyquist numc denc opt nyquist numc denc w opt nyquist style nyquist style id w nyquist 444 LMEPPC User Manual 1999 2008 Calerga Sarl re im nyquist re im w nyquist Description The Nyquist diagram of the continuous time transfer function given by polynomials numc and denc is displayed in the complex plane In con tinuous time the Nyquist diagram is the locus of the complex values of the transfer function evaluated at jw where w is real positive other definitions include the real negative values which gives a symmetric diagram with respec
431. ust be provided for some distributions The distributions are given in the table below Default values for the parameters when mentioned mean that the parameter may be omitted 154 Distribution Name Beta beta Cauchy cauchy X chi x chi2 Y gamma exponential exp F f half normal half normal Laplace laplace lognormal logn normal norm Rayleigh rayl Student s T t uniform unif Weibull weib See also ceil Rounding towards infinity Syntax y ceil x Description LMEPPC User Manual 1999 2008 Calerga Sarl Parameters a and b a and b deg of freedom v deg of freedom v shape and A mean deg of freedom v and v2 9 mean and scale mean 0 and st dev 1 mean 0 and st dev 1 b deg of freedom v limits of the range 0 and 1 a and b ceil x gives the smallest integer larger than or equal to x If the argument is a complex number the real and imaginary parts are han dled separately Examples ceil 2 3 3 ceil 2 3 2 ceil 2 3 4 5j 3 4j LME Reference mathematical functions 155 See also complex Make a complex number Syntax z complex x y Description complex x y makes a complex number from its real part x and imag inary part y The imaginary part of its input arguments is ignored Examples complex 2 3 2 3j complex 1 5 2 14 2j 2 2j 3 2j 44 2j 5 2j See also conj Complex conjugate value Syntax w conj z Description conj z ch
432. ut argument info builtin gives a list of structures which describe each built in function with the following fields name function name module module name trusted true if the function is trusted info operators displays the list of operators With an output argument info operators gives a list of structures like info builtin 96 LMEPPC User Manual 1999 2008 Calerga Sarl info functions displays the list of user defined functions with the library where they are defined Parenthesis denote functions known by LME but not loaded they also indicate spelling errors in function or variable names With an output argument info functions gives a list of structures which describe each user defined function with the following fields library library name name function name loaded true if loaded info methods displays the list of methods With an output argu ment info methods gives a list of structures which describe each method with the following fields library library name class class name name function name loaded true if loaded info variables displays the list of variables with their type and size With an output argument info methods gives a list of struc tures which describe each variable with the following fields name function name defined true if defined info global displays the list of all global variables With an output argument info global gives the list of
433. uture They are replaced with serialdevopen and serialdevset to specify configuration settings serialdevname fclose and fflush serialdevname Serial device name Syntax name serialdevname n list serialdevname 458 LMEPPC User Manual 1999 2008 Calerga Sarl Description serialdevname n returns the name of the n th serial device which can be opened by serialdevopen Argument n must be 1 or higher with other values such as those larger than the number of serial de vices available on your computer serialdevname returns the empty string Without input argument serialdevname gives the list of serial de vice names Examples On a Macintosh with internal modem serialdevname 1 Internal Modem Under Windows serialdevname 1 COM1 See also serlalaevopen serialdevopen Open a serial port Syntax fd fd serialdevopen portname options serialdevopen portname Description serialdevopen portname opens a connection to the serial port whose name is portname and returns a file descriptor fd Names depend on the operating system and can be obtained with serialdevname Some platforms do not provide a complete list of all ports serialdevopen may accept additional device names and pass them directly to the corresponding function of the operating system The second argument of serialdevopen portname options isa structure which contains configuration settings It is set with serialdevset Serial
434. variables but cannot create new ones Examples eval 1 2 3 a eval 1 2 3 a 2 3 5 Il a eval a See also feval exist Existence of a function or variable Syntax b b exist name exist name type LME Reference miscellaneous functions 93 Description exist returns true if its argument is the name of an existing function or variable or false otherwise A second argument can restrict the lookup to builtin functions builtin user functions function or variable variable Examples exist sin true exist cos function false See also into feval Function evaluation Syntax argoutl feval fun arginl Description yl y2 feval fun x1 x2 evaluates function fun with in put arguments x1 x2 etc Output arguments are assigned to yl y2 etc Function fun is specified by either its name as a string a function reference or an inline function Examples y feval sin 3 5 0 1411 0 7568 0 9589 y feval inline sin 2 x 3 5 0 2794 0 9894 0 544 See also 94 LMEPPC User Manual 1999 2008 Calerga Sarl fevalx Function evaluation with array expansion Syntax Y1 fevalx fun X1 Description Y1 Y2 fevalx fun X1 X2 evaluates function fun with input arguments X1 X2 etc Arguments must be arrays which are ex panded if necessary along singleton d
435. ven by the two polynomials num and den If the closed loop system with negative feedback is unstable all output arguments are set to an empty ma trix Otherwise margin calculates the gain margins gm which give the interval of gain for which the closed loop system remains stable the phase margin psi always positive if it exists which defines the sym metric range of phases which can be added to the open loop system while keeping the closed loop system stable the critical frequency as sociated to the gain margins where the open loop frequency response intersects the real axis around 1 and the cross over frequency asso ciated to the phase margin where the open loop frequency response LME Reference dynamical systems 351 has a unit magnitude If the Nyquist diagram does not cross the unit circle psi and wx are empty Examples Stable closed loop Nyquist inside unit circle gm psi wc wx margin 0 5 poly 1 1 1 gm 2 16 psi wc 0 1 7321 wx Stable closed loop Nyquist crosses unit circle gm psi wc wx margin 4 poly 1 1 1 gm 0 25 2 psi 0 4737 we 0 1 7321 wx 1 2328 Unstable closed loop gm psi wc wx margin 10 poly 1 1 1 gm psi we wx Caveats Contrary to many functions margin cannot be used with several trans fer functions simultaneously because not all of them may correspond simultaneously to either stable or unstable c
436. vert back from codes to signal It should be a vector with one more element than partition With a second output argu ment quantiz gives codebook i With a third output argument quantiz computes the distortion be tween input and codebook i i e the mean of the squared error Libraries sigenc 549 Example use sigenc partition 1 0 1 codebook 2 0 5 0 5 2 in randn 1 5 in 0 1799 9 7676e 2 1 1431 0 4986 1 0445 i out dist quantiz in partition codebook l1 2 1 0 1 2 out 0 5 0 5 2 0 5 0 5 dist 0 259 See also Lloyds dpcmenco ulawcompress mu law compressor Syntax use sigenc output ulawcompress input output ulawcompress input mu Description ulawcompress input a compresses signal input with mu law method using parameter mu input can be a real array of any size and dimension The default value of mu is 255 The compressor and its inverse the expander are static nonlin ear filters used to improve the signal noise ratio of quantized signals The compressor should be used before quantization or on a signal represented with a higher precision See also ulLawexpand ja Lawcompress ulawexpand mu law expander 550 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax use sigenc output ulawexpand input output ulawexpand input mu Description ulawexpand input a expands signal input with mu law method us ing parameter a input can be a
437. was used outside of any index sub expression in an expression matrixcol not in an index expression matrixcol was used outside of any index sub expression in an expression matrixrow not in an index expression matrixrow was used outside of any index sub expression in an expression matrixrow or matrixcol used in the wrong index matrixrow was used in an index which was not the first one or matrixcol was used in an index which was not the only one or the second one Compilation overflow Not enough memory during compilation Too many nested subexpressions The number of nested of subexpressions is too high Variable table overflow A single statement attempts to define too many new variables at once Expression too large Not enough memory to compile a large ex pression Too many nested and The maximum depth of nested subexpressions function argument lists arrays and lists is reached Too many nested programming structures Not enough mem ory to compile that many nested programming structures such as if while switch etc Wrong number of input arguments Too few or too many input arguments for a built in function during compilation Wrong number of output arguments Too few or too many out put arguments for a built in function during compilation Too many indices More than two indices for a variable Variable not found A variable is referenced but appears neither in the arguments of the function nor in t
438. x To multiply by the inverse of the left argument use the symbol This is handy to solve a set of linear equations For example to find the values of x and y such that x 2y 2 and 3x 4y 7 type gt 1 2 3 4 277 ans 3 0 5 Hence x 3 and y 0 5 Another way to solve this problem is to use the inv function which return the inverse of its argument It is sometimes useful to multiply or divide matrices element wise The and operators do exactly that Note that the and operators do not need special dot versions because they perform element wise anyway gt 1 2 3 4 x 2 1 5 3 ans 12 7 26 15 gt 1 2 3 4 2 1 5 3 ans 2 2 15 12 Some functions change the order of elements The transpose operator tick reverses the columns and the rows gt 1 2 3 4 5 6 ans 135 246 When applied to complex matrices the complex conjugate transpose is obtained Use dot tick if you just want to reverse the rows and columns The flipud function flips a matrix upside down and fliptr flips a matrix left right gt flipud 1 2 3 4 ans 3 4 12 gt fliptr 1 2 3 4 ans 21 4 3 To sort the elements of each column of a matrix or the elements of a row vector use the sort function Tutorial 19 gt sort 2 4 8 7 1 3 ans 123478 To get the size of a matrix you can use the size function which gives you both the number of rows and the number of columns unless you specif
439. x y z creates the quaternion object w ix x j y k z With three real arguments quaternion x y z creates the pure quaternion object i x j y k z In all these cases the arguments may be scalars or arrays of the same size With two arguments quaternion w v creates a quaternion object whose real part is w and imaginary parts is array v v must have one more dimension than w for the three imaginary parts LME Reference Quaternions 321 Without argument quaternion returns the zero quaternion object The real or imaginary parts of a quaternion can be accessed with field access such aS g w q x q y q Z and q v Examples q quaternion 1 2 3 4 q 1 21 3j 4k q 5 6 21 3j 4k q q 28 41 6 8k Q q 2 2 q 5 2x2 quaternion array 0 0 quaternion 1 5 3 7 a2alaw lt 1 51 3j 7k NWwWuc See also rpy2q Conversion from attitude angles to quaternion Syntax q rpy2q pitch roll yaw Description rpy2q pitch roll yaw gives the quaternion corresponding to a rotation of angle yaw around the z axis followed by a rotation of angle pitch around the y axis followed by a rotation of angle roll round the x axis All angles are given in radians The result is a normalized quaternion whose real part is cos 9 2 and imaginary part sin 9 2 Vxi Vyj vzk for a rotation of 9 around unit vector 322 LMEPPC User Manual 1999 2008 Calerga Sarl Vx Vy ve The rotation is applied to a point xyz given
440. xt 1 1 pl tr text 1 1 p2 bl Text with font specification font fontset Font Times Bold true Size 18 Color 1 0 0 text 1 1 4 2 Abc font See also title Subplot title Syntax title string Description title string sets or changes the title of the current subplot See also 3 35 3D Graphics Three dimension graphic commands enable the representation of ob jects defined in three dimensions x y and z on the two dimension screen The transform from the 3D space to the screen is performed as if there were a virtual camera in the 3D space with a given posi tion orientation and angle of view related to the focal length in a real camera 404 LMEPPC User Manual 1999 2008 Calerga Sarl 3 36 Projection The projection is defined by the following parameters Target point The target point is a 3D vector which defines the position where the camera is oriented to Projection kind Two kinds of projections are supported ortho graphic and perspective View point The view point is a 3D vector which defines the posi tion of the camera For orthographic projection it defines a direc tion independent from the target position for perspective projec tion it defines a position and the view orientation is defined by the vector from view point to target point Up vector The up vector is a 3D vector which fixes the orientation of the cam
441. y list list or structure inline inline function funref function reference Examples ol class struct fld1 1 fld2 rand 4 cl1 o2 class struct fld3 abc c2 ol class o2 c2 LME Reference objects 333 See also isa Test for an object of a given class Syntax b isa object classname Description isa object classname returns true of object is an object of class class directly or by inheritance Example isa pi double true See also Class isobject methods isobject Test for an object Syntax b isobject a Description object a returns true if a is an object created with class See also methods List of methods for a class 334 LMEPPC User Manual 1999 2008 Calerga Sarl Syntax methods classname list methods classname Description methods classname displays the list of methods defined for class classname Inherited methods and private methods are ignored With an output argument methods gives produces a list of strings See also 3 26 Logical Functions all Check whether all the elements are true Syntax all A all A dim all v v v b Description all A performs a logical AND on the elements of the columns of array A or the elements of a vector If a second argument dim is provided the operation is performed along that dimension all can be omitted if its result is us
442. y which of them you want in the optional second argument gt size rand 13 17 ans 13 17 gt size rand 13 17 1 ans 13 gt size rand 13 17 2 ans 17 2 4 Polynomials LME handles only numerical values Therefore it cannot differenti ate functions like f x sin e However a class of functions has a paramount importance in numerical computing the polynomials Poly nomials are weighted sums of powers of a variable such as 2x 3x 5 LME which handles only matrices stores the coefficients of poly nomials in row vectors i e 2x 3x 5 is represented as 2 3 5 and 2x 3x as 2 0 0 0 3 0 Adding two polynomials would be like adding the coefficient vectors if they had the same size in the general case however you had better use the function addpol which can also be used for subtraction gt addpol 1 2 3 7 ans 49 gt addpol 1 2 2 4 5 ans 257 gt addpol 1 2 2 4 5 ans 2 3 3 Multiplication of polynomials corresponds to convolution no need to understand what it means here of the coefficient vectors gt conv 1 2 2 4 5 ans 2 8 13 10 Hence x 2 2x 4x 5 2x34 8x 13x 10 20 LMEPPC User Manual 1999 2008 Calerga Sarl 2 5 Strings You type strings by bracketing them with single quotes gt Hello World ans Hello World If you want single quotes in a string double them gt Easy isn t it ans Ea
443. your whole program For instance let us use one of the variables of magicSum gt mage 77 magc 77 24 LMEPPC User Manual 1999 2008 Calerga Sarl gt magicSum 3 magc ans 92 92 92 gt magc magc 77 2 9 Local and Global Variables When a value is assigned to a variable which has never been refer enced a new variable is created It is visible only in the current con text the base workspace for assignments made from the command line interface or the current function invocation for functions The variable is discarded when the function returns to its caller Variables can also be declared to be global i e to survive the end of the function and to support sharing among several functions and the base workspace Global variables are declared with keyword global global x global y z A global variable is unique if its name is unique even if it is declared in several functions In the following example we define functions which implement a queue which contains scalar numbers The queue is stored in a global variable named QUEUE Elements are added at the front of the vector with function queueput and retrieved from the end of the vector with function queueget function queueput x global QUEUE QUEUE x QUEUE function x queueget global QUEUE x QUEUE end QUEUE end Both functions must declare QUEUE as global otherwise the variable would be local even if there exists also a global var

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