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1. llle 17 16 Extended String v89 Obsolete 0 17 17 Small Data Set v89 Obsolete o 17 17 Extended Data Set v89 Obsolete 17 19 Matrix v92 Obsolete llle 17 20 String v92 Obsolete 2 17 20 Data Set v92 Obsolete 0 o ee 17 21 MaAWIKVIOG 2 2 24 4 62426684 car ee S 17 22 DataSetv96 2 222 17 23 GAUSS Data Archive een 17 24 18 Foreign Language Interface 18 1 Writing FLI Functions gt lt o s ses ossa rera ee ee RET RS 18 2 18 2 Creating Dynamic Libraries llle 18 3 19 Data Transformations 19 1 Data Loop Statements o e o 19 2 19 2 Using Other Statements 19 3 19 3 Debugging Data Loops lt o esa cem 9 a ee RR 3 Ro 19 3 19 3 1 Translation Phase llle 19 3 19 3 2 Compilation Phase lt lt lt 19 3 193 3 Execution Phase eo lt a racea aoea eoa ea ea ea eee 19 4 19 4 Reserved Variables noaoae 19 4 20 The GAUSS Profiler 20 1 Using the GAUSS Profiler aaa aaa 20 1 20 4 4 Collection lt ssa saa i ama a a aa a aaa ee 20 1 20 1 2 JANAIVSIS 24 coooa cra eee ee hA OE ok AE E eee Ae d 20 2 xiii GAUSS User Guide 21 Publication Quality Graphics 21 1 21 2 21 3 21 4 21 5 21 6 General Design lel 21 1
2. 10 e19dO GAUSS User Guide Exclusive Or X Y XxorY T T F T F T FIT T FIF F Equivalence X Y XeqvY T T T T F F FIT F FIF T For complex matrices the logical operators consider only the real part of the matrices The following operators require scalar arguments These are the ones to use in if and do statements e Complement z not x e Conjunction z x and y e Disjunction Z x or y e Exclusive or Z X xor y Operators e Equivalence Z Xx eqv y If the logical operator is preceded by a dot the result will be a matrix of 1 s and 0 s based upon an element by element logical comparison of x and y e Element by element logical complement z not x Element by element conjunction z x and y Element by element disjunction Z Xx or y e Element by element exclusive or Zz x xor y e Element by element equivalence Z Xx eqv y 7 5 Other Operators Assignment Operator Assignments are done with one equal sign y 3 s10 e1adoO GAUSS User Guide Comma Commas are used to delimit lists clear x y Z to separate row indices from column indices within brackets y x 3 5 and to separate arguments of functions within parentheses y momentd x d Period Dots are used in brackets to signify all rows or all columns y x 5 Space Spaces are used inside of index brackets to separate indices
3. 21 4 Publication Quality Graphics xlabel X Axis X axis label title Example xy Graph main title xy x y call to main routine Example 3 In this example two graphics panels are drawn The first is a full sized surface representation and the second is a half sized inset containing a contour of the same data located in the lower left corner of the window library pgraph activate pgraph library Generate data for surface and contour plots x sega 10 0 1 71 note x is a row vector y sega 10 0 1 71 note y is a column vector z cos 5 sin x y zis a 71x71 matrix begwind initialize graphics windows makewind 9 6 855 0 0 0 first window full size makewind 9 2 6 855 2 1 1 0 second window inset to first setwind 1 activate first window graphset reset global variables _pzclr 1 2 3 4 set Z level colors titleC cos 5 sin x y set main title xlabel X Axis set X axis label ylabel Y Axis set Y axis label scale3d miss 0 0 miss 0 0 5 5 scale Z axis surface x y z call surface routine nextwind activate second window graphset reset global variables pzclr 1 2 3 4 set Z level colors _pbox 15 white border contour x y Z call contour routine endwind Display windows 21 5 90d GAUSS User Guide While
4. Result Left Operator Right dense sparse dense dense dense dense sparse sparse sparse dense dense sparse Element by Element Multiplication Result Left Operator Right sparse sparse D dense dense dense i dense sparse sparse S sparse sparse dense a sparse Element by Element Division Result Left Operator Right sparse sparse J dense dense dense Pi dense dense sparse el sparse dense dense sparse 9 6 Sparse Matrices Other Numeric Operators Matrix Multiplication Result Left Operator Right dense sparse Y dense dense dense dense sparse sparse x sparse Linear Solve Result Left Operator Right dense dense dense dense dense sparse Note that at this time the dense dense sparse case is defined only for real data When either of its arguments are sparse the operator uses a tolerance to determine the result which may be read or set using the sysstate function case 39 The default tolerance is le 14 Relational Operators Since the results of element by element dot comparison operators depend largely on the kind of data inputted there are both both dense returning and sparse returning versions of the dot comparison operators when one or both arguments is a sparse matrix The regular dot comparison operators and their alphabetic counterparts always return dense matrices and there is a new set of alphabetic dot co
5. e mo 28 50 28 13 Error Handling and Debugging o e e eee eee 28 50 28 14 String Handling lt RR xot Se Ee ew pS 28 51 28 15 Time and Date Functions eo 28 53 28 16 Console VO c svo eas eee ems EY Swe nir eee eee eS 28 55 28 17 Output FUNGIIONS s a ces eae a o m eee ee ee ee 28 56 28 18 GIaphil6S asd dom dee ye whe Soe Gone eri ee ee Boe ee eo 28 57 29 Command Reference D Obsolete Commands E Colors Index xvil List of Figures List of Figures 3 1 Command Page 3 2 Command Page Toolbar 3 3 Working Directory Toolbar 3 4 Command History Toolbar 3 5 Run Debug and Edit ButionS 5 2 x c kx 3 6 Command Page Widgets 3 7 Command History Window 3 8 Source Page 3 9 Programming Editor 3 10 Autocomplete 3 11 Tooltips 3 12 Find and Replace 3 13 Find and Replace Regular Expression 2 o 3 14 Data Page 3 15 Data Page Toolbar 3 16 The Struct Editor 3 17 Debug Toolbar 3 18 Debug Window 3 19 Watch Window 3 20 Help Page 12 1 Structure tree forel 22 1 Graphics Editor Workspace 22 2 Graphics Editor Toolbar 22 3 Graphics Editor Status Bar 3 2 3 4 3 5 3 5 3 7 3 8 3 11 3 11 3 12 3 12 3 14 3 16 3 17 3 18 3 20 3 21 3 22 3 25 3 26 12 7 22 2 22 3 22 3 xix Introduction 1 1 Product Overview GAUS
6. cmmult xr xi yr yi cminv tr ti This is completely general so the following program is legal proc 2 cmcplx x local r c r rows x c cols x retp x zeros r c endp 8 12 Procedures and Keywords proc 2 cminv xr xi local ixy zr zi ixy inv xr xi zr inv xr xi ixy real part of inverse zi ixy zr imaginary part of inverse retp zr zi endp proc 2 cmmult xr xi yr yi local zr zi zr zi xr yr xi yi xr yi xi yr retp zr zi endp xr xi yr yi zr zi qr qi wr wi cmcplx rndn 3 3 cmcplx rndn 3 3 cmmult cminv xr xi cminv yr yi cmmult yr yi cminv yr yi cmmult yr yi cminv cmmult cminv xr xi yr yi 8 7 Saving Compiled Procedures When a file containing a procedure definition is run the procedure is compiled and is then resident in memory The procedure can be called as if it were an intrinsic function If the new command is executed or you quit GAUSS and exit to the operating system the compiled image of the procedure disappears and the file containing the procedure definition will have to be compiled again If a procedure contains no global references that is if it does not reference any global matrices or strings and it does not call any user defined functions or procedures it can be saved to disk in compiled form in a fcg file with the save command and loaded late
7. This saves the vector of instances in a file called p2 fsr retc will be zero if the save was successful otherwise nonzero 12 8 Structures 12 1 7 Loading an Instance from the Disk The syntax for loading a file containing an instance or matrix of instances is instance retc loadstruct file_name structure_name For example include trade sdf struct DS p3 p3 retc loadstruct p2 ds 12 1 8 Passing Structures to Procedures Structures or members of structures can be passed to procedures When a structure is passed as an argument to a procedure it is passed by value The structure becomes a local copy of the structure that was passed The data in the structure is not duplicated unless the local copy of the structure has a new value assigned to one of its members Structure arguments must be declared in the procedure definition struct rectangle matrix ulx matrix uly matrix lrx matrix lry proc area struct rectangle rect retp rect lrx rect ulx rect uly rect lry endp Local structures are defined using a struct statement inside the procedure definition 12 9 sa4ni9n1s GAUSS User Guide proc center struct rectangle rect struct rectangle cent cent lrx rect lrx rect ulx 2 cent ulx cent lrx cent uly rect uly rect lry 2 cent lry cent uly retp cent endp 12 2 Structure Pointers A structure pointer is a separate data typ
8. 0 3 always 0 4 7 always OXEECDCDCD 8 11 reserved 12 15 reserved 16 19 reserved 20 23 0 real matrix 1 complex matrix 24 27 number of dimensions 0 scalar row vector 2 column vector matrix 28 31 header size 128 number of dimensions 4 padded to 8 byte boundary 32 127 reserved If the data is a scalar the data will directly follow the header If the data is a row vector an unsigned integer equaling the number of columns in the vector will precede the data along with 4 padding bytes If the data is a column vector or a matrix there will be two unsigned integers preceding the data The first will represent the number of rows in the matrix and the second will represent the number of columns The data area always begins on an even 8 byte boundary Numbers are stored in double precision 8 bytes per element 16 if complex For complex matrices all of the real parts are stored first followed by all the imaginary parts 17 5 8 String v92 Obsolete Offset Description 0 3 always 0 4 7 always OXEECFCFCF 17 20 File I O Offset Description 8 11 reserved 12 15 reserved 16 19 reserved 20 23 size of string in units of 8 bytes 24 27 length of string plus null terminator in bytes 28 127 reserved The size of the data area is always divisible by 8 and is padded with nulls if the length of the string is not evenly divisible by 8 If the length of the string is evenly divisible by 8 the d
9. 201GAUSS s If this is set to a null string no date will be printed For more information on using fonts within strings see GRAPHICS TExT ELEMENTS Section 21 4 Mx9 matrix draws one error bar per row of the input matrix If scalar 0 no error bars will be drawn Location values are in plot coordinates M 1 x location M 2 left end of error bar M 3 right end of error bar M 5 bottom of error bar M 4 y location M 6 top of error bar M 7 line type dashed dotted short dashes closely spaced dots dots and dashes solid Duna WN M 8 color see Corons Section 21 5 M 9 line thickness This value may be 0 or greater A value of 0 is normal line width To create one error bar using solid lines use _perrbar 1 0 2 2 1 3 6 2 86 2x1 vector controls frame around axes area On 3 D plots this is a cube surrounding the 3 D workspace 21 20 Publication Quality Graphics _pgrid _plctrl 1 1 frame on 0 frame off 2 1 tick marks on frame 0 notick marks The default is a frame with tick marks 2x1 vector to control grid 1 grid through tick marks 0 nogrid 1 dotted grid 2 fine dotted grid 3 solid grid 2 grid subdivisions between major tick marks 0 nosubdivisions 1 dotted lines at subdivisions 2 tick marks only at subdivisions The default is no grid and tick marks at subdivisions scalar or Kx1 vector to control whether lines and or symbols w
10. G3 2 6 2 and will result in a 2x2 matrix because the arithmetic operators have precedence over concatenation N o A For more information see OPERATOR PRECEDENCE Section 7 7 The let command is used to initialize matrices with constant values let x 2 2 12 3 4 Unlike the concatenation operators it cannot be used to define matrices in terms of expressions such as y x1 x2 x2 x3 3 x4 The statement y x 1 3 5 8 6 16 Language Fundamentals will put the intersection of the first three rows and the fifth through eighth columns of x into the matrix y The statement y x 1 3 1 5 5 9 will create a 3x3 matrix y with the intersection of the specified rows and columns pulled from x in the indicated order The following code let r 1 3 1 let c 5 5 9 y x r c will have the same effect as the previous example but is more general The statement y 2 4 3 will set the 2 4 element of the existing matrix y to 3 This statement is illegal if y does not have at least 2 rows and 4 columns The statement x con 3 2 will cause the following prompt to be printed in the window 1 1 6 17 s ejuawepuny oDenbue GAUSS User Guide indicating that the user should enter the 1 1 element of the matrix Entering a number and then pressing ENTER will cause a prompt for the next element of the matrix to appear Pressing will display a help screen and pressing
11. k y fish The result will be a 3X1 matrix with each element containing catfish If we then use k created above t k 1 1 The result will be a string containing catfish If we used the same k to create z as follows z dog k 1 1 The resulting z will be a string containing dogcatfish String Array Concatenation Vertical string array concatenation Operators x dog y fish k x y print k dog fish Horizontal string array concatenation x dog y fish k x 7 y print k dog fish String Variable Substitution In a command like the following create f1 olsdat with x 4 2 by default GAUSS will interpret olsdat as the literal name of the GAUSS data file you want to create It will also interpret x as the literal prefix string for the variable names x1 x2 x3 x4 To get the data set name from a string variable the substitution operator could be used as follows dataset olsdat create f1 dataset with x 4 2 To get the data set name from a string variable and the variable names from a character vector use the following 7 19 10 e19dO GAUSS User Guide dataset olsdat vnames age pay sex create f1 dataset with vnames 0 2 The general syntax is variable name Expressions are not allowed The following commands are currently supported with the substitution operator in t
12. y x 1 3 5 3 5 9 No extraneous spaces are allowed immediately before or after the comma or immediately after the left bracket or before the right bracket Spaces are also used in print and lprint statements to separate the separate expressions to be printed Operators print x 2 2 sqrt x No extraneous spaces are allowed within expressions in print or 1print statements unless the expression is enclosed in parentheses print x 2 2 sqrt x Colon A colon is used within brackets to create a continuous range of indices y x 1 5 Ampersand The 8 ampersand operator will return a pointer to a procedure proc function fn or structure struct It is used when passing procedures or functions to other functions when indexing procedures and when initializing structure pointers For more information see INDEXING PROCEDURES Section 8 5 or STRUCTURE PoINnTERS Section 12 2 String Concatenation x dog y cat Z xX y print z dogcat If the first argument is of type string the result will be of type string If the first argument is of type matrix the result will be of type matrix Here are some examples 7 17 s10 e1ado GAUSS User Guide y 0 caterpillar The result will be a 1x1 matrix containing caterpil y zeros 3 1 cat The result will be a 3x1 matrix each element containing cat If we use the y created above in the following
13. To open Find and Replace we enter CTRL F in out open text editor In the Find and Replace widget select the check box next to Regex to enable regular expression searching One of the most simple regular expression options is to add a The means any character So if we search for rnd that will find any string that contains rnd followed by any character such as rnda rndb rndc rndn rndu etc Now enter rndKMu in the replace box and click Replace All Now all instances of rndu and rndn should be replaced with rndKMu 3 5 4 Changing Editor Properties Programming editor preferences can be accessed by selecting Tools Preferences from the menu bar From the Preferences window select Source from the tree on the left Here you can customize the programming editor s behavior 3 15 onul IND GAUSS User Guide File Edit Debug Tools View Window Help ye Xub O 8 4 O C gauss11 lib usericg CAgaussl1 lib gauss icg 40 0 M Or ur b CUN e nau Find mem E lt E El wnote word E match case Replace radu HJ le Ex Replace Al bd C gauss11 newprogram gss Ln 9 Col 3 dock ino em Figure 3 13 Find and Replace Regular Expression 3 5 5 Command Input Window The Command Input Window can be accessed by toggling the Input button on the right side of the status bar For details regarding the features and us
14. cdfLogisticInv 29 94 cdfm src 29 96 29 97 29 98 29 100 29 102 29 104 cdfMvn 29 94 cdfMvn2e 29 97 cdfMvnce 29 95 cdfMvne 29 96 cdfMvt2e 29 103 cdfMvtce 29 99 cdfMvte 29 101 cd N 29 105 cd N2 29 108 cd Nc 29 105 commandnamecdfNegBinomial 29 107 commandnamecdfNegBinomialInv 29 108 cd Ni 29 110 commandnamecdfPoisson 29 110 commandnamecdfPoissonInv 29 111 cdfRayleigh 29 112 cdfRayleighInv 29 113 cdfTc 29 113 cdfTci 29 115 cdfTnc 29 116 cdf Tvn 29 117 cdfWeibull 29 118 cdfWeibullInv 29 119 cdir 29 120 ceil 29 120 change font 3 3 change working directory 3 3 ChangeDir 29 121 characteristic polynomial 29 623 chdir 29 122 chi square 29 79 chi square noncentral 29 81 chiBarSquare 29 122 chol 29 124 choldn 29 125 Cholesky decomposition 0 1 7 5 29 124 29 810 cholsol 29 126 cholup 29 127 chrs 29 128 circles 21 22 clear breakpoints 3 21 clear working directory history 3 3 clear 29 129 clearg 29 130 close 3 10 close all 3 10 close 29 130 closeall 29 132 cls 29 134 code dataloop 29 137 code folding 3 12 code 29 134 coefficient of determination 29 584 29 589 coefficients 29 583 29 589 coefficients standardized 29 583 29 589 colon 6 39 color 21 19 21 25 Colors 0 1 colors 0 1 cols 29 138 colsf 29 139 columns in a matrix 29 138 combinate 29 139 combinated 29 140 comlog 29
15. endp A particular application may require setting other members of the DS instance for particular purposes but in general you may use them for your own purposes For example dO dname could be set to a GAUSS dataset name from which you read the data in the objective function procedure or d0 vnames could be set to the variable names of the columns of the data stored in d0 dataMatrix or dQ type could be an indicator variable for the elements of a vector of DS instances The following are complete examples of the use of the PV and DS structures The first example fits a set of data to the Micherlitz model It illustrates packing and unpacking by index include sqpsolvemt sdf struct DS Y Y dsCreate Y dataMatrix 3 183 13 8 Run Time Library Structures 059 871 622 541 184 110 875 018 903 770 762 556 PrRFRPRPFNNNNNN WN Ww struct DS X X dsCreate X dataMatrix seqa 1 1 13 struct DS Z Z reshape Z 2 1 Z 1 Y Z 2 X struct SQPsolveMTControl cl c1 sqpSolveMTcontrolCreate initializes EJ default values cl bounds 0 100 constrains parameters to be positive cl CovType 1 cl output 1 cl printIters 0 cl gradProc amp grad struct PV parl parl pvCreate 13 9 sa4ni9n1s 118 GAUSS User Guide start 2 4 2 parl pvPacki parl start Parameters 1 struct SQPsolveMTout out1
16. ord 10 10 5 3 Y y areshape rndu prodc ord 1 ord The quick and dirty method above uses the linear congruential generator which is fast but doesn t have the properties required for serious Monte Carlo work For series simulation you will need to use the KM generator sdo 345678 ord 10 10 5 3 z sd rndKMu prodc ord 1 sd0 y areshape z ord s eJIy uw DupJoM GAUSS User Guide Expanding a Matrix into an Array Vector of Matrices For computing the log likelihood of a variance components model of panel data it is necessary to expand a TXT matrix into an NTXT array of these matrices This is easily accomplished using areshape For example e n e Nue ore Ren a a r areshape m 3 3 3 print r Plane 1 1 0000 0 3000 0 2000 0 3000 1 0000 0 1000 0 2000 0 1000 1 0000 Plane 2 1 0000 0 3000 0 2000 0 3000 1 0000 0 1000 0 2000 0 1000 1 0000 1 0000 0 3000 0 2000 0 3000 1 0000 0 1000 0 2000 0 1000 1 0000 11 1 2 aconcat aconcat creates arrays from conformable sets of matrices or arrays With this function contents are completely specified by the user This example tries three concatenations one along each Working with Arrays dimension rndseed 345678 x1 rndn 2 2 x2 arrayinit 2 2 1 a aconcat xl x21 print a 0 4300 0 2878 1 0000 1 0000 0 1327 0 0573 1 0000 1 0000 a aconcat x1 x2 2 print a 0 4300
17. 0 1327 1 0000 1 0000 px a aconcat x1 x2 3 print a Plane 1 along the first dimension or rows along the second dimension or columns 0 2878 0 0573 1 0000 1 0000 along the third dimension TEM s eJIy uw DupJoM GAUSS User Guide 0 4300 0 2878 0 1327 0 0573 Plane 2 1 0000 1 0000 1 0000 1 0000 11 1 3 aeye aeye creates an array in which the principal diagonal of the two trailing dimensions is set to one For example ord 2 3 3 a aeye ord print a Plane 1 1 00000 0 00000 0 00000 0 00000 1 00000 0 00000 0 00000 0 00000 1 00000 Plane 2 1 00000 0 00000 0 00000 0 00000 1 00000 0 00000 0 00000 0 00000 1 00000 11 1 4 arrayinit arrayinit creates an array with all elements set to a specified value For example ord 3 2 3 Working with Arrays a arrayinit ord 1 print a Plane 1 1 0000 1 0000 1 0000 1 0000 Plane 2 1 0000 1 0000 1 0000 1 0000 Plane 3 1 0000 1 0000 1 0000 1 0000 11 1 5 arrayalloc 1 1 1 1 1 1 0000 0000 0000 0000 0000 0000 arrayalloc creates an array with specified number and size of dimensions without setting elements to any values This requires a vector specifying the order of the array The length of the vector determines the number of dimensions and each element determines the size of the corresponding dimensions The array wi
18. 17 13 O I 9113 GAUSS User Guide The save command takes a matrix in memory adds a header that contains information on the number of rows and columns in the matrix and stores it on disk Numbers are stored in double precision just as they are in matrices in memory These files have the extension fmt Matrix files can be no larger than a single matrix No variable names are associated with matrix files GAUSS matrix files can be load ed into memory using the load or loadm command or they can be opened with the open command and read with the readr command With the readr command a subset of the rows can be read With the load command the entire matrix is load ed GAUSS matrix files can be open ed for read but not for append or for update If a matrix file has been opened and assigned a file handle rowsf and colsf can be used to determine how many rows and columns it has without actually reading it into memory seekr and readr can be used to jump to particular rows and to read them into memory This is useful when only a subset of rows is needed at any time This procedure will save memory and be much faster than load ing the entire matrix into memory 17 5 File Formats This section discusses the GAUSS binary file formats There are four currently supported matrix file formats Version Extension Support Small Matrix v89 fmt Obsolete use v96 Extended Matrix v89 fmt Obsolete use v96 Matrix v92 fmt Obs
19. Another example is a symbol that is declared as a local and then declared as a local procedure or function later in the same procedure definition This allows doing arithmetic on local function pointers before calling them For more information see INDEXING PROCEDURES Section 8 5 8 1 3 Body of Procedure The body of the procedure can have any GAUSS statements necessary to perform the task the procedure is being written for Other user defined functions and other procedures can be referenced as well as any global matrices and strings 8 4 Procedures and Keywords GAUSS procedures are recursive so the procedure can call itself as long as there is logic in the procedure to prevent an infinite recursion The process would otherwise terminate with either an Insufficient workspace memory message or a Procedure calls too deep message depending on the space necessary to store the locals for each separate invocation of the procedure 8 1 4 Returning from the Procedure The return from the procedure is accomplished with the retp statement retp retp expression expression2 expressionN The retp statement can have multiple arguments The number of items returned must coincide with the number of rets in the proc statement If the procedure was defined with no items returned the retp statement is optional The endp statement that ends the procedure will generate an implicit retp with no objects returned If the procedure return
20. File listed in library not found A file listed in a library could not be opened Procedure has no definition The procedure was not initialized Define it Error opening temporary file One of the temporary files could not be opened The directory may be full Error writing temporary file One of the temporary files could not be written to The disk may be full Can t raise negative number to nonintegral power File handle must be a scalar Syntax error in library 25 17 soDesso y 10413 GAUSS User Guide G0302 G0317 G0336 G0339 G0341 G0347 G0351 G0352 G0355 G0360 G0364 G0365 File has been truncated or corrupted getname File header cannot be read load Cannot read input file or file header cannot be read open File size does not match header specifications or file header cannot be read Can t open temp file Disk full Can t debug compiled program File too big Can t allocate that many globals Warning Not reinitializing declare The symbol is already initialized It will be left as is Warning Reinitializing declare The symbol is already initialized It will be reset Wrong size line matrix Write error Paging error Unsupported executable file type 25 18 Error Messages G0368 G0369 G0370 G0371 G0372 G0373 G0374 G0375 G0376 G0377 G0378 G0379 G0380 G0381 G0382 Unable to allocate translati
21. The graphics window border and fill colors may be set using their respective Color buttons Once the file has been selected and the user presses OK the graphics window is created in a default size located at the top left corner of the page At this time the window object may be modified Creating a Text Object To create a text object select the Text menu item from the Draw menu or press the Draw text button on the toolbar Next position the mouse where you want the top left corner of your text then press and hold the left mouse button You may also move the object by pressing and holding the right mouse button while keeping the left button depressed Drag the mouse to the bottom left corner and let up on the mouse button 22 11 101p3 soiydeiy GAUSS User Guide The text region will be redrawn in the current background fill color and contain a text cursor inside At this point you may enter your text at the cursor using the last selected text font If the text requires more lines than the current bounding box allows the box will be resized as needed To save your text when you have finished typing press the OK icon on the text toolbar indicated by a green check mark or press the SHIFT ENTER key Clicking the mouse button outside the text window will also save the text and complete the operation The box will be redrawn with the proper font background border color and margin settings To cancel out of the text and
22. dsCreate d0 dataMatrix loadd maxfact output file sqpfact out reset struct SQPsolveMTOut out0 out SQPsolveMT amp lpr par90 d0 c0 lambdahat pvUnpack out par lambda phihat pvUnpack out0 par phi psihat pvUnpack out0 par psi print estimates print print lambda lambdahat 12 31 sa4ni9n1s GAUSS User Guide print print phi phihat print print psi psihat struct PV stderr stderr outQ par if not scalmiss out0 moment stderr pvPutParVector stderr sqrt diag out0 moment lambdase pvUnpack stderr lambda phise pvUnpack stderr phi psise pvUnpack stderr psi print standard errors print print lambda lambdase print print phi phise print print psi psise endif output off proc lpr struct PV parl struct DS datal local lambda phi psi sigma logl lambda pvUnpack par1 lambda phi pvUnpack parl phi psi pvUnpack parl psi sigma lambda phi lambda psi logl lnpdfmvn datal dataMatrix sigma retp logl endp proc ineq struct PV parl struct DS datal 12 32 Structures local lambda phi psi sigma e lambda pvUnpack par1 lambda phi pvUnpack parl phi psi pvUnpack parl psi sigma lambda phi lambda psi e eigh sigma 001 eigenvalues of sigma e e eigh phi 001 eigenvalues of phi retp e endp 12 33 sa4ni9n1s
23. fewer elements than x has columns it will be if scalerr cm cm inv x endif is located in the examples subdirectory as explained under create see OPERATOR PRECEDENCE Section 7 7 1 2 Getting Started 2 1 Installation Under UNIX Linux 1 Make a directory to install GAUSS in 2 cd to that directory 3 Gunzip the gz file if there is one 4 Untar the tar file 5 Run the executable script ginstall 6 Put the installation directory in the executable path 7 Put the installation directory in the shared library search path 8 Install the license To receive a license and license installation instructions email license aptech com For last minute information see README term 2 1 paviels Buna GAUSS User Guide 2 2 Installation Under Windows 2 2 1 Machine Requirements e A Pentium or AMD computer or equivalent e Operating System and Memory RAM requirements Windows XP 256 MB minimum 512 MB recommended Windows Vista 32 bit 512 MB minimum 1 GB recommended Windows Vista 64 bit 1 GB minimum 2 GB or more recommended Windows 7 32 bit 1 GB minimum 2 GB or more recommended Windows 7 64 bit 2 GB minimum 3 GB or more recommended e Minimum of 100 MB free hard disk space more may be needed depending on the size of matrices and the complexity of the program e Monthly defragmenting is recommended 2 2 2 Inst
24. x lt y z x le y z x lt y e Equal to ZX Y 7 10 Operators Z x ed y z x y e Not equal Ze xf Y z xne y z x y e Greater than or equal to z x gt y zZz x ge y Z x gt y e Greater than Z Xx gt y Z Xx gt y z x gt y If the relational operator IS preceded by a dot then the result will be a matrix of 1 s and 0 s based upon an element by element comparison of x and y e Element by element less than ISN aly Z x s1t y zx lt y s10 e1adoO GAUSS User Guide e Element by element less than or equal to Zz x lt y z x le y Z x lt y e Element by element equal to GS ie SS ys Z Xx eq y SA y e Element by element not equal to zax y Z x ne y z x y e Element by element greater than or equal to Z x gt y Z x ge y z x gt y e Element by element greater than Z x gt y3 Z x gt y Z x gt y Operators 7 4 Logical Operators The logical operators perform logical or Boolean operations on numeric values On input a nonzero value is considered TRUE and a zero value is considered FALSE The logical operators return a 1 if TRUE and a 0 if FALSE Decisions are based on the following truth tables Complement not X F T dx Conjunction X Y XandY TT T TF F FT F F F F Disjunction X o lt Tono HX pii iis s ii ias MHA
25. 0 00000 1 0000 Plane 3 3 0000 3 0000 3 0000 3 0000 11 2 7 setArray setArray enters a subarray matrix or scalar into an N dimensional array in place a arrayinit 3 2 2 3 setarray a 2 eye 2 print b Plane 1 3 0000 3 0000 3 0000 3 0000 Plane 2 1 0000 0 0000 0 0000 1 0000 11 16 Working with Arrays Plane 3 3 0000 3 0000 3 0000 3 0000 11 3 Looping with Arrays When working with arrays for loops and do loops may be used in the usual way In the following let Y be an Nx1XL array of L time series X an Nx1xK array of K independent variables Ba KXL matrix of regression coefficients phi a PXLxL array of garch coefficients theta a QxLxL array of arch coefficients and omega a LxL symmetric matrix of constants The log likelihood for a multivariate garch BEKK model can be computed using the index operator yord getOrders Y xord getOrders X gord getOrders phi aord getOrders theta N yord 1 No of observations L yord 3 No of time series K xord 3 No of independent variables in mean equation P gord 1 order of garch parameters Q aord 1 order of arch parameters r maxc P Q E Y amult X areshape B N K L Sigma areshape omega N L L for i r 1 N 1 for 3 1 0 1 W amult theta j atranspose E i j 1 3 2 sigma i sigma i amult W atranspose W 1 3 2
26. 24 27 OxFFFFFFFF for forward bit order 0 for backward bit order 28 31 OxABCDEF02 32 35 version currently 1 36 39 reserved 40 43 floating point type 1 for IEEE 754 44 47 12 signed 2 byte integer 1004 single precision floating point 1008 double precision float 48 51 2 4 or 8 the size of an element in bytes 52 55 0 real matrix 1 complex matrix 56 59 1 imaginary part of matrix follows real part standard GAUSS style 2 imaginary part of each element immediately follows real part FORTRAN style 60 63 always 2 64 67 1 for row major ordering of elements 2 for column major 17 23 O I 9113 GAUSS User Guide Offset Description 68 71 always 0 72 75 header size 128 columns 33 padded to 8 byte boundary 76 79 reserved 80 83 rows in data set 84 87 columns in data set 88 127 reserved The variable names begin at offset 128 and are stored 32 bytes each in ASCII format Each name corresponds to one column of data Names less than 32 characters are padded on the right with bytes of zero The variable type flags immediately follow the variable names They are 1 byte binary integers one per column padded to an even 8 byte boundary A 1 indicates a numeric variable and a 0 indicates a character variable Contents of the data set follow the header and start on an 8 byte boundary Data is either 2 byte signed integer 4 byte single precision floating point or 8 byte double precision floating po
27. 29 158 corrxs 29 159 cos 29 159 cosh 29 160 cosine inverse 29 29 counts 29 161 countwts 29 163 create 29 164 cropping 21 19 cross product 29 170 29 568 crossprd 29 170 Crout decomposition 29 171 29 172 Crout LU decomposition 0 1 crout 29 171 croutp 29 172 csrcol 29 174 csrlin 29 174 cumprodc 29 175 cumsumc 29 176 Index 5 xepu Index cumulative distribution function 29 68 cumulative products 29 175 cumulative sums 29 176 cursor 29 174 29 534 curve 29 177 cut 3 3 3 4 cvtos 29 178 D data coding 28 38 data handling 28 33 data loop 19 1 data page 3 17 data sets 17 7 28 36 data transformations 19 1 29 134 29 201 data writing 29 965 datacreate 29 179 datacreatecomplex 29 181 datalist 29 183 dataload 29 184 dataloop translator 5 6 dataloop 29 185 dataopen 29 185 datasave 29 187 date 21 20 29 188 date 23 2 29 188 datestr 29 189 datestring 29 189 datestrymd 29 190 dayinyr 29 191 dayofweek 29 191 debug 3 4 debug button 3 6 debug page 3 21 debug 29 192 debugger 3 22 debugging 5 7 16 3 28 50 29 511 declare 29 193 delete dataloop 29 200 delete 29 198 DeleteFile 29 200 deletion 29 229 29 230 29 569 29 612 delif 29 201 delimited 24 1 delimited files 17 3 delimited hard 24 6 delimited soft 24 5 denseToSp 29 202 denseToSpRE 29 203 denToZero 29 204 derivatives 29 404 deriva
28. 3 3 1 3 3 2 4 1 1 4 1 2 4 2 1 4 2 2 4 3 1 4 3 2 A complex N dimensional array is stored in memory in the same way Like complex matrices complex arrays are stored with the entire real part first followed by the entire imaginary part 10 1 shey GAUSS User Guide Every N dimensional array has a corresponding Nx1 vector of orders that contains the sizes of each dimension of the array This is stored with the array and can be accessed with getorders The first element of the vector of orders corresponds to the slowest moving dimension and the last element corresponds to the fastest moving dimension refer to the sectionnameGlossary of Terms at the end of the chapter for clear definitions of these terms The vector of orders for a 6x5x4x3x2 array which has 5 dimensions is the following 5x1 vector NU Bu 0 Two terms that are important in working with N dimensional arrays are dimension index and dimension number A dimension index specifies a dimension based on indexing the vector of orders Itis a scalar 1 to N where 1 corresponds to the dimension indicated by the first element of the vector of orders of the array the slowest moving dimension and N corresponds to the dimension indicated by the last element of the vector of orders the fastest moving dimension A dimension number specifies dimensions by numbering them in the same order that one would add dimensions to an array In other words the dimen
29. 4 closely spaced dots 5 dots and dashes 6 solid 21 15 90d GAUSS User Guide _parrow3 M 11 controls thickness of lines used to draw arrow This value may be zero or greater A value of zero is normal line width To create two single headed arrows located using inches use 2 _parrow 1 1 11 10 2 6 0 3 4 2 6 0 2 3 0 2 2 3 0 2 11 10 2 T5 Mx12 matrix draws one 3 D arrow per row of the input matrix for a total of M arrows If scalar zero no arrows will be drawn M 1 x starting point in 3 D plot coordinates M 2 y starting point in 3 D plot coordinates M 3 z starting point in 3 D plot coordinates M 4 x ending point in 3 D plot coordinates M 6 z ending point in 3 D plot coordinates M 7 ratio of the length of the arrow head to half its width M 8 size of arrow head in inches M 5 y ending point in 3 D plot coordinates M 9 type and location of arrow heads This integer number will be interpreted as a decimal expansion mn For example if 10 then m 1 n 0 m type of arrow head 0 solid 1 empty 2 open 3 closed n location of arrow head 0 none 1 atthe final end 2 at both ends M 10 color of arrow see Coors Section 21 5 21 16 Publication Quality Graphics _paxes _paxht _pbartyp M 11 line type 1 dashed 2 dotted 3 short dashes 4 closely spaced dots 5 dots and dashes 6 solid M 12 controls thickness of li
30. 6 10 7 Assignment Statements a 6 39 6 10 8 Function ArQUINents s seos mol EE a a 6 40 6 10 9 Indexing Matrices llle 6 40 6 10 10 Arrays of Matrices and Strings 0 o 6 41 6 10 11 Arrays Of Procedures o e 2 e 6 42 7 Operators 7 1 Element by Element Operators o 7 1 72 Matix Operators s cies eee hw Ae e a a eS 7 4 7 2 1 Numeric Operators llle 7 4 7 2 2 Other Matrix Operators llle 7 8 7 3 RelationdlOperators llle 7 9 7 4 LogicalOperatorS 259 olco to Ron RR REA REGES 7 13 7 5 Other Operators ss cu se ne rc hono RR RUE RR R E n mg 7 15 7 6 Using Dot Operators with Constants 0 7 20 7 7 Operator Precedence llle 7 22 viii Contents 8 Procedures and Keywords 8 1 8 2 8 3 8 4 8 5 8 6 8 7 Defining a Procedure eee ee 8 2 8 1 1 Procedure Declaration o 0 e len 8 3 8 1 2 Local Variable Declarations l l 8 3 8 1 3 Body of Procedure o a 8 4 8 1 4 Returning from the Procedure o e 8 5 8 1 5 End of Procedure Definition 2 004 8 5 Galinga Procedure lt a oea YR ee ale ee Ge ee XL UR Rd 8 6 IGVWOIOS rr yd hae wm ele a bee Se Eas Oh ws oe 8 7 8 3 1 Defining a Keyword lens 8 7 8 3 2 Calling a Keyword
31. G0409 G0410 G0411 recode Variable is a Number recode Variable is Procedure Cannot recode External Variable Cannot recode String Constant Invalid keep statement Invalid drop statement Cannot define Number Cannot define String Invalid select statement Invalid delete statement Invalid outtyp statement outtyp already defaulted to 8 Character data has been found in the output data set before an outtyp 2 or outtyp 4 statement This is a warning only outtyp must equal 2 4 or 8 outtyp override precision set to 8 Character data has been found in the output data set after an outtyp 2 or outtyp 4 statement This is a warning only 25 21 soDesso y 10413 GAUSS User Guide G0412 default not allowed in recode statement default allowed only in code statement G0413 Missing file name in dataloop statement G0414 Invalid listwise statement G0415 Invalid lag statement G0416 lag variable is a number G0417 lag variable is a procedure G0418 Cannot lag External Variable G0419 Cannot lag String Constant G0421 Command not supported in Run Time Module G0428 Cannot use debug command inside program G0429 Invalid number of subdiagonals G0431 Error closing dynamic library G0432 Error opening dynamic library G0433 Cannot find DLL function G0434 Error opening default dynamic library G0435 Invalid mode 25 22 Error Messages G0436 G0437 G0438 G0439 G0440 G0441 G044
32. G0510 G0514 G0515 G0516 G0517 G0518 Licensing failure Missing right parenthesis Cannot create temporary filename Cannot assign matrix to scalar member Invalid structure member Invalid structure redefinition Structure assignment mismatch Undefined structure Structure argument mismatch Too many structure members Duplicate name for structure member Not supported for structures Too many values in locator Too many dimensions in result Too many dimensions in argument Not implemented for complex 25 25 soDesso y 10413 GAUSS User Guide G0519 G0520 G0521 G0522 G0523 G0524 G0525 G0526 G0529 G0531 G0532 G0533 G0534 G0538 G0541 G0542 Illegal dereference of structure array Arguments not conformable Argument must be real Illegal indexing of dereferenced structure Numeric argument must be integer Found comma expecting index Argument contains NaNs Argument must be compact format Array orders must be gt 1 Two trailing dimensions of argument must be the same size Both dimensions of argument must be the same size 1 dimensional argument must contain only 1 element Cannot create file Zero illegal in for loop increment Illegal assignment to FOR loop counter Object too large for 32 bit version 25 26 Error Messages G0543 G0547 G0548 G0549 G0550 G0551 G0553 G0554 G0555 G0556 G0
33. Incdfbvn2 29 515 Incdfmvn 29 517 Incdfn 29 517 Incdfn src 29 94 29 109 Incdfn2 29 518 Incdfnc 29 519 Infact 29 519 lngammacplx 29 520 lnpdfmvn 29 521 lnpdfmvt 29 522 lnpdfn 29 522 Inpdft 29 523 load 29 524 loadarray 29 529 loadd 29 531 loadf 29 524 loadk 29 524 loadm 29 524 loadp 29 524 loads 29 524 loadstruct 29 532 loadwind 29 532 local variable declaration 8 3 local variables 6 8 8 3 29 533 local 8 2 29 533 locate 29 534 loess 29 534 loessmt 29 535 loessmtControlCreate 29 536 log coordinates 29 538 log factorial 29 519 log gamma 29 519 log 29 537 log base 10 29 537 log natural 29 513 logging commands 29 142 logical operators 7 13 logistic 29 93 29 94 29 617 loglog 29 538 logx 29 538 logy 29 539 looping 6 32 28 45 29 215 looping with arrays 11 17 Index 13 xapul Index loopnextindex 11 19 29 540 lower triangular matrix 29 542 lower 29 541 lowmat 29 542 lowmat1 29 542 1t 7 10 lt 7 11 ltrisol 29 543 LU decomposition 7 5 29 544 lu 29 544 lusol 29 545 M machEpsilon 29 545 machine epsilon 29 105 29 902 29 907 machine requirements 2 2 magnification 21 29 make dataloop 29 546 makevars 29 546 makewind 29 548 margin 29 549 matalloc 29 550 matinit 29 551 matrices indexing 6 40 matrix conformability 7 1 matrix files 17 13 matrix manipulation 28 24 matrix creat
34. Plane 1 2 500 6 500 10 500 Plane 2 14 500 11 31 s eJIy uw DupJoM GAUSS User Guide 18 500 22 500 means computed down columns c amean a 2 print c Plane 1 5 000 6 000 7 000 8 000 Plane 2 17 000 18 000 19 000 20 000 J means computed along 3rd dimension d amean a 3 print d Plane 1 7 000 8 000 9 000 10 000 11 000 12 000 13 000 14 000 15 000 16 000 17 000 18 000 11 6 A Panel Data Model Suppose we have N cases observed at T times Let y be an observation on a dependent variable for the i case at time t X an observation of k independent variables for the i case at time t B a 11 32 Working with Arrays Kx1 vector of coefficients Then Yu Xi B ui En is a variance components model where u is a random error term uncorrelated with e but which is correlated within cases This implies an NTXNT residual moment matrix that is block diagonal with N TxT moment matrices with the following form 2x52 2 2 Tq ECs 4 Ty Ti DA o i 2 2 2 2 om e gustu The log likelihood for this model is InL 0 5 NTIn 2n In O Y XByQ Y XB where 2 is the block diagonal moment matrix of the residuals Computing the Log likelihood Using GAUSS arrays we can compute the log likelihood of this model without resorting to do loops Let Y be a 100x3x1 array of observations on the dependent variable and X a 100
35. Suppress the sign on banner output only Turn the dataloop translator on Turn the dataloop translator off 5 1 eur puewwog GAUSS User Guide 5 1 Viewing Graphics GAUSS generates tkf files for graphical output The default output for graphics is graphic tkf On Windows you can use vwr exe to view the graphics file on UNIX Linux Mac you can use vwrmp Two functions are available to convert tkf files to PostScript for printing and viewing with external viewers the tkf2ps function will convert tkf files to PostScript ps files and the tkf2eps function will convert tkf files to encapsulated PostScript eps files For example to convert the file graphic tkf to a postscript file named graphic ps use ret tkf2ps filename tkf filename ps If the function is successful it returns 0 5 2 Command Line History and Command Line Editing When you run a command at the TGAUSS prompt it is added to your command line history which is stored in a file called gauss prompt history in your HOME directory on UNIX Linux or in your CHOMEDRIVE HOMEPATH directory on Windows A separate history for commands entered in the command line debugger is stored in a file called gauss debug prompt history in the same directory By default the last 500 commands executed at the TGAUSS and debugger command lines are stored in these files You can change this number by changing prompt hist num in your
36. The file will have a gcg extension The compile command will compile an entire program to a compiled file An attempt to edit a compiled file will cause the source code to be loaded into the editor if it is available to the system The run command assumes a compiled file if no extension is given and that a file with a gcg extension is in the src_path A saveall command is available to save the current contents of memory in a compiled file for instant recall later The use command will instantly load a compiled program or set of procedures at the beginning of an ASCII program before compiling the rest of the ASCII program file Since the compiled files are encoded binary files the compiler is useful for developers who do not want to distribute their source code 16 1 Jajidwoy GAUSS User Guide 16 1 Compiling Programs Programs are compiled with the compile command 16 1 1 Compiling a File Source code program files that can be run with the run command can be compiled to gcg files with the compile command compile qxy e All procedures global matrices arrays strings and string arrays and the main program segment will be saved in the compiled file The compiled file can be run later using the run command Any libraries used in the program must be present and active during the compile but not when the program is run If the program uses the dlibrary command the d11 files must be present when the program is run and the
37. _pline3d _plotshf M 6 ending point of radius M 7 angle in radians M 8 color see Corons Section 21 5 M 9 controls line thickness This value may be zero or greater A value of zero is normal line width Mx9 matrix Allows extra lines to be added to an xyz or surface graph in 3 D plot coordinates M 1 x starting point M 2 y starting point M 3 z starting point M 4 x ending point M 5 y ending point M 6 z ending point M 7 color M 8 line type dashed dotted short dashes closely spaced dots dots and dashes solid M 9 line thickness 0 normal width M 10 hidden line flag 1 obscured by surface 0 not obscured Du WN m 2x1 vector distance of plot from lower left corner of output page in inches 1 x distance 2 y distance If scalar 0 there will be no shift Default is 0 Note Used internally For the same functionality see axmargin in the GAUSS LANGUAGE REFERENCE This is used by the graphic panel routines The user must not set this when using the graphic panel procedures 21 24 Publication Quality Graphics _plotsiz _pltype _plwidth _pmcolor 2x1 vector size of the axes area in inches If scalar 0 the maximum size will be used Note Used internally For the same functionality see axmargin in the GAUSS LANGUAGE REFERENCE This is used by the graphic panel routines The user must not set this when using the gra
38. is legal 8 3 Keywords A keyword like a procedure is a subroutine that can be called interactively or from within a GAUSS program A keyword differs from a procedure in that a keyword accepts exactly one string argument and returns nothing Keywords can perform many tasks not as easily accomplished with procedures 8 3 1 Defining a Keyword A keyword definition is much like a procedure definition Keywords always are defined with 0 returns and 1 argument The beginning of a keyword definition is the keyword statement keyword name strarg name Name of the keyword up to 32 alphanumeric characters or an underscore beginning with an alpha or an underscore strarg Name that will be used inside of the keyword for the argument that is passed to the keyword when it is called There is always one argument The name is known only in the keyword being defined Other keywords can use the same name but they will be separate entities This will always be a string If the keyword is called with no characters following the name of the keyword this will be a null string The rest of the keyword definition is the same as a procedure definition For more information see DEFINING A PROCEDURE Section 8 1 Keywords always return nothing Any retp statements if used should be empty For example 8 7 Se1npoooJd GAUSS User Guide keyword add s local tok sum if S yo Tg print The argument is a null string retp endif
39. of an array The size of the selected dimension of the resulting array is shrunk to one and contains the means minimums or maximums depending on the function called For example a areshape seqa 1 1 12 2 3 2 print a Plane 1 1 0000 2 0000 3 0000 4 0000 5 0000 6 0000 Plane 2 7 0000 8 0000 9 0000 10 000 11 000 12 000 compute means along third dimension print amean a 3 Plane 1 11 25 s eJIy uw BUMJOM GAUSS User Guide 4 0000 5 0000 6 0000 7 0000 8 0000 9 0000 print means along the second dimension i e down the columns TP print amean a 2 Plane 1 3 0000 4 0000 Plane 2 9 0000 10 000 print the minimums down the columns a print amin a 2 Plane 1 1 0000 2 0000 Plane 2 7 0000 8 0000 print the maximums along the third dimension 11 26 Working with Arrays print amax a 3 Plane 1 7 0000 8 0000 9 0000 10 000 11 000 12 000 11 44 getDims This function returns the number of dimensions of an array a arrayinit 4 4 5 2 0 print getdims a 4 00 11 45 getOrders This function returns the sizes of each dimension of an array The length of the vector returned by getOrders is the dimension of the array a arrayinit 4 4 5 2 0 print getOrders a 11 27 s eJIy uw BUMJOM GAUSS User Guide 11 4 6 arraytomat This function converts an array with two or fewer
40. outl SQPsolveMT Micherlitz par1 Z c1 estimates pvGetParVector outl par print parameter estimates print estimates print print standard errors print sqrt diag outl moment proc Micherlitz struct PV parl struct DS Z local p0 e s2 p0 pvUnpack par1 1 e Z 1 dataMatrix p0 1 p8 2 expC p98 3 7 2 dataMatrix s2 moment e 0 Crows e 1 retp 2 rows e e e s2 1n 2 pi s2 endp proc grad struct PV parl struct DS Z local p0 e el e2 e3 w 9 82 p0 pvUnpack par1 1 w exp p0 3 Z 2 dataMatrix e z 1 dataMatrix p0 1 p0 2 w s2 moment e 0 rows e el ones rows e 1 e2 w e3 p8 2 Z 2 dataMatrix w W 1 e e s2 rows e g e el w e el g g e e2 w e e2 g g Ce e3 w e e3 13 10 Run Time Library Structures retp 4 g Crows e s2 endp This example estimates parameters of a confirmatory factor analysis model include sqpsolvemt sdf lambda 1 0 0 0 0 5 0 0 0 0 1 0 0 0 0 5 lmask 0 6 1 0 0 0 0 1 phi 1 0 0 3 0 3 1 0 theta 0 6 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 6 tmask 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 struct PV par0 par pvCreate par8 pvPackm parQ lambda lambda 1mask par8 pvPacks par0 phi phi par8 pvPacksm par0 theta theta tmask 13 11 sa4ni9n1s 118 GAUSS
41. output outwidth printfm print screen Specify format for printing a matrix Open close rename auxiliary output file or device Set auxiliary output width Formatted matrix print Print matrix or string Turn printing to the window on and off This example illustrates printing a matrix to a file format rd 8 2 outwidth 132 output file myfile asc reset screen off print x output off screen on The numbers in the matrix x will be printed with a field width of 8 spaces per number and with 2 places beyond the decimal point The resulting file will be an ASCII data file It will have 132 column lines maximum A more extended example follows This program will write the contents of the GAUSS file mydata dat into an ASCH file called mydata asc If there is an existing file by the name of mydata asc it will be overwritten output file mydata asc reset screen off format rd 1 8 open fp mydata do until eof fp print readr fp 200 17 5 O I 9113 GAUSS User Guide endo fp close fp end The output reset command will create an auxiliary output file called mydata asc to receive the output The window is turned off to speed up the process The GAUSS data file mydata dat is opened for reading and 200 rows are read per iteration until the end of the file is reached The data read are printed to the auxiliary output mydata asc only because the window is off 17 1 2 General Fil
42. print The argument is s sum 6 do until s tok s token s sum sum stof tok endo format rd 1 2 print The sum is sum endp The keyword defined above will print the string argument passed to it The argument will be printed enclosed in single quotes 8 3 2 Calling a Keyword When a keyword is called every character up to the end of the statement excluding the leading spaces is passed to the keyword as one string argument For example if you type add 1234 5 the keyword will respond The sum is 15 00 8 8 Procedures and Keywords Here is another example add the keyword will respond The argument is a null string 8 4 Passing Procedures to Procedures Procedures and functions can be passed to procedures in the following way proc max x y procedure to return maximum if xy retp x else retp y endif endp proc min x y procedure to return minimum if x lt y retp x else retp y endif endp fn lgsqrt x In sqrt x function to return log of square root 8 9 se1npoooJd GAUSS User Guide proc myproc amp fl amp f2 x y local f1 proc f2 fn zZ z f1 x y retp 2 z endp The procedure myproc takes four arguments The first is a procedure 1 that has two arguments The second is a function 2 that has one argument It also has two other arguments that must be matrices or scalars In the local s
43. the first element of the vector of indices corresponds to the slowest moving dimension of the array the second element to the second slowest moving dimension and so on each unique vector of indices locates a unique subarray In general an N K x1 vector of indices locates a K dimensional subarray that begins at the position indicated by the indices The sizes of the dimensions of the K dimensional subarray correspond to the last K elements of the vector of orders of the N dimensional array For a 6x5x4x3x2 array y the 2x1 vector of indices locates the 4x3x2 subarray in y that begins at 2 5 1 1 1 and ends at 2 5 4 3 2 10 1 Bracketed Indexing Brackets can be used to index N dimensional arrays in virtually the same way that they are used to index matrices Bracketed indexing is slower than the convenience array functions such as getarray and setarray however it can be used to index non contiguous elements In order to index an N dimensional array with brackets there must be N indices located within the brackets where the first index corresponds to the slowest moving dimension of the array and the last index corresponds to the fastest moving dimension 10 3 shey GAUSS User Guide For a 2x3x4 array x such that 1 1 1 through 1 3 4 12 3 4 5 6 7 8 9 10 11 12 2 1 1 through 2 3 4 13 14 15 16 17 18 19 20 21 22 23 24 x 1 2 3 returns a 1x1x1 array containing the 1 2 3 element of x x 3
44. triangular matrix upper 29 939 trigamma 29 928 trimr 29 928 trivariate Normal 29 117 troubleshooting libraries 15 12 TRUE 6 32 7 10 trunc 29 929 truncating 29 929 type 29 930 typecv 29 931 typef 29 932 U unconditional branching 6 35 underdetermined 29 583 29 589 undo 3 3 union 29 933 unionsa 29 934 uniqindx 29 935 uniqindxsa 29 936 unique 29 937 uniquesa 29 938 until 29 215 upmat 29 939 upmat1 29 939 upper triangular matrix 29 939 upper 29 940 use 29 940 user defined function 29 477 29 646 utctodt 29 942 utctodtv 29 943 utrisol 29 944 V vals 29 945 varget 29 946 vargetl 29 947 variable names 29 384 29 385 variables debugging 3 24 variables editing 3 24 variables viewing 3 24 variance 29 229 29 231 variance covariance matrix 29 583 29 589 29 953 varindxi 29 597 varmall 29 948 varmares 29 949 varput 29 949 varputl 29 951 vartypef 29 952 vem 29 953 vems 29 953 vcx 29 953 vcxs 29 953 vec vecr 29 954 vech 29 955 vector dataloop 29 956 vectors 6 40 vget 29 957 view 29 957 viewing graphics 5 2 viewing program output 4 3 viewxyz 29 958 vlist 29 959 vnamecv 29 959 volume 29 960 vput 29 960 Index 23 xapul Index vread 29 961 vtypecv 29 962 W wait 29 962 waitc 29 962 walkindex 29 963 watch window 3 24 Weibull 29 118 29 119 29 619 weighte
45. type char char char char numeric The data set is double precision since character data is explicitly specified Example 3 The third example is a hard delimited ASCII file called cplx asc The file contains six columns of ASCII data 456 4 345 2 533 2 345 5 524 5 257 6 624 3 639 5 826 5 331 4 602 3 333 4 342 1 816 7 452 6 The ATOG command file is cp1x cmd input gauss cplx asc output cplx invar delimit cvar 3 complex The output data set will contain the following information 935 3 376 4 690 8 name cvarl cvar2 cvar3 case 1 456 4 345 21 533 2 345 51 case 2 257 6 624 31 639 5 826 51 case 3 602 3 333 4i 342 1 816 7i 524 5 935 31 331 4 376 41 452 6 690 81 type numeric numeric numeric 24 14 ATOG The data set defaults to single precision since no character data is present and no outtyp command is specified 24 4 Error Messages atog atog atog atog atog atog atog atog Can t find input file The ASCII input file could not be opened Can t open output file The output file could not be opened Can t open temporary file Notify Aptech Systems Can t read temporary file Notify Aptech Systems Character data in output file Setting output file to double precision The output file contains character data The type was set to double precision automatically Character data longer than 8
46. window Partition window into tiled graphic panels makewind Create graphic panel with specified size and position setwind Set to specified graphic panel number 21 8 Publication Quality Graphics nextwind getwind savewind loadwind Set to next available graphic panel number Get current graphic panel number library pgraph graphset begwind window 2 2 0 xsize 9 2 ysize 6 855 2 Save graphic panel configuration to a file Load graphic panel configuration from a file This example creates four tiled graphic panels and one graphic panel that overlaps the other four Create four tiled graphic panels 2 rows 2 columns Create graphic panel that overlaps the tiled graphic panels makewind xsize ysize xsize 2 ysize 2 0 x sega 1 1 1000 Create X data y sin x 1 10 Create Y data setwind 1 Graph 1 upper left corner xy x y nextwind Graph 2 upper right corner logx x y nextwind Graph 3 lower left corner logy x y nextwind Graph 4 lower right corner loglog x y nextwind Graph 5 center overlayed bar x y endwind End graphic panel processing display graph 21 9 90d GAUSS User Guide 21 3 6 Inch Units in Graphic Panels Some global variables allow coordinates to be input in inches If a coordinate value is in inches and is being used in a graphic panel that value will be s
47. 122 3 Using Structure Pointers in Procedures 12 13 1238 Special SMUCUFES s 2 CIT 12 15 12 9 1 The DS Stnucture 4 ca cori ceux x omm m A m ommo 12 15 12 89 2 The PV Sulle uuu gonna coe Sak cm e Rm RU RR Rm Re 12 16 123 3 Miscellaneous PV Procedures e 12 20 12 3 4 Control Structures 2 ccsa c RR IRR ee ee e a 12 22 124 SSgpSOlVelM s ze c s ee ee be ke eek eho ee A A es eS 12 23 124 1 Input Arguments 2 08 6 4684484 ko ba ee eee wo 12 24 12 42 Output Argument 2 000202 eee eee 12 27 124 3 Example x 20 ee ee wee ee AA 12 29 12 4 4 The Command File 2 5 858 224 2842 deep eee Re 12 30 13 Run Time Library Structures 13 1 The PV Parameter Structure es 13 1 19 2 Fast Pack FUNCIONS aa se asarrean a ee we RE RR 13 6 133 The DS Data Structure osi xo e e cuim B moche Rm ces 13 7 14 Multi Threaded Programming in GAUSS 14 The FUNCIONS 2 254442 ess reir AA 3h39 303 R4 O33 14 1 14 GAUSS Threading Concepts s lt s oea sac watas naga ee eee 14 3 14 3 Coding With Threads 2 leen 14 4 14 4 Coding Restrictions 2 2 00 llle 14 6 GAUSS User Guide 15 Libraries 154 Autoloader x mo momo m RR EA eee ew be 15 1 15 1 1 Forward References 2222s 15 2 15 1 2 The Autoloader Search Path 0 15 3 15 2 Global Declaration Fles 2 0 6 5 Rok AOL a eee See Yoox Re 15 9 15 9 Woubleshooung cicle rara RO mu Rip He
48. 142 comma 7 16 command 6 2 command history toolbar 3 5 command history window 3 7 command input window 3 8 3 16 Index 4 Index command line 5 1 command line editing 3 8 5 2 command line history 3 8 5 2 command page 3 2 4 3 command page toolbar 3 4 comments 6 38 comparison functions 29 299 29 300 comparison operator 6 40 compilation phase 19 3 compile 16 1 compile time 6 1 compile 29 143 compiled language 6 1 compiler 16 1 compiler directives 28 42 compiling 28 48 compiling files 16 2 compiling programs 16 2 complex constants 6 14 29 194 29 503 29 862 complex modulus 29 1 complex 24 4 29 144 components and usage 3 22 con 29 145 concatenation matrix 7 8 7 9 concatenation string 7 17 cond 29 148 condition number 29 148 conditional branching 6 34 config 5 5 conformability 7 1 conj 29 149 cons 29 150 ConScore 29 150 constants complex 6 14 29 194 29 503 29 862 continue 29 154 contour levels 21 22 contour 29 155 control flow 6 31 control structures 12 22 conv 29 156 conversion character to ASCII value 29 945 conversion float to ASCII 29 336 29 337 conversion string to floating point 29 862 convertsatostr 29 157 convertstrtosa 29 157 convolution 29 156 coordinates 21 6 copy 3 3 3 4 correlation matrix 29 158 29 159 29 584 29 589 corrm 29 158 corrms 29 159 corrvc 29 158 corrx
49. 2 returns a 2x1x1 array containing 10 22 x 2 1 4 returns a 1x3x2 array containing 13 16 17 20 21 24 10 4 N Dimensional Arrays x 2 1 3 returns a 2x1x3 array containing 17 18 19 10 2 ExE Conformability The following describes rules for EXE conformability of arrays for operators and functions with two or more arguments e Any N dimensional array is conformable to a scalar e An array is conformable to a matrix only if the array has fewer than 3 dimensions and the array and matrix follow the standard rules of EXE conformability e Two arrays are EXE conformable if they comply with one of the following requirements The two arrays have the same number of dimensions and each dimension has the same size The two arrays have the same number of dimensions and each of the N 2 slowest moving dimensions has the same size In this case the 2 fastest moving dimensions of the arrays must follow the EXE comformability rules that apply to matrices Both of the arrays have fewer than 3 dimensions and they follow the EXE conformability rules that apply to matrices 10 3 Glossary of Terms dimensions The number of dimensions of an object vector of orders Nx1 vector of the sizes of the dimensions of an object where N is the number of dimensions and the first element corresponds to the slowest moving dimension 10 5 shey GAUSS User Guide vector of indices 1 to N x1 vector of indic
50. 2 1 Or you can use indexing to reference a subarray of structures e3tmp el e2 3 1 e3 1 12 6 Structures e3 is a 2x1 array e3 isa matrix z matr struct example3 e3 el matrix x matrix y string str struct example2 e2 e2 is a 3x1 array ix z matrix z struct example3 e3 struct example3 e3 xl array e3 is a 3x1 array matrix w string aray sa matrix w matrix w matrix w string aray sa string aray sa string aray sa matrix w matrix w string aray sa string aray sa Figure 12 1 Structure tree for e1 12 7 s n n Ss GAUSS User Guide In this case e3tmp would be an array of 3x1 example3 structures since the 3 1 member of el e2 contains a 3x1 array of example3 structures It is important to remember however that when indexing a structure array on multiple levels only the final index may resolve to an array of structures For example e3tmp el e2 1 e3 2 1 would be invalid since el e2 1 resolves to a 3x1 array of example2 structures 12 1 6 Saving an Instance to the Disk Instances and vectors or matrices of instances of structures can be saved in a file on the disk and later loaded from the file onto the disk The syntax for saving an instance to the disk is ret savestruct instance filename The file on the disk will have an fsr extension For example include ds sdf struct DS pd p0 reshape dsCreate 2 1 retc saveStruct p2 p2
51. 28 9 29 249 eigenvalues and eigenvectors 29 252 eigh 29 250 eighv 29 251 eigv 29 252 elapsedTradingDays 29 254 element by element conformability 7 1 10 5 element by element operators 7 1 else 29 431 elseif 29 431 empty matrix 6 15 29 138 29 504 29 525 29 772 29 784 end of file 29 258 end 29 254 endp 8 2 8 5 29 255 endwind 29 256 envget 29 257 environment search 29 257 eof 29 258 eq 7 10 eq 7 12 Index 7 xepu Index eqSolve 29 259 eqSolvemt 29 263 eqSolvemtControlCreate 29 267 eqSolvemtOutCreate 29 268 eqSolveSet 29 269 eqv 7 14 7 15 eqv 7 15 erf 29 269 erfc 29 269 erfccplx 29 271 ervCInv 29 248 erfcplx 29 271 ervinv 29 248 error bar 21 20 error code 29 271 29 784 error function 29 269 error handling 28 50 error messages 25 1 29 273 29 511 error output window 3 9 3 16 error trapping 29 924 error 29 271 errorlog 29 272 errorlogat 29 273 escape character 6 22 etdays 29 273 ethsec 29 274 etstr 23 5 29 275 EuropeanBinomCall 29 276 EuropeanBinomCall_Greeks 29 277 EuropeanBinomCall ImpVol 29 279 EuropeanBinomPut 29 280 EuropeanBinomPut Greeks 29 281 EuropeanBinomPut ImpVol 29 283 EuropeanBSCall 29 284 EuropeanBSCall Greeks 29 285 EuropeanBSCall_ImpVol 29 286 EuropeanBSPut 29 287 EuropeanBSPut Greeks 29 288 EuropeanBSPut ImpVol 29 289 exctsmpl 29 290 exec 29 291 execbg 29 292 execu
52. 3 21 hyperbolic cosine 29 160 hyperbolic sine 29 808 hyperbolic tangent 29 910 I if 29 431 imag 29 432 imaginary matrix 29 432 inch coordinates 21 6 include 29 433 incomplete beta function 29 68 incomplete gamma function 29 89 indcv 29 434 indefinite 6 28 index variables 29 597 indexcat 29 435 indexing matrices 6 40 7 16 indexing procedures 7 17 indexing array 10 3 indexing structure 12 5 indices 29 437 indices2 29 438 indicesf 29 439 indicesfn 29 440 indnv 29 441 indsav 29 442 infinity 6 28 initialize 8 4 initializing arrays 11 1 inner product 7 5 input ATOG command 24 4 input console 29 145 input keyboard 29 145 installation 2 1 installation UNIX Linux 2 1 installation Windows 2 2 Index 11 xapul Index instruction pointer 6 3 integration 28 3 28 4 29 447 29 450 29 452 29 455 29 458 29 466 interactive commands 5 4 interpreter 6 1 intersection 29 465 intgrat2 29 443 intgrat3 29 445 inthp1 29 447 inthp2 29 449 inthp3 29 452 inthp4 29 455 inthpControlCreate 29 458 intquad1 29 458 intquad2 29 460 intquad3 29 461 intrinsic function 6 8 intrleav 29 463 intrleavsa 29 464 intrsect 29 465 intrsectsa 29 466 intsimp 29 466 inv 29 467 invar ATOG command 24 5 inverse cosine 29 29 inverse sine 29 30 inverse generalized 29 469 29 621 29 622 inverse matrix 29 467 inverse sweep 29
53. 4 2 ne 7 11 ne 7 12 new 3 3 3 4 3 18 new 29 574 nextindex 29 575 nextn 29 576 nextnevn 29 576 nextwind 29 577 nocheck 24 10 Normal distribution 29 94 29 95 29 06 29 97 29 99 29 101 29 103 29 105 29 108 29 514 29 517 29 518 29 519 Normal distribution bivariate 29 72 not 7 13 7 14 not 7 15 null space 29 578 null 29 578 nulli 29 579 numCombinations 29 580 O obsolete commands 0 1 ols 29 580 olsmt 29 585 olsmtControlCreate 29 592 olsqr 29 593 olsqr2 29 594 olsqrmt 29 595 ones 29 595 open 3 3 3 4 open 29 596 operators 6 1 7 4 operators element by element 7 1 optimization 28 17 optn 29 602 optnevn 29 602 or 7 13 7 14 or 7 15 orth 29 604 orthogonal complement 29 578 orthonormal 29 578 29 604 outer product 7 6 output 17 4 output functions 28 56 output 29 604 output ATOG command 24 10 outtyp dataloop 29 608 outtyp ATOG command 24 11 outvar ATOG command 24 11 outwidth 29 608 P pacf 29 609 Index 15 xapul Index packed ASCII 24 1 24 8 packedToSp 29 610 packr 29 612 page organization 3 1 _pageshf 21 14 _pagesiz 21 14 pairwise deletion 7 5 29 229 29 230 29 569 panel data 11 32 _parrow 21 14 _parrow3 21 16 parse 29 613 paste 3 3 3 4 3 5 pause 29 614 _paxes 21 17 _paxht 21 17 _pbartyp 21 17 _pbarwid 21 18 _pbox 21 18 _pboxlim 21 19 _pcolor 21 19 _pcrop
54. 4 single precision 6 7 8 43x10 lt X lt 3 37x10 38 8 double precision 15 16 4 19x1073 lt X lt 1 67x10 308 If the output type is integer the input numbers will be truncated to integers If your data has more than 6 or 7 significant digits specify outtyp as double Character data require outtyp d ATOG automatically selects double precision when character data is specified in the invar statement unless you have specified nocheck The precision of the storage selected does not affect the accuracy of GAUSS calculations using the data GAUSS converts all data to double precision when the file is read outvar Selects the variables to be placed in the GAUSS data set The outvar command needs only the list of variables to be included in the output data set They can be in any order In this example 24 11 SOLV GAUSS User Guide invar name age pay sex var 1 10 x 005 outvar sex age x001 x003 var 1 8 the outvar statement selects the following variables column name data type 1 sex character 2 AGE numeric 3 X001 numeric 4 X003 numeric 5 VARO1 numeric 6 VARO2 numeric 7 VARO3 numeric 8 VARO4 numeric 9 VAROS numeric 10 VARO6 numeric 11 VARO7 numeric N VARO8 numeric outvar is not used with packed ASCII files preservecase Optional preserves the case of variable names The default is nopreservcase which will force variable names for numeric variables to upper case and character variables to l
55. 469 invpd 29 467 invswp 29 469 iscplx 29 470 iscplxf 29 471 isden 29 471 isinfnanmiss 29 472 ismiss 29 472 J Jacobian 29 404 K keep dataloop 29 473 key 29 474 keyav 29 476 keyboard input 29 150 keyboard reading 29 474 keyw 29 476 keyword 8 1 8 7 keyword procedure 29 477 keyword 29 477 keywords 28 46 Kronecker 7 6 L label 6 35 6 39 8 1 29 395 29 398 lag dataloop 29 478 lagi 29 479 lagn 29 479 lambda 29 82 lapeighb 29 480 lapeighi 29 481 lapeigvb 29 482 lapeigvi 29 484 lapgeig 29 485 lapgeigh 29 486 lapgeighv 29 487 lapgeigv 29 488 lapgschur 29 497 lapgsvdcst 29 489 lapgsvds 29 492 lapgsvdst 29 494 Laplace 29 91 29 92 29 616 lapsvdcusv 29 498 Index 12 Index lapsvds 29 500 lapsvdusv 29 501 layout 3 6 3 18 layout and usage 3 10 le 7 10 le 7 12 least squares 7 5 least squares regression 29 580 29 585 left hand side 15 2 legend 21 22 let 29 502 lib 29 507 libraries 15 1 28 47 libraries active 29 509 library 29 508 line numbers 29 511 line thickness 21 16 21 20 21 25 line type 21 25 linear algebra 28 5 linear equation 29 809 linear equation solution 7 5 lines 21 21 21 22 21 24 linesoff 29 511 lineson 29 511 linsolve 29 512 listwise dataloop 29 513 listwise deletion 29 229 29 230 29 569 29 612 literal 6 23 7 19 1n 29 513 Incdfbvn 29 514
56. 879 subvec 29 880 sum 29 882 sumc 29 881 sumr 29 883 surface 29 885 svd 29 887 svd1 29 888 svd2 29 889 svdcusv 29 890 svds 29 891 svdusv 29 892 sweep inverse 29 469 symbol editor 3 20 symbol names 6 39 symbol table 29 803 symbol table type 29 930 symbols allocate maximum number 29 574 syntax 6 37 syntax highlighting 3 12 sysstate 29 893 system 29 908 T t distribution Student s 29 113 tab 29 908 table 7 6 tan 29 909 tanh 29 910 tempname 29 911 tensor 7 6 text files 28 34 TGAUSS 5 1 thickness line 21 16 21 20 21 25 ThreadBegin 29 911 ThreadEnd 29 912 ThreadJoin 29 913 threads 14 1 28 43 ThreadStat 29 914 tick marks 21 28 tilde 7 9 time and date functions 28 53 time 23 2 29 914 time elapsed 29 274 timed iterations 23 6 timedt 29 915 timestr 29 915 timeutc 29 916 timing functions 29 430 title 29 917 tkf2eps 29 917 tkf2ps 29 918 tocart 29 919 todaydt 29 919 Toeplitz matrix 29 920 toeplitz 29 920 toggle auto reload 3 18 toggle breakpoint 3 21 token 29 921 toolbar 3 18 toolbar graphics editor 22 2 toolbars 3 3 3 21 tooltips 3 12 topolar 29 922 trace program execution 29 922 trace 29 922 translation phase 19 3 Index 22 Index transpose 7 8 transpose bookkeeping 7 8 trap flag 29 924 29 926 trap state 29 784 trap 29 924 trapchk 29 926 triangular matrix lower 29 542
57. A real data set with 2 rows and 3 columns will be stored on disk in the following way from the lowest addressed element to the highest addressed 17 18 File I O element 1 1 1 2 1 3 2 1 2 2 2 3 The rows of a complex data set are stored with the real and imaginary parts interleaved element by element A 2x3 complex data set then will be stored on disk in the following way from the lowest addressed element to the highest addressed element 1L 1 r L1 1 2 r 1 2 1 3 r 1 3 2 1 r 2 1 2 2 r 2 2 i 2 3 r 2 3 i 17 5 6 Extended Data Set v89 Obsolete Data sets with more than 8175 columns are saved in an extended format that cannot be read by the 16 bit version These files have a dht descriptor file formatted as follows Offset Description 0 1 EEDA hex identification flag 2 3 data type in dat file 2 4 8 unsigned 2 byte integer 4 7 reserved all 0 s 8 11 columns unsigned 4 byte integer 12 15 row size in bytes unsigned 4 byte integer 16 19 header size in bytes unsigned 4 byte integer 20 23 reserved all 0 s 24 27 reserved all 0 s 28 29 control flags unsigned 2 byte integer 30 127 reserved all 0 s Aside from the differences in the descriptor file and the number of columns allowed in the data file extended data sets conform to the v89 data set description specified above 17 19 O I 9113 GAUSS User Guide 17 5 7 Matrix v92 Obsolete Offset Description
58. Displays the opening screen of Help From the opening screen you can jump to step by step instructions for using the graphics editor and various types of reference information Once you open Help you can click the Contents button whenever you want to return to the opening screen About Displays the copyright notice and version number of this application 22 2 9 Object Action Context Menu Once an object has been selected its action context menu may be displayed by right clicking inside the object The following actions may be selected from this menu Refresh Redraws the object 22 7 J011P3 so1y der GAUSS User Guide Cut Copy Delete Z Order Edit Deselect Properties Removes the currently selected data from the document and put it on the clipboard This command is unavailable if there is no data currently selected Cutting data to the clipboard replaces the contents previously stored there Copies currently selected data onto the clipboard This command is unavailable if there is no data currently selected Deletes currently selected data This command is unavailable if there is no data currently selected Changes the objects position in the z order of the document s list The z order allows the user to control in what order the object is drawn on the page To change select the Z Order menu item from the action context menu and select one of the following Move to Top Moves the object to the top
59. Open Import Save Save As Print Print Preview Opens a new untitled document CTRL N Opens an existing document in a new window CTRL 0 Imports a file of another format Currently only the GAUSS graphics format tkf is supported Saves the active document to its current name and directory When you save a document for the first time the graphics editor displays the Save As dialog box so you can name your document CTRL S If you want to change the name and directory of an existing document before saving it choose the Save As command Saves and names the active document The graphics editor displays the Save As dialog box so you can name your document Prints a document This command presents a Print dialog box where you may specify the ranges of pages to be printed the number of copies the destination printer and other printer setup options CTRL P Displays the active document as it would appear when printed When you choose this command the main window will be replaced with a print preview window in which one or two pages will be displayed in their printed format The print preview toolbar offers you the option to view either one or two pages at a time move back and forth through the document zoom in and out of pages and initiate a print job 22 4 Graphics Editor Print Setup Exit Allows you to select a printer and printer connection This command presents a Print Setup dialog box where you
60. Summary The following commands are supported in ATOG 24 1 SOLV GAUSS User Guide append Append data to an existing file complex Treat data as complex variables input The name of the ASCII input file invar Input file variables column names msym Specify missing value character nocheck Don t check data type or record length output The name of the GAUSS data set to be created outtyp Output data type outvar List of variables to be included in output file preservecase Preserve case of variable names in output file The principle commands for converting an ASCII file that is delimited with spaces or commas are given in the following example input agex asc output agex invar race age pay sex region outvar region age sex pay outtyp d In this example a delimited ASCII file agex asc is converted to a double precision GAUSS data file agex dat The input file has five variables The file will be interpreted as having five columns column name data type 1 race character AGE numeric PAY numeric sex character region character Un RU P2 24 2 ATOG The output file will have four columns since the first column of the input file race is not included in the output variables The columns of the output file are column name data type 1 region character 2 AGE numeric 3 sex character 4 PAY numeric The variable names are saved in the file header Unless preservecase has been sp
61. a 3 1 2 Plane 1 1 0000 3 0000 5 0000 7 0000 9 0000 11 000 Plane 2 2 0000 4 0000 6 0000 8 0000 10 000 12 000 11 42 amult This function performs a matrix multiplication on the last two trailing dimensions of an array The leading dimensions must be strictly conformable and the last two trailing dimensions must be conformable in the matrix product sense For example a areshape seqa 1 1 12 2 3 2 b areshape seqa 1 1 16 2 2 4 c amult a b print a Plane 1 11 23 s eJIy yim DupJoM GAUSS User Guide 1 0000 2 0000 3 0000 4 0000 5 0000 6 0000 Plane 2 7 0000 8 0000 9 0000 10 000 11 000 12 000 print b Plane 1 1 0000 2 0000 3 0000 4 0000 5 0000 6 0000 7 0000 8 0000 Plane 2 9 0000 10 000 11 000 12 000 13 000 14 000 15 000 16 000 print c Plane 1 11 000 14 000 17 000 20 000 23 000 30 000 37 000 44 000 35 000 46 000 57 000 68 000 Plane 2 167 00 182 00 197 00 212 00 211 00 230 00 249 00 268 00 255 00 278 00 301 00 324 00 11 24 Working with Arrays Suppose we have a matrix of data sets a 2x2 matrix of 100x5 data sets that we ve stored in a 2x2x100x5 array called x The moment matrices of these data sets can easily and quickly be computed using atranspose and amult vc amult atranspose x 1 2 4 3 2 11 4 3 amean amin amax These functions compute the means minimums and maximums respectively across a dimension
62. a Wo CcROR E CHOR ck B RR RR EGER E A 3 ES MIEDO Lm A 4 AA COMPE A A a To aE A 5 B Reserved Words Appendix C Singularity Tolerance Appendix o1 C2 Reading and Setting the Tolerance 0 llle C 2 Determining Singularity ie e osea ca srada cocia fani asd C 2 27 Command Reference Introduction 27 1 Documentation Conventions llle 27 2 27 2 Command Components uum acera ansi ee ea eee ee e Ex 27 3 27 3 Using This Manual lt zm RREG EGRE REGEEG cr 27 4 27 4 Global Control Variables 22s 27 5 27 4 1 Changing the Default Values 0 27 5 27 4 2 The Procedure gausset e 000 27 6 28 Commands by Category 28 1 Mathematical Functions o e eo 28 1 28 2 Finance FUNCIONS Dis mum a a aT E 28 23 28 9 Matix Manipulation 3 3 5 rara a ee ees 28 24 28 4 Sparse Matrix Handling o lll 28 29 28 5 N Dimensional Array Handling ll 28 30 28 6 DIUGIIMES ai cuado ls a a A e ad UE CRAT Rn Des 28 32 28 7 Data Handling VO lt lt s mu sscb acadada e de ma eee 28 33 28 8 COMPIE COMON 2 lt a a a e eoo Ea meon a A A A 28 42 25 9 Multi Threading Secciones ieee Peed be td ee hes eo 28 43 xvi Contents 28 10 Program Gontrel ociosa e aosa aa oP a Rum hem a EG Ur hg 28 44 28 11 OS Functions and File Management o o 28 49 28 12 Workspace Management
63. addressed byte of the elements being compared The equality comparison operators lt gt and their dot equivalents can be used to test for missing values and the NaN that is created by floating point exceptions Less than and greater than comparisons are not meaningful with missings or NaN s but equal and not equal are valid These operators are sign insensitive for missings NaN s and zeros The string versions of these operators can also be used to test missings NaN s and zeros Because they do a strict byte to byte comparison they are sensitive to the sign bit Missings NaN s and zeros can all have the sign bit set to 0 or 1 depending on how they were generated and have been used in a program 7 9 s10 e1ado GAUSS User Guide If the relational operator is NOT preceded by a dot then the result is always a scalar 1 or 0 based upon a comparison of all elements of x and y All comparisons must be true for the relational operator to return TRUE By this definition then if x y is interpreted as if every element of x is not equal to the corresponding element of y To check if two matrices are not identical use if not x y For complex matrices the and operators compare both the real and imaginary parts of the matrices all other relational operators compare only the real parts e Less than Z x lt y z x lt y z x lt y e Less than or equal to z
64. analyze the information stored in the tcollect output file you must run the gaussprof executable which is also shipped with GAUSS on that file gaussprof produces an organized report displaying the time usage by procedure and by line Assuming that running myfile e in tcollect produced an output file called gaussprof_001 gco you could analyze the results in that file as follows gaussprof gaussprof_001 gco The syntax for gaussprof is gaussprof flags profile_data_file where flags may be any of the following p profile procedure calls 1 profile line numbers h suppress headers Sp order procedure call sort order where order contains one or more of the folllowing 20 2 The GAUSS Profiler exclusive time total time number of times called procedure name ascending order a Y O A rc o descending order default Columns are sorted all ascending or all descending sl order line number sort order where order contains one or more of the folllowing time spent on line number of times line was executed file name line number ascending order aoe mA ae descending order default Columns are sorted all ascending or all descending The default with no flags is p1 sp dep sl dtf 20 3 19 1J01d Publication Quality Graphics GAUSS Publication Quality Graphics PQG is a set of routines built on the graphics functions in GraphiC by Scientific Endeavors Corporation The main gra
65. as stated above you can reference read only symbols in as many threads within a set as you like but any symbols that are assigned to must be wholly owned by a single thread A symbol that is assigned to by a thread cannot be written or read by any other thread in that set This is the writer must isolate rule So you can do this ThreadStat x y y ThreadStat z y y 14 7 spealyL GAUSS User Guide ThreadStat a b y ThreadJoin You cannot do this ThreadStat x y y Threadstat z x x ThreadStat a b y ThreadJoin This is because the threads within a set run simultaneously Thus there is no way of knowing when an assignment to a symbol has taken place no way of knowing in one thread the state of a symbol in another Let s revisit the nested thread example for a minute and see how the writer must isolate rule applies to it q chol b ThreadBegin x q m ThreadBegin y xxi z qm ThreadEnd ThreadBegin a b x c a cm ThreadEnd ThreadJoin games ThreadEnd ThreadBegin ThreadStat r m m ThreadStat s m inv b main code no threads yet Thi isolates x y z a c q from Th2 Th1 1 isolates y z from 1 2 Th1 2 isolates a c from 1 1 Joins 1 1 1 2 Th2 isolates r s t from Th1 Th2 1 isolates r from 2 2 Th2 2 isolates s from 2 1 14 8 Multi Threaded Programming in GAUSS ThreadJoin Joins 2 1 2 1 t So7r7 s ThreadEnd Thre
66. bar shown below the color boxes Setting the Fill brush Color Right click in one of the color boxes in the dialog bar to set the current fill color The dialog bar is located to the left of the drawing area The fill color is immediately displayed in the sample box at the top of the color box area Transparent Fill To set a transparent fill color right click in the sample box at the top of the color boxes This will cause the drawing object to have no fill associated with it and allow objects beneath it to show through Customizing Dquble clicking in the color box will allow you to customize that particular 22 10 Graphics Editor 22 2 13 Graphical Objects The graphics editor allows the user to interactively create any number of the following graphical objects for composing your document Creating a TKF Graphics window A TKF Graphics Window is a window object containing a GAUSS generated graphics file To create a TKF graphics window select the Graphics Window menu item from the Draw menu or press the Create TKF window icon on the toobar A properties dialog is presented which allows the selection of a GAUSS generated TKF graphics file There are two ways to do this If one or more graphics files are currently being displayed in GAUSS those filenames will appear in the Active Graphs drop down control and may be selected Otherwise pressing the Browse button will present a common open file dialog for selecting the file
67. be helpful to enter an interactive command and or view error output while simultaneously viewing the relevant documentation 3 25 onul IND GAUSS User Guide 1000 O0 8 O Gea i E a 3 a E s o gt User Guide gt Command Reference In gt Commands by Category 4 Command Reference 4 a Next 36 1 2 acf Up 36 1 a Previous 36 1a 36 1 1 abs Purpose Returns the absolute value or complex modulus of x AmericanBino AmericanBino Format AmericanBino AmericanBino AmericanBino AmericanBino y abs x AmericanBSCall AmericanBSCall Input AmericanBSCall AmericanBSPut AmericanBSPut x NxK matrix or sparse matrix or N dimensional array AmericanBSPut dock inp er Figure 3 20 Help Page 3 8 1 Hot Keys Fi CTRL F1 Opens the Command Reference section for the highlighted command Opens a programming editor with the function definition of a highlighted procedure 3 26 Navigating the GAUSS Graphical User Interface Navigation of the GAUSS Graphical User Interface is designed to naturally follow your actions For example if the action you would like to perform is debugging the file that you are editing you can either enter CTRL D to debug or select the file from the Debug Toolbar Button s drop down Action List Both of these options will begin your debugging session and take you to the Debug Page Regardl
68. beep will sound when the graph is finished drawing to the window Default is 1 no beep scalar or Kx1 vector controls symbol used at data points To use a single symbol type for all points set this to one of the following scalar values 1 circle 8 solidcircle 2 square 9 solid square 3 triangle 10 solid triangle 4 plus 11 solid plus 5 diamond 12 solid diamond 6 inverted triangle 13 solid inverted triangle 7 star 14 solid star If this is a vector each line will have a different symbol Symbols will repeat if there are more lines than symbol types Default is 0 no symbols are shown 2x1 vector controls 3 D surface characteristics 1 if 1 show hidden lines Default is 0 2 color for base see Corons Section 21 5 The base is an outline of the X Y plane with a line connecting each corner to the surface If 0 no base is drawn Default is 7 21 27 90d GAUSS User Guide _psym _psym3d _psymsiz _ptek _pticout _ptitlht Mx7 matrix M extra symbols will be plotted M 1 x location M 2 y location M 3 symbol type see _pstype earlier M 4 symbol height If this is 0 a default height of 5 0 will be used M 5 symbol color see Corons Section 21 5 M 6 type of coordinates 1 plot coordinates 2 inchcoordinates M 7 line thickness A value of zero is normal line width Mx7 matrix for plotting extra symbols on a 3 D surface or xyz graph M 1 x lo
69. between any other pages while continuing to observe the program output 4 3 INS y Sunebinen GAUSS User Guide 4 5 F1 Help If your cursor is on the name of a GAUSS command in an editor you can press Fl and it will take you to the Command Reference listing for that command Inside the Help system highlight command names by double clicking them to enable F1 help navigation 4 6 CTRL F1 Source Browsing For procedures that reside in a GAUSS Library 1cg file you can browse to the procedure definition and to the initiation of any global variables with CTRL Fl Like F1 help set your cursor on the procedure or global variable name and enter CTRL F1 If it resides in an active library the source file will be immediately opened in a Programming Editor To learn more about creating a User Library for your procedures see Chapter 15 4 4 Using the Command Line Interface TGAUSS is the command line version of GAUSS The executable file tgauss is located in the GAUSS installation directory The format for using TGAUSS is tgauss flag s program program b 1 logfile e expression Execute file in batch mode and then exit You can execute multiple files by separating file names with spaces Set the name of the batch mode log file when using the b argument The default is tmp gauss log where is the process ID Execute a GAUSS expression This command is not logged when GAUSS is in batch mode
70. bytes were truncated The input file contained character elements longer than 8 bytes The conversion continued and the character elements were truncated to 8 bytes Disk Full The output disk is full The output file is incomplete Found character data in numeric field 24 15 SOLV GAUSS User Guide atog atog atog atog atog atog atog atog atog This is a warning that character data was found in a variable that was specified as numeric The conversion will continue Illegal command An unrecognizable command was found in a command file Internal error Notify Aptech Systems Invalid delimiter The delimiter following the backslash is not supported Invalid output type Output type must be I F or D Missing value symbol not found No missing value was specified in an msym statement No Input file No ASCII input file was specified The input command may be missing No input variables No input variable names were specified The invar statement may be missing No output file No output file was specified The output command may be missing output type d required for character data Character data in output file will be lost Output file contains character data and is not double precision 24 16 ATOG atog atog atog atog atog atog atog atog atog atog Open comment The command file has a comment that is not closed Commen
71. containing the parameter vector Sometimes the matrix or vector is partly parameters to be estimated that is a parameter to be entered in the parameter vector and partly fixed parameters To distinguish between estimated and fixed parameters an additional argument is used in the packing function called a mask which is strictly conformable to the input matrix Its elements are set to 1 for an estimated parameter and 0 for a fixed parameter For example p0 pvPackm p0 1 eye 3 theta eye 3 Here just the diagonal of a 3x3 matrix is added to the parameter vector When this matrix is unpacked the entire matrix is returned with current values of the parameters on the diagonal print pvUnpack p6 theta 0 1000 0 0000 0 0000 0 0000 0 1000 0 0000 0 0000 0 0000 0 1000 Symmetric Matrices Symmetric matrices are a special case because even if the entire matrix is to be estimated only the nonredundant portion is to be put into the parameter vector Thus for them there are special procedures For example 12 18 Structures 1 6 4 6 1 2 4 2 1 Hh pvPacks p0 vc vc vc pod There is also a procedure for masking in case only a subset of the nonredundant elements are to be included in the parameter vector 1 6 4 6 1 2 4 2 1 mas a 110 110 60 1 p0 pvPacksm p0 vc vc mask Fast Unpacking When unpacking matrices using a matrix name pvUnpack has to make a search through a list of
72. creating temporary file Too many locals A procedure has too many local variables 25 8 Error Messages G0085 G0086 G0087 G0088 G0089 G0090 G0091 G0092 G0093 G0094 G0095 G0096 Invalid file type You cannot use this kind of file in this way Error deleting file Couldn t open The auxiliary output file could not be opened Check the file name and make sure there 1s room on the disk Not enough memory to convert the whole string WARNING duplicate definition of local Label undefined Label referenced has no definition Symbol too long Symbols can be no longer than 32 characters Open comment A comment was never closed Locate off screen Argument out of range Seed out of range Error parsing string parse encountered a token that was too long 25 9 soDesso y 10413 GAUSS User Guide G0097 G0098 G0099 G0100 G0101 G0102 G0103 G0104 G0105 G0106 G0107 G0108 String not closed A string must have double quotes at both ends Invalid character for imaginary part of complex number Illegal redefinition of user keyword Internal ERROR Notify Aptech Systems Argument cannot be zero The argument to 1n or log cannot be zero Subroutine calls too deep Too many levels of gosub Restructure your program return without gosub You have encountered a subroutine without executing a gosub Argument must be positiv
73. dlibrary path must be set to the correct subdirectory This will be handled automatically in your configuration file If the program is run on a different computer than it was compiled on the d11 files must be present in the correct location sysstate case 24 can be used to set the dlibrary path at run time 16 2 Saving the Current Workspace The simplest way to create a compiled file containing a set of frequently used procedures is to use saveall and an external statement library pgraph external proc xy logx logy loglog hist saveall pgraph Just list the procedures you will be using in an external statement and follow it with a saveall statement It is not necessary to list procedures that you do not explicitly call but are called from 16 2 Compiler another procedure because the autoloader will automatically find them before the saveall command is executed Nor is it necessary to list every procedure you will be calling unless the source will not be available when the compiled file is use d Remember the list of active libraries is NOT saved in the compiled file so you may still need a library statement in a program that is use ing a compiled file 16 3 Debugging If you are using compiled code in a development situation in which debugging is important compile the file with line number records After the development is over you can recompile without line number records if the maximum possible execution speed
74. edit the values of variables during debugging Viewing Variable Values During Debugging Once the debugger is started the editor window uses floatover variable windows for viewing variable data Floatover variable windows give a quick view of the value a variable currently holds by simply moving your mouse over the variable name in the edit window The floatover variable window is only intended to give a quick view of the data so it may not show all data held by the variable If you need to view more data click on the variable name and type CTRL E or click the Set Watch Variable and enter the variable name Editing Variable Values During Debugging The debugger integrates the Matrix Editor to edit values of loaded variables or to use as a watch window to view the changing values of variables as you step through a program To edit a variable value highlight the variable in the edit window or the Command Input Window and then open the Matrix Editor You can use the menu or toolbar to start the Matrix Editor Making a Watch Window You can make the Matrix Editor a Watch Window allowing you to watch the changing value of a variable as the lines of the program are executed You can activate the Watch Window by clicking Set Watch on the Debug toolbar or by highlighting a variable name in the Debugger Window and pressing CTRL E You use a Watch Window to see how variables change in value during debugging Watch variables can be specified pri
75. editors If you would like to open a second copy of a symbol right click on the symbol in the symbol tree and select Edit Another Copy GAUSS allows you to open more than one copy of each symbol so that you can examine different portions of a large matrix at the same time Special Case Structures To view a structure in the GAUSS Symbol Editor click the next to the Structures node on the Symbol Tree From here you will see a full list of all structures in your current GAUSS workspace Clicking the next to an individual structure will reveal all members of a structure To view the contents of any member of a GAUSS structure first open the structure in a Struct Viewer by either double clicking or right clicking and selecting Edit over the name of the structure in the Symbol Tree Once open in the Struct Viewer individual members of the structure can be accessed for viewing and editing from the Struct Tree The Struct Editor When opened from the Symbol Tree structures will be loaded into a special Struct Editor The Struct Editor is composed of a Struct Tree Widget and a Struct Member Editor The Struct Tree Widget displays the structure being edited and its members names data types and dimensions The Struct Member editor displays the contents of individual struct members The Struct Editor is displayed in the Source Editor docking area like all other Source Editors Individual structure members can be opened for editing or viewing from
76. eee eee 3 3 3 22 Command Page Toolbar llle sn 3 4 3 2 9 Working Directory Toolbar llle 3 4 3 2 4 Command History Toolbar 5h43 ES Pe dae we 3 5 3 2 5 The Run Debug and Edit Buttons 3 6 So Layo t se soss mde me hook 8609 Be ee ies 373 pe ee eed UR 3 6 3 9 1 Command History Window sn 3 7 3 3 2 The Command Input Window 3 8 3 4 Command Line History and Command Line Editing 3 8 3 4 1 MoOVement a zd ak Ro Eas odios 4546 chee m hoe bbe 3 8 3 4 2 Error Output Window llle 3 9 3 5 Source Page Editing Programs 0 e 3 9 95 1 Menus and Toolbars e e e 3 9 3 5 2 Layoutand Usage oa coot a ce cuo bw om Remo s 3 10 GAUSS User Guide 3 6 3 7 3 8 3 0 9 Find and Replace e 4 4 3 5 4 Changing Editor Properties o 3 5 5 Command Input Window e lens 3 5 6 Error Output Window Data Page io c ssa ea a x 3 6 1 Men Baf s so ts aseran ears 3 6 2 Layout 222 sarera Sa Mewes 3 6 3 Symbol BONO 2 20 socs ene eee Sas Debug Page 2 226 eee eee hee eR 3 7 1 Menus and Toolbars 3 7 2 Using Breakpoints 3 7 3 Setting and Clearing Breakpoints 3 7 4 Stepping Through a Program 3 4 5 Viewing and Editing Variables Help Page suc suem done eno oe
77. eem Roa nc Rec de as 15 12 15 9 1 Using dec Files e ssas rmm RI x ER UR RR om ER 15 13 16 Compiler 16 1 Compiling Programs llle 16 2 16 1 1 Comping a Fle us 240046 0a 6 xo 2 ee ee m ko es 16 2 16 2 Saving the Current Workspace o a 16 2 16 3 DEODUIIMO lt lt sem mo Rmo RR aaa a bene re 16 3 17 File O 1450 ZASOIFEIIBS ios egy eves e a LE eg 17 3 Wl Maie Data uude ios ave me oe RR XT ee EU oue le Res 17 3 14 1 2 General File NO 2 c roe aosa eac d em e a a ea Re a 17 6 11 2 Data SelS e ss cmo m o xor OUR a RUE RHEE ERE Be 17 7 T4251 Layout iio noua Eom hee xd ee Re m hm XV LEM Res Aou hg 17 7 17 2 8 Creating Data Sets lll aa 17 8 17 2 3 Reading and Writing e s sa n xm mms 17 8 17 2 4 Distinguishing Character and Numeric Data 17 9 17 3 GAUSS Data Archives 2 2222 17 11 17 3 1 Creating and Writing Variables to GDA s 17 11 17 3 2 Reading Variables from GDA s 17 12 17 3 8 Updating Variables in GDA s o 17 13 17 4 MatrbeElles cs os ee be fA Rm Um be ee a ae RR ee ee ee E 17 13 14 5 EleFormalS uu Raw ee UE eoe OR FO a a a li 17 14 17 5 1 Small Matrix v89 Obsolete 17 15 17 5 2 Extended Matrix v89 Obsolete 17 16 Contents 175 3 17 5 4 17 5 5 17 5 6 17 5 7 17 5 8 17 5 9 17 5 10 17 511 17 5 12 Small String v89 Obsolete
78. for each would be 201 Simplex 202 Complex 203 Microb 204 Simgrma The following example demonstrates how to select a font for use in a string title M201This is the title using Simplex font xlabel 202This is the label for X using Complex font ylabel 203This is the label for Y using Microb font Once a font is selected all succeeding text will use that font until another font is selected If no fonts are selected by the user a default font Simplex is loaded and selected automatically for all text work 21 4 2 Greek and Mathematical Symbols The following examples illustrate the use of the Simgrma font they assume that Simgrma was the fourth font loaded For the available Simgrma characters and their numbers see Appendix A The Simgrma characters are specified by either 1 The character number preceeded by a NX 2 The regular text character with the same number 21 12 Publication Quality Graphics e 99 For example to get an integral sign f in Simgrma embed either a 844 ora in a string that has been set to use the Simgrma font To produce the title f x sin xx the following title string should be used titlec 201f Cx sin 2 204p 201x TEE The p character 112 corresponds to z in Simgrma To number the major X axis tick marks with multiples of 7 4 the following could be passed to asclabel lab 2010 204p 201 4 204p 201 2 3 204p 2
79. gt 1 c ctl endif i i l endo print c Or you could use 26 2 Maximizing Performance c sumc abs x gt 1 print c The do loop takes over 40 times longer 26 3 Memory Usage Computers today can have large amounts of RAM This doesn t mean that large data sets should be read entirely into memory Many GAUSS procedures and applications are written to allow for data sets to be read in sections rather than all at once Even if you have enough RAM to store the data set completely you should consider taking advantage of this feature The speed ups using this feature can be significant For example ols is called using a data set stored in a matrix versus stored on the disk in a GAUSS data set The computer is a 2 8 Megahertz computer with Windows XP y rndn 250000 1 x rndn 250000 100 xlbl 0 X ftocv sega 1 1 100 1 0 lbl Y xlbl call saved y x test 1b1 output 6 t0 date call ols y x tl date t2 date call olsC test Y xlbl t3 date print ethsec t2 t3 100 seconds print print ethsec t0 t1 100 seconds 25 750000 seconds 9 6720000 seconds 26 3 eoueuloJ19d GAUSS User Guide This represents more than a 50 speedup by leaving the data on the disk maxvec maxbytes maxvec is a GAUSS procedure that returns the value of the global variable __maxvec that determines the amount of data to be read in at a time from a GAUSS dat
80. hand side of the equal sign in an expression x 5 Left hand side references since they are assignments are assumed to be matrices In the statement above X is assumed to be a matrix and the code is compiled accordingly If at execution time the expression actually returns a string the assignment is made and the type of the symbol x is forced to string Some commands are implicit left hand side assignments There is an implicit left hand side reference to X in each statement below clear x load x open x myfile Right Hand Side A right hand side reference is usually a reference to a symbol on the right hand side of the equal sign in an expression such as 15 2 Libraries Z 6 y z dog print y In the program above since dog is not previously known to the compiler the autoloader will search for it in the active libraries If it is found the file containing it will be compiled If it is not found in a library the autoload autodelete state will determine how it is handled 15 1 2 The Autoloader Search Path If the autoloader is OFF no forward references are allowed Every procedure matrix and string referenced by your program must be defined before it is referenced An external statement can be used above the first reference to a symbol but the definition of the symbol must be in the main file or in one of the files that are include d No global symbols are deleted automatically If the autol
81. in the course of a program The declare statement used for compile time initialization enforces type checking Short strings of up to 8 bytes can be entered into elements of matrices to form character matrices For details see CHARACTER Matrices Section 6 6 7 6 6 1 Constants The following constant types are supported Decimal Decimal constants can be either integer or floating point values 1 34e 10 1 34e123 1 34e 10 1 34d 10 1 34d10 6 9 s ejuawepuny oDenbue GAUSS User Guide 1 34d 10 123 456789345 Up to 18 consecutive digits before and after the decimal point depending on the platform are significant but the final result will be rounded to double precision if necessary The range is the same as for matrices For details see Matrices Section 6 6 2 String String constants are enclosed in quotation marks This is a string Hexadecimal Integer Hexadecimal integer constants are prefixed with Ox OxOab53def2 Hexadecimal Floating Point Hexadecimal floating point constants are prefixed with Ov This allows you to input a double precision value exactly as you want using 16 hexadecimal digits The highest order byte is to the left Ovfff8000000000000 6 10 Language Fundamentals 6 6 2 Matrices Matrices are 2 dimensional arrays of double precision numbers All matrices are implicitly complex although if it consists only of zeros the imaginary part may ta
82. inside thread Unable to converge in allowed number of iterations Incorrect Argument Number of eigenvalues must be positive Incorrect Argument Number of column vectors must be gt number of eigenvalues 2 and lt rows of input matrix Could not apply shift during an Arnoldi iteration cycle Try increasing size of ncv Invalid Input which must be LM SM LR LI SR or SI and type string Error Return from LAPACK eigenvalue calculation dneupd error 1 contact Aptech Systems Input matrix must be sparse Incorrect Input Number of eigenvalues must be scalar Incorrect Input Tolerance must be scalar No eigenvalues found to specified tolerance in allowed iterations Incorrect Input Max iterations must be scalar Incorrect Input Number of column vectors must be scalar 25 29 soDesso y 10413 GAUSS User Guide G0593 Incorrect Input Third input probability must be gt 0 and lt 1 G0594 Incorrect Input Number of successes input 1 must be less than number of trials input 2 G0595 Incorrect Input State vector cannot have more than 1 column G0596 Incorrect Input Inputs 1 and 2 cols and rows must be scalar or 1x1 matrix G0597 Incorrect Input Input must be dense matrix G0598 Incorrect Input First input may have 1 column only G0599 Incorrect Input Input 2 may not have more columns that input 1 has rows G0600 Incorrect Input Input 1 must be square G0601 Incor
83. is 1 0e 14 You can adjust this as necessary A numerically better method of determining singularity is to use cond to determine the condition number of the matrix If the equation 1 cond x 1 eq 1 is true then the matrix is usually considered singular to machine precision See LAPACK for a detailed discussion on the relationship between the matrix condition and the number of significant figures of accuracy to be expected in the result C 2 Index Index r 7 8 wv 7 8 7 9 7 8 7 6 7 7 7 5 F 7 6 F 7 6 7 4 7 4 7 5 J 7 6 96 7 5 7 6 7 19 7 6 comma 7 16 dot 7 16 colon 7 17 semicolon 6 2 19 3 29 137 29 546 29 720 29 956 29 137 29 546 29 720 29 956 7 19 7 18 7 17 amp 7 17 8 10 6 2 6 12 6 39 7 15 7 11 J 7 12 6 40 7 10 7 12 gt 7 11 7 12 gt 7 11 gt 7 12 lt 7 10 7 11 lt 7 10 lt 7 12 __altnam 29 259 __output 29 259 29 535 29 847 __title 29 259 __Tol 29 259 _eqs_IterInfo 29 259 _eqs_JacobianProc 29 259 _eqs_MaxIters 29 259 _eqs_StepTol 29 259 _eqs_TypicalF 29 259 _eqs_TypicalX 29 259 _loess_Degree 29 535 _loess_NumEval 29 535 _loess_Span 29 535 Index 1 xapul Index _loess_WgtType 29 535 _sqp_A 29 845 _sqp_B 29 845 _sqp_Bounds 29 846 sqp C 29 845 Sqp D 29 845 _sqp_DirTol 29 847
84. is preferred because rows x can be used to determine how many elements were actually loaded and the matrix can be reshape d to the desired form 17 3 O I 9113 GAUSS User Guide load x datl asc if rows x eq 500 x reshape x 100 5 else errorlog Read Error end endif For quick interactive loading without error checking use load x 100 5 datl asc This will load the data into a 1005 matrix If there are more or fewer than 500 numbers in the data set the matrix will automatically be reshaped to 100x5 Writing To write data to an ASCII file the print or print fm command is used to print to the auxiliary output The resulting files are standard ASCII files and can be edited with GAUSS s editor or another text editor The output and outwidth commands are used to control the auxiliary output The print or printfm command is used to control what is sent to the output file The window can be turned on and off using screen When printing a large amount of data to the auxiliary output the window can be turned off using the command screen off This will make the process much faster especially if the auxiliary output is a disk file It is easy to forget to turn the window on again Use the end statement to terminate your programs end will automatically perform screen on and output off The following commands can be used to control printing to the auxiliary output 17 4 File I O format
85. is the first place GAUSS looks when trying to resolve symbol references You can update the user library with the 1ib command as follows lib user myfile src This will update the user library by adding a reference to myfile src No user library is shipped with GAUSS It will be created the first time you use the 1ib command to update it For details on the parameters available with the 1ib command see the GAUSS LANGUAGE REFERENCE g Files If autoload and autodelete are ON and a symbol is not found in a library the autoloader will assume it is a procedure and look for a file that has the same name as the symbol and a g extension For example 1f you have defined a procedure called square you could put the definition in a file called square g in one of the subdirectories listed in your src_path If autodelete is OFF the g file must be listed in an active library for example in the user library 15 8 Libraries 15 2 Global Declaration Files If your application makes use of several global variables create a file containing declare statements Use files with the extension dec to assign default values to global matrices and strings with declare statements and to declare global N dimensional arrays sparse matrices and structures which will be initialized as follows Variable Type Initializes To N dimensional array 1 dimensional array of 1 containing O sparse matrix empty sparse matrix structure 1x1 structu
86. keyword lapsvds lapsvdusv le let lib library license_id line linsolve In Incdfbvn Incdfbvn2 Incdfmvn Incdfn Incdfn2 Incdfnc B 8 Reserved Words Appendix Infact lngamma lnpdfmvn lnpdfmvt lnpdfn lnpdft load loadarray loadd loadexe loadf loadk loadm loadp loads loadstruct loadwind local locate machEpsilon makevars makewind margin matalloc matinit matrix mattoarray maxbytes maxc maxindc maxvec mbesselei mbesselei0 loess loessmt loessmtControlCreate log loglog logx logy loopnextindex lower lowmat lowmat1 lpos lprint lpwidth lshow lt ltrisol lu lusol mbesseleil mbesseli mbesseli0 mbesselil meanc median mergeby mergebysa mergevar minc minindc miss missex missrv B 9 SP IOM P9A19SDH GAUSS User Guide moment momentd movingave nametype ndpchk ndpclex ndpcntrl ne new nextindex oldfft oldffti ols olsmt olsmtControlCreate olsqr olsqr2 olsqrmt ones pacf packr parse pause pdfn movingaveExpwgt movingaveWgt msym nextn nextnevn nextwind not null nulli numCombinations open openpqg optn optnevn or orth output outwidth pi pinv pinvmt plot plotsym Reserved Words Appendix polar polychar polyeval polyint polymake polymat polymroot polymult polyroot pop pagwin prcsn previousindex princomp print printdos printfm printfmt proc prodc push QNewton QNewtonmt QNewt
87. len 8 8 Passing Procedures to Procedures 8 9 Indexing Procedures llle 8 10 Multiple Returns from Procedures 2 o 8 11 Saving Compiled Procedures e 8 13 9 Sparse Matrices 9 1 9 2 9 3 Defining Sparse Matices x od a PES 9 1 Creating and Using Sparse Matrices 9 2 Sparse Support in Matrix Functions and Operators 9 3 9 3 1 Return Types for Dyadic Operators o o 9 5 10 N Dimensional Arrays 10 1 Bracketed Indexing e eee es 10 3 10 2 EXE Contormability lt s s ss aso 2 8664 282 658 8 ooo eS be RR RE 10 5 10 9 Glossary of Terms ck eR Rx ee eRe mx 10 5 11 Working with Arrays Tid Initializing Arrays aoe 2 22 11 1 Ti areshape ia sara cedo nomm uomo RR Rom mcm s 11 2 ix GAUSS User Guide Wel AGOMCAL RTT MAS AY osha e ba Sedeweeee hag GHA eae eh eohL SG TAA anay uo uos ee eh ewe eed eee be 3 TIAS amayalldE cx dos som Se ale XR wae ER wl 112 Assigning Io AM AVS ox rc Soe Ss RS Re a Reds T1321 iWidex operator eno Roos a le bo te Ae eo 11 22 getAITay acera naa He bee eee EU Roe RR ae E 1128 COMIDO diia o Ro Eon Rx a e ohne a mu 11 24 geiMatrix4D 2 20 mo m or ak Oe EGER ee E Romo eee 11 25 getScalar3D getScalar4D 2l lll 11 2 6 qputAmay nase AA JE TES ACC ccu 11 9 Looping with Amrays s rias ie r
88. line are stored The following keystrokes are supported for movement and editing at the command line and for retrieving the command line history 3 4 1 Movement Left Arrow or Moves cursor left one character CTRL B 3 8 Introduction to the GAUSS Graphical User Interface Right Arrow or CTRL F HOME END or CTRL E ALT Left Arrow or CTRL Left Arrow ALT Right Arrow or CTRL Right Arrow Up Arrow Down Arrow Moves cursor right one character Moves cursor to beginning of line Moves cursor to end of line Moves cursor left one word Moves cursor right one word Search up through command history Search down through command history 3 4 2 Error Output Window The Error Output Window shows errors messages from program runs or interactive commands It may be viewed from any page by clicking the Error Output button on the right side of the status bar 3 5 Source Page Editing Programs The Source Page is for creating and editing programs and procedures 3 5 1 Menus and Toolbars Section 3 2 provides details of the main menus and toolbars The Source Page contains the following additional menu options 3 9 onul IND GAUSS User Guide File Menu Save Save As Close Close All Window Menu Split Horizontally Split Vertically Remove Split Close Close All Saves the active file Saves the active file with a new or different file or path name Closes the selected file Cl
89. lose changes press the Cancel icon on the text toolbar indicated by a red X or press the ESCAPE key Note The text object may be rotated at any angle from the Object Properties menu Creating a Line To create a line select the Line menu item from the Draw menu or press the Draw line button on the toolbar This puts the editor into the draw line state indicated by a crosshair cursor Next position the mouse where you want the first end point of the line then press and hold the left mouse button You may also move the line by pressing and holding the right mouse button while keeping the left button depressed Drag the mouse to the location for the second end point and release the mouse button Note Pressing the CTRL key while defining a line or arrow forces the line to be vertical or horizontal The line will be redrawn in the current pen color At any time after the above process you may modify the line object 22 12 Graphics Editor Creating an Arrow To create an arrow select the Arrow menu item from the Draw menu or press the Draw arrow button on the toolbar This puts the editor into the draw arrow state indicated by a crosshair cursor Arrow style controls for defining the arrow appear on the dialog bar to the left of the drawing area Defining the endpoints are identical to the steps for defining a line above However the arrow head size and shape may be set using the additional arrow style controls in the dial
90. lt abs cols gt maxc o gt minc gt print gt rows lt scalerr x show lt type Indexing is also supported for sparse matrices using the same syntax as matrix indexing Note that printing a sparse matrix results in a table of the non zero values contained in the sparse matrix followed by their corresponding row and column indices respectively 9 3 1 Return Types for Dyadic Operators The types of the returns for the dyadic operators were decided on a case by case basis using the following general principles 1 The return type for dyadic operations on two dense arguments is always dense 2 The return type for dyadic operations on two sparse arguments is always sparse unless the result is likely to be significantly less sparse than the sparse arguments 3 The return type for dyadic operations on a dense argument and a sparse argument regardless of order is dense unless the return is likely to be at least as sparse as the sparse argument These general principles have led to the following decisions regarding return types note that only the cases that are displayed in these tables have been implemented at this point S N esieds GAUSS User Guide Element by Element Numeric Operators Element by Element Addition Result Left Operator Right dense sparse dense dense dense dense sparse sparse sparse dense dense sparse Element by Element Subtraction
91. manage using for loops loopnextindex can be faster and more useful The next example compares two ways of extracting a subarray from a 5 dimensional array ord 313131313 a areshape seqa 1 1 prodc ord ord b eye 3 for 1 1 3 1 11 20 Working with Arrays for j 1 3 1 for k 1 3 1 setarray a i jl k b endfor endfor endfor ind 1 1 1 loopi setarray a ind b loopnextindex loopi ind ord Calling each loop 10 000 times and measuring the time each takes we get for loop 1 171 seconds loopnextindex 321 seconds In other words loopnextindex is about four times faster a very significant difference 11 4 Miscellaneous Array Functions 11 4 1 atranspose This function changes the order of the dimensions For example a areshape seqa 1 1 12 2 3 2 print a Plane 1 11 21 s eJIy uw DupJoM GAUSS User Guide 1 0000 2 0000 3 0000 4 0000 5 0000 6 0000 Plane 2 7 0000 8 0000 9 0000 10 000 11 000 12 000 yA swap 2nd and 3rd dimension print atranspose a 1 3 2 Plane 1 1 0000 3 0000 5 0000 2 0000 4 0000 6 0000 Plane 2 7 0000 9 0000 11 000 8 0000 10 000 12 000 swap 1st and 3rd dimension print atranspose a 3 2 1 Plane 1 1 0000 7 0000 3 0000 9 0000 5 0000 11 000 11 22 Working with Arrays Plane 2 2 0000 8 0000 4 0000 10 000 6 0000 12 000 move 3rd into the front print atranspose
92. margin of the window You can stop debugging at any time by clicking the Stop button on the debug toolbar 3 7 2 Using Breakpoints Breakpoints stop code execution where you have inserted them Breakpoints are normally set prior to running the debugger but can also be set or cleared during debugging by clicking the Set Clear Breakpoint command on the Debug menu 3 7 3 Setting and Clearing Breakpoints To set breakpoints in any part of the file not currently being executed just click in the left margin of the line on which you would like the breakpoint Alternatively you can highlight a line then click Toggle Breakpoint To clear a breakpoint in the file click on the breakpoint you would like to remove or click a line of code that has a breakpoint set and then click Set Clear Breakpoint You can clear all breakpoints from the active file by clicking Clear All Breakpoints 3 7 4 Stepping Through a Program GAUSS s debugger includes the ability to step into step out of and step over code during debugging Use Step Into to execute the line of code currently highlighted by the debugger Use Step Out to execute to the end of the current function without pause and return to the calling function Use Step Over to execute the line of code currently highlighted by the debugger without entering the functions that are called 3 23 onul IND GAUSS User Guide 3 7 5 Viewing and Editing Variables GAUSS allows you to view and
93. names for the elements of the parameter vector pvList returns the list of matrix names in the PV instance pvLength the length of the parameter vector struct PV pl p1 pvCreate cov pl pvPacksm p1 cov correlation mask print pvGetParVector p1 5000 pl pvPutParVector p1 8 print pvGetParVector p1 8000 print pvUnpack p1 correlation 1 0000 8000 8000 1 0000 print pvGetParNames p1 correlation 2 1 13 5 s n n sS 118 GAUSS User Guide print pvLength p1 1 0000 Also pvTest tests an instance to make sure it is properly constructed pvCreate generates an initialized instance and pvGetIndex returns the indices of the parameters of an input matrix in the parameter vector This last function is most useful when constructing linear constraint indices for the optimization programs 13 2 Fast Pack Functions Unpacking matrices using matrix names is slow because it requires a string search through a string array of names A set of special packing functions are provided that avoid the search altogether These functions use a table of indices that you specify to find the matrix in the PV instance For example struct PV pl p1 pvCreate y rndn 4 1 x rndn 4 4 pl pvPacki pl y Y 1 pl pvPacki p1 x X 2 print pvUnpack p1 1 3422 0407 5611 0953 print pvUnpack p1 Y 13 6 Run Time Library Structures 3422 0407 56
94. of the list Move to Bottom Moves the object to the bottom of the list Allows you to modify the object This menu item currently applies to text objects only De selects the object Opens the object s property dialog 22 2 10 Page Context Menu The Page Context menu is displayed by pressing the right mouse button when no object is selected The following actions may be selected from this menu Paste Retain Aspect Ratio Copies an object from the clipboard to the page if one is available Check or uncheck the aspect ratio state When checked this forces the object to retain its aspect ratio while sizing it from the top or sides sizing from the corners overrides this setting See MODIFYING THE GRAPHICAL OBJECTS Section 22 2 14 for more information 22 8 Graphics Editor 22 2 11 Setting the Page View Properties The following describes how to set various page and view properties including how to set the page orientation and margins use the zoom feature and set the color options Setting the Page Orientation and Margins Page Orientation The document page orientation of landscape or portrait is set from the Properties dialog under the View menu Measure Units Allows all coordinates and measurements to be in inches or centimeters Reference A reference margin indicating the document s current orientation and Margin margin settings is also available This is useful for customizing your page to be co
95. on nb mes 3 8 1 HotKGyS zc rr 4 Navigating the GAUSS Graphical User Interface 4 1 4 2 4 3 4 4 4 5 4 6 Hot Keys and Shortcuts Navigating Between Pages Switch To Command Page on I O Viewing Program Output from Other Pages 5 Using the Command Line Interface 5 1 5 2 Viewing Graphics o Command Line History and Command Line Editing 5 2 1 Movement 2 522 EANO uox cuu ata e x 5 2 3 History Retrieval 3 14 3 15 3 16 3 16 3 17 3 17 3 18 3 20 3 21 3 21 3 23 3 23 3 23 3 24 3 25 3 26 4 2 4 2 4 3 4 3 4 4 5 2 5 2 5 3 5 3 vi Contents 5 3 5 4 5 5 Interactive Commands 5 3 1 Qui i cus ks 53 2 A 5 3 3 browse 5 3 4 COM dumme Debugging 5 4 1 General Functions 5 4 2 Listing Functions 5 4 3 Execution Functions 5 4 4 View Commands 5 4 5 Breakpoint Commands Using the Source Browser in TGAUSS 0 000000 eee 6 Language Fundamentals 6 1 6 2 6 3 6 4 6 5 6 6 EXPIESSIONMS ura a ae aS DH ep ee ee a a ee ee a E Statements oao sers 6 2 1 Executable Statements 6 2 2 Nonexecutable Statements Programo S eoi a Gente eas a ea a ia See Go oe a 6 3 1 Mai SECUOM s ienee a a Eton ed Boas we GS eee daa 6 3 2 Secondary SectlonS iso gor dy a Roe SE d 9 eod Compil
96. on using the toolbar Displays and hides the Status Bar which describes the action to be executed by the selected menu or depressed toolbar button and keyboard latch state A check mark appears next to the menu item when the Status Bar is displayed See Status Bar Section for help on using the status bar Allows you to change user defined page view settings See SETTING THE PaGE VIEW PROPERTIES Section 22 2 11 for more information Allows you to change user defined zoom control See USING THE ZooM FEATURE Section 22 2 11 for more information 22 2 6 Draw menu commands The Draw menu offers the following commands see GRAPHICAL ObJECTS Section 22 2 13 for more detailed information on each Select TKF Graphics Window Line Arrow Rectangle Ellipse Text Puts the editor into object selection state Opens a GAUSS graphics window Draws a line Draws an arrow Draws a rectangle Draws an ellipse Allows you to enter text 22 6 Graphics Editor 22 2 7 Export menu commands The Export menu offers the following commands see FILE MANAGEMENT Section 22 3 for more detailed information on each Encapsulated Writes an Encapsulated Postscript file Postscript JPEG Image Writes a JPEG compressed image file Windows Writes a Windows Enhanced Metafile Metafile 22 2 8 Help menu commands The Help menu offers the following commands which provide you assistance with this application Help Topics
97. positive definite covariance matrices To do this a procedure is written that returns the eigenvalues of X and minus a small number sqpSolvemt then finds parameters such that these eigenvalues are greater than or equal to that small number 12 29 s n n sS GAUSS User Guide 12 4 4 The Command File This command file can be found in the file sqpfact e in the examples subdirectory include sqpsolvemt sdf lambda 1 0 0 0 0 5 0 0 0 0 1 0 0 0 0 5 lmask 0 6 1 0 0 0 013 phi 1 0 0 3 0 3 1 0 Y psi 0 6 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 6 tmask 1000 0100 0010 000 1 struct PV parQ par pvCreate par8 pvPackm parQ lambda lambda 1mask par8 pvPacks par0 phi phi par8 pvPacksm par0 psi psi tmask struct SQPsolveMTControl c6 12 30 Structures c8 sqpSolveMTcontrolCreate lind pvGetIndex par0 lambda get indices of lambda parameters in parameter vector tind pvGetIndex par0 psi get indices of psi parameters in parameter vector cQ bounds ones pvLength par8 1 1e250 1e250 c6 bounds lind 1 zeros rows lind 1 c6 bounds lind 2 18 ones rows lind 1 c8 bounds tind 1 001 ones rows tind 1 c6 bounds tind 2 100 ones rows tind 1 c0 output 1 cQ printIters 1 cO trustRadius 1 cQ ineqProc amp ineq c0 covType 1 struct DS dQ d
98. produced the following results index operator 2 604 seconds getArray setArray 1 092 seconds Thus the getArray and setArray methods are more than twice as fast 11 3 1 loopnextindex Several keyword functions are available in GAUSS for looping with arrays The problem in the previous section for example can be written using these functions rather than with for loops sigind r 1 sigloop 11 19 s eJIy uw DupJoM GAUSS User Guide sig8ind sigind 1 thetaind 1 thetaloop sig ind sigUind 1 W amult getArray theta thetaind atranspose getArray E sig0ind 2 1 setarray sigma sigind getArray sigma sigind amult W atranspose W 2 1 loopnextindex thetaloop thetaind aord sig ind sigind phiind 1 philoop sig0ind 1 sigGind 1 1 setarray sigma sigind getArray sigma sigind areshape amult amult getArray phi phiind getArray sigma sigUind getArray phi phiind 3 3 loopnextindex philoop phiind gord loopnextindex sigloop sigind sigord The loopnextindex function in this example isn t faster than the for loop used in the previous section primarily because the code is looping only through the first dimension in each loop The advantages of loopnextindex previousindex nextindex and walkindex are when the code is looping through the higher dimensions of a highly dimensioned array In this case looping through an array can be very complicated and difficult to
99. the order in which they are used For example the and operators have a higher precedence than the and operators In expressions that contain the above operators the operand pairs associated with the or operator are evaluated first Whether or is evaluated first depends on which comes first in the particular expression The expression 54 3 4 6 3 1s evaluated as 5 3 4 6 3 Within a term operators of equal precedence are evaluated from left to right The precedence of all operators from the highest to the lowest is listed in the following table 7 22 Operators Operator Precedence Operator Precedence Operator Precedence E 90 gt 65 gt 55 90 65 55 89 lt 65 lt 55 E 85 lt 65 lt 55 E 85 65 55 Cunary 83 gt 65 gt 55 80 65 gt 55 be 80 eq 65 eq 55 V 80 ge 65 ge 55 Mut 80 gt 65 gt 55 80 le 65 le 55 80 lt 65 lt 55 96 75 ne 65 ne 55 4 70 not 64 not 49 70 and 63 and 48 70 or 62 or 47 68 xor 61 xor 46 67 eqv 60 eqv 45 65 55 space 35 lt 65 lt 55 35 lt 65 lt 55 10 65 55 gt 65 gt 55 7 23 10 e19dO Procedures and Keywords Procedures are multiple line recursive functions that can have either local or global variables Procedures allow a large computing task to be written as a collection of smaller tasks These smaller tasks are easier to work with and kee
100. these and other related functions is provided in the table in section 23 2 Another major matrix vector format is the dtv or date and time vector The dtv vector is a 1x8 vector used with the dtvnormal and utctodtv functions The format for the dtv vector is Year Month Day Hour Min Sec DoW DiY 1955 4 21 4 16 0 4 110 Where Year Year four digit integer Month 1 12 Month in year Day 1 31 Day of month Hour 0 23 Hours since midnight Min 0 59 Minutes Sec 0 59 Seconds DoW 0 6 Day of week O Sunday DiY 0 365 Days since Jan 1 of current year dtvnormal normalizes a date The last two elements are ignored for input as shown in the following example They are set to the correct values on output The input can be 1x8 or Nx8 dtv 1954 3 17 4 160 8 QO Y dtv dtvnormal dtv 23 3 91eq pue au GAUSS User Guide 1954 3 17 4 16 0 3 75 dtv 3 dtv 3 400 print dtv 1954 3 417 4 16 0 3 75 dtv dtvnormal dtv print dtv 1955 4 21 4 16 0 4 110 23 2 Time and Date Functions Following is a partial listing of the time and date functions available in GAUSS datestr Formats a Date vector to a string mo dy yr datestrymd Formats a Date vector to an eight character string of the type yyyymmdd dayinyr Returns day number in the year of a given date _daypryr Returns the number of days in the years given as input dtvnormal Normalizes a 1x8 dtv vector etdays Computes the difference
101. vector that contains a set of pointers The local statement is used twice The first tells the compiler that f is a local matrix The i pointer which is just a number is assigned to f Then the second local statement tells the compiler to treat f as a procedure from this point on thus the subsequent statement f x is interpreted as a procedure call 6 43 Tr c m 2 2 o eQ Y 236 5 0 e o o 7 1 Element by Element Operators Operators Element by element operators share common rules of conformability Some functions that have two arguments also operate according to the same rules Element by element operators handle those situations in which matrices are not conformable according to standard rules of matrix algebra When a matrix is said to be EXE conformable it refers to this element by element conformability The following cases are supported matrix matrix scalar matrix vector vector op op op op op op matrix scalar matrix vector matrix vector 7 1 s10 e1ado GAUSS User Guide In a typical expression involving an element by element operator Z x y3 conformability is defined as follows e If x and y are the same size the operations are carried out corresponding element by corresponding element 1 3 2 XS 5 1 3 7 4 2 3 y 3 1 4 6 1 2 3 7 5 z 7 6 5 9 8 6 e If x is a matrix and y is a scalar or vice versa then the scalar is operated on with respect to eve
102. walkindex Get a scalar from a 3 dimensional array Get a scalar form a 4 dimensional array Increment an index vector to the next logical index and jump to the specified label if the index did not wrap to the beginning Change a matrix to a type array Return the index of the next element or subarray in an array Return the index of the previous element or subarray in an array Put a contiguous subarray into an N dimensional array and return the resulting array Set a contiguous subarray of an N dimensional array Walk the index of an array forward or backward through a specified dimension 11 36 Structures 12 1 Basic Structures 12 1 1 Structure Definition The syntax for a structure definition is struct A list of members The list of members can include scalars arrays matrices strings and string arrays as well as other structures As a type scalars are unique to structures and don t otherwise exist For example the following defines a structure containing the possible contents struct generic_example scalar x matrix y 12 1 s n n Ss GAUSS User Guide string sl string array s2 struct other example t 5 A useful convention is to put the structure definition into a file with a sdf extension Then for any command file or source code file that requires this definition put include filename sdf For example Zinclude example sdf These statements create structure d
103. will compute numerical derivatives for all those elements set to missing values in the return vector or matrix Default i e no gradient procedure has been provided scalar pointer to a procedure that computes the Hessian i e the matrix of second order partial derivatives of the function with respect to the parameters When such a procedure has been provided it has two input arguments instances of PV and DS structures and one output argument a vector of computed inequality constraints Default i e no Hessian procedure has been provided Whether the objective function procedure returns a scalar or vector the Hessian procedure must return a KxK matrix Elements set to missing values will be computed numerically by sqpSolvemt scalar maximum number of iterations Default le 5 scalar maximum number of attemps in random search Default 100 scalar convergence tolerance for gradient of estimated coefficients Default le 5 When this criterion has been satisifed sqpSolvemt exits the iterations scalar if 2 QML covariance matrix else if 0 no covariance matrix is computed else ML covariance matrix is computed For a QML covariance matrix the objective function procedure must return an Nx1 vector of minus log probabilities 12 26 Structures FeasibleTest scalar if nonzero parameters are tested for feasibility before computing function in line search If function is defined outside inequality bou
104. x will exit The statement load x b mydata asc will load data contained in an ASCII file into an Nx1 vector x Use rows x to find out how many numbers were loaded and use reshape x N K to reshape it to an NxK matrix The statement load x will load the matrix x fmt from disk using the current load path into the matrix x in memory The statement open dl datl x readr d1 100 will read the first 100 rows of the GAUSS data set dat1 dat 6 6 3 Sparse Matrices Many GAUSS operators and commands support the sparse matrix data type You may use any of the following commands to create a sparse matrix denseToSp Converts a dense matrix to a sparse matrix denseToSpRE Converts a dense matrix to a sparse matrix using a relative epsilon 6 18 Language Fundamentals packedToSp spCreate spEye spOnes spZeros Creates a sparse matrix from a packed matrix of non zero values and row and column indices Creates a sparse matrix from vectors of non zero values row indices and column indices Creates a sparse identity matrix Generates a sparse matrix containing only ones and zeros Creates a sparse matrix containing no non zero values See Sparse MATRICES Chapter 9 for more information 6 6 4 N dimensional Arrays Many GAUSS commands support arrays of N dimensions The following commands may be used to create and manipulate an N dimensional array aconcat aeye areshape arrayall
105. 0 43 floating point type 1 for IEEE 754 44 47 1008 double precision data 48 51 8 the size in bytes of a double matrix 52 55 0 real matrix 1 complex matrix 56 59 1 imaginary part of matrix follows real part standard GAUSS style 2 imaginary part of each element immediately follows real part FORTRAN style 60 63 number of dimensions 0 scalar 1 row vector 2 column vector or matrix 64 67 1 row major ordering of elements 2 column major 68 71 always 0 72 75 header size 128 dimensions 4 padded to 8 byte boundary 76 127 reserved If the data is a scalar the data will directly follow the header If the data is a row vector an unsigned integer equaling the number of columns in the vector will 17 22 File I O precede the data along with 4 padding bytes If the data is a column vector or a matrix there will be two unsigned integers preceding the data The first will represent the number of rows in the matrix and the second will represent the number of columns The data area always begins on an even 8 byte boundary Numbers are stored in double precision 8 bytes per element 16 if complex For complex matrices all of the real parts are stored first followed by all the imaginary parts 17 5 11 Data Set v96 Offset Description 0 3 always OXFFFFFFFF 4 7 always 0 8 11 always OXFFFFFFFF 12 15 always 0 16 19 always OxFFFFFFFF 20 23 OxFFFFFFFF for forward byte order 0 for backward byte order
106. 01 4 204p asclabel 1lab 0 xtics 8 pi pi 4 1 xtics is used to make sure that major tick marks are placed in the appropriate places This example will number the X axis tick marks with the labels 1 72 u 1 yu and 42 lab 204m 201 2 204m 201 1 1 204m m 201 2 asclabel lab 9 This example illustrates the use of several of the special Simgrma symbols _pmsgstr 2041 2011 2 204p 201e 204m 2012 201 2 d 204m This produces vias eds 21 13 90d GAUSS User Guide 21 5 Colors O Black 8 Dark Grey 1 Blue 9 Light Blue 2 Green 10 Light Green 3 Cyan 11 Light Cyan 4 Red 12 Light Red 5 Magenta 13 Light Magenta 6 Brown 14 Yellow 7 Grey 15 White 21 6 Global Control Variables The following global variables are used to control various graphics elements Default values are provided Any or all of these variables can be set before calling one of the main graphing routines The default values can be modified by changing the declarations in pgraph dec and the statements in the procedure graphset in pgraph src graphset can be called whenever the user wants to reset these variables to their default values _pageshf 2x1 vector the graph will be shifted to the right and up if this is not 0 If this is 0 the graph will be centered on the output page Default is 0 Note Used internally For the same functionality see makewind in the GAUSS LANGUAGE REFERENCE This is used by the graphic pan
107. 08 sleep 29 809 soft delimited 24 5 solpd 29 809 sort data file 29 812 sort index 29 815 sort heap sort 29 813 sort multiple columns 29 816 sort quicksort 29 811 sortc 29 811 sortcc 29 811 sortd 29 812 sorthc 29 813 sorthcc 29 813 sortind 29 815 sortindc 29 815 sorting 28 41 sortmc 29 816 sortr sortrc 29 817 Source Browser 5 10 source browsing 4 4 source page 3 9 spaces 7 16 spaces extraneous 6 38 7 16 7 17 sparse matrices 28 29 spBiconjGradSol 29 818 spChol 29 820 spConjGradSol 29 821 spCreate 29 822 spDenseSubmat 29 824 spDiagRvMat 29 825 spEigv 29 827 spEye 29 829 spGetNZE 29 829 spLDL 29 832 spline 29 831 split horizontally 3 10 3 18 split vertically 3 10 3 18 spLU 29 833 spNumNZE 29 835 spOnes 29 836 SpreadsheetReadM 29 837 SpreadsheetReadSA 29 837 spreadsheets 28 33 SpreadsheetWrite 29 838 spScale 29 839 spSubmat 29 840 spToDense 29 841 spTrTDense 29 842 spTScalar 29 842 Index 20 Index spZeros 29 843 sqpSolve 29 844 sqpSolvemt 12 23 sqpSolveMT 29 849 sqpSolvemtControl structure 12 25 sqpSolveMTControlCreate 29 856 sqpSolveMTlagrangeCreate 29 857 sqpSolveMToutCreate 29 858 sqpSolveSet 29 858 sqrt 29 858 square root 29 858 src_path 15 1 standard deviation 29 38 29 40 29 229 29 231 29 859 29 860 standard deviation of residual 29 583 29 589 standard errors 29 583 29 589
108. 1 29 533 29 646 procedure definitions 6 3 8 2 procedures 28 46 procedures indexing 8 10 procedures multiple returns 8 11 procedures passing to other procedures 8 9 prodc 29 647 products 29 648 Profiler 20 1 program 6 4 program control 28 44 program space 29 804 program run 29 774 programming editor 3 10 _protate 21 27 _pscreen 21 27 pseudo inverse 29 621 29 622 psi 29 648 _psilent 21 27 _pstype 21 27 _psurf 21 27 _psym 21 28 _psym3d 21 28 _psymsiz 21 28 _ptek 21 28 _pticout 21 28 _ptitlht 21 28 Publication Quality Graphics 21 1 28 57 putArray 11 15 putarray 29 649 putf 29 650 putvals 29 651 PV structure 12 16 13 1 pvCreate 29 653 _pversno 21 29 pvGetIndex 29 653 pvGetParNames 29 654 pvGetParVector 29 655 pvLength 29 656 pvList 29 656 pvPack 29 657 pvPacki 29 658 pvPackm 29 659 pvPackmi 29 660 pvPacks 29 662 pvPacksi 29 663 pvPacksm 29 664 pvPacksmi 29 666 pvPutParVector 29 668 pvTest 29 670 pvUnpack 29 670 _pxpmax 21 29 _pxsci 21 29 _pypmax 21 29 _pysci 21 29 Index 17 xapul Index _pzclr 21 29 _pzoom 21 29 _pzpmax 21 29 _pzsci 21 29 Q QNewton 29 671 QNewtonmt 29 674 QNewtonmtControlCreate 29 678 QNewtonmtOutCreate 29 679 QNewtonSet 29 679 QProg 29 680 QProgmt 29 681 QProgmtInCreate 29 684 qar 29 684 qqre 29 686 qqrep 29 689 QR decomposition 29 593 29 595 ar 29 691 qre 29 6
109. 11 0953 The call to pvPacki puts an entry in the table associating the matrix in its second argument with the index 1 As indicated above the matrix can be unpacked either by index or by name Unpacking by index however is much faster than by name Note that the matrix can be unpacked using either the index or the matrix name There are index versions of all four of the packing functions pvPacki pvPackmi pvPacksi and pvPacksmi 13 3 The DS Data Structure An instance of the DS data structure contains the following members struct DS dQ d0 dataMatrix MxK matrix data d0 dataArray N dimensional array data d0 type scalar d0 dname string d0 vnames string array The definition and use of the elements of d8 are determined by the particular application and are mostly up to the user A typical use might use a vector of structures For example suppose the objective function requires a vector of observations on a dependent variable as well as on K independent variables Then 13 7 s n n Ss 114 GAUSS User Guide struct DS dQ d dsCreate y rndn 20 1 x rndn 20 5 d6 reshape d0 2 1 d0 1 dataMatrix y d0 2 dataMatrix X The d0 instance would be passed to the optimization program which then passes it to your procedure computing the objective function For example proc lpr struct PV pl struct DS d1 local u u d0 1 dataMatrix d0 2 dataMatrix pvUnpack pl beta retp u u
110. 11 17 s eJIy uw DupJoM GAUSS User Guide endfor for j 1 P 1 sigma i sigma i amult amult phi j sigma i j philj endfor endfor sigmai invpd sigma Indet In det sigma lnl 0 5 L N R asum 1n det sigmai 1 asum amult amult E sigmai atranspose E 1 312 3 Instead of index operators the above computation can be done using getArray and setArray yord getOrders Y xord getOrders X gord getOrders phi aord getOrders theta N yord 1 No of observations L yord 3 No of time series K xord 3 No of independent variables in mean equation P gord 1 order of garch parameters Q aord 1 order of arch parameters r maxc P Q E Y amult X areshape B N K L Sigma areshape omega N L L for i r 1 N 1 for 3 1 0 1 W amult getArray theta j atranspose getArray E i j 2 1 setarray Sigma i getArray sigma i 11 18 Working with Arrays amult W atranspose W 2 1 endfor for j 1 P 1 setarray sigma i getArray sigma i areshape amult amult getArray phi j getArray sigma i j getArray phi j 3 3 endfor endfor sigmai invpd sigma Indet In det sigma lnl 0 5 L N R asum 1n det sigmai 1 asum amult Camult E sigmai atranspose E 1 3 2 3 Putting the two code fragments above into loops that called them a hundred times and measuring the time
111. 18 5 MA GAUSS User Guide CCOPTIONS g xsb xarch v9 KPIC CC cc libhyp so hyp c CC G CCCOPTIONS o hyp c lm Linux CCOPTS indicates any optional compilation flags you might add CCOPTIONS CC g 02 lm lc shared gcc libhyp so hyp cpp CCC CCCOPTIONS o hyp c For details on linking your dynamic library see dlibrary in the GAUSS LANGUAGE REFERENCE 18 6 Data Transformations GAUSS allows expressions that directly reference variables columns of a data set This is done within the context of a data loop dataloop infile outfile drop wagefac wqlec shordelt foobly csed 1n sqrt csed select csed gt 0 35 and married 1 y make chfac hcfac wcfac keep csed chfac stid recsum voom endata GAUSS translates the data loop into a procedure that performs the required operations and then calls the procedure automatically at the location in your program of the data loop It does this by translating your main program file into a temporary file and then executing the temporary file A data loop may be placed only in the main program file Data loops in files that are include d or autoloaded are not recognized 19 1 doo e1eq GAUSS User Guide 19 1 Data Loop Statements A data loop begins with a dataloop statement and ends with an endata statement Inside a data loop the following statements are supported code delete drop extern keep lag list
112. 1p In this case the procedure modifies the structure es1 which es1p is pointing at instead of a local copy of the structure 12 14 Structures 12 3 Special Structures There are three common types of structures that will be found in the GAUSS Run Time Library and applications The DS and PV structures are defined in the GAUSS Run Time Library Their definitions are found in ds sdf and pv sdf respectively in the src source code subdirectory Before structures many procedures in the Run Time Library and all applications had global variables serving a variety of purposes such as setting and altering defaults Currently these variables are being entered as members of control structures 12 3 1 The DS Structure The DS structure or data structure is a very simple structure It contains a member for each GAUSS data type The following is found in ds sdf struct DS scalar type matrix dataMatrix array dataArray string dname string array vnames 5 This structure was designed for use by the various optimization functions in GAUSS in particular sqpSolvemt as well as a set of gradient procedures gradmt hessmt et al These procedures all require that the user provide a procedure computing a function to be optimized or take the derivative of etc which takes the DS structure as an argument The Run Time Library procedures such as sqpSolvemt take the DS structure as an argument and pass it
113. 2 G0445 G0446 G0447 G0454 G0456 G0457 G0458 G0459 G0460 Matrix is empty loadexe not supported use dlibrary instead callexe not supported use dllcall instead File has wrong bit order File has wrong byte order Type vector malloc failed No type vector in gfblock Illegal left hand side reference in procedure Argument is the wrong size vfor called with illegal loop level Failure opening printer for output Failure buffering output for printer Cannot take log of a negative number Attempt to index proc fn keyword as a matrix Missing right brace Unexpected end of statement 25 23 soDesso y 10413 GAUSS User Guide G0461 G0462 G0463 G0465 G0466 G0467 G0468 G0469 G0470 G0472 G0473 G0477 G0486 G0487 G0490 G0491 Too many data items Negative trim value Failure generating graph Redefinition of structure number of elements Redefinition of structure type mismatch Redefinition of structure unrecognized member Structure definition inside procedure definition Cannot create translator temp file Symbol not found Invalid name String not terminated with null byte FOR loops nested too deep Character argument too long License expired License manager initialization error License manager error 25 24 Error Messages G0492 G0497 G0500 G0503 G0504 G0505 G0506 G0507 G0508 G0509
114. 21 19 _pcross 21 19 _pdate 21 20 pdfCauchy 29 614 pdfexp 29 615 pdfGenPareto 29 616 pdfLaplace 29 616 pdflogistic 29 617 pdfn 29 618 pdfRayleigh 29 619 pdfWeibull 29 619 _perrbar 21 20 _pframe 21 20 _pgrid 21 21 pi 29 620 pinv 29 621 pinvmt 29 622 pixel coordinates 21 6 _plctrl 21 21 _plegctl 21 22 _plegstr 21 22 _plev 21 22 _pline 21 22 _pline3d 21 24 plot coordinates 21 6 _plotshf 21 24 _plotsiz 21 25 _pltype 21 25 _plwidth 21 25 _pmcolor 21 25 _pmsgctl 21 26 _pmsgstr 21 26 _pnotify 21 26 _pnum 21 26 _pnumht 21 27 pointer 7 17 8 10 8 11 29 533 pointer instruction 6 3 pointers structure 12 10 polar 29 623 polychar 29 623 polyeval 29 624 polygamma 29 625 polyint 29 626 polymake 29 627 polymat 29 628 polymroot 29 628 polymult 29 630 polynomial 29 627 polynomial interpolation 29 626 polynomial operations 28 10 polynomial regression 29 628 polynomial characteristic 29 623 polynomial evaluation 29 624 Index 16 Index polynomial roots 29 631 polyroot 29 631 pop 29 631 pagwin 29 632 precedence 6 30 precision control 28 22 predicted values 29 594 preferences 3 3 3 18 preservecase 24 12 previousindex 29 633 princomp 29 634 print 3 3 3 4 print setup 3 3 print 29 635 printdos 29 641 printfm 29 642 printfmt 29 645 probability density function Normal 29 618 proc 8 2 29 646 procedure 8
115. 557 G0558 G0559 G0560 G0561 G0562 Array has too many dimensions for matrix assign Array not conformable for indexing Array not conformable for boolean operation Global structure pointer cannot point to local structure Invalid use of Feature not authorized Path too long Unable to create sparse matrix Cannot index uninitialized structure IF nesting limit exceeded ELSE without IF ENDIF without IF Symbol not DEFINE d Too many DEFINE s Duplicate DEFINE Open comment 25 27 soDesso y 10413 GAUSS User Guide G0563 G0564 G0565 G0566 G0567 G0568 G0569 G0570 G0571 G0572 G0573 G0574 G0575 G0576 G0577 Open comment Illegal redefinition of sparse matrix Initializer too large increase maxdeclet in config cfg file Can t create profiler data file Sparse matrix uninitialized Operation not defined for triangular symmetric or Hermitian sparse matrix Argument must be complex Diagonal must be real Diagonal must not contain zeros Argument must be triangular Argument must be symmetric Sparse type mismatch Unable to load variable Threading error Expected THREADSTAT THREADBEGIN or THREADJOIN 25 28 Error Messages G0578 G0579 G0580 G0581 G0582 G0583 G0584 G0585 G0586 G0587 G0588 G0589 G0590 G0591 G0592 A THREADJOIN failed Cannot call RUN from
116. 6 Index 2 Index autocompletion 3 12 autoindenting 3 13 autoloader 6 4 6 5 15 1 29 509 autoreload 3 20 auxiliary output 17 4 29 605 auxiliary output width 29 608 axes 21 17 21 19 axes numbering 21 26 axes reversed 29 978 29 981 axmargin 29 49 B backslash 6 22 balance 29 50 band 29 51 bandchol 29 52 bandcholsol 29 53 bandltsol 29 55 bandrv 29 56 bandsolpd 29 58 bar shading 21 17 bar width 21 18 bar 29 58 base18 29 60 batch mode 5 1 begwind 29 61 besselj 29 61 bessely 29 62 beta function 29 68 beta 29 63 binary file loading 29 381 binary files 17 15 bivariate Normal 29 72 blank lines 6 38 bookmark 3 13 Boolean operators 7 13 box 21 18 box 29 64 boxcox 29 65 branching 28 44 break 29 66 breakpoints 3 23 browse 5 5 C call 29 67 calling a procedure 8 6 caret 7 6 7 19 Cartesian coordinates 29 979 case 6 38 20 541 29 940 Cauchy 29 78 29 614 cdBbeta 29 68 cdfBetaInv 29 70 commandnamecdfBinomial 29 70 commandnamecdfBinomialInv 29 71 cdfBvn 29 72 cdfBvn2 29 74 cdfBvn2e 29 76 cdfCauchy 29 78 cdfCauchyInv 29 78 cdfChic 29 79 cdfChii 29 80 cdfChinc 29 81 commandnamecdfChincInv 29 83 cdfExp 29 83 cdfExpInv 29 84 cdfFc 29 85 cdfFnc 29 87 commandnamecdfFncInv 29 88 cdfGam 29 89 cdfGenPareto 29 91 cdfLaplace 29 91 cdfLaplaceInv 29 92 cdfLogistic 29 93 Index 3 xapul Index
117. 6 File I O Offset Description 0 1 DFDF hex identification flag 2 3 1 unsigned 2 byte integer 4 5 length of string plus null byte unsigned 2 byte integer 6 7 size of file minus 16 byte header unsigned 2 byte integer 8 0 001D hex type of file 10 15 reserved all 0 s The body of the file starts at offset 16 It consists of the string terminated with a null byte The size of the file is the 16 byte header plus the length of the string and null byte rounded up to the next 16 byte paragraph boundary 17 5 4 Extended String v89 Obsolete Strings with more than 65519 characters are saved in an extended format These files have a 16 byte header formatted as follows Offset Description 0 1 EEDF hex identification flag 2 3 001D hex type of file 4 7 1 unsigned 4 byte integer 8 11 length of string plus null byte unsigned 4 byte integer 12 15 size of file minus 16 byte header unsigned 4 byte integer The body of the file starts at offset 16 It consists of the string terminated with a null byte The size of the file is the 16 byte header plus the length of the string and null byte rounded up to the next 8 byte boundary 17 5 5 Small Data Set v89 Obsolete All data sets are created with create v89 data sets consist of two files one dht contains the header information the second dat contains the binary data The data will be one of three types 17 17 O I 9113 GAUSS User Guide 8 byte IEEE
118. 8 Ne escape ASCII 27 AU formfeed ASCII 12 Ng beep ASCII 7 IU line feed ASCII 10 Nr carriage return ASCII 13 NE tab ASCII 9 INN a backslash the ASCII character whose decimal value is HH When entering DOS pathnames in double quotes two backslashes must be used to insert one backslash st c gauss myprog prg An important use of strings and character elements of matrices is with the substitution operator In the command create f1 olsdat with x 4 2 6 22 Language Fundamentals by default GAUSS will interpret the olsdat as a literal that is the literal name of the GAUSS data file you want to create It will also interpret the x as the literal prefix string for the variable names X1 x2 x3 x4 If you want to get the data set name from a string variable the substitution operator could be used as dataset olsdat create f1 dataset with x 4 2 If you want to get the data set name from a string variable and the variable names from a character vector use dataset olsdat let vnames age pay sex create fl dataset with vnames 0 2 The substitution operator works with load and save also lpath gauss procs name mydata load path lpath x name command dir fmt The general syntax is variable name Expressions are not allowed The following commands are supported with the substitution operator 6 23 Tr c m 2 3
119. 9 by Econotron Software Inc All Rights Reserved Worldwide GAUSS GAUSS Engine and GAUSS Light are trademarks of Aptech Systems Inc GEM is a trademark of Digital Research Inc Lotus is a trademark of Lotus Development Corp HP LaserJet and HP GL are trademarks of Hewlett Packard Corp PostScript is a trademark of Adobe Systems Inc IBM is a trademark of International Business Machines Corporation Hercules is a trademark of Hercules Computer Technology Inc GraphiC is a trademark of Scientific Endeavors Corporation Tektronix 1s a trademark of Tektronix Inc Windows is a registered trademark of Microsoft Corporation Other trademarks are the property of their respective owners Part Number 007431 Version 11 Documentation Revision 1047 January 21 2011 Contents Contents 1 Introduction 1 25 JuoducbtOVelVieW x uae oe ee ee ee ewe Te 1 1 1 2 Documentation Conventions 1 2 2 Getting Started 2 1 Installation Under UNIX Linux ee 2 1 2 2 Installation Under Windows lens 2 2 22 Machine Requirements gt o is aac 0 e e 2 2 222 Installation from Download c n 2 2 22 3 Installation from CD s sa sabc o lens 2 2 3 Introduction to the GAUSS Graphical User Interface 3 1 Page Organization Concept e 3 1 3 2 Command Page ccoo cier a ee eH aE 3 2 3 2 1 Menus and Toolbars o 00000
120. 92 qrep 29 695 qrsol 29 697 artsol 29 698 qtyr 29 698 qtyre 29 701 qtyrep 29 704 quadrature 29 458 quantile 29 706 quantiled 29 707 ayr 29 709 ayre 29 710 ayrep 29 712 R radii 21 22 random numbers 28 11 rank of a matrix 29 714 rank 29 714 rankindx 29 715 Rayleigh 29 112 29 113 29 619 readr 29 716 real 29 717 recent files 3 3 recent working directories 3 3 recode dataloop 29 720 recode 29 718 recserar 29 721 recsercp 29 723 recserrc 29 724 recursion 8 5 redo 3 3 reduced row echelon form 29 773 regression 29 580 29 585 regular expressions 3 15 relational operator dot 7 11 7 21 relational operators 7 9 relative error 29 105 29 114 reload 3 18 reload symbol 3 17 remove split 3 10 rerun 29 725 reserved words 0 1 reshape 29 726 residuals 29 583 29 587 29 594 retp 8 2 8 5 29 727 return 29 728 rev 29 728 rfft 29 729 rffti 29 730 rfftip 29 731 rfftn 29 732 rfftnp 29 733 rfftp 29 735 Index 18 Index right hand side 15 2 rndbeta 29 736 rndcon 29 737 rndgam 29 738 rndi 29 740 rndKMbeta 29 740 rndKMgam 29 742 rndKMi 29 743 rndKMn 29 745 rndKMnb 29 746 rndKMp 29 747 rndKMu 29 749 rndKMvm 29 750 rndLCbeta 29 751 rndLCgam 29 753 rndLCi 29 755 rndLCn 29 757 rndLCnb 29 758 rndLCp 29 760 rndLCu 29 762 rndLCvm 29 764 rndmult 29 737 rndn 29 765 rndnb 29 766 rndp 29 767 rnds
121. AUSS User Guide srcline 12 This allows you to place srcline statements in the middle of GAUSS commands so that line numbers are reported precisely as you want them For example Zsrcline 1 print Here is a multi line srcline 2 sentence if it contains a run time error srcline 3 you will know exactly srcline 4 which part of the sentence has the problem The argument supplied to srcfile does not need quotes srcfile gauss test e 6 5 Procedures A procedure allows you to define a new function which you can then use as if it were an intrinsic function It is called in the same way as an intrinsic function y myproc a b c Procedures are isolated from the rest of your program and cannot be entered except by calling them Some or all of the variables inside a procedure can be local variables local variables exist only when the procedure is actually executing and then disappear Local variables cannot get mixed up with other variables of the same name in your main program or in other procedures For details on defining and calling procedures see PROCEDURES AND KEYWORDS chapter 8 6 8 Language Fundamentals 6 6 Data Types There are four basic data types in GAUSS matrices N dimensional arrays strings and string arrays It is not necessary to declare the type of a variable but it is good programming practice to respect the types of variables whenever possible The data type and size can change
122. GAUSS User Guide Aptech Systems Inc Mathematical and Statistical System Information in this document is subject to change without notice and does not represent a commitment on the part of Aptech Systems Inc The software described in this document is furnished under a license agreement or nondisclosure agreement The software may be used or copied only in accordance with the terms of the agreement The purchaser may make one copy of the software for backup purposes No part of this manual may be reproduced or transmitted in any form or by any means electronic or mechanical including photocopying and recording for any purpose other than the purchaser s personal use without the written permission of Aptech Systems Inc Copyright Aptech Systems Inc Black Diamond WA 1984 2010 All Rights Reserved Worldwide SuperLU Copyright 2003 The Regents of the University of California through Lawrence Berkeley National Laboratory subject to receipt of any required approvals from U S Dept of Energy All Rights Reserved See GAUSS Software Product License for additional terms and conditions TAUCS Version 2 0 November 29 2001 Copyright 2001 2002 2003 by Sivan Toledo Tel Aviv University stoledo tau ac il All Rights Reserved See GAUSS Software License for additional terms and conditions Econotron Software Inc beta polygamma zeta gammacplx Ingammacplx erfcplx erfccplx psi gradcp hesscp Functions Copyright 200
123. No square root negative element Illegal index An illegal value has been passed in as a matrix index Index overflow An illegal value has been passed in as a matrix index retp outside of procedure A retp statement has been encountered outside a procedure definition Too many active locals The execution stack is full There are too many local variables active Restructure your program Notify Aptech Systems Procedure stack overflow expression too complex The execution stack is full There are too many nested levels of procedure calls Restructure your program Notify Aptech Systems Index out of range You have referenced a matrix element that is out of bounds for the matrix being referenced exec command string too long Nonscalar index Cholesky downdate failed Zero pivot encountered crout The Crout algorithm has encountered a diagonal element equal to 0 Use croutp instead 25 6 Error Messages G0063 G0064 G0065 G0066 G0068 G0069 G0070 G0071 G0072 G0073 Operator missing An expression contains two consecutive operands with no intervening operator Operand missing An expression contains two consecutive operators with no intervening operand Division by zero Must be recompiled under current version You are attempting to use compiled code from a previous version of GAUSS Recompile the source code under the current version Program compiled under GAUSS 386 real ver
124. Page CTRL 2 Brings up the Source Page CTRL 3 Brings up the Data Page 4 2 Navigating the GAUSS Graphical User Interface CTRL 4 Brings up the Debug Page CTRL 5 Brings up the Help Page CTRL TAB Brings up the next page For example CTRL TAB from the Command Page will bring up the Source Page CTRL TAB from the Help Page will wrap and bring up the Command Page ALT TAB Cycles between any pages that are undocked as well as other open programs WINDOW TAB Windows only Cycles between any pages that are un docked as well as other open programs Mouse Scroll Wheel When floating over any set of tabs the mouse scroll wheel will cycle through the open tabs This will work for pro gramming editor tabs symbol editor tabs and the main page tabs on the left of the main application 4 3 Switch To Command Page on I O Under the Tools gt Preferences gt Command is a check box entitled Switch to Command Page on I O Selecting this option will bring you to the command page if any program output is printed to the Program Output Window or if any input is requested by GAUSS functions key keyw or cons 4 4 Viewing Program Output from Other Pages The Program Output Window may be pulled out of the Command Page by selecting the Program Output banner and dragging it The Program Output Window may then be placed and resized The Program Output Window will remain in place and on the top of the window stack allowing you to navigate freely
125. Run Time Library Structures Two structures are used by several GAUSS Run Time Library functions for handling parameter vectors and data the PV parameter structure and the DS data structure 13 1 The PV Parameter Structure The members of an instance of structure of type PV are all private that is not accessible directly to the user It is designed to handle parameter vectors for threadsafe optimization functions Entering and receiving parameter vectors and accessing properties of this vector are accomplished using special functions Suppose you are optimizing a function containing a KxL matrix of coefficients The optimization function requires a parameter vector but your function uses a KxL matrix Your needs and the needs of the optimization function can be both satisfied by an instance of the structure of type PV For example struct PV pl p1 pvCreate 13 1 s n n sS 114 GAUSS User Guide x zeros 4 3 on input contains start values on exit contains estimates pl pvPack pl x coefficients The pvCreate function initializes p1 to default values pvPack enters the 4x3 matrix stored row wise as a 12x1 parameter vector for the optimization function The optimization program will pass the instance of the structure of type PV to your objective function By calling pvUnpack your 4x3 coefficient matrix is retrieved from the parameter vector For example in your procedure you have x pvUn
126. S isa complete analysis environment suitable for performing quick calculations complex analysis of millions of data points or anything in between Whether you are new to computerized analysis or a seasoned programmer the GAUSS family of products combine to offer you an easy to learn environment that is powerful and versatile enough for virtually any numerical task Since its introduction in 1984 GAUSS has been the standard for serious number crunching and complex modeling of large scale data Worldwide acceptance and use in government industry and the academic community is a firm testament to its power and versatility The GAUSS System can be described several ways It is an exceptionally efficient number cruncher a comprehensive programming language and an interactive analysis environment GAUSS may be the only numerical tool you will ever need 1 1 uononpoauu GAUSS User Guide 1 2 Documentation Conventions The following table describes how text formatting is used to identify GAUSS programming elements Text Style Use Example regular text narrative text formatting is used bold text emphasis not supported under UNIX italic text variables If vnames is a string or has monospace monospace monospace bold SMALL Caps code example filename path etc reference to a GAUSS command or other programming element within a narrative paragraph reference to section of the manual
127. S User Guide If you require a matrix result and if the result has one or two dimensions use arraytomat to convert to a matrix or use getMatrix or getMatrix4D Or if the result is a scalar use getScalar3D or getScalar4D 11 2 2 getArray getArray is an additional method for extracting arrays a areshape seqa 1 1 12 3 2 2 b getarray a 2 1 print a Plane 1 1 0000 2 0000 3 0000 4 0000 Plane 2 5 0000 6 0000 7 0000 8 0000 Plane 3 9 0000 10 000 11 000 12 000 print b 5 0000 6 0000 getArray can only extract a contiguous part of an array To get non contiguous parts you must use the index operator 11 12 Working with Arrays 11 23 getMatrix If the result is one or two dimensions getMatrix returns a portion of an array converted to a matrix getMatrix is about 20 percent faster than the index operator a areshape seqa 1 1 12 3 2 2 b getMatrix a 2 print b 5 0000 6 0000 7 0000 8 0000 11 24 getMatrix4D This is a specialized version of getMatrix for 4 dimensional arrays It behaves just like getMatrix but is dramatically faster for that type of array The following illustrates the difference in timing a arrayinit 100 100 10 10 1 t8 date for 1 1 100 1 for j 1 100 1 b a i j endfor endfor tl date el ethsec t6 t1 print el print t2 date for 1 1 100 1 11 13 s eJIy uw BUMJOM GAUSS User Guide fo
128. SS User Guide Indexing matrices Assignment operator Vertical concatenation Horizontal concatenation con Numeric input from keyboard cons Character input from keyboard declare Compile time matrix or string initialization let Matrix definition statement load Load matrix same as loadm readr Read from a GAUSS matrix or data set file save Save matrices procedures and strings to disk saved Convert a matrix to a GAUSS data set stof Convert string to matrix submat Extract a submatrix writer Write data to a GAUSS data set Following are some examples of matrix definition statements An assignment statement followed by data enclosed in braces is an implicit let statement Only constants are allowed in let statements operators are illegal When braces are used in let statements commas are used to separate rows The statement let x 123 456 789 or 6 12 Language Fundamentals x 123 456 789 will result in ll NaN fre Nn ON The statement let x 3 3 21234 567 89 will result in aj Il aN fre oo tA N NO NW Ww The statement let x 3 3 1 will result in The statement let x 3 3 6 13 sj ejuawepuny oDenbue GAUSS User Guide will result in gt Il ooo ooo ooo The statement letx 1234567809 will result in s OMmAANDNDNHPWN KE Complex constants can be entered in a let statement In the following example the or is not a ma
129. SS programming language Error messages generated by library functions are not included here G0002 File too large load Input file too large getf Input file too large G0003 Indexing a matrix as a vector A single index can be used only on vectors Vectors have only one row or only one column G0004 Compiler stack overflow too complex An expression is too complex Break it into smaller pieces Notify Aptech Systems 25 1 soDesso y 10413 GAUSS User Guide G0005 G0006 G0007 G0008 G0009 G0010 G0011 G0012 G0013 G0014 G0015 G0016 File is already compiled Statement too long Statement longer than 4000 characters End of file encountered Syntax error Compiler Unrecognizable or incorrect syntax Semicolon missing on previous statement create Unrecognizable statement in command file or numvar or outvar statement error Compiler pass out of memory Compiler pass has run out of memory Notify Aptech Systems Can t open output file Compiled file must have correct extension GAUSS requires a gcg extension Invalid drive specifier Invalid filename File not found Directory full Too many include s include d files are nested too deep 25 2 Error Messages G0017 G0018 G0019 G0020 G0021 G0022 G0023 G0024 G0025 G0026 G0027 G0028 WARNING local outside of procedure A local statement has been found outside a pro
130. The call to getnamef in this example returns a string array rather than a character vector so you can print it without the prefix 17 10 File I O Using the Uppercase Lowercase Convention v89 Data Sets Historically some GAUSS Application programs recognized an uppercase lowercase convention if the variable name was uppercase the variable was assumed to be numeric and if it was lowercase the variable was assumed to be character However this is now obsolete use vartypef and v96 data sets to be compatible with future versions 17 3 GAUSS Data Archives The GAUSS Data Archive GDA is extremely powerful and flexible giving you much greater control over how you store your data There is no limitation on the number of variables that can be stored in a GDA and the only size limitation is the amount of available disk space Moreover GDA s are designed to hold whatever type of data you want to store in them You may write matrices arrays strings string arrays sparse matrices and structures to a GDA and the GDA will keep track of the type size and location of each of the variables contained in it Since GAUSS now supports reading and writing to GDA s that were created on other platforms GDA s provide a simple solution to the problem of sharing data across platforms See Section 17 5 12 for information on the layout of a GDA 17 3 1 Creating and Writing Variables to GDA s To create a GAUSS Data Archiv
131. User Guide struct SQPsolveMTControl c6 c8 sqpSolveMTcontrolCreate lind pvGetIndex par0 lambda get indices of lambda parameters in parameter vector tind pvGetIndex par0 theta get indices of theta parameters in parameter vector c bounds ones pvLength parQ 1 1e250 1e250 c6 bounds lind 1 zeros rows lind 1 c6 bounds lind 2 18 ones rows lind 1 c6 bounds tind 1 001 ones rows tind 1 c6 bounds tind 2 100 ones rows tind 1 cQ ineqProc amp ineq c covType 1 struct DS d6 dQ dsCreate dQ dataMatrix loadd maxfact struct SQPsolveMTOut out0 out SQPsolveMT 1pr par0 d0 c0 lambdahat pvUnpack out6 par lambda phihat pvUnpack out6 par phi thetahat pvUnpack out0 par theta print estimates print print lambda lambdahat print 13 12 Run Time Library Structures print phi phihat print print theta thetahat struct PV stderr stderr out0 par if not scalmiss out0 moment stderr pvPutParVector stderr sqrt diag out9 moment lambdase pvUnpack stderr lambda phise pvUnpack stderr phi thetase pvUnpack stderr theta print standard errors print print lambda lambdase print print phi phise print print theta thetase endif proc lpr struct PV parl struct DS datal local lambda phi theta sigma logl lambda pvUnpack p
132. Using Publication Quality Graphics 21 2 21 2 1 Getting Started lt sa s ea aoso a Se R RE LE 21 2 21 2 2 Graphics Coordinate System o 21 6 Eirhecui pc 21 7 21 3 1 Tiled Graphic Panels 2 252 840 680 e ee mA 21 7 21 3 2 Overlapping Graphic Panels lll 21 7 21 8 3 Nontransparent Graphic Panels o 21 8 21 8 4 Transparent Graphic Panels o o 21 8 21 8 5 Using Graphic Panel Functions lll 21 8 21 8 6 Inch Units in Graphic Panels lll 21 10 21 8 7 Saving Graphic Panel Configurations 21 10 Graphics Text Elements e 21 10 214 1 Selecting FOM S oie ae ra e a e a 21 11 21 42 Greek and Mathematical Symbols 21 12 AAN 21 14 Global Control VanableS s asue a ee Se A e eds 21 14 22 Graphics Editor 22 1 22 2 Introduction to the Graphics Editor us so Rex eee Ge REOR S Roms 22 1 22 1 4 Overview 1 a a a a a a E a G EAE e a 22 1 Graphics Editor Workspace a a eee ee ee 22 2 22 231 TODA ess eon Soe a Be a e d ene os Be a 3 etes 22 2 2222 SAUS Bar e es re gee e bee Sue Gee See heed were E 22 3 22 2 3 File menu commands 22 4 22 2 4 Editmenucommands 0 00052 ee eae 22 5 22 2 5 View menu commands 22 5 22 2 6 Draw menu commands 22 6 22 2 7 E
133. Ww wait waitc walkindex while winclear wincleararea winclearttylog winclose wincloseall winconvertpqg window wingetactive wingetattributes wingetcolorcells wingetcursor winmove winopenpqg winopentext winopentty x indcv xlabel xor xpnd ylabel winpan winprint winprintpqg winrefresh winrefresharea winresize winsetactive winsetbackground winsetcolor winsetcolorcells winsetcolormap winsetcursor winsetforeground winsetrefresh winsettextwrap winwrite winzoompqg writer xtics xy XYZ ytics B 16 Reserved Words Appendix zeros zlabel ztics SP IOM P9A19SDH Singularity Tolerance Appendix The tolerance used to determine whether or not a matrix is singular can be changed The default value is 1 0e 14 for both the LU and the Cholesky decompositions The tolerance for each decomposition can be changed separately The following operators are affected by a change in the tolerance Crout LU Decomposition crout x croutp x inv x det x y x when neither x nor y is scalar and x is square Cholesky Decomposition chol x invpd x solpd y x y x when neither x nor y is scalar and x is not square C 1 wte nBuis GAUSS User Guide C 1 Reading and Setting the Tolerance The tolerance value may be read or set using the sysstate function cases 13 and 14 C 2 Determining Singularity There is no perfect tolerance for determining singularity The default
134. _sqp_EqProc 29 845 _sqp_FeasibleTest 29 847 _sqp_GradProc 29 846 _sqp_HessProc 29 847 _sqp_IneqProc 29 846 _sqp_MaxIters 29 847 _sqp_ParNames 29 847 _sqp_PrintIters 29 847 _sqp_RandRadius 29 847 A abs 29 1 absolute value 29 1 acf 29 2 aconcat 11 4 29 3 additive sequence 29 794 aeye 11 6 29 5 algebra linear 28 5 amax 11 25 29 6 amean 11 25 29 8 AmericanBinomCall 29 10 AmericanBinomCall_Greeks 29 11 AmericanBinomCall_ImpVol 29 13 AmericanBinomPut 29 14 AmericanBinomPut_Greeks 29 15 AmericanBinomPut_ImpVol 29 17 AmericanBSCall 29 18 AmericanBSCall_Greeks 29 19 AmericanBSCall ImpVol 29 20 AmericanBSPut 29 21 AmericanBSPut Greeks 29 22 AmericanBSPut ImpVol 29 23 amin 11 25 29 24 ampersand 7 17 amult 11 23 29 26 and 7 13 7 14 and 7 15 annualTradingDays 29 28 append ATOG command 24 3 arccos 29 29 arcsin 29 30 areshape 11 2 29 31 arguments 6 40 8 3 8 7 array indexing 10 3 arrayalloc 11 7 29 32 arrayindex 29 33 arrayinit 11 6 29 34 arrays 10 1 11 1 28 30 arrays of structures 12 4 arraytomat 11 28 29 35 arrows 21 14 21 16 ASCII files 24 1 ASCII files packed 24 8 ASCII files reading 17 3 ASCII files writing 17 4 asciiload 29 36 asclabel 29 37 assigning to arrays 11 8 assignment operator 6 2 6 39 7 15 astd 29 38 astds 29 40 asum 29 42 atan 29 44 atan2 29 45 atog 17 3 ATOG 24 1 atranspose 11 21 29 4
135. a set This value can be modified for a particular run by setting __maxvec in your command file to some other value The value returned by a call to maxvec can be permanently modified by editing system dec and changing the value of __maxvec The value returned when running GAUSS Light is always 8192 maxbytes is a GAUSS procedure that returns the value of a scalar global __maxbytes that sets the amount of available RAM This value can be modified for a particular run by setting __maxbytes in your command file to some other value The value returned by a call to maxbytes can be permanently modified by editing system dec and changing the value of __maxbytes If you wish to force GAUSS procedures and applications to read a GAUSS data set in its entirety set __maxvec and __maxbytes to very large values 26 3 1 Hard Disk Maintenance The hard disk used for the swap file should be optimized occasionally with a disk optimizer Use a disk maintenance program to ensure that the disk media is in good shape 26 3 2 CPU Cache There is a line for cache size in the gauss cfg file Set it to the size of the CPU data cache for your computer This affects the choice of algorithms used for matrix multiply functions This will not change the results you get but it can radically affect performance for large matrices 26 4 Fonts There are four fonts available in the Publication Quality Graphics System Simplex standard sans serif font Simgrma Sim
136. aches the specified line in the current file The debugger will stop at every line in the named file The debugger will stop when it reaches the specified line in the current file The debugger will stop every period times it reaches the first line in a called procedure The debugger will stop every time it reaches the first line in a called procedure Executes code to a specified line procedure or period in the file without stopping at breakpoints The optional arguments are the same as g listed above Executes code to the execution count specified number without stopping at breakpoints Executes the remainder of the current procedure or to a breakpoint and stops at the next line in the calling procedure 5 8 Using the Command Line Interface 5 4 4 View Commands v vars v vars Searches for a local variable then a global variable and displays the value of a specified variable Searches for a local variable then a global variable and displays the specified character matrix The display properties of matrices and string arrays can be set using the following commands Specifies the number of rows to be shown Specifies the number of columns to be shown Specifies the indices of the upper left corner of the block to be shown Specifies the width of the columns to be shown Specifies the precision shown Specifies the format of the numbers as decimal scientific or auto format Quits the
137. adJoin Joins Thi Th2 X r s q z t The main point here is that any symbols a thread or its children assign to must be isolated from all the other threads and their children of the same nesting level in that set On the other hand the children of a thread can freely read write symbols that are read written by their parent because there is no risk of simultaneity they must only isolate written symbols from their siblings and siblings offspring If you break the writer must isolate rule your program and probably GAUSS will crash Worse until it crashes it will be happily producing indeterminate results Finally the ThreadEnd command is what tells a thread to terminate so you mustn t write code that keeps a thread from reaching it For example don t retp from the middle of a thread ThreadStat m imt 9 ThreadBegin x q 1 ifx 1 retp z else r Z 2 endif ThreadEnd ThreadJoin And don t use goto to jump into or out of the middle of a thread retry ThreadBegin err x fna q if err 14 9 spealy GAUSS User Guide goto badidea endif x fnb x ThreadEnd ThreadStat y fnb y ThreadJoin z fnc x y save Z end badidea errorlog Error computing fna q q fnd q goto retry Basically don t do anything that will keep a thread from reaching its ThreadEnd command That s the only way it knows its work is done end and stop are okay to call tho
138. ade sdf struct option p0 p1 p2 p0 optionCreate pl optionCreate p2 pl pd 12 1 5 Structure Indexing Structure indexing may be used to reference a particular element in a structure array The syntax follows that of matrix indexing For example given the following structure definition struct examplel matrix x matrix y string str 3 you could create an array of examplel structures and index it as follows struct examplel ela struct examplel elb ela ela elb ela 2 1 y rndn 25 10 In this example ela and e1b are concatenated to create a 2x1 array of example structures that is assigned back to ela Then the y member of the 2 1 element of e1a is set to a random matrix Indexing of structure arrays can occur on multiple levels For example let s define the following structures struct example3 12 5 s n n Ss GAUSS User Guide matrix w string array sa J struct example2 matrix Z struct example3 e3 5 and let s redefine example1 to include an instance of an example2 structure struct examplel matrix x matrix y string str struct example2 e2 Let s assume that we have an example1 structure el like the one displayed in Figure 12 1 We could then index the structure as follows r el e2 3 1 e3 2 1 w You can also use indexing to reference the structure itself rather than a member of that structure struct example3 e3tmp e3tmp el e2 3 1 e3
139. age of the Command Input Window see Section 3 3 2 3 5 6 Error Output Window The Error Output Window can be accessed by toggling the Error Output button on the right side of the status bar For details regarding the features and usage of the Error Output Window see Section 3 4 2 3 16 Introduction to the GAUSS Graphical User Interface 3 6 Data Page Section 3 2 1 provides details of the main menus and toolbars The Data Page contains the following changes to the toolbar and menu options d sauss i IS HEN e Bo Q9 w H O sx gt Symbols B5 X x matrix 5x5 auto sync 4 Active Symbols Dec Sd Hex Chr 1 f Matrices 1 2 3 1 0 364429 0 394827 0 173242 SB command c4 Sparse Matrices Strings String A si ici 3 0 796406 0 258487 1 26757 structures 2 0214176 1 247 0 710351 y Source 4 1 56874 0 724864 0 675488 5 319714 0 615048 0 335485 Qe 18 vebug E bata Figure 3 14 Data Page 3 6 1 Menu Bar Symbol Editor Menu Edit Symbol Opens an active symbol from your current GAUSS workspace in a symbol editor Save Symbol Saves changes to the symbol in the active symbol editor Reload Reloads a symbol that is out of sync with the GAUSS symbol table Symbol Note This only applies if auto reload mode is turned off Toggle Turns on off autoreload for the active symbol editor 3 17 onul IND GAUSS User Guide Auto r
140. age return line feed if applicable Records must be fixed length format start length prec where start starting position of the field in the record 1 is the first position The default is 1 length the length of the field in bytes The default is 8 prec optional a decimal point will be inserted automatically prec places in from the RIGHT edge of the field 24 8 ATOG If several variables are listed after a format definition each succeeding field will be assumed to start immediately after the preceding field If an asterisk is used to specify the starting position the current logical default will be assumed An asterisk in the length position will select the current default for both length and prec This is illegal 3 8 The type change characters and are used to toggle between character and numeric data type Any data in the record that is not defined in a format is ignored The examples below assume a 32 byte record with a carriage return line feed occupying the last 2 bytes of each record The data below can be interpreted in different ways using different invar statements ABCDEFGHIJ12345678901234567890 lt CR gt lt LF gt BA 4 position 1 10 20 30 31 32 This example invar record 32 1 3 group dept 11 4 2 x 3 5 y will result in variable value type group ABC character dept DEF character XI 12 34 numeric X2 56 78 numeric X3 90 12 numeric Y 34567 numeric This example
141. allation from Download For download instructions email info aptech com 2 2 3 Installation from CD Insert the GAUSS compact disc into the CD ROM drive and setup should start automatically If setup does not start automatically browse to the CD ROM drive and double click on the msi file to launch the installer You can use this procedure for the initial installation of GAUSS and for additions or modifications to GAUSS components To receive a license and license installation instructions email license aptech com and include your serial number and hostid 2 2 Introduction to the GAUSS Graphical User Interface 3 1 Page Organization Concept The GAUSS graphical user interface is organized into separate pages Pages are separate customizable main windows with their own set of widgets Each page is designed to facilitate the performance of one of the common tasks performed in GAUSS entering commands interactively editing a program examining data debugging a program and accessing the help system Each page is a tab on the main application allowing you to instantly access a window custom configured for the task you wish to perform The GAUSS graphical user interface is composed of five different pages Command Page For executing interactive commands Source Page For editing program files Data Page For examining and editing GAUSS matrices and other data Debug Page For interactively debugging your programs H
142. als from within procedures that have locals with the same name The local statement does not initialize set to a value the local variables If they are not passed in as parameters they must be assigned some value before they are accessed or the program will terminate with a Variable not initialized error message All local and global variables are dynamically allocated and sized automatically during execution Local variables including those that were passed as parameters can change in size during the execution of the procedure Local variables exist only when the procedure is executing and then disappear Local variables cannot be listed with the show command The maximum number of locals is limited by stack space and the size of workspace memory The limiting factor applies to the total number of active local symbols at any one time during execution If cat has 10 locals and it calls dog which has 20 locals there are 30 active locals whenever cat is called There can be multiple local statements in a procedure They will affect only the code in the procedure that follows Therefore for example it is possible to refer to a global x in a procedure and follow that with a local statement that declares a local x All subsequent references to x would be to the local x This is not good programming practice but it demonstrates the principle that the local statement affects only the code that is physically below it in the procedure definition
143. and second unpacking the PV structure in the user provided procedure for use in computing the objective function For example to pack parameters into a PV structure include sqpsolvemt sdf starting values b0 1 constant in mean equation garch 1 1 garch parameters arch 1 1 arch parameters omega 1 constant in variance equation 12 16 Structures struct PV pd p0 pvPack pvCreate b0 b0 p0 pvPack p8 garch garch p0 pvPack p0 arch arch p0 pvPack p0 omega omega fe data EJ z loadd tseries struct DS dQ d0 dataMatrix z Next in the user provided procedure for computing the objective function in this case minus the log likelihood the parameter vector is unpacked proc ll struct PV p0 struct DS dQ local b0 garch arch omega p q h u vc w b0 pvUnpack p0 b0 garch pvUnpack p8 garch arch pvUnpack p0 arch omega pvUnpack p0 omega rows garch rows arch p q u d0 dataMatrix b0 vc moment u 0 rows u w omega zeros q q shiftr u ones 1 q seqa q 1 1 q arch h recserar w vc ones p 1 garch logl 0 5 u w h 1n 2 pi Indh retp 1ogl 12 17 s n n Ss GAUSS User Guide endp Masked Matrices The pvUnpack function unpacks parameters into matrices or arrays for use in computations The first argument is a PV structure
144. ar1 lambda phi pvUnpack parl phi theta pvUnpack par1 theta Sigma lambda phi lambda theta logl lnpdfmvn datal dataMatrix sigma retp logl endp 13 13 sa4ni9n1s 118 GAUSS User Guide proc ineq struct PV parl struct DS datal local lambda phi theta sigma e lambda pvUnpack parl lambda phi pvUnpack par1 phi theta pvUnpack parl theta sigma lambda phi lambda theta e eigh sigma 001 eigenvalues of sigma e e eigh phi 001 eigenvalues of phi retp e endp 13 14 Multi Threaded 4 Programming in GAUSS The term thread comes from the phrase thread of execution simply it denotes a section of code that you want to execute A single threaded program has only one thread of execution i e the program itself A multi threaded program is one that can have multiple threads sections of code executing simultaneously Since these threads are part of the same program they share the same workspace and see and operate on the same symbols Threads allow you to take full advantage of the hardware processing resources available on hyper threaded multi core and multi processor systems executing independent calculations simultaneously combining and using the results of their work when done 14 1 The Functions GAUSS includes four keywords for multi threading your programs ThreadStat Marks a single statement to be executed as a t
145. are NaN s but this procedure tests only for indefinite proc isindef x retp not x __INDEFn endp Be sure to call gausset before calling isindef gausset will initialize the value of the global __INDEFn to a platform specific encoding The procedure normal will return a matrix with all denormals and unnormals set to zero proc normal x retp x abs x gt 4 19e 307 endp The procedure isinf will return 1 true if the matrix passed to it contains any infinities proc isinf x local plus minus plus INFp 6 29 s ejuawepuny oDenbue GAUSS User Guide minus __INFn retp not x plus or not x minus endp Be sure to call gausset before calling isinf gausset will initialize the values of the globals __INFn and __INFp to platform specific encodings 6 7 Operator Precedence The order in which an expression is evaluated is determined by the precedence of the operators involved and the order in which they are used For example the and operators have a higher precedence than the and operators In expressions that contain these operators the operand pairs associated with the or operator are evaluated first Whether or is evaluated first depends on which comes first in the particular expression For a listing of the precedence of all operators see OPERATOR PRECEDENCE Section 7 7 The expression 54 3 4 6 3 is evaluated as 5 3 4 6 3 Within a te
146. are unique to 6 36 Language Fundamentals the procedure that the subroutine is in For details see gosub in the GAUSS LANGUAGE REFERENCE 6 9 Functions Single line functions that return one item can be defined with the fn statement Je fn area r pi r r These functions can be called in the same way as intrinsic functions The above function could be used in the following program sequence diameter 3 radius 3 2 a area radius 6 10 Rules of Syntax This section lists the general rules of syntax for GAUSS programs 6 10 1 Statements A GAUSS program consists of a series of statements A statement is a complete expression or command Statements in GAUSS end with a semicolon with one exception from the GAUSS command line the final semicolon in an interactive program is implicit if it is not explicitly given gauss x 5 z rndn 3 3 y x z 6 37 s ejuawepuny oDenbue GAUSS User Guide Column position is not significant Blank lines are allowed Inside a statement and outside of double quotes the carriage return line feed at the end of a physical line will be converted to a space character as the program is compiled A statement containing a quoted string can be continued across several lines with a backslash as follows s This is one really long string that would be difficult to assign in just a single line 6 10 2 Case GAUSS does not distinguish between upperca
147. art is the initial value stop is the final value and step is the increment break and continue are also supported by for loops For more information see for in the GAUSS LANGUAGE REFERENCE 6 8 2 Conditional Branching The if statement controls conditional branching if scalar expression statements elseif scalar expression Statements 6 34 Language Fundamentals else statements endif The scalar_expression is any expression that returns a scalar result The expression will be evaluated as TRUE if its real part is nonzero and FALSE if it is zero GAUSS will test the expression after the if statement If it is TRUE then the first list of statements is executed If it is FALSE then GAUSS will move to the expression after the first elseif statement if there is one and test it It will keep testing expressions and will execute the first list of statements that corresponds to a TRUE expression If no expression is TRUE then the list of statements following the else statement is executed After the appropriate list of statements is executed the program will go to the statement following the endif and continue on Use the relational and logical operators without the dot in the expression that controls an if or elseif statement These operators always return a scalar result if statements can be nested One endif is required per if clause If an else statement is used there may be only one per if clause Th
148. ata area will be the length of the string plus 8 The data area follows immediately after the 128 byte header 17 5 9 Data Set v92 Obsolete Offset Description 0 3 always 0 4 7 always OXEECACACA 8 11 reserved 12 15 reserved 16 19 reserved 20 23 rows in data set 24 27 columns in data set 28 3 0 real data set 1 complex data set 32 35 type of data in data set 2 4 or 8 36 39 header size in bytes is 128 columns 9 40 127 reserved The variable names begin at offset 128 and are stored 8 bytes each in ASCII format Each name corresponds to one column of data Names less than 8 characters are padded on the right with bytes of zero The variable type flags immediately follow the variable names They are 1 byte binary integers one per column padded to an even 8 byte boundary A 1 indicates a numeric variable and a 0 indicates a character variable 17 21 O I 9I 4 GAUSS User Guide The contents of the data set follow the header and start on an 8 byte boundary Data is either 2 byte signed integer 4 byte single precision floating point or 8 byte double precision floating point 17 5 10 Matrix v96 Offset Description 0 3 always OXFFFFFFFF 4 7 always 0 8 11 always OxFFFFFFFF 12 15 always 0 16 19 always OXFFFFFFFF 20 23 OxFFFFFFFF for forward byte order 0 for backward byte order 24 27 OxFFFFFFFF for forward bit order 0 for backward bit order 28 31 always OXABCDEFOI 32 35 currently 1 36 39 reserved 4
149. ate array filled with specified scalar value arrayalloc Allocate array with no specified contents 11 1 1 areshape areshape is a method for creating an array with specified contents arrayinit creates an array filled with a selected scalar value areshape will do the same but with a matrix For example given a matrix areshape will create an array containing multiple copies of that matrix reshape seqa 1 1 4 2 2 ord 3 2 2 a areshape x ord print a x I Q I Plane 1 1 0000 2 0000 3 0000 4 0000 Plane 2 1 0000 2 0000 3 0000 4 0000 Plane 3 1 0000 2 0000 3 0000 4 0000 Reading Data from the Disk into an Array areshape is a fast way to re dimension a matrix or array already in memory For example suppose we have a GAUSS data set containing panel data and that it s small enough to be read in all at once Working with Arrays panel areshape loaddC panel 5 100 10 mn amean panel 2 5x1x10 array of means of each panel mm moment panel 80 5x10x10 array of moments of each panel xu yc is a 5x10x10 array of covariance matrices vc mm 100 amult atranspose mn 1 3 2 mn panel is a 5x100x10 array and in this context is 5 panels of 100 cases measured on 10 variables Inserting Random Numbers into Arrays A random array of any dimension or size can be quickly created using areshape Thus for a 10x10x5x3 array
150. ators Section 7 2 or the GAUSS LANGUAGE REFERENCE Result too large The size of the result of an expression is greater than the limit for a single matrix Not all the eigenvalues can be computed Matrix must be square to invert Not all the singular values can be computed 25 4 Error Messages G0041 G0042 G0043 G0044 G0045 G0046 G0047 G0048 G0049 G0050 G0051 Argument must be scalar A matrix argument was passed to a function that requires a scalar Matrix must be square to compute determinant Not implemented for complex matrices Matrix must be real Attempt to write complex data to real data set Data sets unlike matrices cannot change from real to complex after they are created Use create complex to create a complex data set Columns don t match The matrices must have the same number of columns Rows don t match The matrices must have the same number of rows Matrix singular The matrix is singular using the current tolerance Target matrix not complex Out of memory for program The main program area is full To increase the main program space see new in the GAUSS LANGUAGE REFERENCE Program too large The main program area is full To increase the main program space see new in the GAUSS LANGUAGE REFERENCE 25 5 soDesso y 10413 GAUSS User Guide G0052 G0053 G0054 G0055 G0056 G0057 G0058 G0059 G0060 G0061 G0062
151. based file and is considered the best method for export import on the Microsoft Windows platform To create a Windows Enhanced Metafile select the Windows Metafile menu item from the Export menu Autoscale Checking this option forces the translated to automatically scale the Enhanced Metafile This is the best setting for most applications for importing However some applications require a more precise format If the importing application has trouble uncheck this option 22 18 Time and Date GAUSS offers a comprehensive set of time and date functions These functions afford the user the ability to return the current time and date to carry out most related calculations and format the results for output GAUSS also allows the user to perform timed iterations In the year 1 AD the calendar in general use was the Julian calendar The Gregorian calendar that we use today was not invented until the late 1500 s This new calendar changed the method of calculating leap years on century marks With the Julian system simply every fourth year was a leap year The Gregorian system made every fourth year a leap year with the exception of century marks which are only leap years if divisible by 400 The British adoption of this calendar which the GAUSS date functions are based on did not happen until the year 1752 In that year eleven days were removed September 2 1752 was followed by September 14 1752 dtvnormal and utctodtv are accurate bac
152. caled to graphic panel inches and positioned relative to the lower left corner of the graphic panel A graphic panel inch is a true inch in size only if the graphic panel is scaled to the full window otherwise X coordinates will be scaled relative to the horizontal graphic panel size and Y coordinates will be scaled relative to the vertical graphic panel size 21 3 7 Saving Graphic Panel Configurations The functions savewind and loadwind allow the user to save graphic panel configurations Once graphic panels are created using makewind and window savewind may be called This will save to disk the global variables containing information about the current graphic panel configuration To load this configuration again call loadwind See loadwind in the GAUSS LANGUAGE REFERENCE 21 4 Graphics Text Elements Graphics text elements such as titles messages axes labels axes numbering and legends can be modified and enhanced by changing fonts and by adding superscripting subscripting and special mathematical symbols To make these modifications and enhancements the user can embed escape codes in the text strings that are passed to title xlabel ylabel and asclabel or assigned to _pmsgstr and _plegstr The escape codes used for graphics text are 000 String termination character null byte Enter superscript mode leave subscript mode Enter subscript mode leave superscript mode Interpret next character as
153. canBinomPut ImpVol AmericanBSCall AmericanBSCall Greeks AmericanBSCall ImpVol AmericanBSPut AmericanBSPut Greeks AmericanBSPut ImpVol amin amult and annualTradingDays arccos arcsin arctan B 1 SP IOM P9A19SDH GAUSS User Guide arctan2 areshape arrayalloc arrayindex arrayinit arraytomat asclabel balance band bandchol bandcholsol bandltsol bandrv bandsolpd bar calcbox call callexe cdfbeta cdfbvn cdfbvn2 cdfbvn2e cdfchic cdfchii cdfchinc cdffc cdffnc cdfgam cdfmvn asin asum atan atan2 atranspose axmargin base10 begwind besselj bessely box boxcox break cdfn cdfn2 cdfnc cdfni cdftc cdftci cdftnc cdftvn cdir ceil cfft cffti changedir chdir B 2 Reserved Words Appendix checkinterrupt chol choldn cholsol cholup chrs cint clear clearg close closeall cls cmsplit cmsplit2 code color cols colsf combinate combinated comlog commandeerm commandeersa compile complex con cond conformed conj datacreate datacreatecomplex datalist dataload cons continue contour conv convertsatostr convertstrtosa coreleft corrm corrms corrvc corrx corrxs cos cosh counts countwts create crossprd crout croutp csrcol csrlin csrtype cumprodc cumsumc curve cvtos cvtosa dataopen datasave date datestr B 3 SP IOM P9A19SDH GAUSS User Guide datestring datestrymd dayinyr dayOfWeek debug d
154. cation in plot coordinates M 2 y location in plot coordinates M 3 z location in plot coordinates M 5 symbol height If this is 0 a default height of 5 0 will be used M 6 symbol color see CoLors Section 21 5 M 4 symbol type see _pstype earlier M 7 line thickness A value of 0 1s normal line width Use psym for plotting extra symbols in inch coordinates scalar or Kx1 vector symbol size for the symbols on the main curves This is NOT related to _psym If 0 a default size of 5 0 is used string name of Tektronix format graphics file This must have a tkf extension If this is set to a null string the graphics file will be suppressed The default is graphic tkf scalar If 1 tick marks point outward on graphs Default is 0 scalar the height of the title characters in inches If this is O a default height of approx 0 13 inch will be used 21 28 Publication Quality Graphics _pversno _pxpmax _pxsci _Pypmax _pysci _pzclr _pzoom _pzpmax _pzsci string the graphics version number scalar the maximum number of places to the right of the decimal point for the X axis numbers Default is 12 scalar the threshold in digits above which the data for the X axis will be scaled and a power of 10 scaling factor displayed Default is 4 scalar the maximum number of places to the right of the decimal point for the Y axis numbers Default is 12 scalar th
155. cedure definition The local statement will be ignored Read error in program file Can t edit gcg file Not implemented yet Command not supported in this implementation use must be at the beginning of a program User keyword cannot be used in expression Illegal attempt to redefine symbol to an index variable Invalid use of gt probably should be Undefined symbol A symbol has been referenced that has not been given a definition Too many symbols The global symbol table is full To set the limit see new in the GAUSS LANGUAGE REFERENCE Invalid directory Can t open configuration file GAUSS cannot find the configuration file 25 3 soDesso y 10413 GAUSS User Guide G0029 G0030 G0031 G0032 G0033 G0034 G0035 G0036 G0037 G0038 G0039 G0040 Missing left parenthesis Insufficient workspace memory The space used to store and manipulate matrices and strings is not large enough for the operations attempted To make the main program space smaller and reclaim enough space to continue see new in the GAUSS LANGUAGE REFERENCE Execution stack too deep expression too complex An expression is too complex Break it into smaller pieces Notify Aptech Systems fn function too large Missing right index bracket Missing arguments Argument too large Matrices are not conformable For a description of the function or operator being used and conformability rules see MATRIX Oper
156. cedure retp statement 5 End of procedure definition endp statement There is always one proc statement and one endp statement in a procedure definition Any statements that come between these two statements are part of the procedure Procedure definitions cannot be nested local and retp statements are optional There can be multiple local and retp statements in a procedure definition Here is an example proc 3 regress x y local xxi b ymxb sse sd t xxi invpd x x b xxi x y ymxb y xb sse ymxb ymxb rows x cols x sd sqrt diag sse xxi t b sd retp b sd t endp This could be used as a function that takes two matrix arguments and returns three matrices as a result For example is b sd t regress x y Following is a discussion of the five parts of a procedure definition 8 2 Procedures and Keywords 8 1 1 Procedure Declaration The proc statement is the procedure declaration statement The format is proc Crets name larg arg2 argN rets Optional constant number of values returned by the procedure Acceptable values here are 0 1023 the default is 1 name Name of the procedure up to 32 alphanumeric characters or an underscore beginning with an alpha or an underscore arg Names that will be used inside the procedure for the arguments that are passed to the procedure when it is called There can be 0 1023 arguments These names will be known only in the
157. crob 39 A2 05 O Rod ON OU Oo U01010 010 0101 010101 01 o d OOO 0 Ci CF OQ C 4 OCI S 0m 20 7 61 62 65 64 65 66 67 68 69 70 71 72 73 74 75 76 CF 78 79 80 81 82 83 84 85 86 87 88 A C Icxomomnmmoou ug v xe co CHAHwH DA TO Z ET 89 90 91 92 93 94 YD 96 97 98 99 100 101 102 103 104 105 106 107 108 109 no RK WN Jzn 100000 1 E PAIN ORS x gt c 07520002 3 NA N NN NH NH FW NO nO OO pare ee ONE Se a ee eS A 4 Fonts A 4 Complex C4 C4 C4 C4 C4 CN GN O Oo OA CI O ON DORWN OC anna O Q 4 ONARWN O 56 57 58 59 60 Qo N Wat AEP wd See oOmArNAUMUA WNP Os 61 62 63 64 65 66 67 68 69 70 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 M umnuocoou 3g TN Y O U N U O ey ud 89 90 91 92 95 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 mNoaRWN O 000 Tp YTN XK ga 3 0 UO O DB d Uu 17 18 19 20 22 23 24 23 26 E ME E NE a 2 A 5 u04 Reserved Words Appendix The following words are used for GAUSS functions You cannot use these names for variables or procedures in your programs abs acf aconcat acos aeye amax amean AmericanBinomCall AmericanBinomCall_Greeks AmericanBinomCall ImpVol AmericanBinomPut AmericanBinomPut Greeks Ameri
158. ct the Ellipse menu item from the Draw menu or press the Draw ellipse button on the toolbar This puts the editor into the draw ellipse state indicated by a crosshair cursor Next position the mouse where you want the center of the circle then press and hold the left mouse button You may also move the object by pressing and holding the right mouse button while keeping the left button depressed Drag the mouse to the desired radius and release the mouse button The circle will be redrawn in the current background fill and border color At any time after the above process you may modify the circle to any other elliptical size and shape 22 2 14 Modifying the Graphical Objects First ensure you are in selection mode by pressing the Select toolbar button or choosing the Select item in the Draw menu Selection mode is indicated with an arrow cursor Next select the object you want to modify by left clicking anywhere inside or on the object It will then become highlighted Once selected it may be sized moved or modified with one of the actions listed in the object s action context menu 22 14 Graphics Editor Aspect Ratio You can force an object s aspect ratio to be retained while sizing it by checking this menu item from the Page Context menu When this is checked all the sides of the object are sized by the same amount as the side being moved eliminating the need to resize all sides independently If the object
159. cted text and places it on the clipboard Copies selected text to the clipboard Copies the clipboard contents to the cursor position Prints selected text Runs the file at the top of the Action List Debugs the file at the top of the Action List Opens the file at the top of the Action List Stops a running GAUSS program 3 2 3 Working Directory Toolbar The Working Directory Toolbar contains a dropdown list that shows your current working directory and a history of recent directories The Change Working Directory button allows you to browse for and select a new working directory 3 4 Introduction to the GAUSS Graphical User Interface Current Working Directory C gauss 11 x pen Change Working Directory Figure 3 3 Working Directory Toolbar 3 2 4 Command History Toolbar Search Run Previous Histor mx La le yy Paste Search Next Figure 3 4 Command History Toolbar Run Executes the highlighted command from the command history Paste Pastes the highlighted command to the Command Input Window for further editing Search Previous Searches the Command Output Window for previous executions of a command and its output Search Next Searches the Command Output Window for the next execution of a command and its output 3 5 onul IND GAUSS User Guide 3 2 5 The Run Debug and Edit Buttons Pn En O et Q P Debug Stop Figure 3 5 Run Debug and Edit Button
160. current location of the instruction pointer Here are two examples declare matrix x 1234 external matrix ybar Procedure definitions are nonexecutable They do not generate executable code at the current location of the instruction pointer Here is an example Tr c m 2 2 o eQ Y 236 5 0 e o o GAUSS User Guide zed rndn 3 3 proc sqrtinv x local y y sqrt x retp yt inv x endp zsi sqrtinv zed There are two executable statements in the example above the first line and the last line In the binary code that is generated the last line will follow immediately after the first line The last line is the call to the procedure This generates executable code The procedure definition generates no code at the current location of the instruction pointer There is code generated in the procedure definition but it is isolated from the rest of the program It is executable only within the scope of the procedure and can be reached only by calling the procedure 6 3 Programs A program is any set of statements that are run together at one time There are two sections within a program 6 3 1 Main Section The main section of the program is all of the code that is compiled together WITHOUT relying on the autoloader This means code that is in the main file or is included in the compilation of the main file with an include statement ALL executable code should be in the main section There m
161. d deindenting Autoindenting not only simplifies the process of writing code but also encourages the creation of readable code 6 Bookmarks Bookmarks allow quick navigation to often visited lines of code To insert a bookmark hold down the SHIFT key and left click in the left margin of the file on the line where you would like to set the bookmark If a file contains more than one bookmark you may use F2 to navigate to the next bookmark in the file To navigate between bookmarks in multiple files use the bookmark window The bookmark window contains a list of all of your bookmarks Double click on a listed bookmark and GAUSS will bring you to the file and line of your bookmark regardless of whether the file is already open for editing or not Programming Editor Hot Keys CTRL A CTRL C CTRL D CTRL F CTRL G CTRL L CTRL N CTRL O CTRL P Select All Copy Debug current file Find and replace Go to Line Delete line Open new file Open existing file Print file 3 13 onul IND GAUSS User Guide CTRL Q Used for block commenting CTRL R Run current file CTRL S Save current file CTRL T Switches current line with the line above CTRL V Paste CTRL W Closes the current file CTRL Z Undo CTRL Y Redo CTRL Cycles through open editor windows 3 5 3 Find and Replace From the Edit Menu selecting Find and Replace or pressing CTRL F will bring up the find and replace widget at the bo
162. d gdacreate gdadstat gdadstatmat gdagetindex gdagetname gdagetnames gdagetorders gdagettype gdagettypes gdagetvarinfo gdaiscplx gdapack fonts fontunload fontunloadall fopen for format formatcv formatnv fputs fputst fseek fstrerror ftell ftocv ftos ftostrc gdaread gdareadbyindex gdareadsome gdareportvarinfo gdaupdate gdaupdateandpack gdawrite gdawritesome gdtfastcat ge getarray getdims getf getmatrix getmatrix4d getname B 6 Reserved Words Appendix getnamef getNextTradingDay getNextWeekDay getnr getnrmt getorders getpath getPreviousTradingDay getPreviousWeekDay getscalar3d getscalar4d getwind hardcopy hasimag header headermt hess hessMT hessMTg hessMTgw if imag indcv indexcat indices indices2 indicesf indicesfn gosub goto gradMT gradMTm gradp graph graphgpg graphinit graphprt graphset graphsev3 gt hessMTm hessMTmw hessMTw hessp hist histf histp hsec indnv indsav int intgrat2 intgrat3 inthp intHP1 intHP2 B 7 SP IOM P9A19SDH GAUSS User Guide intHP3 intHP4 inthpControlCreate intquad1 intquad2 intquad3 intrleav intrleavsa intrsect intrsectsa key keyav keymatchmc lag lag1 lagn lapeighb lapeighi lapeighvb lapeighvi lapgeig lapgeigh lapgeighv lapgeigv lapgschur lapgsvdcst lapgsvds lapgsvdst lapsvdcusv intsimp inv invpd invswp iscplx iscplxf isinfnanmiss ismiss isSparse keyw
163. d count 29 163 while 29 215 window 17 4 window 29 964 window clear 29 134 workbox 29 958 29 960 working directory toolbar 3 4 workspace 29 199 29 804 writer 29 965 X xlabel 29 966 xlsGetSheetCount 29 967 xlsGetSheetSize 29 968 xlsGetSheetTypes 29 968 xlsMakeRange 29 969 xlsReadM 29 970 xlsReadSA 29 971 xlsWrite 29 973 xlsWriteM 29 974 xlsWriteSA 29 975 xor 7 14 XOr 7 15 xpnd 29 977 xtics 29 978 xy 29 979 xyz 29 979 Y ylabel 29 980 ytics 29 980 Z zeros 29 981 zeta 29 982 zlabel 29 982 zooming graphs 21 29 ztics 29 983 Index 24
164. d here For example cdfnc computes the complement of the Normal cdf for each element of an array just as it would for a matrix See the documentation for these GAUSS functions for information about their behavior with arrays aconcat Concatenate conformable matrices and arrays in a user specified dimension aeye Create an array of identity matrices amax Compute the maximum elements across a dimension of an array amean Compute the mean along one dimension of an array amin Compute the minimum elements across a dimension of an array amult Perform a matrix multiplication on the last two trailing dimensions of an array areshape Reshape a scalar matrix or array into an array of user specified size arrayalloc Create an N dimensional array with unspecified contents arrayinit Create an N dimensional array with a specified fill value arraytomat Change an array to type matrix asum Compute the sum across one dimension of an array atranspose Transpose an N dimensional array getarray Get a contiguous subarray from an N dimensional array getdims Get the number of dimensions in an array getmatrix Get a contiguous matrix from an N dimensional array getmatrix4D Get a contiguous matrix from a 4 dimensional array getorders Get the vector of orders corresponding to an array 11 35 s eJIy uw DupJoM GAUSS User Guide getscalar3D getscalar4D loopnextindex mattoarray nextindex previousindex putarray setarray
165. d number of lines of source code in the current file lc Displays source code in the current file starting with the current line 11 file line Displays source code in the named file starting with the specified line 11 file Displays source code in the named file starting with the first line 11 line Displays source code starting with the specified line File does not change 11 Displays the next page of source code lp Displays the previous page of source code 5 4 3 Execution Functions s number Executes the specified number of lines stepping into procedures 5 7 eur puewwog GAUSS User Guide n number x number g largs j args jx number Executes the specified number of lines stepping over procedures Executes code from the beginning of the program to the specified line count or until a breakpoint is hit Executes from the current line to the end of the program stopping at breakpoints The optional arguments specify other stopping points The syntax for each optional argument is filename line period The debugger will stop every period times it reaches the filename line filename period line period filename line procedure period procedure specified line in the named file The debugger will stop when it reaches the specified line in the named file The debugger will stop every period times it reaches any line in the named file The debugger will stop every period times it re
166. d to the nearest integer This is an element by element operator Factorial y x Computes the factorial of every element in the matrix x Nonintegers are rounded to the nearest integer before the factorial operator is applied This will not work with complex matrices If x is complex a fatal error will be generated Element by element multiplication Jena z If x is a column vector and z is a row vector or vice versa the outer product or table of the two will be computed For comformability rules see ELEMENT BY ELEMENT OPERATORS Section 7 1 Element by element division y x uum Element by element exponentiation ye xz If x is negative z must be an integer Same as Kronecker tensor product 7 6 Operators ku This results in a matrix in which every element in x has been multiplied scalar multiplication by the matrix z For example x y E 8 VS Ad 1 2 34 1456 78 9 X Z 1 2 3 4 6 7 9 4 5 6 8 7 8 9 14 12 15 18 16 21 24 27 28 Horizontal direct product Z Qm Cy 1 2 3 4 5 6 7 8 5 6 10 12 21 24 28 32 10 16 20 32 12 18 24 36 The input matrices x and y must have the same number of rows The result will have cols x cols y columns 7 7 10 e19dO GAUSS User Guide 7 2 2 Other Matrix Operators Transpose operator y xi The columns of y will contain the same values as the rows of x and the rows of y will contain
167. dimensions to a matrix a arrayinit 2 2 0 b arraytomat a type a 21 000 type b 6 0000 11 4 7 mattoarray This function converts a matrix to an array b rndn 2 2 a mattoarray b type b 6 0000 type a 21 000 11 5 Using Arrays with GAUSS functions Many of the GAUSS functions have been re designed to work with arrays There are two general approaches to this implementation There are exceptions however and you are urged to refer to the documention if you are not sure how a particular GAUSS function handles array input 11 28 Working with Arrays In the first approach the function returns an element by element result that is strictly conformable to the input For example cdfnc returns an array of identical size and shape to the input array a areshape seqa 2 5 12 2 3 2 b cdfnc a print b Plane 1 0 9772 0 9331 0 8413 0 6914 0 5000 0 3085 Plane 2 0 1586 0 0668 0 0227 0 0062 0 0013 0 0002 In the second approach which applies generally to GAUSS matrix functions the function operates on the matrix defined by the last two trailing dimensions of the array Thus given a 5x10x3 array moment returns a 5x3x3 array of five moment matrices computed from the five 10x3 matrices in the input array Only the last two trailing dimensions matter i e given a 2X3x4x5x10x6 array moment returns a 2x3x4x5x6x6 array of moment matrices For example in the following th
168. e The limit on the number of rows in a GAUSS data set is determined by disk size The limit on the number of columns is limited by RAM Data can be stored in 2 4 or 8 bytes per number rather than just 8 bytes as in the case of GAUSS matrix files The ranges of the different formats are 17 7 O I 9113 GAUSS User Guide Bytes Type Significant Digits Range 2 integer 4 32768 lt X lt 32767 4 single 6 7 8 43E 37 lt X lt 3 37E 38 8 double 15 16 4 19E 307 lt X lt 1 67E 308 17 2 2 Creating Data Sets Data sets can be created with the create or datacreate command The names of the columns the type of data etc can be specified For details see create in the GAUSS LANGUAGE REFERENCE Data sets unlike matrices cannot change from real to complex or vice versa Data sets are always stored a row at a time The rows of a complex data set then have the real and imaginary parts interleaved element by element For this reason you cannot write rows from a complex matrix to areal data set there is no way to interleave the data without rewriting the entire data set If you must explicitly convert the rows of data first using the real and imag functions see the GAUSS LANGUAGE REFERENCE and then write them to the data set Rows from a real matrix CAN be written to a complex data set GAUSS simply supplies 0 s for the imaginary part To create a complex data set include the complex flag in you
169. e Bad expression or missing arguments Check the expression in question or you forgot an argument Factorial overflow Nesting too deep Break the expression into smaller statements Missing left bracket 25 10 Error Messages G0109 G0110 G0111 G0112 G0113 G0114 G0115 G0116 G0117 G0118 G0120 G0121 G0122 Not enough data items You omitted data in a let statement Found expected Found expected Matrix multiplication overflow Unclosed Unclosed Illegal redefinition of function You are attempting to turn a function into a matrix or string If this is a name conflict delete the function sysstate invalid case Invalid argument Argument must be integer File handles must be integral Illegal type for save Matrix not positive definite The matrix is either not positive definite or singular using the current tolerance Bad file handle The file handle does not refer to an open file or is not in the valid range for file handles 25 11 soDesso y 10413 GAUSS User Guide G0123 File handle not open The file handle does not refer to an open file G0124 readr call too large You are attempting to read too much in one call G0125 Read past end of file You have already reached the end of the file G0126 Error closing file G0127 File not open for write G0128 File already open G0129 File not open for read G0130 No output variable
170. e call gdaCreate which creates a GDA containing only header information It is recommended that file names passed into gdaCreate have a gda extension however gdaCreate will not force an extension To write variables to the GDA you must call gdaWrite A single call to gdaWrite writes only one variable to the GDA Writing multiple variables requires multiple calls to gdaWrite For example the following code ret gdaCreate myfile gda 1 17 11 O I 9113 GAUSS User Guide ret gdaWrite myfile gda rndn 100 50 x1 ret gdaWrite myfile gda This is a string stri1 ret gdaWrite myfile gda 394 x2 produces a GDA containing the following variables Index Name Type Size 1 xl matrix 100 x 50 strl string 16 chars 3 x2 matrix 1x1 17 3 2 Reading Variables from GDA s The following table details the commands that you may use to read various types of variables from a GAUSS Data Archive Variable Type Read Command s matrix array gdaRead string gdaReadB yIndex string array sparse matrix gdaReadSparse structure gdaReadStruct gdaRead gdaReadSparse and gdaReadStruct take a variable name and return the variable data gdaReadByIndex returns the variable data for a specified variable index For example to get the variable x1 out of myfile gda you could call gdaRead myfile gda x1 lt II or y gdaReadByIndex myfile gda 1 17 12 File I O If you want
171. e I O getf will read a file and return it in a string variable Any kind of file can be read in this way as long as it will fit into a single string variable To read files sequentially use fopen to open the file and use fgets fputs and associated functions to read and write the file The current position in a file can be determined with ftell The following example uses these functions to copy an ASCII text file proc copy src dest local fin fout str fin fopen src rb if not fin retp 1 endif fout fopen dest wb if not fin call close fin retp 2 endif do until eof fin 17 6 File I O str fgets fin 1024 if fputs fout str 1 call close fin call close fout retp 3 endif endo call close fin call close fout retp 0 endp 17 2 Data Sets GAUSS data sets are the preferred method of storing data contained in a single matrix for use within GAUSS Use of these data sets allows extremely fast reading and writing of data Many library functions are designed to read data from these data sets If you want to store multiple variables of various types in a single file see GAUSS Data ARCHIVES Section 17 3 17 2 1 Layout GAUSS data sets are arranged as matrices that is they are organized in terms of rows and columns The columns in a data file are assigned names and these names are stored in the header or in the case of the v89 format in a separate header fil
172. e curves is separated by a null byte 000 For example _plegstr Curve 11000Curve 21000Curve 3 Mx 1 vector user defined contour levels for contour Default is 0 See contour in the GAUSS LANGUAGE REFERENCE Mx9 matrix to draw lines circles or radii Each row controls one item to be drawn If this is a scalar zero nothing will be drawn Default is 0 M 1 item type and coordinate system 21 22 Publication Quality Graphics line in plot coordinates line in inch coordinates line in pixel coordinates circle in plot coordinates circle in inch coordinates radius in plot coordinates NA na WN radius in inch coordinates M 2 line type dashed dotted short dashes closely spaced dots dots and dashes 6 solid M 3 7 coordinates and dimensions if item type is line 1 lt _pline M 1 lt 3 ak oU N M 3 x starting point M 4 y starting point M 5 x ending point M 6 y ending point M 7 0 if this is a continuation of a curve 1 if this begins a new curve if item type is circle _pline M 1 4 or _pline M 1 5 M 3 x center of circle M 4 y center of circle M 5 radius M 6 starting point of arc in radians M 7 ending point of arc in radians if item type is radius _pline M 1 6 or _pline M 1 7 M 3 x center of circle M 4 y center of circle M 5 beginning point of radius O is the center of the circle 21 23 90d GAUSS User Guide
173. e result is a 2x3 array of 3x1 vectors of singular values of a 2x3 array of 6x3 matrices a areshape seqa 1 1 108 2 3 6 3 b svds a print b 11 29 s eJIy uw BUDO GAUSS User Guide Plane 1 1 45 894532 1 6407053 1 2063156e 015 Plane 1 2 118 72909 0 63421188 5 8652600e 015 Plane 1 3 194 29063 0 38756064 1 7162751e 014 Plane 2 1 270 30524 0 27857175 1 9012118e 014 Plane 2 2 346 47504 0 21732995 1 4501098e 014 Plane 2 3 422 71618 0 17813229 1 6612287e 014 It might be tempting to conclude from this example that in general a GAUSS function s behavior 11 30 Working with Arrays on the last two trailing dimensions of an array is strictly analogous to the GAUSS function s behavior on a matrix This may be true with some of the functions but not all For example the GAUSS meanc function returns a column result for matrix input However the behavior for the GAUSS amean function is not analogous This function takes a second argument that specifies on which dimension the mean is to be taken That dimension is then collapsed to a size of 1 Thus a areshape seqa 1 1 24 2 3 4 print a Plane 1 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 9 000 10 000 11 000 12 000 Plane 2 13 000 14 000 15 000 16 000 17 000 18 000 19 000 20 000 21 000 22 000 23 000 24 000 means computed across rows b amean a 1 print b
174. e that contains the address of a structure and is used to reference that structure 12 2 1 Creating and Assigning Structure Pointers Given the following structure type definition struct example struct matrix x matrix y E a pointer to an example struct structure can be created with the following syntax struct example struct esp However at this point esp is not yet pointing at anything It has only been defined to be the kind of pointer that points at example struct structures To set it to point at a particular structure instance we must first create the structure instance 12 10 Structures struct example_struct es and then we can set esp to point at es by setting esp to the address of es esp amp es The following code struct example_struct es2 es2 esp copies the contents of the structure that esp is pointing at i e the contents of es to es2 It is the same as struct example_struct es2 es2 es 12 2 2 Structure Pointer References To reference a member of a structure we use a dot syntax For example we might use the following code to set the x member of es es x rndn 3 3 To reference a member of a structure using a pointer to that structure we use an arrow syntax For example we might use the following code to set the x member of es using the pointer esp esp gt x rndn 10 5 12 11 sa4ni9n1s GAUSS User Guide This code will modify
175. e threshold in digits above which the data for the Y axis will be scaled and a power of 10 scaling factor displayed Default is 4 scalar row vector or Kx2 matrix Z level color control for procedures surface and contour See surface in the GAUSS LANGUAGE REFERENCE 1x3 row vector magnifies the graphics display for zooming in on detailed areas of the graph If scalar 0 no magnification is performed Default is 0 1 magnification value 1 is normal size 2 horizontal center of zoomed plot 0 100 3 vertical center of zoomed plot 0 100 To see the upper left quarter of the screen magnified 2 times use _pzoom 2 25 75 scalar the maximum number of places to the right of the decimal point for the Z axis numbers Default is 3 scalar the threshold in digits above which the data for the Z axis will be scaled and a power of 10 scaling factor displayed Default is 4 21 29 90d Graphics Editor 22 1 Introduction to the Graphics Editor The GAUSS graphics editor is a utility for composing pages containing GAUSS graphics files Its primary purpose is to provide the user with a toolbox for creating and annotating graphs created by GAUSS using all of the fonts available on your Windows system It is not meant to be a full featured publishing tool but rather a supplemental utility for dynamically importing and easily arranging multiple graphics files on a single page 22 1 4 Overview The graphics editor allows the u
176. ecified the names of character variables will be saved in lowercase and the names of numeric variables will be saved in uppercase The in the invar statement specifies that the variables that follow are character type The specifies numeric If and are not used in an invar statement the default is numeric Comments in command files must be enclosed between characters 24 2 Commands A detailed explanation of each command follows append Instructs ATOG to append the converted data to an existing data set append No assumptions are made regarding the format of the existing file Make certain that the number order and type of data converted match the existing file ATOG creates v96 format data files so will only append to v96 format data files 24 3 SOLV GAUSS User Guide complex Instructs ATOG to convert the ASCH file into a complex GAUSS data set complex Complex GAUSS data sets are stored by rows with the real and imaginary parts interleaved element by element ATOG assumes the same structure for the ASCII input file and will thus read TWO numbers out for EACH variable specified complex cannot be used with packed ASCII files input Specifies the file name of the ASCII file to be converted The full path name can be used in the file specification For example the command input data raw will expect an ASCII data file in the current working directory The command input
177. eclare delete deletefile delif denseSubmat design det detl dfft dffti dfree diag diagrv digamma disable dlibrary dllcall do dos doswincloseall doswinopen dotfeq dotfeqmt ed edit editm eig eigcg dotfge dotfgemt dotfgt dotfgtmt dotfle dotflemt dotflt dotfltmt dotfne dotfnemt draw dsCreate dstat dstatmt dstatmtControlCreate dtdate dtday dttime dttodtv dttostr dttoutc dtvnormal dtvtodt dtvtoutc dummy dummybr dummydn eigcg2 eigch eigch2 eigh eighv B 4 Reserved Words Appendix eigrg eigrg2 eigrs eigrs2 eigv elapsedTradingDays else elseif enable end endfor endif endo endp endwind envget eof eq eqSolve eqSolvemt eqSolvemtControlCreate eqSolvemtOutCreate eqSolveSet eqv erf fcheckerr fclearerr feq feqmt fflush fft ffti fftm erfc error errorlog etdays ethsec etstr EuropeanBinomCall EuropeanBinomCall Greeks EuropeanBinomCall ImpVol EuropeanBinomPut EuropeanBinomPut Greeks EuropeanBinomPut ImpVol EuropeanBSCall EuropeanBSCall Greeks EuropeanBSCall ImpVol EuropeanBSPut EuropeanBSPut Greeks EuropeanBSPut ImpVol exctsmpl exec execbg exp expr external eye fftmi fftn fge fgemt fgets fgetsa fgetsat fgetst B 5 SP IOM P9A19SDH GAUSS User Guide fgt fgtmt fileinfo files filesa fix fle flemt floor flt fltmt fmod fn fne fnemt font fontload gamma gammaii gausset gdaappen
178. edure definition A proc statement was encountered inside a procedure definition G0156 Illegal redefinition of procedure You are attempting to turn a procedure into a matrix or string If this is a name conflict delete the procedure G0157 Illegal redefinition of matrix G0158 endp without proc You are attempting to end a procedure that you never started G0159 Wrong number of parameters You called a procedure with the wrong number of arguments G0160 Expected string variable G0161 User keywords return nothing G0162 Can t save proc keyword fn with global references Remove the global references or leave this in source code form for the autoloader to handle See library in the GAUSS LANGUAGE REFERENCE 25 14 Error Messages G0163 G0164 G0165 G0166 G0167 G0168 G0169 G0170 G0171 G0172 G0173 G0174 Wrong size format matrix Bad mask matrix Type mismatch or missing arguments Character element too long The maximum length for character elements is 8 characters Argument must be column vector Wrong number of returns The procedure was defined to return a different number of items Invalid pointer You are attempting to call a local procedure using an invalid procedure pointer Invalid use of ampersand Called symbol is wrong type You are attempting to call a local procedure using a pointer to something else Can t resize temporary file varindx failed during open The g
179. eed 29 737 rndu 29 768 rndvm 29 769 rotater 29 770 round down 29 316 round up 29 121 round 29 771 rows 29 771 rowsf 29 772 rref 29 773 rules of syntax 6 37 run 3 4 3 5 run button 3 6 run to cursor 3 21 run 29 774 Run Time Library structures 13 1 S satostrC 29 776 save 3 10 3 18 save as 3 10 save symbol 3 17 save 29 776 saveall 29 778 saved 29 779 savestruct 29 780 savewind 29 781 saving the workspace 16 2 scalar error code 29 271 29 784 scalar expression 6 32 scale 29 782 scale3d 29 783 scalerr 29 784 scalinfnanmiss 29 785 scaling 29 782 29 783 scalmiss 29 786 schtoc 29 787 schur 29 788 scientific functions 28 1 screen 29 789 search next 3 5 search previous 3 5 searchsourcepath 29 790 secondary section 6 5 seekr 29 791 select dataloop 29 792 selif 29 792 semicolon 6 2 sega 29 794 Index 19 xapul Index seqm 29 794 sequence function 29 794 sequence functions 28 22 series functions 28 22 set difference function 29 796 setArray 11 16 setarray 29 795 setdif 29 796 setdifsa 29 797 setvars 29 798 setvwrmode 29 799 setwind 29 800 shell 29 800 shi ftr 29 801 shortcuts 4 2 show 29 802 Simpson s method 29 466 sin 29 805 sine inverse 29 30 singleindex 29 806 singular value decomposition 29 888 29 890 29 892 singular values 29 887 29 891 singularity tolerance 0 1 sinh 29 8
180. efinitions that persist until the workspace is cleared They do not create structures only structure type definitions The next section describes how to create an instance of a structure 12 1 2 Declaring an Instance To use a structure it is necessary to declare an instance The syntax for this is struct structure type structure name For example Zinclude example sdf struct generic example p0 12 2 Structures 12 1 3 Initializing an Instance Members of structures are referenced using a dot syntax p0 x rndn 20 3 The same syntax applies when referred to on the right hand side mn meanc p0 x Initialization of Global Structures Global structures are initialized at compile time Each member of the structure is initialized according to the following schedule scalar O a scalar zero matrix an empty matrix with zero rows and zero columns array 0 a 1 dimensional array set to zero string a null string 9999 string array a 1x1 string array set to null If a global already exists in memory it will not be reinitialized It may be the case in your program that when it is rerun the global variables may need to be reset to default values That is your program may depend on certain members of a structure being set to default values that are set to some other value later in the program When you rerun this program you will want to reinitialize the global structure To do this make an ass
181. el routines The user must not set this when using the graphic panel procedures _pagesiz 2x1 vector size of the graph in inches on the printer output Maximum size is 9 0x6 855 inches unrotated or 6 855x9 0 inches rotated If this is 0 the maximum size will be used Default is 0 Note Used internally For the same functionality see makewind in the GAUSS LANGUAGE REFERENCE This is used by the graphic panel routines The user must not set this when using the graphic panel procedures _parrow Mx11 matrix draws one arrow per row of the input matrix for total of M arrows If scalar zero no arrows will be drawn 21 14 Publication Quality Graphics M 1 x starting point M 2 y starting point M 3 x ending point M 5 ratio of the length of the arrow head to half its width M 6 size of arrow head in inches M 4 y ending point M 7 type and location of arrow heads This integer number will be interpreted as a decimal expansion mn for example if 10 then m 1 n 0 m type of arrow head 0 solid 1 empty 2 open 3 closed n location of arrow head 0 none 1 atthe final end 2 atboth ends M 8 color of arrow see Corons Section 21 5 M 9 coordinate units for location 1 x y starting and ending locations in plot coordinates 2 x y starting and ending locations in inches 3 xy starting and ending locations in pixels M 10 line type 1 dashed 2 dotted 3 short dashes
182. eload Preferences Window Menu Split Horizontally Split Vertically Toolbar New Save Reload 3 6 2 Layout Brings up preference dialog for changing the settings of open symbol editors Tiles open symbol editors horizontally Tiles open symbol editors vertically Edit Reload Sym bol Sym bol 5 Bo Save Symbol Figure 3 15 Data Page Toolbar Opens an active symbol from your current GAUSS workspace in a symbol editor Saves changes to the symbol in the active symbol editor Reloads an out of sync symbol editor Note This applies only if autoreload is disabled The Data Page has two main widgets the symbol tree and the source editor docking area The Command Input and Error Windows are also accessible from the toggle buttons on the right side of the status bar 3 18 Introduction to the GAUSS Graphical User Interface The Symbol Tree window lists all of your active symbols organized by type To view your active symbols click on the node expander or right click and select Symbol View from the context menu Hovering over a symbol in the Symbol Tree will produce a tooltip with a preview of the symbol s contents To view the entire contents of a symbol double click the symbol or right click the symbol and select Edit The symbol will now appear in a symbol editor see Section 3 6 3 Symbol Editor Double clicking an already open symbol will bring that symbol to the top of the stack of open symbol
183. elp Page For accessing the GAUSS HTML help system 3 1 onul IND GAUSS User Guide Each page may be undocked and from the main application and redocked by toggling the Dock button on the right side of the status bar Navigation between undocked pages may be accomplished with ALT TAB and ALT SHIFT TAB To navigate between docked pages use CTRL TAB to cycle forward and CTRL SHIFT TAB to cycle backwards between pages Each page has its own toolbars and menus The menus and toolbars facilitate intuitive navigation through the GUI as well as performing desired functions For example clicking the New toolbar from any page in the GUI will bring the Source Page to the top of the window stack with a new file opened ready for editing More details on navigating the GUI are in Section 4 NAVIGATING THE GAUSS GRAPHICAL USER INTERFACE 3 2 Command Page The Command Page is for entering interactive commands to GAUSS dg cuss EN file Edt ooh View Help dat X Jj E O 9 4 gt Hstwy Program Output 5 o Figure 3 1 Command Page 3 2 Introduction to the GAUSS Graphical User Interface 3 2 1 Menus and Toolbars Command Page File Menu Edit Menu Tools Menu View Menu Help Menu New Open Print Print Setup Recent Files Exit Undo Redo Cut Copy Paste Preferences Change Font Change Working Directory Clear Working Directory History Recent Working Directories Creates a n
184. else fendif directives allow you to conditionally compile sections of a program depending on whether a particular flag variable has been define d For example ifdef log_10 y log x else y ln z endif This allows the same program to calculate answers using different base logarithms depending on whether or not the program has a define log_10 statement at the top undef allows you to undefine text replacement or flag variables so they no longer affect a program or so you can define them again with a different value for a different section of the program If you use definecs to define a case sensitive variable you must use the right case when undef ing it With lineson linesoff srcline and srcfile you can include line number and file name records in your compiled code so that run time errors will be easier to track down srcline and srcfile are currently used by GAUSS when doing data loop translation For more information on line number tracking see DEBUGGING Section 16 3 and see DEBUGGING Data Loops Section 19 3 See also lineson in the GAUSS LANGUAGE REFERENCE The syntax for srcfile and srcline is different than for the other directives that take arguments Typically directives do not take arguments in parentheses that is they look like keywords define red 4 srcfile and srcline however do take their arguments in parentheses like procedures 6 7 s ejuawepuny oDenbue G
185. em e Whenever possible declare variables in a file that contains only declare statements When your program is run again without clearing the workspace the file containing the variable declarations will not be compiled and declare warnings will be prevented e Provide a function containing regular assignment statements to reinitialize the global variables in your program if they ever need to be reinitialized during or between runs Put this in a separate file from the declarations 15 13 S9I118 1Q17 GAUSS User Guide proc 0 globset _vname Jo ue _con _row _title endp I rell e Never declare any global in more than one file e To avoid meaningless redefinition errors and declare warnings never declare a global more than once in any one file Redefinition error messages and declare warnings are meant to help you prevent name conflicts and will be useless to you if your code generates them normally By following these guidelines any declare warnings and redefinition errors you get will be meaningful By knowing that such warnings and errors are significant you will be able to debug your programs more efficiently 15 14 Compiler l 6 GAUSS allows you to compile your large frequently used programs to a file that can be run over and over with no compile time The compiled image is usually smaller than the uncompiled source GAUSS is not a native code compiler rather it compiles to a form of pseudocode
186. er DIrectiVOS scs x mom xo Yom OE Xo9 PRY AES Rw Ee Xx Procedures 2l o rns DCN PL r 6 6 1 nico PC LLC rc 6 6 2 MatniG S i nu oco Rd RE ERS REE HERES ERE RES 6 6 3 sparse Matices o oue 64 5644 Saas oe See Dee Xo Re es 6 6 4 N dimensional Arrays 2 2 2 e e 6 6 5 Sg rs PE ee Aa eR Be a c 6 6 6 String ArfayS i 6 0644 oo gone Rx Sk ae A RR 6 6 7 Character Matrices 2s ko mo Rex ba eee 6 6 8 Date and Time Formats 5 4 5 4 5 5 5 5 5 5 5 7 5 7 5 7 5 7 6 1 6 2 6 3 6 3 6 4 6 4 6 5 6 8 6 9 6 9 6 11 6 18 6 19 6 20 6 24 6 26 6 27 Vil GAUSS User Guide 6 6 9 Special Data Types o o e o 6 28 6 7 Operator Precedence o llle 6 30 6 8 Flow Control cux cono RR bee abe ee wd be ROM a hee ee 6 31 6 8 1 LOOPING a aer Saag ee os eae path ae te a is ld BAS 6 32 6 8 2 Conditional Branching 2 gt a e 046 440 0243 2 ae XE 6 34 6 8 3 Unconditional Branching o lt s e sasos sasa o rens 6 35 6 9 FUNCIONS ss snsd kest sip m komo E a PARR AAA 6 37 6 10 Rules of Syntax lll ee 6 37 6 10 11 Statements 2x o mom doo Box RB E x Rep ae 6 37 O02 ASE a red d e Be Ge Bee Ae oe ee d 6 38 6 10 3 Comments 222 6 38 6 10 4 Extraneous Spaces e 22 agai 6 38 6 10 5 Symbol Names s Are aroe ath ade a a ao A BUR Robe ee 6 39 6 10 6 LabelS o ag surea doa ade ra 6 39
187. er Guide The format for config is config Run Menu Translator Translator line number tracking Line number tracking Compile Menu Autoload Autodelete GAUSS Library User Library Declare Warnings Compiler Trace Toggles on off the translation of a file using dataloop The translator is not necessary for GAUSS program files not using dataloop Toggles on off execution time line number tracking of the original file before translation Toggles on off the execution time line number tracking If the translator is on the line numbers refer to the translated file Toggles on off the autoloader Toggles on off autodelete Toggles on off the GAUSS library functions Toggles on off the user library functions Toggles on off the declare warning messages during compiling Includes the following options Off Turns off the compiler trace function File Traces program file openings and closings Line Traces compilation by line Symbol Creates a report of procedures and the local and global symbols they reference Using the Command Line Interface 5 4 Debugging The debug command runs a program under the source level debugger The format for debug is debug filename 5 4 1 General Functions Displays a list of available commands q Esc Exits the debugger and returns to the GAUSS command line Disables the last command repeat function 5 4 2 Listing Functions 1 number Displays a specifie
188. er the minimum line width value if you want to darken the lines in width the exported file Note About Fonts Although the fonts you select for your text box may appear fine in the graphics editor it is possible the target application importing it may not interpret them correctly Every application has its own EPS interpreter and the availability of your font depends on it If you are having problems of this type try using the Enhanced Metafile format conversion This format has no such font limitations Writing a JPEG Image A JPEG image file is a widely used bitmap format for inclusion in web pages due to its compression characteristics To write a JPEG file select the JPEG Image File menu item from the Export menu Note Because JPEG is a bitmap format the image written to the file is exactly as seen on the display Thus you may be requried to zoom out on some lower resolution displays to obtain an image of the entire document 22 17 101p3 soiydeiy GAUSS User Guide Writing a TIFF Image A TIFF Tag Image File Format image file is an older but widely used bitmap format To write a TIFF file select the TIFF Image File menu item from the Export menu Note Because TIFF is a bitmap format the image written to the file is exactly as seen on the display Thus you may be required to zoom out on some lower resolution displays to obtain an image of the entire document Windows Metafile An enhanced metafile is a vector
189. ere inside the object Drag the object to the new location and lift the mouse button The object is then redrawn in the new location If the object is a line or arrow then it may also be moved during the sizing operation 22 3 File Management The graphics editor stores the document as a list of vector based graphical objects These are binary files and cannot be edited by hand It uses a default extension of pge See the FILE MENU COMMAND for available file operations You may export your document to other formats for inclusion in web pages word processors and publishing applications 22 3 4 Exporting Files The Export menu enables you to easily export graphic files to some of the most frequently used graphic formats 22 16 Graphics Editor Writing an Encapsulated Postscript Image To write an Encapsulated Postscript file select the Encapsulated Postscript menu item from the Export menu This displays the entire file dialog Filename Enter or browse to the desired output filename The default extension is eps Convert lines Check this item if you want to convert all colors in the image to black to Black Scale Factor Enter a scale factor if necessary By default the graphics editor uses a very high internal resolution for the best possible quality However some applications are unable to correctly scale the data when importing This may be worked around by scaling the data during the export stage Minimum line Ent
190. ere may be as many elseif s as are required There need not be any elseif s or any else statement within an if clause 6 8 3 Unconditional Branching The goto and gosub statements control unconditional branching The target of both a goto and a gosub is a label goto A goto is an unconditional jump to a label with no return 6 35 s ejuawepuny oDenbue GAUSS User Guide label goto label Parameters can be passed with a goto The number of parameters is limited by available stack space This is helpful for common exit routines goto errout Matrix singular goto errout File not found errout pop errmsg errorlog errmsg end gosub With a gosub the address of the gosub statement is remembered and when a return statement is encountered the program will resume executing at the statement following the gosub Parameters can be passed with a gosub in the same way as a goto With a gosub it is also possible to return parameters with the return statement Subroutines are not isolated from the rest of your program and the variables referred to between the label and the return statement can be accessed from other places in your program Since a subroutine is only an address marked by a label there can be subroutines inside of procedures The variables used in these subroutines are the same variables that are known inside the procedure They will not be unique to the subroutine but they may be locals that
191. es since esp is merely a pointer to es Structure pointers cannot be members of a structure The following is illegal struct example_struct_2 matrix Z struct example struct ep Therefore since a structure pointer will never be a member of a structure neither spl gt sp2 gt x nor s spl gt x will ever be valid sp1 and sp2 are assumed to be structure pointers S a structure instance and x a matrix The arrow gt will only be valid if it is used for the first or furthest left dereference as in spl st x At this point we do not support indexing of structure pointers Thus a structure pointer should point at a scalar structure instance not a matrix of structures However you may index members of that scalar structure instance So for example let us suppose that you defined the following structure types struct sb matrix y matrix Z 12 12 Structures struct sa matrix x struct structb s and then created an instance of an sa structure a0 setting a0 s to a 3x2 matrix of sb structures The following would be legal struct sa sap sap amp aQ sap gt s 3 1 y rndn 3 3 12 2 3 Using Structure Pointers in Procedures Structure pointers are especially useful in cases where structures are passed into and out of procedures If a procedure takes a structure as an argument and modifies any members of that structure then it makes a local copy of the entire st
192. es into an array where the first element corresponds to the first element in a vector of orders dimension number Scalar 1 to N where 1 corresponds to the fastest moving dimension and N to the slowest moving dimension dimension index Scalar 1 to N where 1 corresponds to the first element of the vector of orders or vector of indices locator 1 to N x1 vector of indices into an array used by array functions to locate a contiguous block of the array 10 6 Working with Arrays 11 1 Initializing Arrays The use of N dimensional arrays in GAUSS is an additional tool for reducing development time and increasing execution speed of programs There are multiple ways of handling N dimensional arrays and using them to solve problems and these ways sometimes have implications for a trade off between speed of execution and development time We will try to make this clear in this chapter The term arrays specifically refers to N dimensional arrays and must not be confused with matrices Matrices and arrays are distinct types even if in fact they contain identical information Functions for conversion from one to the other are described below There are five basic ways of creating an array depending on how the contents are specified areshape Create array from specified matrix aconcat Create array from matrices and arrays aeye Create array of identity matrices s eJIy uw BUMJOM GAUSS User Guide arrayinit Alloc
193. ess may be 0 or greater If 0 use normal line width string contains a set of messages to be printed on the plot Each message is separated from the next by a null byte 000 The number of messages must correspond to the number of rows in the _pmsgctl control matrix This can be created as follows _pmsgstr Message one 1000Message two scalar controls window output during the creation of the graph Default is 1 0 no activity to the window while writing tkf file 1 display progress as fonts are loaded and tkf file is being generated scalar 2x1 or 3x1 vector for independent control for axes numbering The first element controls the X axis numbers the second controls the Y axis numbers and the third if set controls the Z axis numbers Default is 1 If this value is scalar it will be expanded to a vector 0 no axes numbers displayed 1 axes numbers displayed vertically oriented on axis 21 26 Publication Quality Graphics _pnumht _protate _pscreen _psilent _pstype _psurf 2 axes numbers displayed horizontally oriented on axis For example _pnum 0 2 3 no X axis numbers horizontal on Y axis scalar size of axes numbers in inches If 0 a size of 13 will be used Default is 0 scalar If 0 no rotation if 1 plot will be rotated 90 degrees Default is 0 scalar If 1 display graph in window if 0 do not display graph in window Default is 1 scalar If 0 a
194. ess of the method you choose to initiate the action debugging in this case the navigation is done for you The same automatic and intuitive navigation is enabled for many common GAUSS actions such as opening a new or existing file for editing or using the F1 help Since GAUSS program output can be viewed in many ways such as symbol editors on the Data Page or graphic files running a program or executing a command does not automatically navigate to the Command Page However if the Program Output Window from the Command Page is your modality of choice the option to automatically navigate to the Command Page can be selected as an option under Tools gt Preferences 4 1 INS y Sunebinen GAUSS User Guide 4 1 Hot Keys and Shortcuts F2 Navigates to the next bookmark in the Active File F3 Find again FS Run file at top of Action List F6 Debug file at top of Action List Inside a debug session F6 will cause the debugger to run to the next breakpoint or the end of the file if no breakpoint is set F7 Edit file at top of Action List F8 Step in During a debug session F9 Step over During a debug session F10 Step out During a debug session The Control Keys operate on a file that is being edited or is open in a Programming Editor and has focus This file is referred to as the Active File CTRL R Run the Active File CTRL D Debug the Active File 4 2 Navigating Between Pages CTRL 1 Brings up the Command
195. ew untitled file in a programming editor on the Source Page Opens an existing file in a programming editor on the Source Page Prints selected text Specifies the printer to use and other options such as paper tray and page orientation Holds a selectable dropdown list of recently edited files Exits a GAUSS session Restores your last unsaved change Re inserts changes removed with undo Removes selected text and copies it to the clipboard Copies selected text to the clipboard Copies the clipboard contents to the cursor position Allows you to configure the GAUSS user environment Allows you to specify a new font Aptech recommends using a monospaced font such as Courier Allows you to browse for a new working directory Deletes the contents of your working directory history Contains a dropdown list of your most recent working directories The View menu lets you toggle on or off the windows on the current page Goto Help About GAUSS Takes you to the Help Page Provides information regarding your version of GAUSS 3 3 onul IND GAUSS User Guide isi Print Copy de amp A dy L Dd n cut Paste Figure 3 2 Command Page Toolbar 3 2 2 Command Page Toolbar New Open Cut Copy Paste Print Run Debug Edit Stop Program Opens a new untitled document in a programming editor on the Source Page and brings you to the Source Page Opens an existing file for editing Removes sele
196. fine Define a case insensitive text replacement or flag variable 6 5 sj ejuawepuny oDenbue GAUSS User Guide definecs Define a case sensitive text replacement or flag variable undef Undefine a text replacement or flag variable ifdef Compile code block if a variable has been define d ifndef Compile code block if a variable has not been define d iflight Compile code block if running GAUSS Light ifdos Compile code block if running DOS ifos2win Compile code block if running OS 2 or Windows ifunix Compile code block if running UNIX else Else clause for if else endif code block endif End of if else endif code block include Include code from another file in program flineson Compile program with line number and file name records linesoff Compile program without line number and file name records srcfile Insert source file name record at this point currently used when doing data loop translation srcline Insert source file line number record at this point currently used when doing data loop translation The define statement can be used to define abstract constants For example you could define the default graphics page size as define hpage 9 define vpage 6 6 6 Language Fundamentals and then write your program using hpage and vpage GAUSS will replace them with 9 0 and 6 855 when it compiles the program This makes a program much more readable The ifdef f
197. floating point 4 byte IEEE floating point 2 byte signed binary integer twos complement Numbers are stored row by row The dht file is used in conjunction with the dat file as a descriptor file and as a place to store names for the columns in the dat file Data sets with up to 8175 columns have a dht file formatted as follows Offset Description 0 1 DADA hex identification flag 2 5 reserved all 0 s 6 7 columns unsigned 2 byte integer 8 9 row size in bytes unsigned 2 byte integer 10 11 header size in bytes unsigned 2 byte integer 12 13 data type in dat file 2 4 8 unsigned 2 byte integer 14 17 reserved all 0 s 18 21 reserved all O s 22 23 control flags unsigned 2 byte integer 24 127 reserved all 0 s Column names begin at offset 128 and are stored 8 bytes each in ASCII format Names with less than 8 characters are padded on the right with bytes of 0 The number of rows in the dat file is calculated in GAUSS using the file size columns and data type This means that users can modify the dat file by adding or deleting rows with other software without updating the header information Names for the columns should be lowercase for character data to be able to distinguish them from numeric data with vartype GAUSS currently examines only the 4 s bit of the control flags This bit is set to O for real data sets 1 for complex data sets All other bits are 0 Data sets are always stored a row at a time
198. followed by the string array data in row major order with each element null terminated A struct satable consists of two members Member Type Description off size t offset of element data from beginning of string array data len size t length of element data including null terminating byte On a 32 bit machine a size_t is 4 bytes On a 64 bit machine it is 8 bytes Arrays are written with the orders sizes of each dimension followed by the array data For example the following 2x3x4 array 17 25 O I 9113 GAUSS User Guide 1 1 1 through 1 3 4 12 3 4 5 6 7 8 9 10 11 12 2 1 1 through 2 3 4 13 14 15 16 17 18 19 20 21 22 23 24 would be written out like this 1234567891011 12 13 14 15 16 17 18 19 20 21 22 23 24 Variable Structures The variable data is followed by an array of variable descriptors For each variable in the GDA there is a corresponding variable descriptor in this array A variable descriptor is laid out as follows Offset Type Description 0 3 32 bit unsigned integer variable type 4 7 32 bit unsigned integer data type 10 for 8 byte floating point 8 11 32 bit unsigned integer dimensions used only for arrays 12 15 32 bit unsigned integer complex flag 1 for real data 0 for complex 16 19 32 bit unsigned integer size of pointer indicates whether the variable was written on a 32 bit or 64 bit platform 17 26 File I O Offset Type Description 20 23 32 bit un
199. func double arg Functions can be written to take a list of up to 100 arguments or a vector in C terms a 1 dimensional array of up to 1000 arguments This does not affect how the function is called from GAUSS the d11call statement will always appear to pass the arguments in a list That is the dllcall statement will always look as follows dllcall func a b c d e D For details on calling your function passing arguments to it getting data back and what the return value means see d1lcall in the GAUSS LANGUAGE REFERENCE 18 2 Foreign Language Interface 18 2 Creating Dynamic Libraries The following describes how to build a dynamic library called hyp d11 on Windows or libhyp so on UNIX Linux from the source file hyp c As mentioned in the previous section your FLI functions may take only pointers to doubles as arguments Therefore you should define your FLI functions to be merely wrapper functions that cast their arguments as necessary and then call the functions that actually do the work This is demonstrated in the source file hyp c include lt stdio h gt include lt stdlib h gt include lt math h gt This code is not meant to be efficient It is meant to demonstrate the use of the FLI this does all the work not exported static int hypo double x double y double h int r int c double wx double wy double dp double spl double sp2 int i elems elem
200. gauss cfg file The following keystrokes are supported for movement and editing at the command line and for retrieving the command line history 5 2 1 Movement Left Arrow or CTRL B Moves cursor left one character Right Arrow or CTRL F Moves cursor right one character 5 2 Using the Command Line Interface HOME or CTRL A END or CTRL E ALT Left Arrow or CTRL Left Arrow ALT Right Arrow or CTRL Right Arrow 5 2 2 Editing DELETE OR CTRL D BACKSPACE or CTRL H CTRL U CTRL K CTRL X ESC Win only CTRL V CTRL T 5 2 3 History Retrieval Up Arrow or CTRL P Down Arrow or CTRL P Moves cursor to beginning of line Moves cursor to end of line Moves cursor left one word Moves cursor right one word Deletes character at cursor Deletes character left of cursor Cuts all characters left of cursor Cuts all characters right of cursor including cursor Cuts whole line Deletes whole line Pastes text from buffer to left of cursor Transposes character at cursor and character left of cursor Retrieves previous line in history Retrieves next line in history 5 3 eur puewwog GAUSS User Guide PAGE UP or CTRL W Retrieves previous line in history that matches text to left of cursor PAGE DOWN or Retrieves next line in history that matches text to left of CTRL S cursor ALT H or Prints prompt history to screen OPTION H MAC only Runs last line in history Inum Runs the num line in histor
201. he 2 1 element and the 3 3 element like this 456 4 345 2 533 2 624 3 639 5 602 3 333 4 If N delimiters had been specified this file would be interpreted as having two rows and a final incomplete row that is dropped 456 4 345 2 533 2 624 3 639 5 The spaces were shown only for clarity and are not significant in delimited files so BILL 222 3 123 2 456 4 345 2 533 2 STEVE 624 3 340 3 624 3 639 5 TOM 244 2 834 3 602 3 333 4 822 5 would work just as well Linefeeds are significant only if n is specified as the delimiter or when using r This example 24 7 SOLV GAUSS User Guide invar delimit r name var 5 will expect a file with no comma after the final element in each row BILL 222 3 123 2 456 4 345 2 533 2 STEVE 624 3 340 3 245 3 624 3 639 5 TOM 244 2 834 3 602 3 333 4 822 5 Packed ASCII Files Packed ASCU files must have fixed length records The record subcommand is used to specify the record length and variables are specified by giving their type starting position length and the position of an implicit decimal point if necessary outvar is not used with packed ASCII files Instead invar is used to specify only those variables to be included in the output file For packed ASCII files the syntax of the invar command is as follows invar record reclen format variables format variables where reclen the total record length in bytes including the final carri
202. he current version create f1 dataset with vnames 0 2 create f1 dataset using cmdfile open f1 dataset output file outfile load x datafile load path lpath x y z t w loadexe buf exefile save name x save path spath dos cmdstr run prog msym mstring 7 6 Using Dot Operators with Constants When you use those operators preceded by a dot operators with a scalar integer constant insert a space between the constant and any following dot operator Otherwise the dot will be interpreted as part of the scalar that is the decimal point For example 7 20 Operators let y 1 2 3 X 2 lt y will return x as a scalar 0 not a vector of 0 s and 1 s because X 2 lt y is interpreted as x 2 lt y and not as x 2 lt y Be careful when using the dot relational operators lt lt gt gt The same problem can occur with other dot operators also For example let x 11 1 y x 2 x will return y as a scalar 5 rather than a vector of 5 s because y x 2 x is interpreted as y x 2 x 7 21 s10 e1adoO GAUSS User Guide not y x 2 x The second division then is handled as a matrix division rather than an element by element division 7 7 Operator Precedence The order in which an expression is evaluated is determined by the precedence of the operators involved and
203. he one in the argument newp 1 5 2 2 3 3 8 p0 pvPutParVector newp p0 print pvGetParVector p0 5000 2000 2000 3000 3000 8000 eaooo or 12 21 sa4ni9n1s GAUSS User Guide pvGetIndex This procedure returns the indices in the parameter vector of the parameters in a matrix These indices are useful when setting linear constraints or bounds in sqpSolvemt Bounds for example are set by specifying a Kx2 matrix where K is the length of the parameter vector and the first column are the lower bounds and the second the upper bounds To set the bounds for a particular parameter then requires knowing where that parameter is in the parameter vector This information can be found using pvGetIndex For example get indices of lambda parameters in parameter vector lind pvGetIndex par0 lambda set bounds constraint matrix to unconstrained default cQ bounds ones pvLength par8 1 1e250 1e250 set bounds for lambda parameters to be positive c6 bounds lind 1 zeros rows lind 1 12 3 4 Control Structures Another important class of structures is the control structure Applications developed before structures were introduced into GAUSS typically handled some program specifications by the use of global variables which had some disadvantages in particular preventing the nesting of calls to procedures Currently the purposes served by global variables are now served by
204. he symbol in the GAUSS symbol table If you would like the contents of a particular symbol editor to stay the same even if the value of the symbol is changed by running a program or an interactive command you may disable autoreload for that symbol If the value of a symbol with autoreload disabled is changed in the GAUSS symbol table the symbol editor will display the message out of sync This indicates that the values in the symbol editor are not current 3 20 Introduction to the GAUSS Graphical User Interface 3 7 Debug Page 3 7 1 Menus and Toolbars Go Stop Toggle Breakpoint Clear Breakpoints Set Watch Step Into Step Over Step Out Run to Cursor Runs the program to the next breakpoint Terminates a debugging session Sets Clears a breakpoint at the cursor Clears all breakpoints in a file Opens a watch variable in a symbol editor Runs the next executable line of code in the application and steps into procedures Runs the next executable line of code but does not step into procedures Runs the remainder of the current procedure and stops at the next line in the calling procedure Runs the program until it reaches the cursor position Toggle Set Step Run to Go Breakpoint Watch Over Cursor d z 00835955 Stop Clear Step Step Breakpoint Into Out Figure 3 17 Debug Toolbar 3 2 onul IND GAUSS User Guide Components and Usage The Debug Page is composed of
205. hread ThreadBegin Marks the beginning of a block of code to be executed as a thread 14 1 speoluL GAUSS User Guide ThreadEnd Marks the end of a block of code to be executed as a thread ThreadJoin Completes the definition of a set of threads waits until they are done ThreadStat defines a single statement to be executed as a thread ThreadStat n m m ThreadBegin and ThreadEnd define a multi line block of code to be executed as a thread ThreadBegin y xxi z y y ThreadEnd Together these define sets of threads to be executed concurrently ThreadStat n m m Thread 1 ThreadBegin Thread 2 y xxi z y y ThreadEnd ThreadBegin Thread 3 q r r r q q ThreadEnd ThreadStat p o o Thread 4 Finally ThreadJoin completes the definition of a set of threads It waits for the threads in a set to finish and rejoin the creating the parent thread which can then continue making use of their individual calculations 14 2 Multi Threaded Programming in GAUSS ThreadBegin Thread 1 y x x z y y ThreadEnd ThreadBegin Thread 2 q r r q q ThreadEnd ThreadStat n m m Thread 3 ThreadStat p 0 o Thread 4 ThreadJoin waits for Threads 1 4 to finish b z r n p Using the results 14 2 GAUSS Threading Concepts This is really the one and only thing you need to know about threads threads are separate sections of the same program e
206. idual editor windows can be pulled out of the Source Page by grabbing their banner and dragging them to the desired location Programming editor features 1 Syntax highlighting The GAUSS programming editor will provide syntax highlighting for GAUSS C C Java Fortran R and many other languages 2 Autocompletion Autocompletion is available in the GAUSS programming editor for GAUSS functions Using autocomplete if the characters you enter match items in the autocomplete list a dropdown box will appear containing those functions To navigate the dropdown list press the down arrow or continue typing until only one selection remains Once the desired command is highlighted press the ENTER key to insert the remainder of the word Figure 3 10 Autocomplete 3 Tooltips After a GAUSS command and an opening parenthesis has been entered a tooltip will appear with the argument list for the function Figure 3 11 Tooltips 4 Code folding At the start of code blocks e g procedure definitions do and for loops and if statements the left margin of the programming editor will contain a Clicking the will hide the block of code from view and place a horizontal line across the editor indicating folded code and changing the to a Clicking on the will reveal the hidden code 3 12 Introduction to the GAUSS Graphical User Interface 5 Autoindenting The GAUSS programming editor provides automatic code indenting an
207. ignment to at least one of the members This can be made convenient by writing a procedure that declares a structure and initializes one of its members to a default value and then returns it For example ds src include ds sdf proc dsCreate 12 3 sa4ni9n1as GAUSS User Guide struct DS dQ d0 dataMatrix 6 retp dQ endp Calling this function after declaring an instance of the structure will ensure initialization to default values each time your program is run struct DS dQ d dsCreate Initializing Local Structures Local structures which are structures defined inside procedures are initialized at the first assignment The procedure may have been written in such a way that a subset of structures are used an any one call and in that case time is saved by not initializing the unused structures They will be initialized to default values only when the first assignment is made to one of its members 12 1 4 Arrays of Structures To create a matrix of instances use the reshape command include ds sdf struct DS pd p0 reshape dsCreate 5 1 This creates a 5x1 vector of instances of DS structures with all of the members initialized to default values When the instance members have been set to some other values reshape will produce multiple copies of that instance set to those values Matrices or vectors of instances can also be created by concatenation 12 4 Structures include tr
208. ill be displayed for the main curves This also controls the frequency of symbols on main curves The number of rows K is equal to the number of individual curves to be plotted in the graph Default is O 0 draw line only gt 0 draw line and symbols every _plctr1 points 0 draw symbols only every _plctr1 points allofthe data points will be plotted with no connecting lines This example draws a line for the first curve draws a line and plots a symbol every 10 data points for the second curve and plots symbols only every 5 data points for the third curve _plctrl 0 10 5 21 21 90d GAUSS User Guide _plegctl _plegstr _plev _pline scalar or 1x4 vector legend control variable If scalar 0 no legend is drawn default If nonzero scalar create legend in the default location in the lower right of the page If 1x4 vector set as follows 1 legend position coordinate units 1 coordinates are in plot coordinates 2 coordinates are in inches 3 coordinates are in pixel 2 legend text font size where 1 lt size lt 9 Default is 5 3 x coordinate of lower left corner of legend box 4 y coordinate of lower left corner of legend box This example puts a legend in the lower right corner plegctl 1 This example creates a smaller legend and positions it 2 5 inches from the left and 1 inch from the bottom plegct1 2 3 2 5 1 string legend entry text Text for multipl
209. in days between two dates ethsec Computes the difference between two times in hundredths of a second etstr Formats a time difference measured in hundreths of a second to a string 23 4 Time and Date _isleap Returns a vector of ones and zeros 1 if leap year O if not timestr Formats a Time vector to a string hr mn sc timeutc Universal time coordinate number of seconds since January 1 1970 Greenwich Mean Time utctodtv Converts a scalar number of seconds since or before Jan 1 1970 Greenwich mean time to a dtv vector Below is an example of two ways to calculate a time difference d1 1996 12 19 82 d2 1997 4 28 4248879 3 dif ethsec d1 d2 ds etstr dif dif 1 1274488e 09 ds 130days llhours 48minutes 7 97seconds If only the number of days is needed use etdays d1 1996 12 19 82 y d2 1997 4 28 4248879 3 dif etdays d1 d2 dif 130 00000 The last element of d1 is optional when used as an input for etdays _isleap returns a matrix of ones and zeros ones when the corresponding year is a leap year 23 5 91eq pue au GAUSS User Guide x seqa 1970 1 20 y _isleap x delif x abs y 1 1972 0000 Vector containing all leap years 1976 0000 between 1970 1989 1980 0000 1984 0000 1988 0000 To calculate the days of a number of consecutive years x sega 1983 1 3 y _daypryr x sumc y 1096 0000 To add a porti
210. index operator will put a subarray into an array in a manner analogous to the use of index operators on matrices a arrayinit 3 2 2 0 b arrayinit 3 1 2 1 a 2 b print a Plane 1 0 00000 0 00000 1 0000 1 0000 Plane 2 0 00000 0 00000 1 0000 1 0000 Plane 3 0 00000 0 00000 1 0000 1 0000 s eJIy uw DupJoM GAUSS User Guide As this example illustrates the assignment doesn t have to be contiguous putMatrix and setMatrix require a contiguous assignment but for that reason they are faster The right hand side of the assignment can also be a matrix a 1 rndn 2 2 print a Plane 1 1 7906502 0 61038103 1 2586160 0 47736360 Plane 2 0 00000 0 00000 1 00000 1 00000 Plane 3 0 00000 0 00000 1 00000 1 00000 The index operator will extract an array from a subarray in a manner analogous to the use of index Operators on matrices a areshape seqa 1 1 12 3 2 2 b a 1 print a Plane 1 1 0000 2 0000 3 0000 4 0000 11 10 Working with Arrays Plane 2 5 0000 6 0000 7 0000 8 0000 Plane 3 9 0000 10 000 11 000 12 000 print b Plane 1 1 0000 2 0000 Plane 2 5 0000 6 0000 Plane 3 9 0000 10 000 It is important to note that the result is always an array even if it s a scalar value c al1 1 1 print c Plane 1 1 0000 11 11 s eJIy uw DupJoM GAUS
211. ined by operators An expression returns a result that can be assigned to a s ejuawepuny oDenbue GAUSS User Guide variable with the assignment operator 6 2 Statements A statement is a complete expression or command Statements end with a semicolon y x 3 If an expression has no assignment operator it will be assumed to be an implicit print statement print x 3 or Here is an example of a statement that is a command rather than an expression output on Commands cannot be used as a part of an expression There can be multiple statements on the same line as long as each statement is terminated with a semicolon Language Fundamentals 6 2 1 Executable Statements Executable statements are statements that can be executed over and over during the execution phase of a GAUSS program execution time As an executable statement is compiled binary code is added to the program being compiled at the current location of the instruction pointer This binary code will be executed whenever the interpreter passes through this section of the program If this code is in a loop it will be executed each iteration of the loop Here are some examples of executable statements y 34 25 print y x 13729403 6 2 2 Nonexecutable Statements Nonexecutable statements are statements that have an effect only when the program is compiled compile time They generate no executable code at the
212. ines will be considered missings Otherwise delimiters must be printable characters The dot is illegal and will always be interpreted as a missing value To specify the backslash as a delimiter use NX If Nr is specified as a delimiter the file will be assumed to contain one case or record per line with commas between elements and no comma at the end of the line For hard delimited files the delimit subcommand is used with the invar command The delimit subcommand has two optional parameters The first parameter is the delimiter The default is a comma The second parameter is an N If the second parameter is present ATOG will expect N delimiters If it is not present ATOG will expect N 1 delimiters This example invar delimit N name var 5 will expect a file like this BILL 222 3 123 2 456 4 345 2 533 2 STEVE 624 3 340 3 624 3 639 5 TOM 244 2 834 3 602 3 333 4 822 5 while invar delimit name var 5 or invar delimit name var 5 will expect a file like this 24 6 ATOG BILL 222 3 123 2 456 4 345 2 533 2 STEVE 624 3 340 3 624 3 639 5 TOM 244 2 834 3 602 3 333 4 822 5 The difference between specifying N or N 1 delimiters can be seen here 456 4 345 2 533 2 624 3 639 5 602 3 333 4 If the invar statement specified three variables and N 1 delimiters this file would be interpreted as having three rows containing a missing in t
213. ing data if any For example proc fct struct PV p0 struct DS dQ local y x b0 b e s y d8 1 dataMatrix x d0 2 dataMatrix b0 pvUnpack p6 constant b pvUnpack p0 coefficients e y b0O x b s sqrt e e rows e retp pdfn e s endp Note that this procedure returns a vector rather than a scalar When the objective function is a properly defined log likelihood returning a vector of minus log probabilities permits the calculation of a QML covariance matrix of the parameters The remaining input arguments are structures P a PV structure containing starting values of the parameters O a DS structure containing data if any 12 24 Structures C an sqpSolvemtControl structure The DS structure is optional sqpSolvemt passes this argument on to the user provided procedure that amp fct is pointing to without modification If there is no data a default structure can be passed to it sqpSolvemtControl Structure A default sqpSolvemtControl structure can be passed in the fourth argument for an unconstrained problem The members of this structure are as follows eqProc IneqProc MxK matrix linear equality constraint coecients A0 B where p is a vector of the parameters Mxl1 vector linear equality constraint constants A0 B where p is a vector of the parameters MxK matrix linear inequality constraint coefficients C D where p is a vector of the parameters M
214. int 17 5 12 GAUSS Data Archive A GAUSS Data Archive consists of a header followed by the variable data and finally an array of variable descriptors containing information about each variable Header The header for a GAUSS Data Archive is laid out as follows Offset Type Description 0 3 32 bit unsigned integer always OxFFFFFFFF 4 7 32 bit unsigned integer always 0 8 11 32 bit unsigned integer always OXFFFFFFFF 17 24 File I O Offset Type Description 12 15 32 bit unsigned integer always 0 16 19 32 bit unsigned integer always OXFFFFFFFF 20 23 32 bit unsigned integer OxFFFFFFFF for forward byte order 0 for backward byte order 24 27 32 bit unsigned integer always 0 28 31 32 bit unsigned integer always OxABCDEFOS 32 35 32 bit unsigned integer version currently 1 36 39 32 bit unsigned integer reserved 40 43 32 bit unsigned integer floating point type 1 for IEEE 754 44 55 32 bit unsigned integers reserved 56 63 64 bit unsigned integer number of variables 64 67 32 bit unsigned integer header size 128 68 95 32 bit unsigned integers reserved 96 103 64 bit unsigned integer offset of variable descriptor table from end of header 104 127 64 bit unsigned integers reserved Variable Data After the header comes the variable data Matrices are laid out in row major order and strings are written with a null terminating byte For string arrays an array of rowsxcolumns struct satable s is written out first
215. invar record 32 dept 2 id 5 wage 2 area 24 9 SOLV GAUSS User Guide will result in variable value type dept ABCDEFGH character id IJ character WAGE 12345 numeric AREA 67 numeric msym Specifies the character in the input file that is to be interpreted as a missing value This example msym amp defines the character amp as the missing value character The default dot will always be interpreted as a missing value unless it is part of a numeric value nocheck Optional suppresses automatic checking of packed ASCII record length and output data type The default is to increase the record length by 2 bytes if the second record in a packed file starts with cr lf and any files that have explicitly defined character data will be output in double precision regardless of the type specified output The name of the GAUSS data set A file will be created with the extension dat For example output gauss dat test creates the file test dat on the gauss dat directory 24 10 ATOG outtyp Selects the numerical accuracy of the output file Use of this command should be dictated by the accuracy of the input data and storage space limitations The format is outtyp fmt where fmt is Dor8 double precision For4 single precision default Ior2 integer The ranges of the different formats are bytes data type significant range digits 2 integer 4 32768 lt X lt 32767
216. ion 29 502 matrix empty 6 15 29 138 29 504 29 525 29 772 29 784 matrix ones 29 595 matrix zeros 29 981 mattoarray 11 28 29 551 maxbytes 29 556 maxc 29 552 maximizing performance 26 1 maximum element 29 552 maximum element index 29 553 maxindc 29 553 maxv 29 554 maxvec 29 555 mbesseli 29 556 mean 29 559 meanc 29 559 median 29 560 memory 29 199 memory clear all 29 574 menu bar 3 17 menu edit 3 3 menu file 3 3 3 10 menu help 3 3 menu symbol editor 3 17 menu tools 3 3 menu view 3 3 menu window 3 10 3 18 menus 3 3 3 21 menus graphics editor 22 4 mergeby 29 561 mergevar 29 562 merging 28 41 minc 29 563 minimum element 29 563 minimum element index 29 564 minindc 29 564 minv 29 565 miss 29 566 missex 29 567 missing character 29 573 missing values 7 5 29 229 29 230 29 472 29 566 29 567 29 573 29 612 29 786 missrv 29 566 modulo division 7 5 moment matrix 29 569 29 583 29 588 Index 14 Index moment 29 568 momentd 29 570 Moore Penrose pseudo inverse 29 621 29 622 movement command line history 3 8 movingave 29 571 movingaveExpwgt 29 572 movingaveWgt 29 573 msym 29 573 msym ATOG command 24 10 multi threading 14 1 28 43 multiplication 7 5 multiplicative sequence 29 794 N N dimensional arrays 10 1 11 1 28 30 NaN 6 28 NaN testing for 6 29 7 9 navigating
217. is being sized by a corner point this feature is ignored eliminating the need for the user to check uncheck the aspect ratio menu item needlessly The aspect ratio feature has no effect for lines and arrows Object Properties The properties dialog box allows you to modify various attributes of the object depending on its type See GRAPHICAL OBJECTS Section 22 2 13 for more information about object properties Sizing an Object First select the object Next click and hold the left mouse button in one of the object s highlight points Depending on the type of object the new size is defined by how you move the mouse Lifting the mouse button sets the new size and causes it to be redrawn If the object is a TKF graphics window text object rectangle or ellipse then the aspect ratio may be retained depending on the selection state of the aspect ratio menu item state when grabbing one of the four sides Grabbing the corner of an object allows you to size it in any direction ignoring the state of the aspect ratio menu 22 15 101p3 soiydeiy GAUSS User Guide If the object is a line or arrow then it may be moved during the sizing operation by pressing and holding the right mouse button while still depressing the left mouse button Note A rotated text object may not be sized It may only be sized in a non rotated state Moving an Object First select the object Next click and hold the left mouse button somewh
218. is important If you want to guarantee that all procedures contain line number records put a new statement at the top of your program and turn line number tracking on 16 3 Jajidwoy File I O The following is a partial list of the I O commands in the GAUSS programming language close closeall colsf create eof fcheckerr fclearerr fflush fgets fgetsa Close a file Close all open files Number of columns in a file Create GAUSS data set Test for end of file Check error status of a file Check error status of a file and clear error flag Flush a file s output buffer Read a line of text from a file Read multiple lines of text from a file 17 1 O I 9113 GAUSS User Guide fgetsat fgetst fileinfo files filesa fopen fputs fputst fseek fstrerror ftell getf getname iscplxf load loadd loadm loads open output readr rowsf save Read multiple lines of text from a file discarding newlines Read a line of text from a file discarding newline Return names and information of files matching a specification Return a directory listing as a character matrix Return a list of files matching a specification Open a file Write strings to a file Write strings to a file appending newlines Reposition file pointer Get explanation of last file I O error Get position of file pointer Load a file into a string Get variable names from data set Return whether a data set is real o
219. k to 1 AD The rest of the GAUSS date functions assume a normal Gregorian system regardless of year Thus they will not account for the days taken out in September of 1752 nor will they account for all century marks being leap years before the adoption of the Gregorian system in 1752 The time is given by your operating system daylight savings time is not automatically accounted for by GAUSS in calculations 23 1 91eq pue au GAUSS User Guide 23 1 Time and Date Formats The Time and Date formats in GAUSS fall into one of two major categories matrix vector and string The matrix vector formats can be used for either calculations or if desired for output The string formats are however mostly for use as ouput Some manipulation of strings is possible with the use of the stof function A 4x1 vector is returned by both the date and time functions d date d 1997 00 5 00000 29 0000 56 4700 t time t 10 00 17 00 33 00 13 81 bb Year Month Day Hundredths of a second since midnight Hours since midnight Minutes Seconds Hundredths of a second These vectors can be written to a string of the desired form by passing them through the corresponding function d 1997 5 29 56 47 Y datestr d 5 29 97 datestrymd d 23 2 Time and Date 19970529 t 10 17 33 13 81 timestr t 10 17 33 A list and brief description of
220. ke up no space Matrices are stored in row major order A 2x3 real matrix will be stored in the following way from the lowest addressed element to the highest addressed element 1 1 1 2 1 3 2 1 2 2 2 3 A 2x3 complex matrix will be stored in the following way from the lowest addressed element to the highest addressed element real part 1 1 1 2 1 3 2 1 2 2 2 3 imaginary part 1 1 1 2 1 3 2 1 2 2 2 3 Conversion between complex and real matrices occurs automatically and is transparent to the user in most cases Functions are provided to provide explicit control when necessary All elements of a GAUSS matrix are stored in double precision floating point format and each takes up 8 bytes of memory This is the IEEE 754 format Bytes Data Type Significant Range Digits 8 floating point 15 16 419x107 lt X lt 1 67x10 3 Matrices with only one element 1x1 matrices are referred to as scalars and matrices with only one row or column 1xN or Nx1 matrices are referred to as vectors Any matrix or vector can be indexed with two indices Vectors can be indexed with one index Scalars can be indexed with one or two indices also because scalars vectors and matrices are the same data type to GAUSS The majority of functions and operators in GAUSS take matrices as arguments The following functions and operators are used for defining saving and loading matrices s ejuawepuny oDenbue GAU
221. l positioned 1 inch from the left edge of the page and 1 5 inches from the bottom of the page It will be nontransparent makewind hsize vsize hpos vpos attr 21 7 90d GAUSS User Guide window 2 3 9 makewind 4 2 5 1 1 5 0 21 3 3 Nontransparent Graphic Panels A nontransparent graphic panel is one that is blanked before graphics information is written to it Therefore information in any previously drawn graphic panels that lie under it will not be visible 21 3 4 Transparent Graphic Panels A transparent graphic panel is one that is not blanked allowing the graphic panel beneath it to show through Lines symbols arrows error bars and other graphics objects may extend from one graphic panel to the next by using transparent graphic panels First create the desired graphic panel configuration Then create a full window transparent graphic panel using the makewind or window command Set the appropriate global variables to position the desired object on the transparent graphic panel Use the draw procedure to draw it This graphic panel will act as a transparent overlay on top of the other graphic panels Transparent graphic panels can be used to add text or to superimpose one graphic panel on top of another 21 3 5 Using Graphic Panel Functions The following is a summary of the graphic panel functions begwind Graphic panel initialization procedure endwind End graphic panel manipulations display graphs
222. l return the global matrix y The returned matrix is inverted and assigned to g mvec xyzatH 1 2 g inv varget mvec i 6 41 s ejuawepuny oDenbue GAUSS User Guide The following procedure can be used to index the matrices in mvec more directly proc imvec i retp varget mvec i endp Then imvec i will equal the matrix whose name is in the i element of mvec In the example above the procedure imvec was written so that it always operates on the vector mvec The following procedure makes it possible to pass in the vector of names being used proc get array i retp varget array i endp Then get mvec 3 will return the 3 7 matrix listed in mvec proc put x array i retp varput x array i endp And put x mvec 3 will assign x to the 3 matrix listed in mvec and return a 1 if successful or a O 1f 1t fails 6 10 11 Arrays of Procedures It is also possible to index procedures The ampersand operator amp is used to return a pointer to a procedure Assume that 1 2 and 3 are procedures that take a single argument The following code defines a procedure i that will return the value of the i procedure evaluated at x 6 42 Language Fundamentals nms amp f1 amp f2 amp f3 proc fi x i local f f nms i local f proc retp f x endp fi x 2 will return 2 x The ampersand is used to return the pointers to the procedures nms is a numeric
223. liary output Reshape a matrix or string array to new dimensions Save matrix string array string procedure function or keyword to disk and gives the disk file either a fmt fst or cg extension Display global symbol table Quick sort rows of matrix or string array based on character column Indicate whether variable passed as argument is matrix string or string array Indicate whether variables named in argument are strings string arrays matrices procedures functions or keywords Access the global variable named by a string array Assign the global variable named by a string array Stack columns of a matrix or string array to form a column vector Stack rows of a matrix or string array to form a column vector String arrays are created through the use of the string array concatenation operators Below is a contrast of the horizontal string and horizontal string array concatenation operators 6 25 s ejuawepuny oDenbue GAUSS User Guide age pay sex x y n sa x y n U BSX x 5 agepaysex sa age pay J sex 6 6 7 Character Matrices Matrices can have either numeric or character elements For convenience a matrix containing character elements is referred to as a character matrix A character matrix is not a separate data type but gives you the ability to store and manipulate data elements that are composed of ASCII characters as well as floating point numbers F
224. literal 20n Select font number n see SELECTING Fonts following 21 10 Publication Quality Graphics The escape code L or 1 can be embedded into title strings to create a multiple line title title This is the first line lthis is the second line A null byte N986 is used to separate strings in _plegstr and _pmsgstr _pmsgstr First string 000Second string 900Third string or _plegstr Curve 1 000Curve 2 Use to create the expression M t E e _pmsgstr M t E e tx Use to generate and in an X axis label xlabel Data used for x is data 1 2 3 21 4 4 Selecting Fonts Four fonts are supplied with the Publication Quality Graphics system They are Simplex Complex Simgrma and Microb For a list of the characters available in each font see Appendix A Fonts are loaded by passing to the fonts procedure a string containing the names of all fonts to be loaded For example this statement will load all four fonts 21 11 90d GAUSS User Guide fonts simplex complex microb simgrma The fonts command must be called before any of the fonts can be used in text strings A font can then be selected by embedding an escape code of the form 207 in the string that is to be written in the new font The n will be 1 2 3 or 4 depending on the order in which the fonts were loaded in fonts If the fonts were loaded as in the previous example the escape characters
225. ll 21 2 Publication Quality Graphics Header In order to use the graphics procedures the pgraph library must be activated This is done in the library statement at the top of your program or command file The next line in your program will typically be a command to reset the graphics global variables to their default state For example library mylib pgraph graphset Data Setup The data to be graphed must be in matrices For example seqa 1 1 50 y sin x tad l Graphics Format Setup Most of the graphics elements contain defaults that allow the user to generate a plot without modification These defaults however may be overridden by the user through the use of global variables and graphics procedures Some of the elements that may be configured by the user are axes numbering labeling cropping scaling line and symbol sizes and types legends and colors Calling Graphics Routines The graphics routines take as input the user data and global variables that have previously been set Itis in these routines where the graphics file is created and displayed Following are three PQG examples The first two programs are different versions of the same graph The variables that begin with _p are the global control variables used by the graphics 21 3 90d GAUSS User Guide routines For a detailed description of these variables see GLOBAL CONTROL VARIABLES Section 21 6 Example 1 The routine bei
226. ll then have to be filled using any of several methods described later in this chapter For example to allocate a 2x2x3 array rndseed 345678 ord 3 2 2 a arrayalloc ord 0 for i 1 ord 1 1 ali rndn 2 3 endfor s eJIy uw DupJoM GAUSS User Guide print a Plane 1 0 4300 0 2878 0 1327 0 0573 1 2900 0 2467 Plane 2 1 4249 0 0796 1 2693 0 7530 1 7906 0 6103 Plane 3 1 2586 0 4773 0 7044 1 2544 0 5002 0 3559 The second argument in the call to arrayalloc specifies whether the created array is real or complex arrayinit creates only real arrays 11 2 Assigning to Arrays There are three methods used for assignment to an array index operator The same method as matrices generalized to arrays putArray Put a subarray into an N dimensional array and returns the result setArray Set a subarray of an N dimensional array in place And there are several ways to extract parts of arrays index operator The same method as matrices generalized to arrays Working with Arrays getArray Get a subarray from an array getMatrix Get a matrix from an array getMatrix4D Get a matrix from a 4 dimensional array getScalar4D Get a scalar from a 4 dimensional array The index operator is the slowest way to extract parts of arrays The specialized functions are the fastest when the circumstances are appropriate for their use 11 2 1 index operator The
227. llowed by the structure type name If the symbol type is missing the colon must not be present and the symbol type is assumed to be proc Both library files below are valid Example 1 15 6 Libraries Example 2 we math wx This library lists files and procedures for mathematical routines norm src onenorm proc infnorm proc Enorm proc complex src cmmult proc cmdiv proc cmadd proc cmsoln proc poly src polychar proc polyroot proc polymult proc wa math wx This library lists files and procedures for mathematical routines c gauss src norm src onenorm proc infnorm proc Enorm proc c gauss src complex src cmmult proc cmdiv proc cmadd proc cmsoln proc c gauss src fcomp src feq proc fne proc flt proc fgt proc fle proc 15 7 soueiqiq GAUSS User Guide fge proc c gauss src fcomp dec _fcmptol matrix Once the autoloader finds via the library the file containing your procedure definition everything in that file will be compiled For this reason you should combine related procedures in the same file in order to minimize the compiling of procedures not needed by your program In other words you should not combine unrelated functions in one src file because if one function in a src file is needed the whole file will be compiled user Library This is a library for user created procedures If the autoloader is ON the user library
228. lobal symbol table is full and operators must be inside brackets These operators are for indexing matrices 25 15 soDesso y 10413 GAUSS User Guide G0175 G0176 G0177 G0178 G0179 G0180 G0181 G0182 G0274 G0275 G0276 G0277 G0278 G0286 G0287 String too long to compare Argument out of range Invalid format string Invalid mode for getf Insufficient heap space Trim too much You are attempting to trim more rows than the matrix has Illegal assignment type mismatch 2nd and 3rd arguments different order Invalid parameter for conv Parameter is NaN Not A Number The argument is a NaN see SpeciaL Data Types Section 6 6 9 Illegal use of reserved word Null string illegal here proc without endp You must terminate a procedure definition with an endp statement Multiple assign out of memory Seed not updated 25 16 Error Messages G0288 G0289 G0290 G0291 G0292 G0293 G0294 G0295 G0296 G0300 G0301 The seed argument to rndns and rndus must be a simple local or global variable reference It cannot be an expression or constant These functions are obsolete please use rndlcn and rndlcu Found break not in do loop Found continue not in do loop Library not found The specified library cannot be found on the 1ib_path path Make sure installation was correct Compiler pass out of memory Notify Aptech Systems
229. mat specification getf Load ASCII or binary file into string indcv Find index of element in character vector lower Convert to lowercase stof Convert string to floating point strindx Find index of a string within a second string strlen Length of a string strsect Extract substring of string strsplit Split an Nx1 string vector into an NXK string array of the individual tokens 6 20 Language Fundamentals strsplitPad Split a string vector into a string array of the individual tokens Pads on the right with null strings strtodt Convert a string array of dates to a matrix in DT scalar format strtof Convert a string array to a numeric matrix strtofcplx Convert a string array to a complex numeric matrix upper Convert to uppercase vals Convert from string to numeric vector of ASCII codes Strings can be created like this x example string or X cons keyboard input Or x getf myfile 0 read a file into a string They can be printed like this print x A character matrix must have a prefixed to it in a print statement print x 6 21 s ejuawepuny oDenbue GAUSS User Guide A string can be saved to disk with the save command in a file with a fst extension and then loaded with the load command save X loads x or loads x x fst The backslash is used as the escape character inside double quotes to enter special characters Nb backspace ASCII
230. matrix viewer 5 4 5 Breakpoint Commands lb b args Shows all the breakpoints currently defined Sets a breakpoint in the code The syntax for each optional argument is filename line period The debugger will stop every period times it reaches the specified line in the named file filename line The debugger will stop when it reaches the specified ine in the named file filename period The debugger will stop every period times it reaches any line in the named file 5 0 eur puewwog GAUSS User Guide line period The debugger will stop every period times it reaches the specified line in the current file filename The debugger will stop at every line in the named file line The debugger will stop when it reaches the specified line in the current file procedure period The debugger will stop every period times it reaches the first line in a called procedure procedure The debugger will stop every time it reaches the first line in a called procedure d args Removes a previously specified breakpoint The optional arguments are the same arguments as b listed above 5 5 Using the Source Browser in TGAUSS To start the Source Browser in TGAUSS type BROWSE followed by a symbol name When the Source Browser is active the prompt displays Browse GAUSS searches through all active libraries for the file in which the symbol is defined If found the file containing the source code is opened in the default edi
231. mparison operators that all return sparse matrices Element by Element Dot Comparison Operators Operation Dense Returning Sparse Returning Equal to eq speq Not equal to J ne spne Less than lt lt splt Less than or equal to lt le sple Greater than gt Spgt Greater than or equal to gt ge Spge S9DMILIN esieds GAUSS User Guide Since the element by element non dot comparison operators lt lt gt gt and their alphabetic counterparts eq ne It le gt ge all return scalars there are no sparse returning versions of them Other Matrix Operators Horizontal Concatenation Result Left Operator Right dense dense dense sparse sparse sparse Vertical Concatenation Result Left Operator Right dense dense dense sparse sparse sparse N Dimensional Arrays In GAUSS internally matrices and arrays are separate data types Matrices which are 2 dimensional objects are stored in memory in row major order Therefore a 3x2 matrix is stored as follows 1 1 1 2 2 1 2 2 3 1 3 2 The slowest moving dimension in memory is indexed on the right and the fastest moving dimension is indexed on the left This is true of N dimensional arrays as well A 4x3x2 array is stored in the following way 1 1 1 1 1 2 1 2 1 1 2 2 1 3 1 1 3 2 2 1 1 2 1 2 2 2 1 2 2 2 2 3 1 2 3 2 3 1 1 3 1 2 3 2 1 3 2 2
232. mpatible with the printer currently in use Because printer margins vary from one printer to another it is useful to be able to set your page to the margins that most accurately match your printer The reference margin settings are available in the Properties dialog under the View menu Reset Colors Pushing this button will reset the available colors to the initial IBM 16 color scheme Each color may be set to a custom color see PEN FILL PROPERTIES Section 22 2 12 for more information Using the Zoom Feature To set the zoom click the zoom drop down control on the toolbar or select Zoom in the View menu Setting the Color Options You may reset the colors to the original IBM 16 color scheme by pressing the Reset Colors to Initial button 22 9 J011P3 so1y der GAUSS User Guide 22 2 12 Setting the Pen Fill Properties All drawing is done with a currently selected pen and brush The current pen has a width attribute and color attribute The current brush for painting object backgrounds has a color attribute Setting the Pen Color Left click in one of the color boxes in the dialog bar to set the current color The dialog bar is located to the left of the drawing area The color is immediately displayed in the sample box at the top of the color box area Double clicking in the color box will allow you you to customize that particular color Setting the Pen Width Left click in one of the width boxes in the dialog
233. n Arguments The arguments to functions are enclosed in parentheses y 7 sqrt x 6 10 9 Indexing Matrices Brackets are used to index matrices x 211223 375 374 895 6 1 8 y x 3 3 z x 1 2 4 1 3 Vectors can be indexed with either one or two indices v 1234567809 k v 3 j v 1 6 9 6 40 Language Fundamentals x 2 3 returns the element in the second row and the third column of x x 1 3 5 4 7 returns the submatrix that is the intersection of rows 1 3 and 5 and columns 4 and 7 x 3 returns the third column of x x 3 5 returns the submatrix containing the third through the fifth rows of x The indexing operator will take vector arguments for submatrix extraction or submatrix assignments y x rv cv y rv cv x rv and cv can be any expressions returning vectors or matrices The elements of rv will be used as the row indices and the elements of cv will be used as the column indices If rv is a scalar 0 all rows will be used if cv is a scalar 0 all columns will be used If a vector is used in an index expression it is illegal to use the space operator or the colon operator on the same side of the comma as the vector 6 10 10 Arrays of Matrices and Strings It is possible to index sets of matrices or strings using the varget function In this example a set of matrix names is assigned to mvec The name y is indexed from mvec and passed to varget which wil
234. named with a src extension but you may use any name and any file extension In this file put all the definitions of related procedures you wish to use Here is an example of such a file It is called norm src norm src This is a file containing the definitions of three procedures which return the norm of a matrix x The three norms calculated are the 1 norm the inf norm and the E norm proc onenorm x retp maxc sumc abs x endp proc infnorm x 15 5 soueiqiq GAUSS User Guide retp maxc sumc abs x endp proc Enorm x retp sumc sumc x x endp Next create a library file that contains the name of the file you want access to and the list of symbols defined in it This can be done with the 1ib command For details see 1ib in the GAUSS LANGUAGE REFERENCE A library file entry has a filename that is flush left The drive and path can be included to speed up the autoloader Indented below the filename are the symbols included in the file There can be multiple symbols listed on a line with spaces between The symbol type follows the symbol name with a colon delimiting it from the symbol name The valid symbol types are fn user defined single line function keyword keyword proc procedure matrix matrix numeric or character array N dimensional array string string sparse matrix sparse matrix struct structure A structure is always denoted by struct fo
235. names which is relatively time consuming This can be alleviated by using an index rather than a name in unpacking To do this though requires using a special pack procedure that establishes the index p0 pvPacki p0 b0 b0 1 p0 pvPacki p0 garch garch 2 p0 pvPacki p0 arch arch 3 p0 pvPacki p0 omega omega 4 Now they may be unpacked using the index number b8 pvUnpack p0 1 garch pvUnpack p0 2 arch pvUnpack p0 3 omega pvUnpack p0 4 When packed with an index number they may be unpacked either by index or by name but unpacking by index is faster 12 19 s n n Ss GAUSS User Guide 12 3 3 Miscellaneous PV Procedures pvList This procedure generates a list of the matrices or arrays packed into the structure pO pvPack p0 b0 b0 p0 pvPack p0 garch garch p0 pvPack p0 arch arch p0 pvPack p0 omega omega print pvList p0 bO garch arch omega pvLength This procedure returns the length of the parameter vector print pvLength p0 6 0000 pvGetParNames This procedure generates a list of parameter names print pvGetParNames p0 12 20 Structures b0 1 1 garch 1 1 garch 2 1 arch 1 1 arch 2 1 omega 1 1 pvGetParVector This procedure returns the parameter vector itself print pvGetParVector p0 1 0000 0 1000 0 1000 0 1000 0 1000 1 0000 pvPutParVector This procedure replaces the parameter vector with t
236. ndaries then this test can be turned off Default 1 randRadius scalar if zero no random search is attempted If nonzero it is the radius of the random search Default 001 seed scalar if nonzero seeds random number generator for random search otherwise time in seconds from midnight is used trustRadius scalar radius of the trust region If scalar missing trust region not applied The trust sets a maximum amount of the direction at each iteration Default 001 output scalar if nonzero results are printed Default 0 PrintlIters scalar if nonzero prints iteration information Default 0 weights vector weights for objective function returning a vector Default 1 12 4 2 Output Argument The single output argument is an sqpSolvemtOut structure Its definition is struct SQPsolveMTOut struct PV par scalar fct struct SQPsolveMTLagrange lagr scalar retcode matrix moment matrix hessian matrix xproduct 5 The members of this structure are 12 27 s n n Ss GAUSS User Guide par instance of a PV structure containing the parameter estimates are placed in the matrix member par fct scalar function evaluated at final parameter estimates lagr an instance of an SQPLagrange structure containing the Lagrangeans for the constraints For an instance named lagr the members are lagr lineq MXx1 vector Lagrangeans of linear equality constraints lagr nlineq Nxl vector Lagrangeans of
237. nes used to draw arrow This value may be zero or greater A value of zero is normal line width To create two single headed arrows located using plot coordinates use 1 _parrow3 1 1 3 4 5 2 2 2 3 0 2 2 2 2 3 0 2 11 10 scalar 2x1 or 3X1 vector for independent control for each axis The first element controls the X axis the second controls the Y axis and the third if set controls the Z axis If 0 the axis will not be drawn Default is 1 If this is a scalar it will be expanded to that value For example _paxes 1 0 turn X axis on Y axis off _paxes Q turn all axes off _paxes 1 turn all axes on scalar size of axes labels in inches If 0 a default size will be computed Default is 0 1x2 or Kx2 matrix Controls bar shading and colors in bar graphs and histograms The first column controls the bar shading 0 no shading 1 dots 21 17 90d GAUSS User Guide _pbarwid _pbox _pboxctl vertical cross hatch diagonal lines with positive slope diagonal lines with negative slope diagonal cross hatch solid Du RR WwW NY The second column controls the bar color see Corons Section 21 5 scalar width of bars in bar graphs and histograms The valid range is 0 1 If 0 the bars will be a single pixel wide If 1 the bars will touch each other Default is 0 5 so the bars take up about half the space open to them scalar draws a box border around the entire g
238. ng called here is a simple XY plot The entire window will be used Four sets of data will be plotted with the line and symbol attributes automatically selected This graph will include a legend title and a time date stamp time stamp is on by default library pgraph activate PGRAPH library graphset reset global variables x sega 1 1 100 generate data y sin x y y y 8 y 6 y 4 4 curves plotted against x _plegctl 1 legend on title Example xy Graph Main title xy x y Call to main routine Example 2 Here is the same graph with more of the graphics format controlled by the user The first two data sets will be plotted using symbols at data points only observed data the data points in the second two sets will be connected with lines predicted results library pgraph activate PGRAPH library graphset reset global variables x sega 1 1 100 generate data y sin x y y y 8 y 6 y 4j 4 curves plotted against x _pdate date is not printed _plctrl 1 1 0 8 2 curves w symbols 2 without _pltype 1 2 6 6 dashed dotted solid lines _pstype 1 2 0 8 symbol types circles squares _plegctl 2 3 1 7 4 5 legend size and locations _plegstr Sin wave 1 0 4 lines legend text Sin wave 8 0 Sin wave 6 0 Sin wave 4 ylabel Amplitude Y axis label
239. ng example illustrates nested do loops that use counter variables format rdn 1 0 space comma EE ID do while i lt 4 j 1 6 32 Language Fundamentals do while j lt 3 print space i comma j j j 1 endo qu 1 print endo This will print 1 1 1 2 1 3 2 1 2 2 2 3 3 1 3 2 3 3 4 1 4 2 4 3 Use the relational and logical operators without the dot in the expression that controls a do loop These operators always return a scalar result break and continue are used within do loops to control execution flow When break is encountered the program will jump to the statement following the endo This terminates the loop When continue is encountered the program will jump up to the top of the loop and reevaluate the while or until expression This allows you to reiterate the loop without executing any more of the statements inside the loop do until eof fp continue jumps here x packr readr fp 100 if scalmiss x continue iterate again endif S S sumc x count count rows x if count gt 10000 break break out of loop endif endo mean s count break jumps here 6 33 s ejuawepuny oDenbue GAUSS User Guide for loop The fastest looping construct in GAUSS is the for loop for counter start stop step Statements endfor counter is the literal name of the counter variable start stop and step are scalar expressions st
240. nonlinear equality constraints lagr linineq Pxl vector Lagrangeans of linear inequality constraints lagr nlinineq Qx1 vector Lagrangeans of nonlinear inequality constraints lagr bounds Kx2 matrix Lagrangeans of bounds Whenever a constraint is active its associated Lagrangean will be nonzero For any constraint that is inactive throughout the iterations as well as at convergence the corresponding Lagrangean matrix will be set to a scalar missing value retcode return code normal convergence forced exit maximum number of iterations exceeded function calculation failed gradient calculation failed 0 1 2 3 4 5 Hessian calculation failed 6 line search failed 7 error with constraints 8 function complex 9 feasible direction couldn t be found 12 28 Structures 12 4 3 Example Define Y An 0 where A is a KXL matrix of loadings y an Lx1 vector of unobserved latent variables and 6 a Kxl vector of unobserved errors Then x ADAY where is the LxL covariance matrix of the latent variables and Y is the KxK covariance matrix of the errors The log likelihood of the i observation is logP i 5 KIn 2z t n z 4Y XY iy Not all elements of A and V can be estimated At least one element of each column of A must be fixed to 1 and Y is usually a diagonal matrix Constraints To ensure a well defined log likelihood constraints on the parameters are required to guarantee
241. not necessarily ordered by index see gdaUpdate the variable descriptors are Therefore the indices are always in ascending order 17 27 O I 9I 4 Foreign Language Interface The Foreign Language Interface FLI allows users to create functions written in C FORTRAN or other languages and call them from a GAUSS program The functions are placed in dynamic libraries DLLs also known as shared libraries or shared objects and linked in at run time as needed The FLI functions are dlibrary Link and unlink dynamic libraries at run time dllcall Call functions located in dynamic libraries GAUSS recognizes a default dynamic library directory a directory where it will look for your dynamic link libraries when you call dlibrary You can specify the default directory in gauss cfg by setting dlib_path As it is shipped gauss cfg specifies GAUSSDIR dlib as the default directory 18 1 14 GAUSS User Guide 18 1 Writing FLI Functions Your FLI functions should be written to the following specifications 1 Take 0 or more pointers to doubles as arguments This does not mean you cannot pass strings to an FLI function Just recast the double pointer to a char pointer inside the function 2 Take those arguments either in a list or a vector 3 Return an integer In C syntax then your functions would take one of the following forms 1 int func void 2 int func double arg double arg2 3 int
242. nt New Graph Ellipse Print Preview oem Text 6a da x Gg amp IA NDOA new Cut Aer Line Open TR Zoom Arrow Save Paste Rectangle Figure 22 2 Graphics Editor Toolbar 22 2 2 Status Bar The status bar is displayed at the bottom of the graphics editor window To display or hide the status bar use the Status Bar command in the View menu The left area of the status bar describes actions of menu items as you use the arrow keys to navigate through menus This area similarly shows messages that describe the actions of toolbar buttons as you depress them before releasing them If after viewing the description of the toolbar command you wish not to execute the command then release the mouse button while the pointer is off the toolbar button In addition the status bar provides short hints while using the graphical interface such as defining sizing and moving objects Status Bar X Y Mouse Position NUM l 7 55 0 71 NUM N CAPS SCRL Figure 22 3 Graphics Editor Status Bar Indicator Description The remaining status bar panes indicate the following 22 3 mo E 23 O o GAUSS User Guide The x y mouse position on the page in units specified in the View Properties menu CAPS indicates the CAPS LOCK key is latched down NUM indicates the NUM LOCK key is latched down SCRL indicates the SCROLL LOCK key is latched down 22 2 3 File menu commands The File menu offers the following commands New
243. o eQ Y 236 5 0 e E o GAUSS User Guide create fl dataset with vnames 0 2 create fl dataset using cmdfile open f1 dataset output file outfile load x datafile load path lpath x y z t w loadexe buf exefile save name x save path spath dos cmdstr run prog msym mstring 6 6 6 String Arrays String arrays are NXK matrices of strings Here is a partial list of the functions for manipulating string arrays Vertical string array concatenation operator Horizontal string array concatenation operator Extract subarrays or individual strings from their corresponding array or assign their values Transpose operator V Bookkeeping transpose operator declare Initialize variables at compile time delete Delete specified global symbols fgetsa Read multiple lines of text from a file fgetsat Reads multiple lines of text from a file discarding newlines 6 24 Language Fundamentals format fputs fputst let loads lprint lshow print reshape save show sortcc type typecv varget varput vec vecr Define output format for matrices string arrays and strings Write strings to a file Write strings to a file appending newlines Initialize matrices strings and string arrays Load a string or string array file fst file Print expressions to the printer Print global symbol table to the printer Print expressions on window and or auxi
244. oader is ON GAUSS searches for unresolved symbol references during compilation using a specific search path as outlined below If the autoloader is OFF an Undefined symbol error message will result for right hand side references to unknown symbols When autoload is ON the autodelete state controls the handling of references to unknown symbols The following search path will be followed to locate any symbols not previously defined Autodelete ON 1 user library 2 user specified libraries 3 gauss library 4 current directory then src path for files with a g extension Forward references are allowed and g files need not be in a library If there are symbols that cannot be found in any of the places listed above an Undefined symbol error message will be 15 3 S9118 1Q17 GAUSS User Guide generated and all uninitialized variables and all procedures with global references will be deleted from the global symbol table This autodeletion process is transparent to the user since the symbols are automatically located by the autoloader the next time the program is run This process results in more compile time which may or may not be significant depending on the speed of the computer and the size of the program Autodelete OFF 1 user library 2 user specified libraries 3 gauss library All g files must be listed in a library Forward references to symbols that are not listed in an active library are not allowed Fo
245. oc arrayinit mattoarray Concatenate conformable matrices and arrays in a user specified dimension Create an N dimensional array in which the planes described by the two trailing dimensions of the array are equal to the identity Reshape a scalar matrix or array into an array of user specified size Create an N dimensional array with unspecified contents Create an N dimensional array with a specified fill value Convert a matrix to a type array See N DIMENSIONAL Arrays Chapter 10 for a more detailed explanation 6 19 s ejuawepuny oDenbue GAUSS User Guide 6 6 5 Strings Strings can be used to store the names of files to be opened messages to be printed entire files or whatever else you might need Any byte value is legal in a string from 0 255 The buffer where a string is stored always contains a terminating byte of ASCII 0 This allows passing strings as arguments to C functions through the Foreign Language Interface Here is a partial list of the functions for manipulating strings Combine two strings into one long string Interpret following name as a variable not a literal chrs Convert vector of ASCII codes to character string dttostr Convert a matrix containing dates in DT scalar format to a string array ftocv Character representation of numbers in NXK matrix ftos Character representation of numbers in 1x1 matrix ftostrC Convert a matrix to a string array using a C language for
246. og bar Once the second endpoint is defined the arrow will be redrawn in the current pen color At any time after the above process you may modify the arrow object Arrow Styles There are a combination of two styles of arrows Open Closed and Single Double headed arrows A closed arrow is one whose arrowhead is filled in with the current pen color An open one has no fill A single headed arrow is a line with an arrowhead on one end A double headed arrow has an arrowhead at both ends Creating a Rectangle To create a rectangle object select the Rectangle menu item from the Draw menu or press the Draw rectangle button on the toolbar This puts the editor into the draw rectangle state indicated by a crosshair cursor Next position the mouse where you want the top left corner then press and hold the left mouse button You may also move the object by pressing and holding the right mouse button while keeping the left button depressed Drag the mouse to the bottom left corner and release the mouse button The rectangle will be redrawn in the current background fill and border color 22 13 101p3 soiydeiy GAUSS User Guide At any time after the above process you may modify the rectangle object Creating an Ellipse Note a circle is first created when defining an ellipse After the circle has been defined it may be dynamically reshaped into an ellipse of the desired size using the mouse To create the circle sele
247. olete use v96 Universal Matrix v96 fmt Supported for read write There are four currently supported string file formats 17 14 File I O Version Extension Support Small String v89 fst Obsolete use v96 Extended String v89 fst Obsolete use v96 String v92 fst Obsolete use v96 Universal String v96 fst Supported for read write There are four currently supported data set formats Version Extension Support Small Data Set v89 dat Obsolete use v96 dht Extended Data Set v89 dat Obsolete use v96 dht Data Set v92 dat Obsolete use v96 Universal Data Set v96 dat Supported for read write 17 5 1 Small Matrix v89 Obsolete Matrix files are binary files and cannot be read with a text editor They are created with save Matrix files with up to 8190 elements have a fmt extension and a 16 byte header formatted as follows Offset Description 0 1 DDDD hex identification flag 2 3 rows unsigned 2 byte integer 4 5 columns unsigned 2 byte integer 6 7 size of file minus 16 byte header unsigned 2 byte integer 8 9 type of file 0086 hex for real matrices 8086 hex for complex matrices 10 15 reserved all O s The body of the file starts at offset 16 and consists of IEEE format double precision floating point numbers or character elements of up to 8 characters Character elements take up 8 bytes and are padded on the right with zeros The size of the body of the file is 8 rows cols rounded u
248. ommand These values are created by the following operations e 00 plus oo e 00 minus 00 e co minus oo e 0 oco e 00 00 e 0 0 Operations where one or both operands is a NaN e Trigonometric functions involving oo INF When the math coprocessor overflows the result will be a properly signed infinity Subsequent calculations will not deal well with an infinity it usually signals an error in your program The result of an operation involving an infinity is most often a NaN 6 28 Language Fundamentals DEN UNN When some math coprocessors underflow they may do so gradually by shifting the significand of the number as necessary to keep the exponent in range The result of this is a denormal DEN When denormals are used in calculations they are usually handled automatically in an appropriate way The result will either be an unnormal UNN which like the denormal represents a number very close to zero or a normal depending on how significant the effect of the denormal was in the calculation In some cases the result will be a NaN Following are some procedures for dealing with these values These procedures are not defined in the Run Time Library If you want to use them you will need to define them yourself The procedure isindef will return 1 true if the matrix passed to it contains any NaN s that are the indefinite mentioned earlier The GAUSS missing value code as well as GAUSS scalar error codes
249. on of the following year g 1986 2 23 0 dy dayinyr g sumc y dy 1150 0000 For more information on any of these functions see their respective pages in the command reference 23 2 1 Timed Iterations Iterations of a program can be timed with the use of the hsec function in the following manner 23 6 Time and Date et hsec Start timer Segment of code to be timed et hsec et 100 Stop timer convert to seconds In the case of a program running from one day into the next you would need to replace the hsec function with the date function The ethsec function should be used to compute the time difference a straight subtraction as in the previous example will not give the desired result dstart date Start timer Segment of code to be timed dend date Stop timer dif ethsec dstart dend 100 Convert time difference to seconds 23 7 ojeq pue au ATOG ATOG is a stand alone conversion utility that converts ASCII files into GAUSS data sets ATOG can convert delimited and packed ASCII files into GAUSS data sets ATOG can be run from a batch file or the command line it is not run from a GAUSS prompt but rather from a command prompt window The syntax is atog cmdfile where cmdfile is the name of the command file If no extension is given cmd will be assumed If no command file is specified a command summary will be displayed 24 1 Command
250. on space Unable to allocate buffer Syntax Error in code statement Syntax Error in recode statement Token verify error Notify Aptech Systems Procedure definition not allowed A procedure name appears on the left side of an assignment operator Invalid make statement make Variable is a Number make Variable is Procedure Cannot make Existing Variable Cannot make External Variable Cannot make String Constant Invalid vector statement vector Variable is a Number vector Variable is Procedure 25 19 soDesso y 10413 GAUSS User Guide G0383 G0384 G0385 G0386 G0387 G0388 G0389 G0390 G0391 G0392 G0393 G0394 G0395 G0396 G0397 Cannot vector Existing Variable Cannot vector External Variable Cannot vector String Constant Invalid extern statement Cannot extern number Procedures always external A procedure name has been declared in an extern statement This is a warning only extern variable already local A variable declared in an extern statement has already been assigned local status String constant cannot be external Invalid code statement code Variable is a Number code Variable is Procedure Cannot code Existing Variable Cannot code External Variable Cannot code String Constant Invalid recode statement 25 20 Error Messages G0398 G0399 G0400 G0401 G0402 G0403 G0404 G0405 G0406 G0407 G0408
251. on to the user provided procedure without modification Thus the user can put into that structure whatever might be needed as data in the procedure To initialize an instance of a DS structure the procedure dsCreate is defined in ds src 12 15 s n n Ss GAUSS User Guide include ds sdf struct DS d0 d dsCreate 12 3 2 The PV Structure The PV structure or parameter vector structure is used by various optimization modelling and gradient procedures in particular sqpSolvemt for handling the parameter vector The GAUSS Run Time Library contains special functions that work with this structure They are prefixed by pv and defined in pv src These functions store matrices and arrays with parameters in the structure and retrieve various kinds of information about the parameters and parameter vector from it Packing into a PV Structure The various procedures in the Run Time Library and applications for optimization modelling derivatives etc all require a parameter vector Parameters in complex models however often come in matrices of various types and it has been the responsibility of the programmer to generate the parameter vector from the matrices and vice versa The PV procedures make this problem much more convenient to solve The typical situation involves two parts first packing the parameters into the PV structure which is then passed to the Run Time Library procedure or application
252. onmtControlCreate QNewtonmtOutCreate qnewtonset QProg QProgmt qprogMTInCreate qqr qqre qqrep qr putarray putf pvCreate pvgetindex pvgetparnames pvgetparvector pvLength pvList pvnumoffsets pvoffsets pvPack pvPacki pvPackm pvPackmi pvPacks pvPacksi pvPacksm pvPacksmi pvputparvector pvtest pvunpack qre qrep qrsol qrtsol qtyr qtyre qtyrep quantile quantiled quantilem quantilemd qyr B 11 SP IOM P9A19SDH GAUSS User Guide qyre rank rankindx readr real recode recserar recsercp recserrc register_off register_on register_reset register_show renamefile replay rerun reshape retp return rev rfft rffti rfftip rfftn rfftnp rfftp rndbeta rndcon rndgam rndi rndKMbeta rndKMgam qyrep rndkmi rndkmn rndKMnb rndKMp rndkmu rndKMvm rndLCbeta rndLCgam rndlci rndlcn rndLCnb rndLCp rndlcu rndLCvm rndmod rndmult rndn rndnb rndns rndp rndseed rndu rndus rndvm rotater round rows rowsf rref run Reserved Words Appendix satocv satostrC save saveall saved savestruct savewind scale scale3d scalerr scalinfnanmiss scalmiss schtoc schur screen scroll searchsourcepath seekr selif seqa seqm setarray setcnvrt setdif setdifsa setvars setvmode setvwrmode setwind shell shiftr show showpqg sin singleindex sinh sleep solpd sortc sortcc sortd sorthc sorthcc sortind sortindc sortindmc sortmc sortr sortrc spa
253. oo e rem Ree R9 m eae ea bom mew 119 1 Joophextinde x eo crucis eee PS AMAR ARA 11 4 Miscellaneous Array Functions o lll ThA aWanspOSe s 000 006 eee we A oe ox e WAZ aMule tae toe Rb keene Shas bea eee 8 238 be es 11 4 3 Ameany amin AM cuum mos bee hee ta be 11 4 4 QeiDIMS a 2226 ee omo oom ee Ro em x ee eee Tis5 gelOdels uut E ee are o ee XO NOR eis TIMO alraytomal lt erc e dE Eon xim deme ox emp 11 4 7 matoaray 222 5 me a a oe ae ee NR 11 5 Using Arrays with GAUSS functions 0 0 11 6 A Panel Data Model 2x 2c mob REG RR casar Wis Appendbe 2 co mos m RR Rx xo mohobox REOR RR OR AEG REO EX 12 Structures 124 Basic StTUCIINES x cd aod ome ome DERE RUE m As ee E E a 12 1 1 Structure Definition uu s xm omo ned x EUR a RR ER 121 2 Declaring an Instance lll 12 1 3 Initializing a Instance gt lt s 2er 12 1 4 Arrays of Structures aoaaa 02000005 12 1 12 1 12 2 12 3 12 4 Contents 12 1 5 Structure Indexing o eee eee 12 5 12 1 6 Saving an Instance tothe Disk 12 8 12 1 7 Loading an Instance from the Disk 12 9 12 1 8 Passing Structures to Procedures o 12 9 12 2 Structure PoOnters lt aire Aves eee RR Ree RR RR eee a 12 10 12 2 1 Creating and Assigning Structure Pointers 12 10 12 2 2 Structure Pointer References 0 12 11
254. oops can be turned on and off When the translator is on there are three distinct phases in running a program Translation Translation of main program file to temporary file Compilation Compilation of temporary file Execution Execution of compiled code 19 3 1 Translation Phase In the translation phase the main program file is translated into a temporary file Each data loop is translated into a procedure and a call to this procedure is placed in the temporary file at the same location as the original data loop The data loop itself is commented out in the temporary file All the data loop procedures are placed at the end of the temporary file Depending upon the status of line number tracking error messages encountered in this phase will be printed with the file name and line numbers corresponding to the main file 19 3 2 Compilation Phase In the compilation phase the temporary file is compiled Depending upon the status of line number tracking error messages encountered in this phase will be printed with the file name and 19 3 doo eieq GAUSS User Guide line numbers corresponding to both the main file and the temporary file 19 3 3 Execution Phase In the execution phase the compiled program is executed Depending on the status of line number tracking error messages will include line number references from both the main file and the temporary file 19 4 Reserved Variables The following local variables are crea
255. or example you may want to concatenate a column vector containing the names of the variables in an analysis onto a matrix containing the coefficients standard errors t statistic and p value You can then print out the entire matrix with a separate format for each column with one call to the function printfm The logic of the programs will dictate the type of data assigned to a matrix and the increased flexibility allowed by being able to bundle both types of data together in a single matrix can be very powerful You could for instance create a moment matrix from your data concatenate a new row onto it containing the names of the variables and save it to disk with the save command Numeric matrices are double precision which means that each element is stored in 8 bytes A character matrix can thus have elements of up to 8 characters GAUSS does not automatically keep track of whether a matrix contains character or numeric information The ASCII to GAUSS conversion program ATOG will record the types of variables in a data set when it creates it The create command will also The function vartypef gets a vector of variable type information from a data set This vector of ones and zeros can be used by printfm when printing your data Since GAUSS does not know whether a matrix has character or 6 26 Language Fundamentals numeric information it is up to you to specify which type of data it contains when printing the contents of the mat
256. or the negation of all elements depending on context Matrix multiplication or multiplication y xx 2 When z has the same number of rows as x has columns this will perform matrix multiplication inner product If x or z are scalar this performs standard element by element multiplication Division or linear equation solution x b A If A and b are scalars this performs standard division If one of the operands is a matrix and the other is scalar the result is a matrix the same size with the results of the divisions between the scalar and the corresponding elements of the matrix Use for element by element division of matrices If b and A are conformable this operator solves the linear matrix equation Ax b Linear equation solution is performed in the following cases e If A is a square matrix and has the same number of rows as b this statement will solve the system of linear equations using an LU decomposition e If A is rectangular with the same number of rows as b this statement will produce the least squares solutions by forming the normal equations and using the Cholesky decomposition to get the solution Ab AA If trap 2 is set missing values will be handled with pairwise deletion x Modulo division 7 5 10 e19dO GAUSS User Guide y x Kz For integers this returns the integer value that is the remainder of the integer division of x by z If x or z is noninteger it will first be rounde
257. or to running the debugger or during a debugging session The debugger searches for a watch variable using the following order 3 24 Introduction to the GAUSS Graphical User Interface SEN P I 1 2 9z 3 D gt 4k mdn 5 5 5 y rndu 5 5 6 7 2 0lsqr y x 8 9 Y gt C gauss11 x matrix 5x5 auto sync Dec Sd Hex Chr 1 2 113734 0 854312 0 0684091 1 55481 0 612153 117791 0 335641 142571 0 632142 0 823892 3 0 0330848 0 396146 0 0870946 0 871266 0 261012 4 0 73255 0 102078 0 710724 242207 1 04139 5 0 321678 0 18923 0 207681 0 82713 1 83705 Figure 3 19 Watch Window 1 A local variable within a currently active procedure 2 A global variable mme A watch variable can be the name of a matrix a scalar a string array or a string For a matrix or a string array the first element is displayed If a matrix element is clicked the Matrix Editor is loaded with the matrix The matrix elements can be changed during the debugging session 3 8 Help Page The Help Page gives you access to the entire GAUSS help system in HTML format The table of contents tree is on the left Click the symbol to expand a particular section of the contents and double click on the title to view the page As on the other pages the Command Input Window and the Error Window are available via toggle buttons on the status bar It can
258. oses all open files Tiles any open programming editors horizontally Tiles any open programming editors vertically Removes any editor window tiling Closes the selected file Closes all open files 3 5 2 Layout and Usage The Source Page contains four separate window components Programming Editor Individual programming editors are opened in the editor docking area The editor docking area allows tabbing of multiple open files with the option to tile editors with a horizontal or vertical split Select Window gt Split Horizontally or Window gt Split Vertically to tile open editor windows 3 10 Introduction to the GAUSS Graphical User Interface TG causs 11 File Edt Debug Tools View Window Help e Xu 7 0 Active Libraries B X newprogram gss CA gauss11 lib usericg ET CAgaussl1 lib gauss lcg i e E pata j Source 9s al CAgaussi1 newprogram gss Ln1 Coll dock Cine Cer O nep Figure 3 8 Source Page rndseed 345346 x mdn 100 5 y mdu 100 1 output file ols output b reset print in ols e call ols y x 90 O0 UC i 0N output off print print Results of this run stored in ols output bt file print The file will be found in your working directory print Figure 3 9 Programming Editor 3 11 onul IND GAUSS User Guide Indiv
259. ote the writer must isolate rule only applies to the threads within a given set including any child thread sets they may create It does not apply between thread sets that have no chance of running simultaneously For threads defined in the main code the writer must isolate rule applies to the global symbols For threads defined in procedures or keywords it applies to the global symbols local symbols and the procedure keyword arguments 14 3 Coding With Threads There are two main points to coding with threads One you can define threads anywhere You can define them in the main code you can define them in proc s and keyword s and yes you can define them inside other threads Two you can call proc s and keyword s from threads This is what really ties everything together You can call a proc from a thread and that proc can create threads and any of those threads can call proc s and any of those proc s can create threads and you get the picture So you can do things like this q chol b ThreadBegin x q m ThreadBegin y xxi z q m ThreadEnd ThreadBegin a b x c a cm ThreadEnd ThreadJoin q mc ThreadEnd 14 4 Multi Threaded Programming in GAUSS ThreadBegin ThreadStat r ThreadStat s ThreadJoin tol r ss ThreadEnd ThreadJoin X r s q z t m m m inv b More importantly you can do things like this proc bef x local y t ThreadStat y ThreadS
260. ousTradingDay 29 390 getPreviousWeekDay 29 391 getRow 29 391 getScalar3D 11 14 getscalar3D 29 392 getScalar4D 11 14 getscalar4D 29 393 getTrRow 29 394 getwind 29 394 global control variables 27 5 global variable 8 3 go 3 21 Goertzel algorithm 29 208 gosub 29 395 goto help 3 3 goto 29 398 gradcplx 29 404 gradient 29 404 gradMT 29 399 gradMTm 29 400 gradMTT 29 401 gradMTTm 29 403 gradp 29 404 graphic panels 21 7 graphic panels nontransparent 21 8 graphic panels overlapping 21 7 graphic panels tiled 21 7 graphic panels transparent 21 8 graphical objects graphics editor 22 11 graphics editor 22 1 graphics publication quality 21 1 graphprt 29 405 graphset 29 408 grid 21 21 grid subdivisions 21 21 Index 10 Index gt 7 11 gt 7 12 H hard delimited 24 6 hasimag 29 408 hat operator 7 6 7 19 header 29 410 headermt 29 410 help facility 29 511 help hot keys 3 26 help page 3 25 help F1 4 4 hermitian matrix 29 251 hess 29 411 hesscplx 29 425 Hessian 29 425 hessMT 29 413 hessMTg 29 414 hessMTgw 29 415 hessMTm 29 416 hessMTmw 29 418 hessMTT 29 419 hessMTTg 29 420 hessMTTgw 29 421 hessMTTm 29 423 hessMTw 29 424 hessp 29 425 hidden lines 21 27 hist 29 427 histf 29 428 histogram 29 427 29 428 histp 29 429 horizontal direct product 7 7 hot keys 4 2 hot keys programming editor 3 13 hsec 29 430 html
261. ow dock me Gems tnt Colt Figure 3 6 Command Page Widgets 3 3 1 Command History Window The Command History Window contains a list of recently executed commands Commands in the command history can be executed by double clicking them or highlighting a command and clicking the Run button from the Command History toolbar Commands can be sent to the Command Input Window for further editing before executing by highlighting a command and clicking the Paste button The Search Next and Search Previous buttons will search the Command Output Window forward or backwards for previous executions of that command so that you may inspect its output To remove commands from the command history right click over a command and select Delete to remove only the highlighted command or Delete All to remove the entire contents of the command history 3 7 onul IND GAUSS User Guide Search o Run Previous v His Bx c amp 9 i le cJ x rndn 5 5 p cdfB ta x3 2 j Source Paste Search Next Figure 3 7 Command History Window 3 3 2 The Command Input Window The Command Input Window is where you enter interactive commands in GAUSS The Command Input Window provides a command history with fully featured command line editing 3 4 Command Line History and Command Line Editing When you run a command at the GAUSS prompt it is added to your command line history The last 1 000 commands executed at the GAUSS command
262. ower case 24 3 Examples Example 1 The first example is a soft delimited ASCII file called agex1 asc The file contains seven columns of ASCII data 24 12 ATOG Jan 167 3 822 4 6 34E06 yes 84 3 100 4 Feb 165 8 987 3 5 63E06 no 22 4 65 6 Mar 165 3 842 3 7 34E06 yes 65 4 78 3 The ATOG command file is agex1 cmd input gauss agex1 asc output agexl invar month temp pres vol true var 02 outvar month true temp pres vol The output data set will contain the following information name month true TEMP PRES VOL casel Jan yes 167 3 822 44 6 34e 6 case2 Feb no 165 8 987 3 5 63e 6 case3 Mar yes 165 3 842 3 7 34e 6 type char char numeric numeric numeric The data set is double precision since character data is explicitly specified Example 2 The second example is a packed ASCII file xlod asc The file contains 32 character records AEGDRFCSTy02345678960631567890 lt CR gt lt LF gt EDJTAJPSTn12395863998064839561 lt CR gt lt LF gt GWDNADMSTy19827845659725234451 lt CR gt lt LF gt position 1 The ATOG command file is xlod cmd 10 20 30 31 32 24 13 SOLV GAUSS User Guide input gauss dat xlod asc output xlod2 invar record 32 1 3 client 2 zone 1 reg 20 5 zip The output data set will contain the following information name client client2 zone reg ZIP case 1 AEG DRF CST y 60631 case 2 EDJ TAJ PST n 98064 case 3 GWD NAD MST y 59725
263. p the details of their operation from the other parts of the program that do not need to know them This makes programs easier to understand and easier to maintain A procedure in GAUSS is basically a user defined function that can be used as if it were an intrinsic part of the language A procedure can be as small and simple or as large and complicated as necessary to perform a particular task Procedures allow you to build on your previous work and on the work of others rather than starting over again and again to perform related tasks Any intrinsic command or function may be used in a procedure as well as any user defined function or other procedure Procedures can refer to any global variable that is any variable in the global symbol table that can be shown with the show command It is also possible to declare local variables within a procedure These variables are known only inside the procedure they are defined in and cannot be accessed from other procedures or from the main level program code All labels and subroutines inside a procedure are local to that procedure and will not be confused with labels of the same name in other procedures 8 1 se1npoooJd GAUSS User Guide 8 1 Defining a Procedure A procedure definition consists of five parts four of which are denoted by explicit GAUSS commands 1 Procedure declaration proc statement 2 Local variable declaration local statement 3 Body of procedure 4 Return from pro
264. p to the next 16 byte paragraph boundary Numbers are stored row by row A 2x3 real matrix will be 17 15 O I 9I 4 GAUSS User Guide stored on disk in the following way from the lowest addressed element to the highest addressed element 1 1 1 2 1 31 2 1 2 2 2 3 For complex matrices the size of the body of the file is 16 rows cols The entire real part of the matrix is stored first then the entire imaginary part A 2x3 complex matrix will be stored on disk in the following way from the lowest addressed element to the highest addressed element real part 1 1 1 2 1 3 2 1 2 2 2 3 imaginary part 1 1 1 2 1 3 2 1 2 2 2 3 17 5 2 Extended Matrix v89 Obsolete Matrices with more than 8190 elements are saved in an extended format These files have a 16 byte header formatted as follows Offset Description 0 1 EEDD hex identification flag 2 3 type of file 0086 hex for real matrices 8086 hex for complex matrices 4 7 rows unsigned 4 byte integer 8 11 columns unsigned 4 byte integer 12 15 size of file minus 16 byte header unsigned 4 byte integer The size of the body of an extended matrix file is 8 rows cols not rounded up to a paragraph boundary Aside from this the body is the same as the small matrix v89 file 17 5 3 Small String v89 Obsolete String files are created with save String files with up to 65519 characters have a 16 byte header formatted as follows 17 1
265. pack pl coefficients and now x is a 4x3 matrix of coefficients for your use in calculating the object function Suppose that your objective function has parameters to be estimated in a covariance matrix The covariance matrix is a symmetric matrix where only the lower left portion contains unique values for estimation To handle this use pvPacks For example struct PV p1 p1 pvCreate cov 1 pl pvPacks pl cov covariance Only the lower left portion of cov will be stored in the parameter vector When the covariance matrix is unpacked the parameters in the parameter vector will be entered into both the lower and upper portions of the matrix There may be cases where only a portion of a matrix being used to compute the objective function are parameters to be estimated In this case use pvPackm with a mask matrix that contains ones where parameters are to be estimated and zeros otherwise For example 13 2 Run Time Library Structures struct PV pl p1 pvCreate cov pl pvPacksm p1 cov correlation mask Here only the one element in the lower left of cov is stored in the parameter vector Suppose the optimization program sends a trial value for that parameter of say 45 When the matrix is unpacked in your procedure it will contain the fixed values associated with the zeros in the mask as well as the trial value in that part of the matrix associated with the ones Thus print unpack pl cor
266. phic panel procedures scalar or Kx1 vector line type for the main curves If this is a nonzero scalar all lines will be this type If scalar 0 line types will be default styles Default is 0 dashed dotted short dashes 1 2 3 4 closely spaced dots 5 dots and dashes 6 solid The default line types come from a global vector called _p1sel This vector can be changed by editing pgraph dec to change the default line types plsel is not documented elsewhere scalar or Kx1 vector line thickness for main curves This value may be zero or greater A value of zero is normal single pixel line width Default is 0 9x1 vector color values to use for plot see Corons Section 21 5 1 axes 2 axes numbers 3 X axis label 4 Y axis label 5 Z axis label 6 title 7 box 8 date 9 background 21 25 90d GAUSS User Guide _pmsgctl _pmsgstr _pnotify _pnum If this is scalar it will be expanded to a 9x1 vector Lx7 matrix of control information for printing the strings contained in _pmsgstr L 1 horizontal location of lower left corner of string L 2 vertical location of lower left corner of string L 3 character height in inches L 4 angle in degrees to print string This may be 180 to 180 relative to the positive X axis L 5 location coordinate system 1 location of string in plot coordinates 2 location of string in inches L 6 color L 7 font thickn
267. phics routines include xy xyz surface polar and log plots as well as histograms bar and box graphs Users can enhance their graphs by adding legends changing fonts and adding extra lines arrows symbols and messages The user can create a single full size graph inset a smaller graph into a larger one tile a window with several equally sized graphs or place several overlapping graphs in the window Graphic panel size and location are all completely under the user s control 21 1 General Design GAUSS PQG consists of a set of main graphing procedures and several additional procedures and global variables for customizing the output All of the actual output to the window happens during the call to these main routines 90d GAUSS User Guide bar box contour draw hist histp histf loglog logx logy polar surface xy XYZ Bar graphs Box plots Contour plots Draw graphs using only global variables Histogram Percentage histogram Histogram from a vector of frequencies Log scaling on both axes Log scaling on X axis Log scaling on Y axis Polar plots 3 D surface with hidden line removal Cartesian graph 3 D Cartesian graph 21 2 Using Publication Quality Graphics 21 2 1 Getting Started There are four basic parts to a graphics program These elements should be in any program that uses graphics routines The four parts are the header data setup graphics format setup and graphics ca
268. plex greek math Microb bold and boxy complex standard font with serif The following tables show the characters available in each font and their ASCII values For details on selecting fonts for your graph see SELECTING Fonts Section 21 4 1 u04 GAUSS User Guide A 1 Simplex C4 C4 C4 C4 C4 CA WG 00 Oo 0 A CI OMONDORWN 0 NOaaanawnnnna a OO ON DUOBRWN O T Qe N 6 um X UR ORAS MES RS OO Oo 0 NN 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 mIMoUOD Yr Dp aL 4G O XE lt XCAIODO C 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 NoOBRWN O jeu EE mE X o0 o O0 O O2 O 0 03 3 Ce 17 18 19 20 22 25 24 25 26 joco dE INPOUMES CE A 2 Fonts A 2 Simgrma Bae oe 61 4 89 y 17 v 34 d 62 2 90 z 18 35 63 91 19 o 36 2 64 u 92 20 37 4 65 4 93 21 Y 38 v 66 1 94 A OD ce 39e Y 67 H B i 23 4 40 c 68 A 96 24 f 41 gt 69 97 a 25 42 x 70 98 26 3 4 zw Tr 99 y 44 f yy X 100 6 5 F 73 3 101 e 46 74 1 102 p 47 x 75 3 103 y 48 V 76 104 x 49 Y 77 8 105 4 50 78 1 106 51 lt 79 4 107 x 52 gt 80 m 108 A Ed of 81 109 y 54 3 82 P 110 y 55 l 83 Y 1 o 56 e 84 2 m 57 85 T 3 8 58 gt 86 e 4 p 59 e 87 Q 5 o 60 lt 88 6 T A 3 u04 GAUSS User Guide A 3 Mi
269. procedure being defined Other procedures can use the same names but they will be separate entities 8 1 2 Local Variable Declarations The local statement is used to declare local variables Local variables are variables known only to the procedure being defined The names used in the argument list of the proc statement are always local The format of the local statement is local x y f proc g fn z h keyword Local variables can be matrices or strings If proc fn or keyword follows the variable name in the local statement the compiler will treat the symbol as if it were a procedure function or keyword respectively This allows passing procedures functions and keywords to other procedures For more information see PAssiNG PROCEDURES TO PROCEDURES Section 8 4 Variables that are global to the system that is variables listed in the global symbol table that can be shown with the show command can be accessed by any procedure without any redundant declaration inside the procedure If you want to create variables known only to the procedure 8 3 Se1npoooJd GAUSS User Guide being defined the names of these local variables must be listed in a local statement Once a variable name is encountered in a local statement further references to that name inside the procedure will be to the local rather than to a global having the same name See clearg varget and varput in the GAUSS LANGUAGE REFERENCE for ways of accessing glob
270. r complex Load matrix file or small ASCII file same as loadm Load a small GAUSS data set into a matrix Load matrix file or small ASCII file Load string file Open a GAUSS data set Control printing to an auxiliary output file or device Read a specified number of rows from a file Number of rows in file Save matrices strings procedures 17 2 File I O saved Save a matrix in a GAUSS data set seekr Reset read write pointer in a data set sortd Sort a data set typef Return type of data set bytes per element writer Write data to a data set 17 1 ASCII Files GAUSS has facilities for reading and writing ASCII files Since most software can also read and write ASCII files this provides one method of sharing data between GAUSS and many other kinds of programs 17 1 1 Matrix Data Reading Files containing numeric data that are delimited with spaces or commas and are small enough to fit into a single matrix or string can be read with load Larger ASCII data files can be converted to GAUSS data sets with the ATOG utility program see ATOG Chapter 24 ATOG can convert packed ASCII files as well as delimited files For small delimited data files the load statement can be used to load the data directly into a GAUSS matrix The resulting GAUSS matrix must be no larger than the limit for a single matrix For example load x datl asc will load the data in the file dat1 asc into an Nx1 matrix x This method
271. r create command 17 2 3 Reading and Writing The basic functions in GAUSS for reading data files are open and readr open f1 datl x readr f1 100 The call to readr in this example will read in 100 rows from dat1 dat The data will be assigned to a matrix X loadd and saved can be used for loading and saving small data sets 17 8 File I O The following example illustrates the creation of a GAUSS data file by merging horizontally concatenating two existing data sets filel dat1 file2 dat2 outfile daty open finl filel for read open fin2 file2 for read varnames getname filel getname file2 otyp maxc typef finl typef fin2 create fout outfile with varnames 0 otyp nr 400 do until eof finl or eof fin2 yl readr finl nr y2 readr fin2 nr r maxc rows yl rows y2 y yl l r y2 1 r call writer fout y endo closeall finl fin2 fout In this example data sets dat1 dat and dat2 dat are opened for reading The variable names from each data set are read using getname and combined in a single vector called varnames A variable called otyp is created which will be equal to the larger of the two data types of the input files This will insure that the output is not rounded to less precision than the input files A new data set daty dat is created using the create with command Then on every iteration of the loop 400 rows are read in from each of the
272. r example rndn 10 10 sym x Forward reference to sym X y proc sym x retp x x endp Use an external statement for anything referenced above its definition if autodelete is OFF external proc sym x rndn 10 10 y sym x proc sym x retp x x endp 15 4 Libraries When autodelete is OFF symbols not found in an active library will not be added to the symbol table This prevents the creation of uninitialized procedures in the global symbol table No deletion of symbols from the global symbol table will take place Libraries The first place GAUSS looks for a symbol definition is in the active libraries A GAUSS library is a text file that serves as a dictionary to the source files that contain the symbol definitions When a library is active GAUSS will look in it whenever it is looking for a symbol it is trying to resolve The library statement is used to make a library active Library files should be located in the subdirectory listed in the 1ib_path configuration variable Library files have an 1cg extension Suppose you have several procedures that are all related and you want them all defined in the same file You can create such a file and with the help of a library the autoloader will be able to find the procedures defined in that file whenever they are called First create the file that is to contain your desired procedure definitions By convention this file is usually
273. r j 1 100 1 b getMatrix4d a i j endfor endfor t3 date e2 ethsec t2 t3 print e2 print print ftostrC 100 el e2 e1 percent difference 6 21 13 000008 5 0000000 percent difference 61 54 11 2 5 getScalar3D getScalar4D These are specialized versions of getMatrix for retrieving scalar elements of 3 dimensional and 4 dimensional arrays respectively They behave just like getMatrix with scalar results but are much faster For example a arrayinit 100 10 10 1 t8 date for 1 1 100 1 for j 1 10 1 for k 1 10 1 b alij kl endfor endfor endfor 11 14 Working with Arrays tl date el ethsec t6 t1 print el print t2 date for 1 1 100 1 for j 1 10 1 for k 1 10 1 b getscalar3d a i j k endfor endfor endfor t3 date e2 ethsec t2 t3 print e2 print print ftostrC 100 el e2 e1 percent difference 6 21 7 0000000 2 0000000 percent difference 71 43 11 2 6 putArray putArray enters a subarray matrix or scalar into an N dimensional array and returns the result in an array This function is much faster than the index operator but it requires the part of the array being assigned to be contiguous a arrayinit 3 2 2 3 putarray a 2 eye 2 o Il 11 15 s eJIy uw DupJoM GAUSS User Guide print b Plane 1 3 0000 3 0000 3 0000 3 0000 Plane 2 1 0000 0 00000
274. r with the loadp command 8 13 se1npoooJd GAUSS User Guide whenever it is needed This will usually be faster than recompiling For example save path c gauss cp procl proc2 proc3 loadp path c gauss cp procl proc2 proc3 The name of the file will be the same as the name of the procedure with a cg extension For details see loadp and save in the GAUSS LANGUAGE REFERENCE All compiled procedures should be saved in the same subdirectory so there is no question where they are located when it is necessary to reload them The loadp path can be set in your startup file to reflect this Then to load in procedures use loadp proc1 proc2 proc3 Procedures that are saved in cg files will NOT be automatically loaded It is necessary to explicitly load them with loadp This feature should be used only when the time necessary for the autoloader to compile the source is too great Also unless these procedures have been compiled with lineson debugging will be more complicated 8 14 Sparse Matrices The sparse matrix data type stores only the non zero values of a 2 dimensional sparse matrix which makes working with sparse matrices faster and more efficient 9 1 Defining Sparse Matrices The sparse matrix data type is strongly typed in GAUSS which means that a variable must be defined as a sparse matrix variable before it may be used as such Once a variable has been defined as a sparse matrix it may not be
275. raph Set to desired color of box to be drawn Use 0 if no box is desired Default is 0 5x1 vector controls box plot style width and color Used by procedure box only 1 box width between 0 and 1 If O the box plot is drawn as two vertical lines representing the quartile ranges with a filled circle representing the 50 percentile 2 box color see Corons Section 21 5 If 0 the colors may be individually controlled using global variable _pcolor 3 min max style for the box symbol One of the following 1 minimum and maximum taken from the actual limits of the data Elements 4 and 5 are ignored 2 statistical standard with the minimum and maximum calculated according to interquartile range as follows intqrange 75 25 min 25 1 5 intgrange max 75 1 5 intqrange Elements 4 and 5 are ignored 3 minimum and maximum percentiles taken from elements 4 and 5 4 minimum percentile value 0 100 if _ pboxct1 3 3 5 maximum percentile value 0 100 if _ pboxct1 3 3 21 18 Publication Quality Graphics _pboxlim _pcolor _pcrop _pcross 5xM output matrix containing computed percentile results from procedure box M corresponds to each column of input y data 1 M minimum whisker limit according to pboxct1 3 2 M 25th percentile bottom of box 3 M 50th percentile median 4 M 75th percentile top of box 5 M maximum whisker limit according to pboxct1 3
276. re containing empty and or zeroed out members In order to declare structures in a dec file you must include the file s containing the definitions of the types of structures that you wish to declare at the top of your dec file For example if you have the following structure type definition in a file called mystruct sdf struct mystruct matrix m array a scalar scal string array sa 3 You could declare an instance of that structure type called ms in a dec file as follows include mystruct sdf declare struct mystruct ms See declare in the CommManp REFERENCE Chapter 29 for more information A file with a ext extension containing the same symbols in external statements can also be created and include d at the top of any file that references these global variables An 15 9 S9118 1Q17 GAUSS User Guide appropriate library file should contain the name of the dec files and the names of the globals they declare This allows you to reference global variables across source files in an application Here is an example that illustrates the way in which dec ext 1cg and src files work together Always begin the names of global matrices or strings with _ to distinguish them from procedures src File fcomp src These functions use _fcmptol to fuzz the comparison operations to allow for roundoff error The statement y feq a b is equivalent to y a eq b Returns a scalar res
277. rect Input Input 2 must be square G0602 Incorrect Input 1 lt il lt iu and iu lt rows of x G0603 Failure to converge 25 30 Maximizing Performance 26 These hints will help you maximize the performance of your new GAUSS System 26 1 Library System Some temporary files are created during the autoloading process If you have a tmp path configuration variable or a tmp environment string that defines a path on a RAM disk the temporary files will be placed on the RAM disk For example set tmp f tmp tmp path takes precedence over the tmp environment variable A disk cache will also help as well as having your frequently used files in the first path in the src path 26 1 2DUBUIIOJ19d GAUSS User Guide You can optimize your library 1cg files by putting the correct drive and path on each file name listed in the library The 1ib command will do this for you Use the compile command to precompile your large frequently used programs This will completely eliminate compile time when the programs are rerun 26 2 Loops The use of the built in matrix operators and functions rather than do loops will ensure that you are utilizing the potential of GAUSS Here is an example Given the vector x with 8000 normal random numbers x rndn 8000 1 you could get a count of the elements with an absolute value greater than 1 with a do loop like this c 9 Lecis do while i lt rows x if abs x i
278. relation 1 0000 4500 4500 1 0000 A mask may also be used with general matrices to store a portion of a matrix in the parameter vector struct PV pl p1 pvCreate m 90 5 1 5 0 3 mask 0 1 1 1 0 07 pl pvPackm p1 m coefficients mask 13 3 SOINJONNS 118 GAUSS User Guide A PV instance can of course hold parameters from all these types of matrices symmetric masked symmetric rectangular and masked rectangular For example lambda 1 0 0 0 0 5 0 0 0 0 1 0 0 0 0 5 lmask 0 0 1 0 0 0 0 1 phi 1 0 0 3 0 3 1 0 theta 0 6 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 6 tmask 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 struct PV parQ par pvCreate par8 pvPackm par0 lambda lambda 1mask par8 pvPacks par0 phi phi par8 pvPacksm parQ theta theta tmask It isn t necessary to know where in the parameter vector the parameters are located in order to use them in your procedure calculating the objective function Thus lambda pvUnpack par1 lambda 13 4 Run Time Library Structures phi pvUnpack parl phi theta pvUnpack parl theta sigma lambda phi lambda theta Additional functions are available to retrieve information on the properties of the parameter vector pvGetParVector and pvPutParVector get and put parameter vector from and into the PV instance pvGetParNames retrieves
279. research data myfile asc specifies a file to be located in the research data subdirectory 24 4 ATOG invar Soft Delimited ASCII Files Soft delimited files may have spaces commas or cr lf as delimiters between elements Two or more consecutive delimiters with no data between them are treated as one delimiter For example invar age name sex pay var 1 10 x 005 The invar command above specifies the following variables column name data type 1 AGE 2 name 3 sex 4 PAY 5 VAROI 6 VARO2 7 VARO3 8 VARO0A 9 VAROS 10 VARO6 11 VARO7 12 VAROS 13 VARO9 14 VAR10 15 X001 16 X002 17 X003 18 X004 19 X005 numeric character character numeric numeric numeric numeric numeric numeric numeric numeric numeric numeric numeric numeric numeric numeric numeric numeric As the input file is translated the first 19 elements will be interpreted as the first row observation the next 19 will be interpreted as the second row and so on If the number of elements in the file is not evenly divisible by 19 the final incomplete row will be dropped and a warning message will be given 24 5 SOLV GAUSS User Guide Hard Delimited ASCII Files Hard delimited files have a printable character as a delimiter between elements Two delimiters without intervening data between them will be interpreted as a missing If Nn is specified as a delimiter the file should have one element per line and blank l
280. rix For details see print and print fm in the GAUSS LANGUAGE REFERENCE Most functions that take a string argument will take an element of a character matrix also interpreting it as a string of up to 8 characters 6 6 8 Date and Time Formats DT Scalar Format The DT scalar format is a double precision representation of the date and time In the DT scalar format the number 20010421183207 represents 18 32 07 or 6 32 07 PM on April 21 2001 DTV Vector Format The DTV vector is a 1x8 vector The format for the DTV vector is 1 Year 2 Month 1 12 3 Day of month 1 31 4 Hour of day 0 23 5 Minute of hour 0 59 6 Second of minute 0 59 7 Day of week 0 6 where 0 is Sunday 8 Day since beginning of year 0 365 UTC Scalar Format The UTC scalar format is the number of seconds since January 1 1970 Greenwich Mean Time 6 27 sje u wepuny oDenbue GAUSS User Guide 6 6 9 Special Data Types The IEEE floating point format has many encodings that have special meaning The print command will print them accurately so that you can tell if your calculation is producing meaningful results NaN There are many floating point encodings which do not correspond to a real number These encodings are referred to as NaN s NaN stands for Not A Number Certain numerical errors will cause the math coprocessor to create a NaN called an indefinite This will be printed as a NaN when using the print c
281. rm operators of equal precedence are evaluated from left to right The term 27377 6 30 Language Fundamentals is evaluated ay In the expression 1 x 2 y f1 is evaluated before f2 Here are some examples Expression Evaluation a b c d 2 4 6 inv 8 9 3 14 5 6 2 sqrt 3 4 a b c 2 a b c d e a b c d a b d c a b c d 2 4 2 3 6 8 Flow Control a b c d 2 4 6 inv 8 9 3 14 6 Q sqrt 3 4 a b a b c d e aX d a b d c a c d 245 2 3 A computer language needs facilities for decision making and looping to control the order in which computations are done GAUSS has several kinds of flow control statements 6 31 sj ejuawepuny oDenbue GAUSS User Guide 6 8 1 Looping do loop The do statement can be used in GAUSS to control looping do while scalar expression loop if expression is true statements endo also do until scalar expression loop if expression is false statements endo The scalar_expression is any expression that returns a scalar result The expression will be evaluated as TRUE if its real part is nonzero and FALSE if it is zero There is no counter variable that is automatically incremented in a do loop If one is used it must be set to its initial value before the loop is entered and explicitly incremented or decremented inside the loop The followi
282. rseCols sparseEye sparseFD sparseFP sparseHConcat sparseNZE sparseOnes sparseRows sparseScale sparseSet sparseSolve sparseSubmat sparseTD sparseTranspose sparseTrTD sparseTscalar sparseVConcat spline spline1D spline2D sqpmt_feasible B 13 SP IOM P9A19SDH GAUSS User Guide sqpmt_meritFunct sqpSolve SQPsolveMT sqpSolveMTcontrolCreate sqpSolveMTlagrangeCreate sqpSolveMToutCreate sqpSolveset sqrt stdc stocv stof stop strcombine strindx string strlen strput strrindx strsect strsplit strsplitpad strtodt strtodtd strtof tab tan tanh tempname ThreadBegin ThreadEnd ThreadJoin ThreadStat time strtofcplx strtriml strtrimr strtrunc strtruncl strtruncpad strtruncr struct submat subscat substute subvec sumc sumr surface svd svdl svd2 svdcusv svds svdusv sysstate system timedt timestr timeutc title tkf2eps tkf2ps tkf2ps_margin tocart todaydt Reserved Words Appendix toeplitz token topolar trace trap trapchk trigamma union unionsa uniqindmc uniqindx uniqindxsa unique uniquemc uniquesa vals varget vargetl varmall varmares varput varputl vartype vartypef vcm vcms vcx VCXS trim trimr trunc type typecv typef until upmat upmat1 upper use utctodt utctodtv utrisol vec vech vecr vfor vget view viewxyz vlist vnamecv volume vput vread vtypecv B 15 SP IOM P9A19SDH GAUSS User Guide
283. ructure before modifying it Thus if you want to have the modified copy of the structure after running the procedure you need to pass the structure out of the procedure as one of its return arguments For example struct example_struct matrix x matrix y matrix Z Hr proc product struct example struct es es z es x es y retp es endp struct example struct esl 12 13 s n n Ss GAUSS User Guide es1 x rndn 1000 109 esl y rndn 1000 1 esl product es1 In this example the structure es1 is passed into the procedure copied and modified The modified structure is then passed out of the procedure and assigned back to es1 Structure pointers allow you to avoid such excessive data copying and eliminate the need to pass a structure back out of a procedure in cases like this When you pass a structure pointer into a procedure and then modify a member of the structure that it references the actual structure is modified rather than a local copy of it Thus there is no need to pass the modifed structure back out of the procedure For example the above example could be accomplished using structure pointers as follows struct example struct matrix x matrix y matrix Z proc 80 product struct example struct esp esp z esp x esp y endp struct example struct esl struct example struct eslp eslp esl es1 x rndn 1000 109 esl y rndn 1000 1 product esi
284. ry element in the matrix For example x 2 will add 2 to every element of x 13 2 x 45 1 3 7 4 y 2 3 5 4 z 6 7 3 5 9 6 7 2 Operators e If x is an Nx1 column vector and y is an NxK matrix or vice versa the vector is swept across the matrix vector matrix 1 2 4 3 4 gt 3 1 4 3 6 1 2 result 3 5 4 7 5 8 9 4 5 e If xis an 1xK column vector and y is an NxK matrix or vice versa then the vector is swept down the matrix vector 2 4 3 de Y Y 2 4 3 matrix 3 1 4 6 1 2 4 8 6 result 5 5 7 8 5 5 e When one argument is a row vector and the other is a column vector the result of an element by element operation will be the table of the two 7 3 s10 e1adoO GAUSS User Guide row vector 2 4 3 1 315 7 6 4 column vector 2 4 6 5 3 5 7 9 8 6 If x and y are such that none of these conditions apply the matrices are not conformable to these operations and an error message will be generated 7 2 Matrix Operators The following operators work on matrices Some assume numeric data and others will work on either character or numeric data 7 2 1 Numeric Operators For details on how matrix conformability is defined for element by element operators see ELEMENT BY ELEMENT OPERATORS Section 7 1 Addition Y XxX 2 Performs element by element addition Subtraction or negation y x zZ y k 7 4 Operators Performs element by element subtraction
285. s Immediately to the right of the Run Debug and Edit buttons is a downward pointing triangle Clicking on this triangle reveals the Action List The Action List is a selectable drop down list of your most recently acted upon files The Run Debug and Edit buttons share the same Action List You may add a file to the Action List by running it from the command line or while editing a file click on the drop down menu from Run Debug or Edit and select Current File Clicking on the Run button will run the file on the top of the Action List Placing your mouse over the Run Button produces a tooltip indicating which file will be run To run one of the other files in the list access the Action List by clicking on the triangle next to the Run button and select the name of the file you wish to run The Debug and Edit buttons work in the same manner 3 3 Layout The Command Page contains four widgets the Program Output Window the Command History Window the Command Input Window and the Error Output Window The Command Output Window shows the output from interactive commands and programs It is also the location for user input requested by the GAUSS functions keyw and cons 3 6 Introduction to the GAUSS Graphical User Interface dg cass Fila Edi Tooh View Help dae ADE g v 4 y Hst x Program Output o Program Output Window Command History Window Command Input S X Error Outut Command Input Error Output Window Wind
286. s r c malloc work arrays if wx double malloc elems sizeof double NULL return 30 out of memory if wy double malloc elems sizeof double NULL i 18 3 MA GAUSS User Guide free wx return 30 out of memory dp wx spl x square x into work area wx for i 0 i lt elems i dp spl spl spl dp dp wy sp2 y square y into work area wy for i 0 i lt elems i dp sp2 sp2 Sp2 dp dp h spl wx sp2 wy compute hypotenuse into h which was allocated by GAUSS for i 0 i lt elems i dp sqrt spl sp2 sp1 Sp2 dp 18 4 Foreign Language Interface free whatever you malloc free wx free wy return 6 exported wrapper all double arguments calls the real function with whatever data types it expects int hypotenuse double x double y double h double r double c return hypo x y h Cint r int c The following Makefiles contain the compile and link commands you would use to build the dynamic library on various platforms For explanations of the various flags used see the documentation for your compiler and linker Windows Solaris hyp dll hyp obj link dll out hyp dll hyp obj hyp obj hyp c cl c MD GX hyp c CCOPTS indicates any optional compilation flags you might add
287. s one or more objects there must be an explicit retp statement There can be multiple retp statements in a procedure and they can be anywhere inside the body of the procedure 8 1 5 End of Procedure Definition The endp statement marks the end of the procedure definition endp An implicit retp statement that returns nothing is always generated here so it is impossible to run off the end of a procedure without returning If the procedure was defined to return one or more objects executing this implicit return will result in a Wrong number of returns error message and the program will terminate 8 5 se1npoooJd GAUSS User Guide 8 2 Calling a Procedure Procedures are called like this dog i j k no returns y catGi j k one return x y z bat i j lO multiple returns call bat i j k ignore any returns Procedures are called in the same way that intrinsic functions are called The procedure name is followed by a list of arguments in parentheses The arguments must be separated by commas If there is to be no return value use proc 8 dog x y z when defining the procedure and use dog ak 4 3 Or call dog ak 4 3 when calling it The arguments passed to procedures can be complicated expressions involving calls to other functions and procedures This calling mechanism is completely general For example 8 6 Procedures and Keywords y dog cat 3 x bird x y 2 2 1
288. s specified G0131 Can t create file too many variables G0132 Can t write disk probably full G0133 Function too long G0134 Can t seekr in this type of file G0135 Can t seek to negative row G0136 Too many arguments or misplaced assignment operator You have an assignment operator where you want a comparison operator or you have too many arguments 25 12 Error Messages G0137 G0138 G0139 G0140 G0141 G0142 G0143 G0144 G0145 G0146 G0147 G0148 G0149 G0150 G0151 Negative argument erf or erfc User keyword must have one argument Negative parameter Incomplete Beta Invalid second parameter Incomplete Beta Invalid third parameter Incomplete Beta Nonpositive parameter gamma NaN or missing value cdfchic Negative parameter cdfchic Second parameter lt 1 0 cdfchic Parameter too large Incomplete Beta Bad argument to trig function Angle too large to trig function Matrices not conformable For a description of the function or operator being used and conformability rules see MATRIX OPERATORS Section 7 2 or the GAUSS LANGUAGE REFERENCE Matrix not square Sort failure 25 13 soDesso y 10413 GAUSS User Guide G0152 Variable not initialized You have referenced a variable that has not been initialized to any value G0153 Unsuccessful close on auxiliary output The disk may be full G0154 Illegal redefinition of string G0155 Nested proc
289. scalar or Kx1 vector colors for main curves in xy xyz and log graphs To use a single color set for all curves set this to a scalar color value If 0 use default colors Default is 0 The default colors come from a global vector called _pcsel This vector can be changed by editing pgraph dec to change the default colors see Coors Section 21 5 _pcsel is not documented elsewhere scalar or 1x5 vector allows plot cropping for different graphic elements to be individually controlled Valid values are O disabled or 1 enabled If cropping is enabled any graphical data sent outside the axes area will not be drawn If this is a scalar it is expanded to a 1x5 vector using the given value for all elements All cropping is enabled by default 1 crop main curves symbols 2 crop lines generated using _pline 3 crop arrows generated using _parrow 4 crop circles arcs generated using _pline 5 crop symbols generated using _psym This example will crop main curves and lines and circles drawn by _pline _pcrop 1101 0 scalar If 1 the axes will intersect at the 0 0 X Y location if it is visible Default is 0 meaning the axes will be at the lowest end of the X Y coordinates 21 19 90d GAUSS User Guide _pdate _perrbar _pframe date string If this contains characters the date will be appended and printed The default is set as follows the first character is a font selection escape code _pdate
290. se and lowercase except inside double quotes 6 10 3 Comments This comments out all text between the and the end of the line This kind of comment can be nested We consider this kind of comment to be obsolete but it is supported for backwards compatibility 6 10 4 Extraneous Spaces Extraneous spaces are significant in print and 1print statements where the space is a delimiter between expressions print x y Z 6 38 Language Fundamentals In print and lprint statements spaces can be used in expressions that are in parentheses print x y x y 6 10 5 Symbol Names The names of matrices strings procedures and functions can be up to 32 characters long The characters must be alphanumeric or an underscore The first character must be alphabetic or an underscore 6 10 6 Labels A label is used as the target of a goto or a gosub The rules for naming labels are the same as for matrices strings procedures and functions A label is followed immediately by a colon here The reference to a label does not use a colon goto here 6 10 7 Assignment Statements The assignment operator is the equal sign EI Multiple assignments must be enclosed in braces Y 6 39 sj ejuawepuny oDenbue GAUSS User Guide mant pow basel0 x The comparison operator equal to is two equal signs if x A y print x is equal to y endif 6 10 8 Functio
291. se matrix from vectors of non zero values row indices and column indices spDenseSubmat Returns a dense submatrix of sparse matrix spDiagRvMat Inserts submatrices along the diagonal of a sparse matrix spEigv Computes a specified number of eigenvalues and eigenvectors of a square sparse matrix spEye Creates a sparse identity matrix spGetNZE Returns the non zero values in a sparse matrix as well as their corresponding row and column indices spLDL Computes the LDL decomposition of a symmetric sparse matrix spLU Computes the LU decomposition of a sparse matrix with partial pivoting spNumNZE Returns the number of non zero elements in a sparse matrix spOnes Generates a sparse matrix containing only ones and zeros spSubmat Returns a sparse submatrix of sparse matrix spToDense Converts a sparse matrix to a dense matrix spTrTDense Multiplies a sparse matrix transposed by a dense matrix spTScalar Multiplies a sparse matrix by a scalar spZeros Creates a sparse matrix containing no non zero values See CoMMAND REFERENCE Chapter 29 for detailed information on each command 9 3 Sparse Support in Matrix Functions and Operators Support for the sparse matrix data type has also been added to many matrix functions and operators The following is a complete list of the matrix functions and operators that currently support the new sparse matrix type sooey esieds GAUSS User Guide 9 4 Sparse Matrices
292. ser to interactively create any number of graphical objects for composing documents It is launched by selecting Tools from the GAUSS menu bar then Graphics Editor or by clicking on the Graphics Editor icon on the GAUSS toolbar Once the document has been created it may be saved for later modification All of the objects and their respective properties contained in the document are preserved The document may also be exported to other formats 22 1 101p3 soiydeiy GAUSS User Guide 22 2 Graphics Editor Workspace The graphics editor workspace is a window allowing access to a single page with tools for composing the document The page is defined by user defined properties such as page orientation and margin settings It provides a dialog bar for user selection of the current pen and brush properties Zoom capability is provided for detailed accuracy and accomodating a wide variety of computer display resolutions Menu Bar A Untitled Page F e Edt View Draw Export Help Toolbar OSG SR Ide NM OV x OOA Pena Pen Fill E i Properties EH a a an Wr a Status Bar Figure 22 1 Graphics Editor Workspace 22 2 4 Toolbar The toolbar is displayed across the top of the application window below the menu bar The toolbar provides quick mouse access to many tools used in the graphics editor 22 2 Graphics Editor To hide or display the toolbar choose Toolbar from the View menu ALT V T Select ri
293. signed integer huge flag indicates whether the variable is larger than INT MAX 24 3 64 bit unsigned integer rows for matrices and string arrays 32 39 64 bit unsigned integer columns for matrices and string arrays length for strings including null terminating byte 40 47 64 bit unsigned integer index of the variable in the GDA 48 55 64 bit unsigned integer offset of variable data from end of header 56 63 64 bit unsigned integer length of variable data in bytes 64 143 string name of variable null terminated The variable type bytes 0 3 may be any of the following 20 array 30 matrix 40 string 50 string array The size of pointer element bytes 16 19 is the size of a pointer on the machine on which the variable was written to the GDA It will be set to 4 on 32 bit machines and 8 on 64 bit machines This element is used only for string array variables If a GDA containing string arrays is created on a 32 bit machine and then read on a 64 bit machine or vice versa then the size of pointer element indicates how the members of the struct satable s must be converted in order to be read on the current machine The huge flag bytes 20 23 is set to 1 if the variable size is greater than INT MAX which is defined as 2147483647 A variable for which the huge flag is set to 1 may not be read into GAUSS on a 32 bit machine The variable index element bytes 40 47 contains the index of the variable in the GDA Although the variable data is
294. sion Program compiled under GAUSS 386i complex version Procedure calls too deep You may have a runaway recursive procedure Type mismatch You are using an argument of the wrong data type e g inputting a matrix when a string 1s called for Too many files open The limit on simultaneously open files is 10 Redefinition of declare An attempt has been made to initialize a variable that is already initialized This is an error when declare is used declare or declare may be a better choice for your application 25 7 soDesso y 10413 GAUSS User Guide G0074 G0075 G0076 G0077 G0078 G0079 G0080 G0081 G0082 G0083 G0084 declare An attempt has been made to redefine a string as a matrix or procedure or vice versa delete the symbol and try again If this happens in the context of a single program you have a programming error If this is a conflict between different programs use a new statement before running the second program let A string is being forced to type matrix Use an external matrix symbol statement before the let statement Can t run program compiled under GAUSS Light gscroll input vector the wrong size Call Aptech Systems Technical Support New size cannot be zero You cannot reshape a matrix to a size of zero vargetl outside of procedure varputl outside of procedure File handle must be an integer Error renaming file Error reading file Error
295. sions of an N dimensional array are numbered such that the fastest moving dimension has a dimension number of 1 and the slowest moving dimension has a dimension number of N A 6x5x4x3x2 array has 5 dimensions so the first element of the vector of orders in this case 6 refers to the size of dimension number 5 Since the index of this element in the vector of orders is 1 the dimension index of the corresponding dimension dimension number 5 is also 1 You will find references to both dimension index and dimension number in the documentation for the functions that manipulate arrays There are a number of functions that have been designed to manipulate arrays These functions allow you to manipulate a subarray within the array by passing in a locator vector to index any subarray that comprises a contiguous block of memory within the larger block A vector of indices of an N dimensional array is a 1 to N x1 vector of base 1 indices into the array where the first element corresponds to the first element in a vector of orders An Nx1 vector of indices locates the 10 2 N Dimensional Arrays scalar whose position is indicated by the indices For a 4x3x2 array x the 3x1 vector of indices o indexes the 3 2 1 element of x A 2x1 vector of indices for this 3 dimensional example references the 1 dimensional array whose starting location is given by the indices Because the elements of the vector of indices are always in the same order
296. specify the printer and its connection Ends the graphics editor session The graphics editor prompts you to save documents with unsaved changes ALT F4 22 2 4 Edit menu commands The Edit menu offers the following commands Undo Cut Copy Paste Reverses the last editing action if possible CTRL Z or ALT BACKSPACE The name of the command changes depending on what the last action was The Undo command changes to Can t Undo on the menu if the last action cannot be reversed Removes the currently selected data from the document and put it on the clipboard CTRL X This command is unavailable if there is no data currently selected Cutting data to the clipboard replaces the contents previously stored there Copies currently selected data onto the clipboard CTRL C This command is unavailable if there is no data currently selected Copying data to the clipboard replaces the contents previously stored there Inserts a copy of the clipboard contents at the insertion point CTRL V This command is unavailable if the clipboard is empty 22 2 5 View menu commands The View menu offers the following commands Toolbar Displays and hides the Toolbar which includes buttons for some of the most common commands such as File Open A check mark appears next to the 22 5 101p3 soiydeiy GAUSS User Guide Status Bar Properties Zoom menu item when the Toolbar is displayed See TooLBAR Section for help
297. statement 6 2 6 37 statement executable 6 3 statement nonexecutable 6 3 statistical distributions 28 18 statistical functions 28 14 statistics descriptive 29 228 29 230 status bar graphics editor 22 3 stdc 29 859 stdsc 29 860 step into 3 21 step out 3 21 step over 3 21 stepping through 3 23 Stirling s formula 29 520 stocv 29 861 stof 29 862 stop 3 21 stop program 3 4 stop 29 862 strcombine 29 863 strindx 29 864 string array concatenation 7 18 string arrays 6 24 6 25 string concatenation 7 17 string files 17 16 string handling 28 51 string index 29 864 29 866 string length 29 865 string long 6 38 string substring 29 867 strings graphics 21 26 strlen 29 865 strput 29 865 strrindx 29 866 strsect 29 867 strsplit 29 868 strsplitPad 29 869 strtodt 29 871 strtof 29 872 strtofcplx 29 873 strtriml 29 873 strtrimr 29 874 strtrunc 29 874 strtruncl 29 875 strtruncpad 29 875 strtruncr 29 876 struct editor 3 19 structure definition 12 1 structure indexing 12 5 structure instance 12 2 structure pointers 12 10 structure DS 12 15 13 7 structure PV 12 16 13 1 structures 3 19 12 1 28 32 structures arrays of 12 4 structures control 12 22 submat 29 876 Index 21 xapul Index submatrix 29 876 subroutine 6 36 29 395 subroutines 28 46 subsample 29 290 subscat 29 877 substitution 7 19 substring 29 867 substute 29
298. table code 6 4 executable statement 6 3 execution phase 19 4 execution time 6 1 exit 3 3 exp 29 293 exponential 29 83 29 84 29 615 exponential function 29 293 exponentiation 7 6 export files graphics editor 22 16 expression 6 1 expression evaluation order 6 30 expression scalar 6 32 extern dataloop 29 294 external 29 295 extraneous spaces 6 38 eye 29 297 F F distribution 29 85 29 87 factorial 7 6 FALSE 6 32 fcheckerr 29 297 fclearerr 29 298 feq 29 299 feqmt 29 300 fflush 29 302 fft 29 302 fft 29 302 ffti 29 303 fftm 29 304 fftmi 29 307 Index 8 Index fftn 29 309 fge 29 299 fgemt 29 300 fgets 29 311 fgetsa 29 312 fgetsat 29 312 fgetst 29 313 fgt 29 299 fgtmt 29 300 file formats 17 14 file handle 29 167 29 598 file management graphics editor 22 16 fileinfo 29 314 files 17 3 files binary 17 15 files matrix 17 13 files string 17 16 filesa 29 315 finance functions 28 23 find and replace 3 14 fle 29 299 flemt 29 300 floor 29 316 flow control 6 31 flt 29 299 fltmt 29 300 fmod 29 317 fn 29 318 fne 29 299 fnemt 29 300 fonts 0 1 29 319 fonts 29 318 fopen 29 319 for 29 321 Foreign Language Interface 18 1 format 29 323 formatcv 29 330 formatnv 29 331 forward reference 15 2 Fourier transform 29 302 Fourier transform discrete 29 208 29 209 fourier transforms 28 10 fpu
299. tat t ThreadJoin t tty retp t endp proc abr m nof x dof x x local x y z a b a m m ThreadStat x ThreadStat y ThreadStat z ThreadJoin b chut x y retp inv b endp S inv m bef m dne a 32 rndn 500 500 14 5 spealyL GAUSS User Guide ThreadStat t abr s ThreadStat q abr s 2 ThreadStat r che s ThreadJoin w del t q r print w 1 10 1 10 This means you can multi thread anything you want and call it from anywhere You can multi thread all the proc s and keyword s in your libraries and call them freely anywhere in your multi threaded programs 14 4 Coding Restrictions A few points on coding restrictions First you can t interlace thread definition statements and regular statements You can t do this ThreadStat a b b n q ThreadStat c d d ThreadJoin Or this if k 1 ThreadStat a b b elseif k 2 ThreadStat a c c endif if j 1 ThreadStat d e e elseif j 2 ThreadStat d endif ThreadJoin T m Fh 14 6 Multi Threaded Programming in GAUSS Each set of threads is defined as a group and always completed by a ThreadJoin like this And this n q ThreadStat a b b ThreadStat c d d ThreadJoin ThreadBegin if k 1 a b b elseif k 2 ae Ce endif ThreadEnd ThreadBegin if j 1 d e e elseif j 2 d f f endif ThreadEnd ThreadJoin Second
300. tatement 1 is declared to be a procedure and 2 is declared to be a function They can be used inside the procedure in the usual way 1 will be interpreted as a procedure inside myproc and 2 will be interpreted as a function The call to myproc is made as follows x l myproc max amp lgsqrt 5 7 log of square root of 7 x l myproc min amp lgsqrt 5 7 log of square root of 5 The ampersand amp in front of the function or procedure name in the call to myproc causes a pointer to the function or procedure to be passed No argument list should follow the name when it is preceded by the ampersand Inside myproc the symbol that is declared as a procedure in the local statement is assumed to contain a pointer to a procedure It can be called exactly like a procedure is called It cannot be save d but it can be passed on to another procedure If it is to be passed on to another procedure use the ampersand in the same way 8 5 Indexing Procedures This example assumes there are a set of procedures named 1 f5 that are already defined A 1x5 vector procvec is defined by horizontally concatenating pointers to these procedures A new procedure g xi is then defined to return the value of the yo procedure evaluated at x procvec amp f1 amp f2 amp f3 amp f4 amp f5 8 10 Procedures and Keywords proc g x i local f f procvec i local f proc retp f x endp The local sta
301. ted by the translator and used in the produced code X_CV X iptr x ncol x plag x drop x keep x nlag Xx ptrim x fpin x lval x nrow x shft x fpout x lvar x ntrim x tname xi xn x out x vname x in x name x outtyp x x These variables are reserved and should not be used within a dataloop endata section 19 4 The GAUSS Profiler GAUSS now includes a profiler which enables you to determine exactly how much time your programs are spending on each line and in each called procedure thereby providing you with the information you need to increase the efficiency of your programs The GAUSS Profiler and tcollect are both run from a command prompt window not at a GAUSS prompt 20 1 Using the GAUSS Profiler There are two steps to using the GAUSS Profiler collection and analysis 20 1 1 Collection To collect profiling information you must run your GAUSS program in tcollect an executable shipped with GAUSS that is identical to tgauss except that it generates a file containing profiling information each time it is run 20 1 19 1J01d GAUSS User Guide tcollect b myfile e The output displayed by tcollect includes the name of the output file containing the profiling information tcollect output files have a gaussprof prefix and a gco extension Note that running tcollect on long programs may generate a very large gco output file Thus you may want to delete the gco files on your machine regularly 20 1 2 Analysis To
302. tement is used twice The first time is declared to be a local matrix After has been set equal to the i pointer f is declared to be a procedure and is called as a procedure in the retp statement 8 6 Multiple Returns from Procedures Procedures can return multiple items up to 1023 The procedure is defined like this example of a complex inverse proc 2 cminv xr xi 2 specifies number of return values local ixy zr zi ixy inv xr xi zr inv xr xi ixy real part of inverse zi ixy zr imaginary part of inverse retp zr zi return real part imaginary part endp It can then be called like this zr zi cminv xr xi To make the assignment the list of targets must be enclosed in braces se1npoooJd GAUSS User Guide Also a procedure that returns more than one argument can be used as input to another procedure or function that takes more than one argument proc 2 cminv xr xi local ixy zr Zi ixy inv xr xi zr inv xr xi ixy real part zi ixy zr imaginary retp zr zi endp proc 2 cmmult xr xi yr yi local zr zi zr xr yr xi yi zi xr yi xi yr retp zr zi endp i zr zi cminv cmmult xr xi yr yi of inverse part of inverse The two returned matrices from cmmult are passed directly to cminv in the statement above This is equivalent to the following statements tr ti zr zi
303. the most probable cause 4 9 error G0290 gauss lib prt lcg Library not found The autoloader is looking for a library file called prt 1cg because it has been activated in a library statement Check the subdirectory listed in your lib path configuration variable for a file called prt 1cg error G0292 prt dec File listed in library not found 15 12 Libraries The autoloader cannot find a file called prt dec Check for this file It should exist somewhere along your src path if you have it listed in prt 1cg Undefined symbols PRTVEC gauss src tstprt g 2 The symbol prtvec could not be found Check if the file containing prtvec is in the src_path You may have not activated the library that contains your symbol definition Do so in a library statement gauss src prt dec 3 Redefinition of __vnames proc __vnames being declared external matrix You are trying to illegally force a symbol to another type You probably have a name conflict that needs to be resolved by renaming one of the symbols gauss lib prt lcg 5 error G0301 prt dec Syntax error in library Undefined symbols __VNAMES gauss src prt src 6 Check your library to see that all filenames are flush left and that all the symbols defined in that file are indented by at least one space 15 3 1 Using dec Files Below is some advice you are encouraged to follow when constructing your own library syst
304. the Struct Tree Widget in the same manner as other data types such as matrices are opened from the Symbol Tree Structure members will be opened in a Symbol Editor to the right of the Struct Tree Widget 3 19 onul IND GAUSS User Guide ew Window Help X C gauss11 x sunneyvalley students matrix 1x1 auto sync ax Dec Sd Hex Chr sunneyvalley ax 1 4 sunneyvalley struct T students scalar teachers scalar avg gpa scalar zipcode scalar Figure 3 16 The Struct Editor 3 6 3 Symbol Editor Symbol editors are like spreadsheets that allow viewing and editing data in your workspace Data may be viewed in decimal scientific hexadecimal or character representation Double clicking in a cell allows you to change its contents Navigation throughout the cells can be accomplished with the arrow keys tab and the mouse To highlight multiple cells click on the corresponding row or column header To highlight the entire contents of a symbol editory click in the empty header box that connects the first row header to the first column header Autoreload By default open symbol editors will automatically update when the symbol has been changed programmatically This behavior is referred to as autoreload A symbol editor in autoreload mode will show auto on its header The header will also display sync indicating that the symbol editor s contents are synchronized with the current value of t
305. the same values as the columns of x For complex matrices this computes the complex conjugate transpose If an operand immediately follows the transpose operator the will be interpreted as Thus y x xis equivalent to y x x Bookkeeping transpose operator y x This is provided primarily as a matrix handling tool for complex matrices For all matrices the columns of y will contain the same values as the rows of x and the rows of y will contain the same values as the columns of x The complex conjugate transpose is NOT computed when you use If an operand immediately follows the bookkeeping transpose operator the will be interpreted as Thus y x x is equivalent toy x x Vertical concatenation z xy i 28 dob m ae y27 89 123 z 4 5 7 8 9 7 8 Operators Horizontal concatenation Z xy 12 el 4 5 6 57 g 1256 Z 3478 7 3 Relational Operators For details on how matrix conformability is defined for element by element operators see ELEMENT BY ELEMENT OPERATORS Section 7 1 Each of these operators has two equivalent representations Either can be used for example lt or 1t depending only upon preference The alphabetic form should be surrounded by spaces A third form of these operators has a and is used for comparisons between character data and for comparisons between strings or string arrays The comparisons are done byte by byte starting with the lowest
306. the structure has changed somewhat the four basic elements of the graphics program are all here The additional routines begwind endwind makewind nextwind and setwind are all used to control the graphic panels As Example 3 illustrates the code between graphic panel functions that is setwind or nextwind may include assignments to global variables a call to graphset or may set up new data to be passed to the main graphics routines You are encouraged to run the example programs supplied with GAUSS Analyzing these programs is perhaps the best way to learn how to use the PQG system The example programs are located on the examples subdirectory 21 2 2 Graphics Coordinate System PQG uses a 4190x3120 pixel resolution grid on a 9 0X6 855 inch printable area There are three units of measure supported with most of the graphics global elements Inch Coordinates Inch coordinates are based on the dimensions of the full size 9 0x6 855 inch output page The origin is 0 0 at the lower left corner of the page If the picture is rotated the origin is at the upper left For more information see Inch Uwrrs IN GRAPHIC PANELS Section 21 3 5 Plot Coordinates Plot coordinates refer to the coordinate system of the graph in the units of the user s X Y and Z axes Pixel Coordinates Pixel coordinates refer to the 4096x3120 pixel coordinates of the full size output page The origin is 0 0 at the lower left corner of the page If the pic
307. the use of a control structure For example for sqpSolvemt struct sqpSolvemtControl matrix A matrix B matrix C matrix D scalar eqProc scalar ineqProc 12 22 Structures The members of this structure determine optional behaviors of sqpSolvemt 12 4 sqpSolvemt matrix scalar scalar scalar scalar scalar scalar scalar scalar scalar scalar scalar scalar matrix i bounds gradProc hessProc maxlters dirTol CovType feasibleTest maxTries randRadius trustRadius seed output printIters weights sqpSolvemt is a procedure in the GAUSS Run Time Library that solves the general nonlinear programming problem using a Sequential Quadratic Programming descent method that is it solves min f 0 subject to A0 B C gt D H 0 G 0 gt 0 0j lt 0 lt 0 p linear equality linear inequality nonlinear equality nonlinear inequality bounds 12 23 sa4ni9n1s GAUSS User Guide The linear and bounds constraints are redundant with respect to the nonlinear constraints but are treated separately for computational convenience The call to sqpSolvemt has four input arguments and one output argument out SQPsolveMT 6fct P D C 12 4 4 Input Arguments The first input argument is a pointer to the objective function to be minimized The procedure computing this objective function has two arguments a PV structure containing the start values and a DS structure contain
308. thematical operator but connects the two parts of a complex number There should be no spaces between the or and the parts of the number If a number has both real and imaginary parts the trailing i is not necessary If a number has no real part you can indicate that it is imaginary by appending the i The statement let x 2 2 1 2i 3 4 5 61 will result in 1 2 3 4 5 O 6i x 6 14 Language Fundamentals Complex constants can also be used with the declare con and stof statements An empty matrix is a matrix that contains no data Empty matrices are created with the let statement and braces x Empty matrices are supported by several functions including rows and cols and the concatenation operators x hsecQ hsec do until hsec hsec8 gt 6000 x x data in hsec hsec0 endo You can test whether a matrix is empty by entering rows x cols x and scalerr x If the matrix is empty rows and cols will return a 0 and scalerr will return 65535 The is the horizontal concatenation operator and the is the vertical concatenation operator The statement y 1 2 3 4 will be evaluated as y 1 2 G 4 and will result in a 2x2 matrix because horizontal concatenation has precedence over vertical concatenation U a RN 6 15 s ejuawepuny oDenbue GAUSS User Guide The statement y 14 1 2 2 3 2 6 2 will be evaluated as y 1 1 2 2
309. tives second partial 29 425 descriptive statistics 29 228 29 230 design matrix 29 205 design 29 205 det 29 206 determinant 29 206 detl 29 207 dfft 29 208 dffti 29 209 diag 29 209 diagonal 29 209 diagrv 29 210 differentiation 28 3 digamma 29 211 dimension index 10 2 dimension number 10 2 directory 29 120 division 7 5 dlibrary 18 1 29 212 dllcall 18 1 29 213 do loop 6 32 do until 29 215 do while 29 215 Index 6 Index dos 29 218 doswin 29 220 DOSWinCloseall 29 220 DOSWinOpen 29 221 dot relational operator 7 11 7 21 dotmtfeq 29 223 dotmtfeqmt 29 224 dotfge 29 223 dotfgemt 29 224 dotfgt 29 223 dotfgtmt 29 224 dotfle 29 223 dotflemt 29 224 dotf1t 29 223 dotfltmt 29 224 dotfne 29 223 dotfnemt 29 224 draw 29 226 drop dataloop 29 227 DS structure 12 15 13 7 dsCreate 29 228 dstat 29 228 dstatmt 29 230 dstatmtControlCreate 29 232 dtdate 29 233 dtday 29 233 dttime 29 234 dttodtv 29 235 dttostr 29 236 dttoutc 29 238 dtv vector 23 3 dtvnormal 23 3 29 238 dtvtodt 29 239 dtvtoutc 29 240 dummy variables 29 242 dummy 29 241 dummybr 29 243 dummydn 29 245 Durbin Watson statistic 29 583 29 587 dynamic libraries 18 3 E EXE conformable 7 1 ed 29 246 edit 3 4 edit button 3 6 edit symbol 3 17 edit 29 247 editor 29 247 editor properties 3 15 editor alternate 20 246 eig 29 249 eigenvalues
310. to read only a part of a matrix array string or string array from a GDA call gdaReadSome Sparse matrices and structures may not be read in parts 17 3 3 Updating Variables in GDA s To overwrite an entire variable in a GDA you may call gdaUpdate or gdaUpdateAndPack If the new variable is not the same size as the variable that it is replacing gdaUpdate will leave empty bytes in the file while gdaUpdateAndPack will pack the file from the location of the variable that is being replaced to the end of the file to remove those empty bytes gdaUpdate is usually faster since it does not move data in the file unnecessarily However calling gdaUpdate several times for one file may result in a file with a large number of empty bytes On the other hand gdaUpdateAndPack uses disk space efficiently but it may be slow for large files especially if the variable to be updated is one of the first variables in the file If speed and disk space are both concerns and you are going to update several variables it will be most efficient to use gdaUpdate to update the variables and then call gdaPack once at the end to pack the file The syntax is the same for both gdaUpdate and gdaUpdateAndPack ret gdaUpdate myfile gda rndn 1000 100 x1 ret gdaUpdateAndPack myfile gda rndn 1000 100 x1 To overwrite part of a variable in a GDA call gdaWriteSome 17 4 Matrix Files GAUSS matrix files are files created by the save command
311. tor Wildcard searches can also be used When using wildcard searches each symbol that the string matches will be displayed on screen in a numbered list To select a specific command to view in the default editor select the number from the list The Source Browser will remain active until you type CTRL C to return to the GAUSS prompt 5 10 Language Fundamentals GAUSS is a compiled language GAUSS is also an interpreter A compiled language because GAUSS scans the entire program once and translates it into a binary code before it starts to execute the program An interpreter because the binary code is not the native code of the CPU When GAUSS executes the binary pseudocode it must interpret each instruction for the computer How can GAUSS be so fast if it is an interpreter Two reasons First GAUSS has a fast interpreter and the binary compiled code is compact and efficient Second and most significantly GAUSS is a matrix language It is designed to tackle problems that can be solved in terms of matrix or vector equations Much of the time lost in interpreting the pseudocode is made up in the matrix or vector operations This chapter will enable you to understand the distinction between compile time and execution time two very different stages in the life of a GAUSS program 6 1 Expressions An expression is a matrix string constant function reference procedure reference or any combination of these jo
312. ts 29 332 fputst 29 333 fseek 29 333 fstrerror 29 335 ftell 29 336 ftocv 29 336 ftos 29 337 ftostrC 29 341 function 6 37 29 477 29 646 functions 28 46 fuzzy conditional functions 28 12 G gamma function 29 342 gamma 29 342 gamma incomplete 29 89 gamma log 29 519 gammacp1x 29 343 gammaii 29 344 GAUSS Data Archives 17 11 17 24 28 35 Gauss Legendre quadrature 29 458 gausset 27 6 29 344 gdaAppend 29 345 gdaCreate 29 346 gdaDStat 29 347 gdaDStatMat 29 349 gdaGetIndex 29 352 gdaGetName 29 353 gdaGetNames 29 354 gdaGetOrders 29 354 gdaGetType 29 355 gdaGetTypes 29 356 Index 9 xapul Index gdaGetVarInfo 29 357 gdaIsCplx 29 359 gdaLoad 29 359 gdaPack 29 362 gdaRead 29 363 gdaReadByIndex 29 364 gdaReadSome 29 365 gdaReadSparse 29 366 gdaReadStruct 29 367 gdaReportVarInfo 29 368 gdaSave 29 370 gdaUpdate 29 372 gdaUpdateAndPack 29 373 gdaVars 29 374 gdaWrite 29 375 gdaWrite32 29 376 gdaWriteSome 29 377 ge 7 11 ge 7 12 generalized inverse 29 469 29 621 29 622 Generalized Pareto 29 91 29 616 getarray 29 380 getArray 11 12 getdims 29 380 getDins 11 27 getf 29 381 getmatrix 29 382 getMatrix 11 13 getmatrix4D 29 383 getMatrix4D 11 13 getname 29 384 getnamef 29 385 getNextTradingDay 29 386 getNextWeekDay 29 387 getnr 29 387 getnrmt 29 388 getOrders 11 27 getorders 29 389 getpath 29 390 getPrevi
313. ts must be enclosed in s comment Out of memory Notify Aptech Systems read error A read error has occurred while converting a packed ASCII file Record length must be 1 16384 bytes The record subcommand has an out of range record length Statement too long Command file statements must be less than 16384 bytes Syntax error at There is unrecognizable syntax in a command file Too many input variables More input variables were specified than available memory permitted Too many output variables More output variables were specified than available memory permitted Too many variables More variables were specified than available memory permitted Undefined variable 24 17 SOLV GAUSS User Guide A variable requested in an outvar statement was not listed in an invar statement atog WARNING missing at The parentheses in the delimit subcommand were not closed atog WARNING some records begin with cr 1f A packed ASCII file has some records that begin with a carriage return linefeed The record length may be wrong atog complex illegal for packed ASCII file A complex command was encountered following an invar command with record specified atog Cannot read packed ASCII complex specified An invar command with record specified was encountered following a complex command 24 18 Error Messages The following is a list of error messages intrinsic to the GAU
314. ttom of your open programming editor If a word is highlighted when you access find and replace it will automatically be present in the find box when the find and replace widget is opened Press the ENTER key or gt to search forward Press the lt key to search backwards To close the find and replace widget press ESC or click the x button on the left Search Search Exit Backward Forward ra a Find qns lt x El wnae word E match case E Regex x PONES mw Replace mau usu la udi Replace Al Search Replace Replace Backward Highlighted Search Replace Forward Figure 3 12 Find and Replace 3 14 Introduction to the GAUSS Graphical User Interface The Replace Box has three buttons gt means replace the highlighted expression and search forwards lt means replace the highlighted expression and search backwards and V means replace the highlighted text and do not change the cursor position Regular Expressions Find and Replace in GAUSS supports regular expression searching Regular expression searching gives users tremendous power allowing quick and precise search and replace throughout an entire file For example let us start with a file containing the following commands 100 c 50 x rndn r c y rndu r c z x rndn r c Regular expressions allow you to perform very specific find and replace commands Suppose that we want to find all usages o f rndu and rndn and replace them with rndKMu
315. ture is rotated the origin is at the upper left 21 6 Publication Quality Graphics 21 3 Graphic Panels Multiple graphic panels for graphics are supported These graphic panels allow the user to display multiple graphs on one window or page A graphic panel is any rectangular subsection of the window or page Graphc panels may be any size and position on the window and may be tiled or overlapping transparent or nontransparent 21 3 1 Tiled Graphic Panels Tiled graphic panels do not overlap The window can easily be divided into any number of tiled graphic panels with the window command window takes three parameters number of rows number of columns and graphic panel attribute 1 transparent O nontransparent This example will divide the window into six equally sized graphic panels There will be two rows of three graphic panels three graphic panels in the upper half of the window and three in the lower half The attribute value of 0 is arbitrary since there are no other graphic panels beneath them window nrows ncols attr window 2 3 0 21 3 2 Overlapping Graphic Panels Overlapping graphic panels are laid on top of one another as they are created much as if you were using the cut and paste method to place several graphs together on one page An overlapping graphic panel is created with the makewind command In this example makewind will create an overlapping graphic panel that is 4 inches wide by 2 5 inches tal
316. two input data sets horizontally concatenated and written out to daty dat When the end of one of the input files is reached reading and writing will stop The closeall command is used to close all files 17 2 4 Distinguishing Character and Numeric Data Although GAUSS itself does not distinguish between numeric and character columns in a matrix or data set some of the GAUSS Application programs do When creating a data set it is important to indicate the type of data in the various columns The following discusses two ways of doing this 17 9 O I 9I 4 GAUSS User Guide Using Type Vectors The v89 data set format distinguished between character and numeric data in data sets by the case of the variable names associated with the columns The v96 data set format however stores this type information separately resulting in a much cleaner and more robust method of tracking variable types and greater freedom in the naming of data set variables When you create a data set you can supply a vector indicating the type of data in each column of the data set For example data M 32 21500 F 27 36000 F 28 19500 M 25 32000 vnames Sex Age Pay vtypes 01 1 create f mydata with vnames 3 8 vtypes call writer f data f close f To retrieve the type vector use vartypef open f mydata for read vn getnamef f vt vartypef f print vn print vt Sex Age Pay 0 1 1
317. two windows the Breakpoint List and the Debug Window The Debug Window is a programming editor window specifically configured for debugging programs The Debug Window indicates which line it is on by the gt gt gt located in the left margin This is also the location where breakpoints are added To add a breakpoint click in the left margin of the Debug Window on the line you wish to add the breakpoint Clicking an active breakpoint will remove it H Gauss 11 File Edit Debug Tools View Help 002242425 O 8 F C Cilgaussi1 Tf Breakpoints Bx 1 2 active newprogram gss line 7 3 newprogram gss line 7 4x mdn 5 5 Sy rndu 5 5 6 k olsarty 9 93 Error Output 5 5 o 3 8 Y 3 a 3 e a In lt C gauss11 newprogram gss gt on line 7 Figure 3 18 Debug Window Starting and Stopping the Debugger You can start debugging of a file you are in by pressing CTRL D Click the Debug button to debug the file in the top of the Action List Placing your mouse over the Debug button will reveal a tooltip with the name of this file or click the downward pointing triangle next to the debug button and select a file from the list 3 22 Introduction to the GAUSS Graphical User Interface When the debugger is started it will highlight the first line of code to be run Any breakpoints are shown in the left
318. ugh they will bring the program to an end as usual and terminate all running threads in the process You can use goto and labels to jump around within a thread that is within the confines of a ThreadBegin ThreadEnd pair 14 10 Libraries The GAUSS library system allows for the creation and maintenance of modular programs The user can create libraries of frequently used functions that the GAUSS system will automatically find and compile whenever they are referenced in a program 15 1 Autoloader The autoloader resolves references to procedures keywords matrices and strings that are not defined in the program from which they are referenced The autoloader automatically locates and compiles the files containing the symbol definitions that are not resolved during the compilation of the main file The search path used by the autoloader is first the current directory and then the paths listed in the src_path configuration variable in the order they appear src_path can be defined in the GAUSS configuration file 15 1 S9118 1Q17 GAUSS User Guide 15 1 1 Forward References When the compiler encounters a symbol that has not previously been defined that is called a forward reference GAUSS handles forward references in two ways depending on whether they are left hand side or right hand side references Left Hand Side A left hand side reference is usually a reference to a symbol on the left
319. ult 1 true or 0 false dor y feq a b dor y fne a b Zinclude fcomp ext proc feq a b retp abs a b fcmptol endp proc fne a b retp abs a b gt _fcmptol endp dec File 15 10 Libraries ext File 1cg File fcomp dec global declaration file for fuzzy comparisons declare matrix _fcmptol 1e 14 fcomp ext external declaration file for fuzzy comparisons external matrix _fcmptol JR fcomp lcg fuzzy compare library fcomp dec fcmptol matrix fcomp src feq proc fne proc With the exception of the library 1cg files these files must be located along your src path The library files must be on your lib path With these files in place the autoloader will be able to find everything needed to run the following programs library fcomp x rndn 3 3 xi inv x 15 11 soueiqiy GAUSS User Guide Xix xi x if feq xix eye 3 print Inverse within tolerance else print Inverse not within tolerance endif If the default tolerance of 1e 14 is too tight the tolerance can be relaxed library fcomp x rndn 3 3 xi inv x Xix xi x _fcmptol 1e 12 reset tolerance if feq xix eye 3 print Inverse within tolerance else print Inverse not within tolerance endif 15 3 Troubleshooting Below is a partial list of errors you may encounter in using the library system followed by
320. used as another data type Similarly once a variable has been used as a matrix array or other non sparse data type it may not be redefined as a sparse matrix To define a global sparse matrix you may use either the declare or the let command declare sparse matrix sml let sparse matrix sml 9 1 S9DMILIN esieds GAUSS User Guide or the following implicit let statement sparse matrix sml declare may be used to define multiple sparse matrices in a single statement declare sparse matrix sm1 sm2 sm3 To define a local sparse matrix inside of a procedure use an implicit let statement sparse matrix lsml As neither let nor declare support the initialization of a sparse matrix at this time you must initialize a sparse matrix with an assignment after defining it 9 2 Creating and Using Sparse Matrices Several new functions have been added to allow you to create and manipulate sparse matrices These functions are denseToSp Converts a dense matrix to a sparse matrix denseToSpRE Converts a dense matrix to a sparse matrix using a relative epsilon packedToSp Creates a sparse matrix from a packed matrix of non zero values and row and column indices spBiconjGradSol Solves the system of linear equations Ax b using the biconjugate gradient method spConjGradSol Solves the system of linear equations Ax b for symmetric matrices using the conjugate gradient method Sparse Matrices spCreate Creates a spar
321. ust always be a main section even if it consists only of a call to the one and only procedure called in the program 6 4 Language Fundamentals 6 3 2 Secondary Sections Secondary sections of the program are files that are neither run directly nor included in the main section with include statements The secondary sections of the program can be left to the autoloader to locate and compile when they are needed Secondary sections must have only procedure definitions and other nonexecutable statements include statements are allowed in secondary sections as long as the file being included does not violate the above criteria Here is an example of a secondary section declare matrix tol 1 0e 15 proc feq a b retp abs a b lt tol endp 6 4 Compiler Directives Compiler directives are commands that tell GAUSS how to process a program during compilation Directives determine what the final compiled form of a program will be They can affect part or all of the source code for a program Directives are not executable statements and have no effect at run time They do not take a semicolon at the end of the line The include statement mentioned earlier is actually a compiler directive It tells GAUSS to compile code from a separate file as though it were actually part of the file being compiled This code is compiled in at the position of the include statement Here are the compiler directives available in GAUSS de
322. wise make outtyp recode select vector Create variable based on a set of logical expressions Delete rows observations based on a logical expression Specify variables NOT to be written to data set Allow access to matrices and strings in memory Specify variables to be written to output data set Lag variables a number of periods Control deletion of missing values Create new variable Specify output file precision Change variable based on a set of logical expressions Select rows observations based on a logical expression Create new variable from a scalar returning expression In any expression inside a data loop all text symbols not immediately followed by a left parenthesis C are assumed to be data set variable column names Text symbols followed by a left parenthesis are assumed to be procedure names Any symbol listed in an extern statement is assumed to be a matrix or string already in memory 19 2 Data Transformations 19 2 Using Other Statements All program statements in the main file and not inside a data loop are passed through to the temporary file without modification Program statements within a data loop that are preceded by a are passed through to the temporary file without modification The user familiar with the code generated in the temporary file can use this to do out of the ordinary operations inside the data loop 19 3 Debugging Data Loops The translator that processes data l
323. x3x5 array of observations on the independent variables Further let B be a 5x1 vector of coefficients and sigu and sige be the residual variances of u and e respectively Then in explicit steps we compute N 100 T 3 K 5 11 33 s eJIy uw BUMJOM GAUSS User Guide sigma sigu ones T T sige eye T TxT sigma Sigmai invpd sigma sigma inverse lndet N ln detl E Y amult X areshape B N K 1 residuals Omegai areshape sigmai N T T diagonal blocks stacked in a vector array R1 amult atranspose E 1 3 2 Omegai E Omegai R2 amult R1 E R1 E lnL 0 5 N T 1n 2 pi lndet asum R2 3 log likelhood All of this can be made more efficient by nesting statements which eliminates copying of temporary intervening arrays to local arrays It is also useful to add a check for the positive definiteness of sigma N 100 T 35 K 5 const 0 5 N T 1n 2 pi oldt trapchk 1 trap 1 1 Sigmai invpd sigu ones T T sige eye T trap oldt 1 if not scalmiss sigmai E Y amult X areshape B N K 15 lnl const 0 5 N 1n detl 0 5 asum amult amult atranspose E 1 3 2 areshape sigmai N T T E 3 else lnl error 98 endif 11 34 Working with Arrays 11 7 Appendix This is an incomplete list of special functions for working with arrays Many GAUSS functions have been modified to handle arrays and are not liste
324. xecuting simultaneously operating on the same data In fact it s so fundamental it s worth saying again threads are separate sections of code in a program running at the same time using the same workspace referencing and operating on the same symbols This raises basic issues of workflow and data integrity How do you manage the creation and execution of threads and make use of the work they do And how do you maintain data integrity You do not want two threads assigning to the same symbol at the same time To handle thread workflow GAUSS employs a split and join approach At various points in your program as many as you like you define a set of threads that will be created and run as a group When created the threads in the set execute simultaneously each doing useful work The parent thread waits for the created threads to complete then continues the results of their work now available for further use To maintain data integrity we introduce the writer must isolate informally the any thread can read unless some thread writes programming rule That is to say symbols that are read from but not assigned to can be referenced by as many threads in a set as you like Symbols that are assigned to however must be wholly owned by a single thread No other thread in the set can reference that symbol They cannot assign to it nor can they read from it They cannot refer to it at all 14 3 spealy GAUSS User Guide N
325. xl1 vector linear inequality constraint constants C0 D where p is a vector of the parameters scalar pointer to a procedure that computes the nonlinear equality constraints When such a procedure has been provided it has two input arguments instances of PV and DS structures and one output argument a vector of computed inequality constraints Default i e no inequality procedure scalar pointer to a procedure that computes the nonlinear inequality constraints When such a procedure has been provided it has two input arguments instances of PV and DS structures and one output argument a vector of computed inequality constraints Default i e no inequality procedure 12 25 s n n Ss GAUSS User Guide Bounds GradProc HessProc MaxIters MaxTries DirTol CovType 1x2 or Kx2 matrix bounds on parameters If 1x2 all parameters have same bounds Default 1e256 1e256 scalar pointer to a procedure that computes the gradient of the function with respect to the parameters When such a procedure has been provided 1t has two input arguments instances of PV and DS structures and one output argument the derivatives If the function procedure returns a scalar the gradient procedure returns a 1xK row vector of derivatives If function procedure turns an NX1 vector the gradient procedure returns an NXK matrix of derivatives This procedure may compute a subset of the derivatives sqpSolvemt
326. xportmenucommands 22 7 22 2 8 Help menu commands 22 7 xlv Contents 22 2 9 Object Action Context Menu o e 22 7 22 2 10 Page Context Men s sso e t ER n aa 3 as 22 8 22 2 11 Setting the Page View Properties o 22 9 22 2 12 Setting the Pen Fill Properties 22 10 22 2 13 Graphical Objects eches Roe uSha pee PEE eee ees 22 11 22 2 14 Modifying the Graphical Objects 22 14 22 3 File Management ee ee 22 16 22 9 1 Expor ng les zu ne se o aa e ek xen Rx 22 16 23 Time and Date 23 1 Time and Date Formats 4 oc 4 6 65565 moon eee sa 23 2 23 2 Time and Date Functions lt 2 20 00 be Se eae R9 eo E y 23 4 29 2 1 Timed Iterations oou po einem e ee wee HY 23 6 24 ATOG 24 1 CommandSummary a 24 1 242 COINS ses s 2 os 2 cence bh woe es Oo m 3 226 x09 3 2809 x3 24 3 Zola cac 4 NCC MT 24 12 24 4 Error Messages eacee raapia ena ea rabena e d 24 15 25 Error Messages 26 Maximizing Performance 264 Libraly Systemi Lu se mur a bay a ee hm GI E aO a a 26 1 202 o Cc 26 2 20 3 Memory Usage cs s 0050048002405 RA 3 8S3 UR A 26 3 26 3 1 Hard Disk Maintenance llle 26 4 26 32 OPUS unu coslada 26 4 XV GAUSS User Guide A Fonts Ad lt SIMPIOX ood 4502 05 beh eed bbe E thee eA es a oai nA E A 2 AZ SIMMA o bate uR oe moo ER S moo
327. y num Runs the line num before current line in history is equivalent to text Runs last line in history beginning with text ALT or ALT or Prints help screen OPTION MAC only Note that some of these keystrokes are mapped differently on different computers For example on some computers SHIFT RIGHT ARROW behaves the same as RIGHT ARROW while ALT RIGHT ARROW moves the cursor right one word Therefore multiple keystroke mappings have been supported to maximize the availability of these commands on any given machine 5 3 Interactive Commands 5 3 1 quit The quit command will exit TGAUSS The format for quit is 5 4 Using the Command Line Interface quit You can also use the system command to exit TGAUSS from either the command line or a program see system in the GAUSS LANGUAGE REFERENCE The format for system is system 5 3 2 ed The ed command will open an input file in an external text editor see ed in the GAUSS LANGUAGE REFERENCE The format for ed is ed filename 5 3 3 browse The browse command allows you to search for specific symbols in a file and open the file in the default editor You can use wildcards to extend search capabilities of the browse command The format for browse is browse symbol 5 3 4 config The config command gives you access to the configuration menu allowing you to change the way GAUSS runs and compiles files 5 5 eur puewwog GAUSS Us

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