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pro Fit 5.1 handbook - quantum

1. ccesccecccsceeseceeeeceeeeeeeeeeseeseaeeneeeneeeseneaeeeees 17 Using the Linear Regression alQoritQim c cceccccececeeeeceeeeseeeeeeeeeeeeeeeeseneeeeeeeeaees 18 Using the Polynomial fitting algorithm 0 eee ceceeceeeseeeeeeeeeeeeeeeeeeeeeeeeeeseeeeeeteetees 19 Fitting multiple functions and x values 5c eer ceeded ais eteee el ene 19 Functions with multiple x valuesS x10 ince oak ele deed 19 Multiple functions With one x value 0 0 eceeeeeeeeceeeeececteeeeeeaeeeeseeseeeseeseeeceateeeseeaneeeaees 21 Multiple functions with multiple X VAlUCS eceecceceseeseeeeeeeeeeeeeeceeeeeeeseeeaseeseeeaeeeteees 22 General Hints for fittingen aoe ese sh a A eV Geen ee GR Aloe 24 Starting ACARI GUN nnns ea eet dete E cada catia tial 24 Redundancy Of Parameters scious cecccul tesa clues daca Weel ee akc oA asec at ae aha 24 The errors of the ALAS Ob sec ce she ei eee ee ce nce ae ip ane setae ene ee 24 Defining functions and PLrOGraMMS ccecceeeeceeeeeeeeeeeeeeeeeeeeeeseeeeeeeeeeeeees 1 Simple examples eae ae ee ne ee er ent ee ee eee ae cr eee ne eee eee ee ere 2 Defining HOMGHORGr xcs se cee tet eats la Mattce theta ele ea at athe hatch alae ike 2 Defining Programs peepeener rere sere etary L E E EE A T reer tar meres enn arrea err 5 Table of Contents vii 7 AYES 06 0 Cae exe en gn E EE A EE A En EN 7 On line help for ProGrarmimmMinG 2 c daceecctentercsiecssens cepecencecdedde sacs sdensdavdonnsneeseee dle
2. function NextWindow windowID longint longint Returns the window i e the window ID of the window behind the window having the given windowID If windowID is 0 it returns the frontmost window Returns 0 if no window behind the given window The following example tiles all data text and drawing windows It first cycles through the windows to count them Then it moves them A 42 Appendix A Predefined functions procedures and arrays program TileWindows const hTile 5 horizontal tiling offset vTile 18 vertical tiling offset var windID longint nrWindows integer left top integer begin nrWindows 0 windID FrontWindow while windID lt gt 0 do count the windows begin if windID gt 0 then if a data drawing nrWindows nrWindows tl or text windID NextWindow windID end left nrWindows hTile top nrWindows vTile windID FrontWindow while windID lt gt Odo place the windows begin if windID gt 0 then if a data drawing begin or text PlaceWindow windID 3 left 30 top 0 0 top top vTile left left hTile end windID NextWindow windID end end NrCols function NrCols longint Returns the number of columns numeric and text columns of the current data window Causes a run time error if no data window is open NrRows function NrRows longint Returns the number of rows of the current data window Causes a run time error
3. Type the text you are searching for and the replacement text in the Find and Replace edit fields Use the radio buttons Forward Backward to start the search by moving down from the current insertion point towards the end of your text or up towards the beginning Click the Find button to start a search click Done if you don t want to start a search yet Click Replace All to replace all the occurrences of the text appearing in the Find item with the text appearing in the Replace item Use the menu command Enter Selection to enter the currently selected text in the Find field of the Find amp Replace dialog box Choose Find Again to restart a search the fastest way to find all occurrences of a text is to select it and choose Enter Selection and Find Again in rapid succession Use Replace to replace the current selection with the text in the Replace field of the Find amp Replace dialog 14 4 General features box Replace and Find Again combines the last two commands Replace All is equivalent to the Replace All button in the Find dialog box Note that by using the Enter Selection command or by copying some text and pasting it into the Find and the Replace field you can enter text that you cannot enter by typing in the dialog box such as carriage returns and tabs These commands can be accessed by using the following key combinations Find shift command F Find Again shift command G Enter Selection shift command
4. When you move the mouse over an entry in the menus Help and Const a help balloon is shown giving a short description When you choose an entry and release the mouse its definition is pasted into the function window You can enable disable balloon help for these two menus by choosing the entry Show Balloons from the popup menu Help Note that when choosing Show Balloons from the Help popup menu balloons are only enabled for the two popup menus not for any of the other menus or dialog boxes of pro Fit To switch on balloons for other parts of pro Fit choose Show Balloons from the Apple Help menu the question mark that appears in the menu bar Browsing functions and programs Navigating a lengthy function or program definition can be difficult To get a quick overview of your definition click the popup menu Browse at the bottom left of the function window 9 8 Defining functions and programs program OoataAnalysis var i OUtFi le logout procedure OpenQutput begin outFile CreqteTextFilec myFile 3 DataAnalysis Opendodutput CloseOutput CalculateRow begin end The menu shows a list of all functions procedures and programs defined in the file Choosing an entry from this list takes you there Finding the definition of a symbol If you want to find the definition of a symbol variable our command that appears in a function window double click it while holding down the op
5. 1 In Pascal indices for these arrays run from 1 to 64 2 InC indices for these arrays run from 0 to 63 3 programmers should set the name by calling the function SetPascalStr with a maximum string length of maxParamLength Example SetPascalStr a0 gt name 0 pname maxParamNameLength Func procedure i Func x extended a ParamArray var y extended pb ExtModulesParamBlockPtr This procedure is called to calculate the return value of your function It has the following parameters e x The function s independent variable e a The function s parameters a i Note that the index i ranges from 1 in Pascal but from 0 in C e y The function s return value to be calculated from x and a 10 8 Working with external modules Derivatives procedure Derivatives x extended a ParamArray var dyda ParamArray pb ExtModulesParamBlockPtr This routine calculates the partial derivatives of your function with respect to its parameters You can leave this routine empty if you don t need it or you can calculate only some derivatives You don t need to calculate all of them pro Fit will check if you did not calculate a derivative and will calculate it numeri cally Set hasDerivatives to false in InitializeFunc if you are sure that you will never want to calculate any derivatives yourself Note that a call of Derivatives with a given x value is always preceded by a call of Func with the same x value the
6. 103 100 f fi fi i 0 A fit with percent errors gives a more satisfying visual agreement between curve and data Obviously for serious data fitting you should always specify the real measurement error you expect for every data point Fitting 8 25 9 Defining functions and programs pro Fit allows you to define functions and programs e A function is added to the menu Func It behaves like any of pro Fit s built in functions and you can use it for fitting plotting etc see Chapter 5 Working with functions e A program is added to the menu Prog A program performs a sequence of tasks Programs can be used for scripting pro Fit Both functions and programs can be defined in the same syntax which is based on the Pascal programming language In addition to this programs can be written in Apple Script All commands that can be given to pro Fit using its menus can also be issued through pro Fit s program definition language or through AppleScript You do not need to know much about the syntax of these programming languages in order to do this The command that corresponds to any user action can be generated automatically by switching on recording either in pro Fit or in Apple s Script Editor or other equivalent scripting utilities Programs can be considered to be macros that can be used to automatize tasks However a pro Fit program can do much more than what you would nor
7. Handle Handle Ge Se tCol tCol HandleEvent Ca ncelEvent returns a random number between 0 and 1 checks if the result of a calculation is a valid number return the number of ticks 1 60 seconds since start up and today s date and time lets your computer emit an alert sound lets your computer speak out loud a text string check the mouse button and the keyboard find the last clicked point in the current drawing window find the position of coordinate markers in the preview window execute edit menus execute a menu command redirect output of results window to file set the text displayed in pro FIt s progress window shown during lengthy operations Advanced routines for external modules only conversion find a module s file tell pro Fit that a module is opening a window of its own Get the current x and y data Get and set in one step all the data contained in a column event processing A 12 Appendix A Predefined functions procedures and arrays Alphabetical list Abs function Abs x extended or complex extended Returns the absolute value of x ActivateProFitWindows procedure ActivateProFitWindows External modules only Activates pro Fit s frontmost window and enables the menus Call this routine after closing a window or a dialog that you created from an external module Each call to ActivateProFitWindows must be preceded by a call to Dectiva
8. Maximize function Maximize theFunction Str255 precision extended varyX Boolean var x y extended Boolean Obsolete Use Optimize instead Finds the parameter set that that gives a maximum value for the given function theFunction is the name of the function as it appears in the Func menu This parameter is case sensitive Use an empty string to specify the currently selected function precision defines the accuracy of the calculation Maximize will run repeated iterations until the function value changes by less than precision in consecutive iterations If varyx is true Maximize varies the active parameters as well as the x value of the function if false only the active parameters are varied and the x value is not changed The variables x and y return the x and y values where the maximum is found The algorithm used is the Simplex method Maximum function Maximum name Str255 min max extended extended Obsolete Use Extrema instead Returns the maximum of a function i e the x value where the function s value is largest name is the name of the function as it appears in the Func menu This parameter is case sensitive Use an empty string to specify the currently selected function min and max are the boundaries of the interval where the maximum must be found Maximum starts looking for a maximum only if the slope of the function is positive at x min and negative at x max If no maximum is found the fun
9. This routine is usually called in the procedure Initialize ofa function It allows to set the settings of a parameter that are given in the Parameter window Example SetParameterProperties provides an alternative to the defaults statements for external modules it provides an alternative to setting the various default values and names by hand Appendix A Predefined functions procedures and arrays A 7 function foo procedure Initialize begin initialization of param values etc SetParameterProperties param 1 value sin pi 4 name pi min 0 end begin function definition y a l sin x end mode paramActive max inf Using other functions or programs CallFunction CallProgram SetFunctionParam GetFunctionParam GetFunctionParamMode GetFunctionParamName GetNumFunctionParams SetFunctionProperites GetFunctionName SelectFunction DeleteFunction DeleteProgram GetGlobalData SetGlobalData LoadParameterSet SaveParameterSet UseParameterSet DeleteParameterSet AddParameterSet call a function or execute a program access other functions parameters hide show function in preview window get name of current function select or delete a function or program passing data between programs and or functions controlling the parameter set menu The following example program copies the active parameters of the current functi
10. Check the option Allow dragging of data points if you want to be able to change coordinates in a data window by dragging the corresponding data points in the preview window Uncheck this option to disable this potentially dangerous option Panel Interface Using this panel you can control some aspects of pro Fit s user interface Preferences Use Appearance services for k Dialog boxes alerts and windows Enable dynamic scrolling for Lf Data windows ki Drawing windows ki Text windows Interface Check the box under Use Appearance services for to enable the new three dimensional look introduced with MacOS 8 This makes the background of all dialog boxes gray adds shadows to most controls etc Drawing these elements takes more time than drawing plain black and white elements Therefore if you have a slow computer you may want to uncheck this option The check boxes under Enable dynamic scrolling for control what happens if you click and drag the indicator of a scroll bar If the corresponding checkbox is checked the contents of the window will be scrolled while you drag the scroll bar This provides a more accurate control of scrolling but may be sluggish on slower computers Panel Prefs file Using this panel you can switch between preferences files or create a new preferences file 13 4 Preferences Preferences New Preferences file Use Preferences file Preyiew S 4H Interface
11. Printing A drawing saved as a PICT or EPS file cannot be opened by pro Fit anymore To be able to modify it later save a copy in the pro Fit format Exporting pictures over the clipboard To copy a part of a drawing in order to export it to another application select the objects you want to copy and choose Copy or Cut from the Edit menu Alternatively you can drag the selected objects directly to their destination The current PICT Options will be used to create the exported picture PICT Options are discussed in Chapter 12 Printing Exporting pictures using Publishers To make a portion of a drawing available to other applications or other users you can also use the command Create Publisher in the Edit menu A Publisher creates a picture of a rectangular part of your drawing window e g of a plot of some data Creating a publisher will create an Edition Container a file containing this picture When you change something within the Publisher rectangle e g you add some points to your plot you can tell the Publisher to send this newer Edition of the picture to its Edition Container In this way the Edition Container always contains the latest version of the picture By default the new edition is always sent to the Edition Container when you save your file If you are defining a series of drawings to be included in some publication written by somebody else it is useful to Publish the drawing using this feature and load
12. Sets the label of the given tick mark to the to given string Accesses the current x or y axis use whichAxis xAxis or whichAxis yAxis This routine is usually used after calls to AddTick SetLineColor procedure SetLineColor red green blue longint Sets the line default color to be used for any future drawing in the current drawing window red green blue are integers between 0 and 65535 SetLineStyle procedure SetLineStyle thick extended dash integer Sets the default line style to be used for any future drawing in the current drawing window thick is the line thickness in points 1 72 inches Set it to 0 for leaving it unchanged dash is the dash pattern and its numerical value corresponds to the position of the dash pattern in the dash popup menu The values between 1 and 8 always correspond to 5 _ _6 Z Pix io 8 Values between 9 and 12 correspond to the four last customizable entries in the dash styles menu A value of 0 leaves the dash style unchanged SetNewGraphRect procedure SetNewGraphRect left top right bottom extended Sets the size and position of the next graph generated with createNewGraph PlotData and PlotFunction Subsequent calls to createNewGraph PlotData and PlotFunction will use the normal default position and size i e the effect of SetNewGraphRect only extends to the one graph created next Use SetGraphFrame for setting the size of the current graph Se
13. fontSize Integer The font size to be used in the window Omit for leaving it unchanged nrRows nrCols Integer The number of rows columns Omit for leaving this unchanged SetDefaultCols procedure SetDefaultCols xCol yCol xErrCol yErrCol longint Sets the default columns of the current data window The default x and y columns are those columns that are shown in the preview window Default columns are marked with x y Ax Ay in their column header You can set xErrCol yErrCol to zero to undefine the column Set any of the xCol yCol xErrCol yErrCol to 1 if you don t want to change it y g SetDefaultDirectory procedure SetDefaultDirectory path string Sets the default directory for saving files to the one specified by the given path name Pass the empty string as a paramter to re set the default directory to its original setting i e the directory where the pro Fit application is found SetEBarStyle procedure SetEBarStyle capLength capThick lineThick extended Sets the style of the error bars that will be generated by OpenDataSet AddDataPoint CloseDataSet Error bars are generated by AddDataPoint when the error parameter of OpenDataSet says so o capLength The length of the cap in pixels 1 to make the caps as wide as the data points 2 to get a box works only if x and y errors are ea bar line given capThick lineThic
14. home field home field drag field To change the size of a data window i e the number of rows and columns click the resize field in the top left corner of the window To bring the first cell of the first column into view click the home field to the right of the resize field To insert or delete empty rows or columns click one of the drag fields and drag the mouse To change the width of a column click and drag the separation line between column titles Dragging down the info hook opens an empty area at the top of the data window In this area you can enter general information or comments about your data Working with data 4 1 population data The world s poulation Geo 1 1990 Loi o oz Y da eae T 1500 cee 200 ooon When editing numbers in a data window the arrow keys NIAE p move the selection mark to neighboring data cells If you hold down the option key while pressing or gt the insertion mark moves horizontally within one cell The tab key moves the selection one column to the right The carriage return or enter key moves the selection to the cell below Selecting data You can select a single cell by clicking it e To select a rectangular region of data cells drag the mouse from the top left to the bottom right cell or click the top left cell and then click the bottom right cell while holding down the shift key e To select all cells in a row column click the row column number field To se
15. Data r c removes any number from the cell in column c and row r In the examples above we have used the for loop and the while loop Let us summarize their use and introduce the third kind of loop the repeat loop Defining functions and programs 9 15 Loops pro Fit supports three kind of loops two of which we have already seen for loops and while loops The third one is the repeat loop The loop statements are The while loop while condition do statement The statement of the while loop is executed as long as the expression in condition returns true If more than one statement should be executed in the loop the statements must be enclosed by begin and end The for loop for loopVariable startValue to endValue do statement A for loop executes its statement for all integer values of its variable between startValue and endValue If startValue equals endValue the for loop is executed only once If the startValue is larger than the endValue the for loop is never executed If more than one statement should be run in the loop the sta tements must be enclosed by begin and end An alternative form of the for loop is for loopVariable startValue downto endValue do Statement In this for loop the value of the loop variable is decreased by one after each execution of the loop statement The loop is terminated as soon as loopVariable lt endValue The repeat loop The last kind of loop is the repeat l
16. E Replace shift command R Replace amp Find Again shift command H These command key equivalents are displayed in the Help Balloons for the corresponding menu items Shortcuts and other options Although most of pro Fit s features and commands are readily accessed through its menus there are some more advanced or rarely used features that require the use of modifier keys like the option key the command key or the shift key This is a short list of these features action modifier keys Pressing F shift amp command to select Find from the Edit menu Pressing G shift amp command to select Find Again from the Edit menu Pressing E shift amp command to select Enter Selection from the Edit menu Pressing R shift amp command to select Replace from the Edit menu Pressing H shift amp command to select Replace amp Find Again from the Edit menu Pressing D command Selecting a tool in the tools palette of drawing windows Dragging objects in drawing windows Drawings objects in drawing windows to dismiss the Do you want to save changes to dialog box Keyboard equivalent of typing the Don t Save button option to keep the tool selected after drawing the corresponding object command to constrain the movement along 45 lines shift to constrain the movement to horizontal and vertical directions option to duplicate an o
17. Printing a pro Fit drawing from another application When you copy or drag a drawing into another application or when you create a Publisher that you subscribe to from another application pro Fit creates a picture often called PICT that contains all the information required for drawing the copied objects on the screen However when it comes to printing on a high quality printer with better resolution than the screen more information is needed This additional information must be packed into the picture Since there is no standard method of doing this in a way that works for all printers you should give pro Fit some information about your printer before creating a picture You can give this information by choosing Preferences from the File menu and selecting PICT Options from the list of icons to the left This brings up the following dialog box Printing 12 3 Preferences 3 Normal PICT d Enlarged PICT Embedded PostScript Bitmap d High resolution PICT O Quickdraw GX shape O Add Quickdraw GX for printer only ki Use Quickdraw for Text Standards Preyiew S i TH Interface You can choose between six picture formats Normal PICT Use this option when you don t plan to print your pictures at a high quality Pictures generated with this option look fine on the screen and use a minimum amount of memory Embedded PostScript Use this option when you are planning to print your pictures on a printer that
18. command in the File menu to set various options that determine which kind of picture is created The original definition of the QuickDraw PICT format defined only pictures with the resolution of the original Macintosh screen i e 72 dots per inch To print a picture on a printer with higher resolution additional data must be included in the picture There are several ways of doing this and the choice of method depends on the printer you are using and the application you are working with See Chapter 12 Printing for more details on this subject Saving a drawing as a PICT or EPS file To save a drawing as a picture to be exported to other programs choose Save as from the File menu and click the radio button PICT in the dialog box that appears The current PICT Options will be used for creating the picture PICT Options are discussed in Chapter 12 Printing To save a drawing as an Encapsulated PostScript File choose Save As from the File menu and click the radio button EPS file in the Save As dialog box The size of EPS files created in this way is kept as small as possible This small size is useful when you want to transmit your pictures over e mail to a publisher However keeping a small size introduces some limitations on the number of text formatting options you can use If a certain text formatting option is not supported by the PostScript font you plan to use like Outline or Shadow or Underline then these
19. function PRandom extended External modules name See Random Print procedure Print optional parameter list Shows the Print dialog box for a given window Parameters window Longint or String The name or window ID of the window Default Front window See also PageSetup Random function Random extended Returns a random number evenly distributed between 0 and 1 Re function Re z complex extended Returns the real part of the complex number z To get the imaginary part call function Im ReduceData procedure ReduceData optional parameter list Reduces and or smoothes the data in data window Parameters window String or Longint The window specified by name or window ID Omit for front window action Integer keepSome keep every n th row removeSome remove every n th row average replace n consecutive rows by one single row holding their average smooth replace each row by the average of the row and its n 1 neighbouring rows keepSelRows remove all rows except the ones that are selected removeSelRows remove all rows that are presently selected n is given by the parameter points points Integer additional parameter if action is keepSome removeSome average or smooth selectionOnly Boolean True if only the currently selected cells are to be affected false if all cells in the data window are to be affected Ignored if parameter action is removeSelRows Or keepSelRo
20. mathematical function to it Our data The world s human population is growing rapidly Table 3 1 shows the number of inhabitants of this planet for the period after 1940 Table 3 1 The world s population since 1940 year population in millions 1940 2200 1950 2500 1960 3000 1969 3600 1975 4000 1981 4400 1987 5000 1990 5300 Let us plot and analyze these figures Starting pro Fit First install pro Fit on your computer as described in the Chapter Installation Then e Double click pro Fit pro Fit comes up with the following windows The results window is used to output results of various calculations The parameters window lists the parameters used by the current function and allows you to edit their values The preview window shows a real time preview of the current function and data set Close these windows if you do not want them When you need them again choose their name from the Windows menu Entering the data First you must enter the numbers given in Table 3 1 into a data window To do this you have to open a new data window 1 Choose New Data from the File menu An empty data window appears Getting started 3 3 Untitled Data 1 Data are arranged in horizontal rows and vertical columns The topmost cell of each column shows the name of the column by default Column 1 Column 2 etc The cells below contain the data of each column 2 Click into the first empty c
21. max its lower and upper boundaries SetParamName procedure SetParamName i integer name Str255 Obsolete Use SetParameterProperties instead Sets the name of a parameter of the currently running function i is the parameter index name its new name Appendix A Predefined functions procedures and arrays A 63 SetRange procedure SetRange whichAxis integer min max extended scaling integer Sets the range and scaling of the current x axis if whnichAxis xAxis or y axis if whichAxis yAxis min max is the new range of the axis scaling is its new scaling and can take the values 0 linear scaling 1 logarithmic scaling 2 1 x scaling 3 probability scaling 1 keep scaling unchanged SetTextFileFormat procedure SetTextFileFormat colDelimiter endOfLine Str255 withColTitles copyInfo Boolean noHeaderLines inout longint Sets the default format for loading and saving text files with SaveDataAsText and OpenData colDelimiter and endofLine define the strings to be inserted between columns and between rows Pass an empty string for colDelimiter tu use a tabulator Pass an empty string or r for endOfLine tu use a carriage return colDelimiter and endOfLine can be built by any string of characters For colDelimiter you can use t for a tabulator For endOfLine you can use r and n for a carriage return and a line feed respectively Any other character preceded by is igno
22. respectively The Superscript and Subscript buttons keyboard equivalents and switch to superscript or subscript characters with smaller font size The Normal button keyboard equivalent command key space bar restores the vertical position and the font size to their previous settings To set the vertical position of the selected characters click and drag the baseline indicator black triangle at the right side of the text box To shift the vertical position click the white triangles above and below the baseline indicator Clicking the white triangle above below moves the selected text up down by three points If you hold down the option key while clicking the triangle the offset is only one point The size of the selected text can be set by changing the font size in the size field or to use the pop up menu to its right To increase or decrease the size of all selected text proportionally click one of the triangles at the right of the size pop up menu Doing so increases or decreases the text size by 7 6 Drawing and Plotting approximately 10 20 To increase or decrease it by just one point hold down the option key while clicking the triangles Each text object contains only a single line of text for multiple lines you must create a text object for each new line Hint To write a text having several lines in a drawing window edit the text in a function window or in the results window Then copy or drag and drop it
23. windowID is the window ID of the window such as it is returned by Get WindowID or FrontWindow fileName is the name of the file If fileName contains a simple file name the file is placed in pro Fit s folder If fileName contains a file path e g HD MyFolder file the file is placed in the folder defined in the file path Pass for fileName to bring up a dialog box asking the user where to save the file SaveDrawingAs L bla default is equivalent to SaveWindowAs L bla SaveParameterSet procedure SaveParameterSet optional parameter list Saves the the parameters that currently appear in the Parameter window Parameters set String The name of the set Omit to save all sets belonging to the given function forAll Boolean True if the parameter set is to be available for all functions false if the parameter set is only to be available for the current function Default false file String The file where the parameter set must be saved Omit to save as permanent sets See also AddParameterSet UseParameterSet LoadParameterSet DeleteParameterSet Save procedure Save windowID longint Equivalent to choosing Save from the File menu Causes a run time error the window has never been saved SaveWindow procedure SaveWindow optional parameter list Saves a window Parameters window Longint or String The name or window ID of the window Default Front window file String The file to save the windo
24. xX Table of contents 1 Introduction pro Fit is an interactive tool for the investigation analysis and representation of functions and data It is designed for users in science research engineering and education The key features of proFit 5 1 are e Customized functions and algorithms Very powerful and simple Pascal like syntax for defining mathematical functions data transformation algorithms drawings and general macros e Interactive parameter modeling and curve fitting Intuitive interface for modeling and fitting data Various fitting algorithms Optional restriction of parameter ranges Support for y as well as x errors Statistical error analysis for fitted parameters e Professional plotting Accurate and flexible graphical representations of mathematical functions and numerical data Multiple coordinate axes Linear logarithmic 1 x and normal probability scalings Reverse scaling Coloring of areas between curves and any axis Editing of any part of a plot with standard drawing tools e Drawing editor Support for standard drawing objects B zier curves two different kinds of polygon smoothing texts with sub and superscripts data point symbols and any imported picture Dash patterns are applicable to most drawing objects Arrows are available for smoothed and un smoothed polygons and simple lines The drawing editor supports colors views at different magnifications and extended precision positioning of graphical o
25. 0 0 0 1 2 3 4 5 legend x Editing legends A legend contains a description for each curve or data set of its graph The e istset description consists of a symbol identifying the plot and a text You can change st fit the line and point style of a plot as well as the text by double clicking the respective items in the legend mx 2nd set e Double click the text of a legend to change a the name of a plot 2nd fit e Double click the plot symbol to choose the color plot symbol and line styles for a plot Find more information on this topic later in this chapter To change the space allocated for the plot symbols or the distance between lines in the legend simply resize the legend by dragging its selection points A graph is logically linked to its legend and vice versa If you change the appearance of a plot the change is reflected in both the graph and its legend To mantain this relationship pro Fit does not let you duplicate a legend However you can select a legend and choose Ungroup from the draw menu This transforms the legend into a set of simple drawing shapes which then can be copied If you do not need the legend delete it You can always create a new legend for a graph by double clicking the graph and checking Draw legend in the dialog box that appears Note that you can change the text style font and font size of a legend by selecting it and choosing an appropriate setting from the Style Font and Size s
26. 0 1 0 2 0 2 0 1 0 0 0 1 0 2 0 An unframed and a framed graph To change the appearance of a frame either double click a graph and click the Frame icon or choose Frame from the submenu Graph in the Draw menu In the dialog box that appears you can edit the Line style of the frame and determine if tick marks must be drawn on it The tick positions of the main coordinate axes X1 and Y1 are used If you draw a frame with ticks you usually do not wish to draw the axes ticks as well Uncheck the corresponding check boxes in the axis dialog box Grid Grid lines are horizontal and vertical lines at the positions of the ticks 1000 1000 E o E 100 100 F 0 i o 106 105 E o E P EEE a A e E E 0 2 4 6 8 10 12 0 2 4 6 8 10 12 A graph without and with grid lines To add grid lines to your graph double click a graph and check Draw grid This will add horizontal and vertical grid lines To customize the grid lines click the Grid icon in the same dialog box or choose Grid from the Graph submenu In the Grid editing panel that appears you can define where you want to have horizontal and or vertical grid lines and if you want to see them at minor ticks major ticks or both You can also choose which axes mu
27. 29 You can also fill the region between a curve and one of the axes with a color of your choice To do this check Fill and select the axis towards which the curve must be filled and the fill color using the two popup menus to its right The Coordinate Axes popup menu defines the coordinate axes used by the selected curve or data set With this pop up menu you can change the reference axis of any given curve Doing this for function curves which were drawn with auto step is not recommended If the scaling of the original axis and the one of the destination axis differ considerably the results can be disappointing Remember that a function curve is only defined by a set of points pro Fit calculated these points in an optimized way when it plotted the function for the axis scaling and range on which the function was plotted If you then change scaling or range your curve may loose its smoothness In such a case it is better to redraw the function curve on the new axis Check Appears in legend to make the curve or data set appear as an entry in the legend Uncheck this check box to hide the corresponding entry in the legend When an entry is visible in the legend you will usually change its style by double clicking it When an entry is not visible in the legend you must choose Curves from the Graph submenu to access and change the style of the corresponding curve or data points Click Tabulate to recover the original data points that were
28. 4 000000e 0 t 0 000000e 0 tr 3 234000e 3 t tabove is empty yr z z t 242400e 44t 1 234000e 3 tr 42423dar6 4 tytStart asdfasd Ikjlkjlikjlki IKjIKj Ikj Iki T1111 4 taght EV ELEVEN EV ENE LEVEL E LEVEL EAE e tit yt tabulator n line feed 4r carriage return Line breaks at J LF 0n CR Gr O Wrap long lines Note that special characters such as a tabulator line feed or carriage return are written in a double character form with a backslash as the first character It is possible to display the text with different Line breaks If Wrap long lines is checked the lines will not be cut at the right border but wrapped to the next line Saving text files You can also save data into text files in a custom format To do this choose Save as from the File menu for your data window and choose Text File from the Format pop up In the dialog box that appears select Custom format Appendix C File formats C 5 Saving TEXT File Format Format Custom kf Optimize Size kf Write header lines Copy text from Info field kf Write column tithes Column delimiter Line terminator Tab cr G0 12 ok ok This dialog box is very similar to the one for loading text files Again you can select the Column delimiter and the Line terminator If Write header lines is checked you have the option to either write a single first line with the text specified in the edit field to the right or t
29. 400 nm corresponds to an energy of 3 0996 eV while a wavelength of 1000 nm corresponds to an energy of 1 2398 eV 6 Edit the tick marks Do this by changing the values in the Ticks field Note how the density of ticks tends to increase for larger values Go over to custom ticks and edit the ticks list directly if necessary The end result could be something like this Energy eV 3 0 2 5 2 0 1 7 1 5 1 3 1 0 T 0 8 2 0 6 Ry 2 3 0 4 Q Ss 0 2 lt 0 0 400 500 600 700 800 900 1000 Wavelength nm Note that the top axis which has 1 x scaling has the smallest value to its right and the largest value to its left Click Prefix in the axis dialog box to set pre and postfix for the labels to multiply them with a given factor or to offset them by a given value General Labels Prefix 2 Lines Offset 0 Prefix Postfix I Click Prefix or Postfix to prepend or append a string to each label The value in field Factor is multiplied with the value of each label before its string is generated You may e g enter 100 here to display values between 0 and 1 in percent The vaue in the field Offset is added before the string of the label is generated 7 28 Drawing and Plotting Curves and data points You can change the appearance of curves and data points in a graph in many ways Choose Curves from the Graph submenu Draw menu or click the Curves icon in the Graph Settings box You can also doubl
30. 8 9 2 In the 5th century A D in China Tsu Chung Chih and Tsu Kengh Chih established 3 1415926 lt m lt 3 1415927 PlaceWindow procedure PlaceWindow windowID longint left top right bottom integer Moves the given window to a new place on screen left top right and bottom give the position of the margins of the new window in global coordinates which have their origin at the top left of the main screen PlaceWindow does nothing if the new window position would be off screen If right lt Appendix A Predefined functions procedures and arrays A 47 left the width of the window remains unchanged if bottom lt top the height of the window remains unchanged windowID is the window ID of the window such as it is returned by Get WindowID or FrontWindow Use windowID 0 for the front window PlaceWindow procedure PlaceWindow windowID longint windowRect Rect External modules only Same as the internal function but accepts a Rect data structure as a parameter PlotData procedure PlotData optional parameter list Plots a data set into a graph Parameters xColumn yColumn window autoX autoY xFirst xLast yFirst yLast xScaling yScaling xAxis yAxis new Window newGraph selRowsOnly drawErrors pointType pointSize pointThickness bgPointType bgPointSize connected curveThickness curveDash Longint The x and y columns Longint or St
31. A is the population in the year 1940 so we can set it to 2200 millions tg note the minus it comes from the different definitions of Eqs 3 1 and 3 2 is the time within which the population increases by a factor e 2 71 Looking at the plot of the data in the drawing window we can easily guess it to be between 50 and 200 years Let us set fg to 100 5 Enter the starting values 2200 for A and 100 for to Your parameter window should now look like the one below parameters A 2200 0000 xO 1940 0000 tO 100 0000 canst 0 0000000 lected t y A expl e e 0 10 const See ee ee exponential function tO time constant lower limit none E Use for fitting Intermission Previewing the data and the function Above we have seen how to produce a graphical representation of the data in a drawing window and how to edit it You can have a quick look at the graphical appearance of the data without actively plotting it by using the Preview window This same window also shows you a graphical representation of the current function Select Preview from the Window menu You should see the following window E Floating S5000 Show data E Show function E Auto L Log Se huto C Loo 1350 To the left of the window there are some controls that let you determine what the window must show and if it must be a floating window or a normal window To the right are some tools that can be used to edit and analyze th
32. Fourier transform of this set of data corresponds to the frequency spectrum of the signal Hy corresponds to the amplitude of the signal at frequency n N At Note that the maximum frequency of the frequency domain is fe 1 2At the Nyquist critical frequency The Fourier transform and its inverse can be calculated with two b FFT commands in the submenu Fourier Transform of the Calc menu FFT P and Inverse FFT FFT stands for Fast Fourier Transform an Inverse FFT efficient algorithm for the calculation of the Fourier transform These built in algorithms assume that the data set hx of the time domain is real valued and not complex In this case the frequency domain data set Hy is complex but we have Hn H_y i e the values at positive frequency are the complex conjugate values at negative frequency It is therefore sufficient to calculate only the positive frequency spectrum of the Fourier transform Note The built in Fourier transform works on real valued data in the time domain To work in complex data use the external module FFT that comes with pro Fit To carry out a Fourier transformation bring the data window with your data in the time domain to the front and choose FFT from the Fourier Transform submenu Fourier Transformation Input Data column x Value 2 Data interwal 1 Jreconos Output Real and imaginary parts Amplitude and phase Real part Imaginary part Frequency vf Calcu
33. Plotting below for more details on this However you might also want to use them to achieve some special effect in a drawing For example you can use a triangle or a rectangle to define a point and you can rotate them by any amount You can t do this that easily using the standard drawing tools You can also define closed polygons with any special symmetry The data point symbols you define can then be used as drawing objects in the drawing window their size can be quite big You will be able to resize them as usual by dragging a selection handle and you can always modify them by double clicking them Editing drawing objects You can change many attributes of drawing objects such as color line thickness or background pattern To do this first select the desired object s Then change the attributes using the Fill Pen Dash and Arrow popup menus A fill pattern and a fill color can be specified for all drawing objects except simple lines See Chapter 10 Printing for a list of limitations on patterns when printing with PostScript A line color can be specified for all drawing objects except imported pictures The two Pen popup menus are used to select a thickness and a line color The dash pattern of a line is selected using the Dash popup menu Choose Other from this menu to design your own dash pattern and add it to the Dash menu The line thickness and dash pattern can be specified for all objects containing line
34. Publisher in the Subscriber Options dialog box Choose Subscriber Options form the Edit menu to see this box or double click the Subscriber while holding down the option key If you have resized a Subscriber or rotated it Go to the Subscriber Options dialog box and check Original size and orientation to go back to the original subscriber Plotting pro Fit generates graphical representations of functions and data sets inside drawing objects called graphs The coordinates of the data points are stored in the graph with double precision and can always be recovered from it A graph can have various components read more about this later in this section The most important of these are its coordinate axes A graph can have multiple x and y coordinate axes which can have different ranges and scalings A graph always maintains two special coordinate axes which can never be deleted This are the main coordinate axes and are called X1 and Y1 The other axes are called X2 X3 Y2 Y3 and so on The axes can have linear scaling logarithmic scaling 1 x scaling or probability scaling 8 The linear scaling type is the standard scaling type It indicates that there is a linear 3o relationship between the coordinates of the graph and your paper 4H OL 010 A logarithmic scaling indicates that there is a logarithmic relationship between the E Ff coordinates of the graph and your paper it expands the lower end of an axis and 51
35. Publishers and Subscribers are discussed in the following section Drawing This section describes the general drawing commands and the use of the tools palette General drawing commands General drawing commands apply to all types of drawing objects These commands are probably already known to you if you ever used any drawing application Here we shortly review them one by one Drawing and Plotting 7 3 To select an object in the drawing window 1 Choose the arrow tool in the tools palette by clicking the box containing the arrow symbol 2 Click the object you want to select A selected object has four small black rectangles selection handles at the corners of its va enclosing rectangle a To select multiple objects you can either click on the desired objects while holding down the shift key or you click into an empty part and drag the mouse to generate a dotted selection rectangle every object enclosed by the rectangle will be selected Click on an object while holding down the shift key to deselect it To move an object 1 Click the object and hold down the mouse button 2 Drag If you hold down the shift key while dragging movement is constrained to horizontal or vertical directions If you hold down the command key while dragging movement is constrained to diagonal 45 directions In MacOS 7 5 and later or if you have the Drag and Drop extension installed you have a few more options availa
36. Sets the fill style of the next plotted curve To fill the area between the curve and an x axis or an y axis set whichAxis tO xAxis or yAxis respectively axisID specifies the index of the axis To disable curve filling set axisID to 0 A call to Set CurveFil1 affects all subsequent calls to opencurve and OpenDataSet calls SetData procedure SetData row column longint ex extended External modules only Sets the value of the specified cell of the current data window to ex SetDataPointStyle procedure SetDataPointStyle style integer size extended thickness extended Sets the default data point style This style is used for all subsequent plotting of data points style defines the shape of the data point 0 pixel the smallest point 1 17 0 1 2 3 4 5 6 7 8 X BO 0 9 10 11 12 13 14 15 16 17 OAAW TH a 1 8 the eight custom points in the last row of the point style menu size is the size in points size is the size of the point in pixels thickness is 0 0 25 or 0 5 or 1 0 Use 0 if you want to automatically use smaller lines for smaller points Points can be simple or composite A simple point consists of a single symbol such as the styles 0 13 above Composite points consist of two symbols a foreground and a background one plotted on top of each other such as the styles 14 17 above SetDataPointStyle sets the foreground symbol or if a composite point is used both foreground and backg
37. This will be the data window that is closest to the front Example the Spline function uses the data window that is closest to the front e The commands for curve fitting and for plotting data display dialog boxes where you can choose the data window from a pop up menu Examples Plot Data and Nonlinear Fit The data window containing the data used in a particular operation is called the current data window in this manual The current data window is either the foremost data window or the window you have selected yourself When a data window is used as the current data window by a function or by some commands four of its columns can have a special meaning They are the default x y Av and Ay columns You can define these columns using the pop up menu that appears when you click the column number of a data window while holding down the command key For example the Spline function uses the data in the x and y columns of the foremost of all the data windows other windows of a different kind e g a drawing window can be active A small x y Ax or Ay in the head of a column marks the default columns Working with data 4 11 5 Working with functions Functions supported by pro Fit are of the form y f x and can have one or more parameters You can use these functions for fitting plotting and analysis This chapter gives an overview of what you can do with functions pro Fit has a set of b
38. a Click New Preferences file to create a new preferences file All the settings and extensions stored in the current preferences file are copied to the new preferences file Click Use Preferences file to switch to another existing preferences file pro Fit will scan the folder of the selected preferences file for a folder called pro Fit modules If it finds such a folder any modules stored in this folder are loaded into pro Fit For a more complete discussion of the pro Fit modules folder see Chapter 5 Working with Functions Preferences 13 5 14 General features Getting help pro Fit offers a powerful on line help based on Apple Guide The pro Fit Guide can be accessed by choosing pro Fit Guide from the help menu or by clicking one of the question marks that are present everywhere in pro Fit windows and dialog boxes Balloon help is also supported When defining functions and programs there is a special feature based on a dedicated help menu which is always present in the header of function windows See chapter 9 Defining functions and programs for more information on this help menu Help balloons Switch on balloon help by choosing the Show Balloons command from the Help menu Once you have switched on balloon help helpful comments show up whenever you move the mouse over some interesting item Choose Hide Balloons from the Help menu to switch balloon help off Help Balloons can be switched on locally fo
39. a program use the commands Start Recording and Stop Recording from the Customize menu To record an Apple Script use a scripting application such as Apple s Script Editor The built in programming syntax has undergone major improvements Complex numbers are now fully supported in function and program definitions Arrays and strings are also available All predefined functions work with complex numbers Parameters can passed as var Many new commands have been added for fitting plotting and other operations making every single operation of pro Fit 5 1 accessible by a program Most of the new commands use named parameters i e a name precedes each parameter this lets you omit parameters if you want to use their default values Function parameter sets can be managed in a much more flexible way in pro Fit 5 1 Function parameters can now be stored with the function definition with the function code or with any other file they will become available automatically when a function is added to the Func menu New special purpose fitting algorithms for linear regression and polynomial fit are available Data windows can now have up to 16 million rows and columns as long as sufficient memory is available A command Print Preview in the File menu lets you preview how your data tables functions and drawings will look in print New features are provided for editing graphs Axis labels can have a common prefix and p
40. addcont inuously add to present selection extending it continuously addDiscontinuously add to present selection extending it discontinuously deselectIt deselect the specified rows SelectRows procedure SelectRows top bottom longint select Boolean Obsolete Use Select Row instead Selects all rows between top and bottom if select true deselects them if select false If there are selected rows outside top bottom they remain selected SelectTop function SelectTop longint Returns the row number of the topmost selected cells of the current data window or 0 if no cells are selected Causes a run time error if no data window is open External modules must use Get Selection SelectWindow procedure SelectWindow wind String or Longint Moves the specified window in front of all other windows wind is the windowID or the name of the window A 54 Appendix A Predefined functions procedures and arrays SetArrowStyle procedure SetArrowStyle location integer style integer size extended Specifies the default arrow style for lines and polygons location defines if you want to change the style of the arrow at the beginning of the line Location 1 end 2 or both beginning and end 3 Set style to 0 if there should be no arrow at the specified location Set style to1 12 to select the arrow style corresponding to the entry in the arrow style popup menu style values from 1 to 6 correspond
41. and shift in order not to load the standard preferences file Another commonly used shortcut is typing a period while holding down the command key This is equivalent to typing the escape key and it interrupts most of the calculations Use it to stop the plotting of a function to stop fitting to cancel printing or to interrupt lengthy calculations The combination Command key period is also interpreted as typing Cancel in dialog boxes The escape character is also interpreted as Cancel Return or Enter are always interpreted as clicking the outlined button 14 8 General features Appendix A Predefined functions procedures and arrays When programming in pro Fit you can use a large number of predefined functions and procedures The first part of this appendix gives a short list of these functions and procedures ordered in functional groups The second part of this appendix provides a full description of each function or procedure in alphabetical order Note that the pro Fit compiler ignores upper lower case i e Set ColumnName is identical to setcolumnnamE An exception to the above rule applies when you call other functions or want to execute menu commands In that case the strings you specify for the names of the functions or menu commands are case sensitive All the predefined functions and procedures described here are also available to external modules In some cases to avoid conflicts with the names of Mac O
42. and to select the type and size of the arrow s use the arrow pop up menu in the tools palette To smooth polygons 1 Select the polygon you want to smooth 2 Choose the appropriate smoothing method in the Smooth submenu in the Draw menu The two possibilities for smoothing can be seen in the figure below You can either select a standard B zier curve that does not touch the corners of the polygon or you can select a smoothed curve that goes through all the corners of the polygon Mow My An unsmoothed polygon and its two smoothed versions To reshape polygons 1 Select the polygon you want to reshape 2 Make sure it is in reshape mode If the selection marks of a polygon appear at the corners m m of its enclosing rectangle the polygon is not in reshape mode If the selection marks appear at its corners it is in reshape mode 3 If the polygon is not in reshape mode choose Reshape from the Draw menu double click it or type the Enter key This puts the polygon into reshape mode To move one of the corner points of a polygon click and drag it To remove one of the corner points click it while holding down the option key To add a corner point click a line of the polygon while holding down the option key Note that you can only add points to unsmoothed polygons 7 8 Drawing and Plotting Points When plotting data the data points are represented by special symbols You can create such plot symbols manua
43. are visible Graph size The horizontal and vertical size of the graph length of the coordinate axes Graph coordinates and zooming Normally you can look at coordinates and analyze data sets and function using the Preview window However options similar to the ones available in the preview window although more limited can be used when editing graphs Hold down the command and option key simultaneously and click and 4 0 41 y 0 80 drag over a graph object the graph must not be part of a group pro Fit displays the mouse location in the main axes coordinate system The coordinates are displayed to the right of the cursor and in the bottom left corner of the drawing window If you now press the shift key you can select a part of the graph The ranges of the graph will be changed to display only this part This is useful for zooming in on some part of the plotted data set 7 34 Drawing and Plotting 8 Fitting This chapter describes what pro Fit does when you perform a fit Fitting the parameters of a function to a data set roughly means finding those parameters that make the function s curve follow the data points as closely as possible There are various possible definitions of the term as closely as possible The correct definition is often determined by the origin and characteristics of the data set to be fitted For example a data set might be subject to large errors in the x coordinate and to smaller er
44. be varied Pass 2 for varying xMin 1 for varying xMax however these two options hardly ever will make sense from Real The start value of the parameter to be varied to Real The end value of the parameter to be varied step Value Integer The step for increasing the parameter subintervals Integer The number of sub intervals to be searched in the x interval When the function s sign changes over a sub interval the sub interval is searched for a root A 68 Appendix A Predefined functions procedures and arrays y Value Real The desired y value Omit or set to 0 if finding the x value where the function becomes zero See also Root Tan function Tan x extended extended Returns the tangent of x tan x sin x cos x Tanh function Tanh x extended extended Returns the hyperbolic tangent of x tanh is defined by X X e e sinh x tanh x a e e cosh x TenTo function TenTo x extended extended Returns 10 to the power of x tento x 10 TestData function TestData row column longint Boolean External modules name See Dat aOK TestStop function TestStop Boolean External modules only Returns true if the current operation should be interrupted because of user wish or pro Fitwish TickCount function TickCount extended Returns the number of 1 60 seconds since your computer was started It can be useful for timing your programs or f
45. column pop up menu to select the column that contains the x values of your data You can only select one x column at a time Use the Y columns list to select the columns that contain the y values of your data You can select multiple columns by holding down the shift key while clicking To plot only part of the data in the x and y columns check Selected rows only In this case only the data in the currently selected rows will be used for plotting To use this feature first select the rows you want to plot in the data window or with the help of the Preview window and then choose Plot Data from the Draw menu Use the Point style pop up menu to select a plot symbol If you are plotting multiple data sets only the first set will be drawn with this symbol The symbols of subsequent sets are chosen according to the current graph style See section Styles later in this chapter for further information about graph styles Check Connected if you want to draw connecting lines between your data points The data points will be connected according to the order in which they appear in the data window not in ascending order of x values If necessary use the command Sort in the Calc menu to sort your data before plotting 7 20 Drawing and Plotting Graphs and legends graph When you plot data or functions you create a graph object and a legend object 2 0 y x05 Graphs and legends are the most o data important drawing objects 1 0
46. compiled as la gt x and b gt y U Use brackets to clarify what you want a gt x and b gt y Note In contrast to some other programming languages all the expressions in a composite logical expression of the form condition l and condition2 and condition 3 will be evaluated even if condition 1 returns false Function definition syntax If you want to define a function of your own to use it for fitting or plotting you must write a function definition The structure of a function definition is the same as the structure of a program definition but it can optionally contain additional information about the parameters and the contents of the parame ters window This additional information is placed right at the beginning of the function definition A function definition starts with the keyword function instead of program Then follows optional information on the parameters and the parameters window 9 20 Defining functions and programs function myFunc function myFunc ampl freq real description textl text2 parameters 4 defaults appl jsetl 2 aGkive a 2 3 0 inactive name a 3 2 0 constant a 4 1 active i 0O INF defaults ampl 1 2 active fregq 3 0 constant const Cue D9 OES var temp extended myVar t integer the name of the function myFunc will appear in the Func menu optional definition of parameter names that will be used to access parameters in
47. cr mre a a aae a Ee A en rene tree eer 21 Editing legends x rec ska hte aa ea tesa Pec a edd a a aa a aa aaa 21 Editing graphs sin a A eee aor erree tt tree 22 LA E ce E E E E E E E E A 23 Curves and data points chee ect Sat eae Baas aes eaet carat eset 29 vi Table of contents Grid 32 Graph VSG ninian tat ccc lata me SS tl ah al aeaaaee aodannan anai 32 Graph coordinates and ZOOMING ascceiicssstocecseccececot teven dpe crascsncdsaiespeibeaediceenuemteeeraatanss 34 FIUNO eiiie e a a tad E E a E a a aaae AEA SEEE 1 Mathematical DaCKG round fc x cat tec tale ie eet chan Ae tical eee at 1 Distribution functions and Gata WeEIQNKS c ccecceeeeeeeeceeeeeeeeeeeeeeeeeeeeesaeeeaeeeeeeteaeeeaes 1 The mean square deviation Chi SQuared eceseceeceseeeeseteeeeeeeeeeeceateeeeeeaneeeaees 4 ZO PC IOUS wie rected es AE cae Peete Raa tse ee ince ative ee Sat en ee eet Se 4 The usual case Chi squared and zero X E rrOPs csccsceecceceeeceeeseeeseeseseeneeaeeaes 4 Error analysis and Confidence intervals ceccecccceceeeceeeeeeeceeaeeeceeeaeeeseeeeeeeeeeteseeeates 5 Fitting algorithiniS e aa aaaeeeaa a annA EEE ar aaa Ea AE 5 THe Monte Carlo algorthM cisien aa aaa a a a aaa 6 The Levenberg Marquardt algorithm ccescceeceeesceeeeeeeeeeeeeeaeeeeeeesaeeeaeeeneeeeeneaees 6 Peat ath Gti V ey GS acct cas cos tsetse hacer iste etc cos a at Mele es lee eei ce acne 7 Estimation of parameter SrrOrsy ices cect ee
48. current data window contains a numeric value returns false if the cell is empty if it is part of a text column or if it lies outside the data window Use this function before reading a data cell Example if DataOK i j then myVariable data i jl DataOK Causes a run time error if no data window is open The external module name for this function is TestData Appendix A Predefined functions procedures and arrays A 21 DateString function DateString format integer String Returns a string with today s date format defines the formatting of the string and can take the following values shortDate 1 31 92 abbrevDate Fri Jan 31 1992 longDate Friday January 31 1992 See also TimeString DeactivateProFitWindows procedure DeactivateProFitWindows External modules only For advanced programmers only Deactivates all of pro Fit s windows and disables all menus Call this routine before showing a window or creating a dialog Each call to DectivateProFitWindows must be matched with a call to ActivateProFitWindows Delete procedure Delete s String first length integer Deletes 1ength characters in s starting from character first To delete all characters until the end of the string pass 255 for length Example s hi there Delete s 4 2 WriteLn s writes hi ere DeleteAxis procedure DeleteAxis whichAxis integer axisID integer Delete
49. decimal point Fixed exponent Use the Font field to specify the text font size and style to be used for the labels of the current axis The Location popup menu defines where the labels of an axis are above graph drawn The edit field to its right defines the distance between the labels above axis and the axis or the frame of the graph The value in this field is in points below axis 1 72 inch or 0 35 mm Note that it can also be negative Click Lines to change the appearance of the lines used for drawing the axis and its tick marks and to set the position where the tick marks are drawn The inner part of the dialog box now looks like this 7 26 Drawing and Plotting General Labels Prefix Lines Axis line style JIE Ticks location top Kiajor ticks Minor ticks Use the Ticks location popup menu to set the position of the tick marks In the Major ticks and Minor ticks fields you can set the line style length and color of major and minor tick marks The line style used to draw the axis can be edited using the Axis line style popup menus All the options outlined above for editing axes let you create many different kinds of graphs Note that you can create new axes and change their scaling tick marks etc also if you don t use them to plot any curve For example you can uncheck the Same as X1 check box 400 101 102 103 in the X2 axis panel and edit it to reflect a completely 1 0 different sca
50. e ParamName holds the name of a parameter as it appears in the parameters window e ParamArray ParamModeArray and ParamNameArray are the arrays with the parameters values modes and names e DefaultParamInfo contains all the arrays with the initial values limits modes and names of the parameters e ExtModulesParamBlock This record contains low level parameters to be passed between an external module and pro Fit In most cases you will not need the information stored here There are only two fields that you might find useful v and globals These are described in the following section Global variables e globalScratch A pointer to a data area shared by all modules internally defined functions and programs as well as external modules From programs and functions defined within pro Fit you can access this area through the predefined array globalData 0 99 e moduleFile A file specifier for the file that the module is in You can e g use this specifier for accessing a resource stored in your module Global variables Global variables or static variables as they are often called by C programmers are variables that remain statically in memory Their values are preserved between individual calls to your module 10 12 Working with external modules If you are programming for the Power Macintosh you can define global variables in the way you are used to In Pascal you declare them globally within your
51. end Using Windows and Documents NewDataWindow NewFunctionWindow NewDrawingWindow GetWindowID FrontWindow FrontmostWindow GetWindowType SetCurrentWindow GetCurrentWindow NextWindow GetWindowTitle SelectWindow OpenFile SaveWindow GetFileDirectory SetDefaultDirectory CloseWindow DataImportOptions DataExportOptions SetWindowProperties Compile DoScript PageSetup Print GetResult fittedParameter i open a new data function or drawing window obtain a unique identification number for a window from its title obtain the ID of the document window in front of all others check if a window is a drawing window a data window or a function window change the window currently used for program input output access the title of a window Bring window in front of all other windows open a document and put it inside a new window save a window s contents into an existing or a new pro Fit document Get the directory where a given file resides Set the default directory used to save files without a full path name close a window set the format for loading and exporting text files Set the info text size title position etc of a window compile run the contents of a function window specify document format and print A 10 Appendix A Predefined functions procedures and arrays Note Windows are usually accessed by window ID A window ID is a unique long integer
52. evaluate Return the value of a regular Pascal expression evaluate string the expression Result real the result of the expression integrate finds the integral of the given function integrate reference the function to be used xMin real lower bound of the integration interval Apple Script 11 9 xMax real upper bound of the integration interval iterations integer number of iterations used print results boolean true if comments are to be printed in Results window inverse FFT inverse Fourier transform from complex to real numbers see also FFT inverse FFT window the data window inputColl integer input column 1 real part or amplitude in frequeny domain inputCol2 integer input column 2 imaginary part or phase in frequeny domain outputCol integer output column data in time domain reallmaginary boolean true if input columns contain real and imaginary parts false if amplitude and phase outTimeCol integer time output column calculated from frequenyInterval frequencyInterval real frequency interval between input data points print results boolean true if comments are to be printed in Results window load parameter set Loads a saved parameter set load parameter set string the name of the parameter set Omit to load all parameter sets of the given function for string name of the function the parameter set belongs to omit for global sets from alias the file from which
53. expressions as parameters They will be written into the Results window Example Write x value is x Note The format fields of standard Pascal x y after numerical values or x after all other values are not supported The number of digits after the decimal point for the write and writeln procedures can be specified by choosing Preferences from the File menu Use SetOptions decimals for setting it from a program or function You can redirect the ouput of Write to a text file using the routines CreateTextFile and WriteToTextFile Writeln procedure Writeln string or expressions This procedure writes strings and numbers into the Results window Then it moves the insertion mark to a new line It uses the same parameters as the procedure write Example The following writes the value of the top left data cell of the current data window into the results window Writeln data cell 1 1 data 1 1 You can redirect the ouput of writeln to a text file using the routines CreateTextFile and WriteToTextFile WritelnString procedure WritelnString s Str255 External modules only Writes the string s to the results window and starts a new line WriteNumber procedure WriteNumber r extended External modules only Writes the number r to the results window A 70 Appendix A Predefined functions procedures and arrays WritelInt procedure WriteInt n longint External modules only Wr
54. freq phase real begin y ampl cos freq x phase end If you do this parameters retain their numbering defined by their sequence when you define them ampl freq phase The a i remain available as synonims a 1 ampl a 2 freq a 3 phase and the parameter numbers can still be used in predefined function such as SetParamName Example 1 You want to define the function y a In a2 x2 Your definition looks like this function logSquare begin y a l sqrt a 2 cosh x end This is a function in its most simple form If you work with it often you may want to assign default values to the parameters You will also see that a2 should not be negative You might therefore improve the above definition as follows function LogSquare defaults afl 1 active al a 2 1 active a2 0 INF begin y a l1 sqrt a 2 cosh x end The first line after the keyword defaults defines the default value default mode active means that it will be varied in a fit and name of aj The second lines defines the default value mode and name as well as the lower and upper limit of a2 Example 2 You want to define the function 1 00 7 y a sinc x x a2 sinc x x2 ao with sinc x sin x x Loa lI a 20 0 20 The value of the function sinc is not defined for x 0 but it converges to 1 for x gt 0 When calculating sinc we must test if its argument is 0 to handle this special
55. from the Customize menu A submenu lists all the functions and programs that can be removed from the menus Select the name of the function or of the program you want to remove Note you cannot remove any of pro Fit s built in functions Spline Polynom etc Loading modules automatically on startup Imagine you have one or more modules or Apple Scripts that you use often You can make them available automatically whenever you start pro Fit Put the modules you want to add permanently to pro Fit into a folder named pro Fit Modules This folder must be located in the same folder as pro Fit s or in the Preferences folder of your System Folder When you create the folder pro Fit Modules type the name exactly as given here otherwise pro Fit will not find it Whenever pro Fit starts up it checks if a folder named pro Fit Modules is located in the same folder as the application itself and tries to load all modules it finds there Then pro Fit looks for a folder pro Fit Modules in the Preferences folder of the System folder and again tries to load all modules it finds there If you are running pro Fit directly from a server the modules found in the pro Fit Modules folder in the application folder on the server will be available to all users the modules in the pro Fit Modules folder of your system s Preferences folder will only be available to you Loading a set of modules together with a new preference
56. in the data window will be rearranged according to the new order in the sort column To order only the selected part of the data window check Selection only Note that you can only sort by columns that contain numerical data You cannot sort by columns that contain text Transposing data The command Transpose in the Calc menu exchanges the rows and columns in the active window It automatically resizes the data window to make sure that all the data fits into it Statistical analysis of a data set The command Statistics in the Calc menu lets you calculate statistical data of a one dimensional data set Statistics id Single column population in millio All columns C Selected rows only Selected cells ki Basic information data sum mean variance standard deviation mean absolute deviation ki Median Minimum Maximum ki Skewness and Kurtosis Working with data 4 7 The data set that will be analyzed by the statistical algorithms can either be a Single column use the popup menu to define it All columns or only the Selected Cells If you specify a single column or all columns you can check Selected rows only to only use the data in the selected rows The following statistical values are calculated from a set of data x1 xN and are printed to the results window e The number of valid values N in the data set e The median of the sorted data set central value for odd N or average of the two cen
57. into the drawing window each line is converted to a text object If your original text contains tabulators pro Fit will use them as column delimiters to order the text in a table Ungroup the resulting text group if you want to edit the position of the columns You can set the justification of a text object right justified left justified or centered by using the align commands in the Draw menu left right center horizontally The default justification is centered If you have several lines of text objects use distribute in the align menu to make equidistant lines you can set the justification of these texts and then group them They will preserve their justification when the group is resized or the texts are changed within the group by double clicking them If your text object is part of a group object it is not resized when the group is resized If you want to resize the text objects within a group you must hold down the command key while resizing the group Kerning and ligatures Typesetters often use a special technique called kerning to make text appear more regular During kerning letters with a lot of white space between them such as a o following a T are moved closer to each other Furthermore some characters will be transferred into a single character when following each other fl will e g be turned into fl Trifle Trifle Text without kerning and ligatures left and with right When you have QuickDr
58. is the one with the circle in its center the stop button is the one with the square the play button is the one with the triangle To record your actions click the record button pro Fit will automatically generate a Pascal script for nearly everything you do When you have finished recording click the stop button Then you can replay what you did by clicking the play button 99 oe Alternatively you can use the commands Start Recording Stop Recording and Run or Run Selection from the Customize menu If you only want to run a part of a script first select it and then click the play button or choose Run Selection from the Customize menu If you don t select a part of the script before clicking the play button then the whole script is run If there are function or program definitions in the midst of the script they will be added to pro Fit s menus The recorded commands appear at the current insertion point in the text window You cannot edit the text window while it is recording 9 10 Defining functions and programs You can record new commands at any place inside an existing program definition Simply position the cursor where you want the new commands to appear and click the record button Syntax of function and program definitions This section gives a full description of the elements of pro Fit s syntax for function and program definitions Information on how to define progra
59. lower left part of the window gives a short description of the function the lower right part lists some properties of the currently selected parameter What you can do here Working with functions 5 1 editing To change a parameter click its value field and enter the desired value Hit the tab key or the enter key to move to the next parameter copy paste You can copy and paste parameter values between the parameters window and data or text windows using the Copy Cut and Paste commands from the Edit menu If you choose Copy with no parameter value selected all parameters are copied to the clipboard separated by tabulators If you choose Paste with no parameter value selected the text on the clipboard is assumed to contain several values separated by spaces tabs or carriage returns which are then used to change all parameter values limits A parameter can have upper and lower limits which are displayed in the lower right part of the Parameters window These limits are used to constrain the parameter during fitting and function optimization To change a limit of a parameter select the parameter and enter the limit in the corresponding field To remove a limit select the parameter and clear its limit fitting mode To change the fitting mode of a parameter check or uncheck the option Use for fitting in the lower right part of the window If you check this option the parameter will be varied during fitting and optimization othe
60. nrRows of window data or set nrRows of table data pro Fit will automatically cast one class type into the other Note however that there are some situations where the words are not equivalent e g set name of front window to data set name of front table to data The first example sets the name of the front window the second the name of the front most data window Class drawing Window a drawing window access by index or name Properties name string the title of the window lt Inheritance gt base class properties r o Class parameter a parameter of a function Properties name string the name of the parameter value real the value of the parameter min real the minimum value of the parameter or none max real the maximum value of the parameter or none mode inactive active constant the mode of the parameter lt Inheritance gt base class properties r o Class program A program or apple script access by name or index Properties name string r o the name of the column lt Inheritance gt base class properties r o Class row A row in a data window access by index Plural form rows Class textWindow a function or program window access by index or name Properties name string the title of the window lt Inheritance gt base class properties r o Class window a window access by index or name Plural form windows Properties name string the title of the window
61. of iterations the current values of chi squared and the current values of the best parameter set You can see the progress of the fit graphically if you open the Preview Window and check the Show Function check box During a fit pro Fit will periodically draw the function corresponding to the best parameter set This allows you to see how the function approaches the data set during a successful fit Because of this previewing feature you will notice soon enough if the fit is not converging correctly and will then be able to interrupt it If your function performs many lengthy calculations redrawing the function periodically can slow down the fit Hide the Preview Window or uncheck Show Function if fitting speed matters Error analysis and confidence intervals Check Error Analysis in the Fit dialog box to get more information on the confidence intervals of the parameters When Error analysis is checked two more edit fields appear in the Fitting Setup dialog box 8 14 Fitting Fitting Setup Data _ AR bse Nast choice Window Untitled Data 1 O Selected rows only X column column population in milli Error 4 Error analysis Iterations 500 confidence intervals 68 3 ef Print full description O Print active parameters only The Error Analysis algorithm simulates a number of data sets equal to the value specified in the iterations edit field For each iteration the corresponding
62. of the axis Drawing and Plotting 7 17 Check Auto range to let pro Fit automatically calculate the ranges of the axes starting from the y values returned by your function or from the range of the selected data If you plot into an existing graph the ranges of the axes you use for the plot will be extended if necessary from to are the ranges of the axes Plotting a function To plot a function 1 Choose the function you want to plot from the Func menu 2 Set its parameters in the parameters window 3 Choose Plot Function from the Draw menu The Plot Function dialog box appears Plot Function Polynom f Plot into current graph _ Open new window Y axis L Use fitted parameters Steps From Xmin to X max Line _ OFrom i _jto zo The top part of this dialog box has already been discussed above Here we go on to explain the rest of its contents The function can be plotted over the whole given range Alternatively you can specify start point and end point manually using the From to edit items at the bottom left of the dialog box oN IA 1 2 3 4 5 1 2 3 4 5 A graph with its curve from min to max left and a graph created using the From To option If Use fitted parameters is checked the function is plotted using the parameter values calculated in the last fit If Use fitted parameters is not checked the parameter values in the parameters window are u
63. of x such as sin a 2 a 3 they will still be recalculated for each new value of x wasting a lot of time You can evaluate these expressions in the procedure First and store their values in variables used by the main part of the function Another use of the procedure First is to perform some task before pro Fit starts to use a function This is less common for functions defined inside pro Fit but it is often used when defining external modules see Chapter 10 that need to allocate and deallocate memory only used while a function is running The following is a small example of this particular use of First that also demonstrates a possible use of the procedure last function Foo var firstTime boolean datall extended sinDiff extended multiplier extended procedure Initialize begin firstTime true initialize to true end procedure First begin if firstTime then begin the statements in this block are executed only once before any other function call firstTime false datall data 1 1 perform here other calculations that do not depend on parameter values and do not depend on x end sinDiff sin a 2 a 3 multiplier datall a 1 perform here other calculations that do not depend on x but depend on the parameter values end procedure Last begin finished using function firstTime true reset firstTime to true end begin the main part of the function y multiplie
64. parameter given in the optional parameters lowLimit and highLimit See the detailed description of the defaults keyword later in this chapter Once you have successfully defined a function and you have added it to the Func menu you can save it as a module A module is a file that contains the computer code for your function and that can be loaded by pro Fit at start up or at any other time Go to the last section of this chapter for more information on modules Defining programs Programs are generally used to create or transform data in a data window or for scripting pro Fit operations In the following we give some very simple examples of programs In a first step we will write a program that fills the first column of a data window with the powers of two 2 4 8 16 etc 1 Choose New Function from the File menu This opens a new empty function window 2 Enter the definition of your program in the new window Enter the following definition program PowersOf2 var i integer begin NewDataWindow for i 1 to nrRows do data i 1 2 i end Note that a program definition starts with the keyword program followed by its name After that we first have a variable declaration for the variable i which is of type integer The body of our program between begin and end starts with the call NewDat aWindow which tells pro Fit to open a new empty data window Then follows a so called for loop which takes the general f
65. parameter set will be determined by the fitting algorithm you selected either the Robust algorithm or the Levenberg Marquardt algorithm You should always use the Levenberg Marquardt algorithm when performing error analysis Using the Robust algorithm is not recommended because this algorithm is inherently slower than the Levenberg Marquardt algorithm Since error analysis can need thousands of iterations the convergence speed of the algorithm is very important All parameter sets generated during error analysis will be collected and displayed in a data window once Error Analysis is completed You can then use them for a more complete analysis of the distribution of each parameter Based on the simulated parameter sets pro Fit estimates confidence intervals You must specify which confidence interval you want pro Fit to calculate by entering the corresponding probability in the confidence intervals field pro Fit calculates a confidence interval in such a way that the given percent of the simulated parameter values are contained inside it During error analysis pro Fit shows the status of the calculation in its progress window Fitting 8 15 Error analysis ampl 0 269786 0 270562 delay 1 109271 1 109222 type to interrupt The window shows the status of the calculation and the confidence interval estimations based on the currently available data The calculation is a Monte Carlo calculation so the boundaries of each conf
66. parameters standardDeviation standard deviation of fitted parameters nriterations number of used iterations goodnessOfFit goodness of fit nrDataPoints number of fitted data points sumOfDeviations sum of deviations only after robust fit correlation linear correlation between x and y values only after linear fit probCorrelation significance of linear correlation only after linear fit Appendix A Predefined functions procedures and arrays A 27 Pass parameter index 1 based as second argument to GetResult Pass matrix indices 1 based as second and third arguments to GetResult Note The old definition procedure Fit funcName String xCol yCol errCol longint errVal extended selectionOnly Boolean is still supported but obsolete do not use it in new programs FittedParams function FittedParams i integer extended Obsolete Use GetResult fittedParameters i instead Returns the parameter values obtained in the last fit i is the parameter index Causes a run time error if i is out of range or if the last fit was not a successful fit FFT procedure FFT optional parameter list Performs a Fourier transform on a data window Input is a column of real values in the time domain output are two columns of real imaginary or amplitude phase in the frequency domain Parameters window String or Longint Data window specified by name or window ID inputCol Longint Input column outputColl Long
67. sets obtained in every single fit store them in a dedicated data window You can copy them from the parameters window and paste them into a single row of the data window or you can write a small macro a pro Fit program that transfers the fitted parameters directly to their data window See chapter 9 Defining functions and programs to see how to do this An example program for transferring parameter values to a data window is found on the pro Fit distribution disks Using the various fitting algorithms pro Fit provides three different fitting algorithms The Monte Carlo Robust and Levenberg Marquarat algorithms They are described in the preceding section 8 16 Fitting The following sections describe how each of these fitting algorithms is used and what particular options you can set for each algorithm Using the Levenberg Marquardt algorithm To start a fit with the Levenberg Marquardt algorithm choose Fit from the Calc menu after having selected the appropriate function from the Func menu The Fitting Setup dialog box appears with Levenberg Marquardt pre selected in the Algorithm popup menu See the preceding section for a description of this dialog box When you define errors the Distribution popup menu is dimmed and set to a Gaussian distribution The Levenberg Marquardt algorithm can only work if the errors of the data set are normally distributed The Levenberg Marquardt fit stops running when the chi squared deter
68. sum begin sum 0 for i 1 to nrRows do if dataOK i 1 then sum sum data i 1 writeln sum of col 1 sum end tell application pro Fit compile myProg compiles the above definition run program test and runs it end tell copy Copies the current selection to the clipboard copy cut Cuts the current selection to the clipboard cut Note To get the clipboard of pro Fit use get clipboard data export options Sets the options for exporting data as text files data export options mode withtitles withouttitles custom Base format titles boolean Write column titles copyInfo boolean Write info as header lines optimize boolean Optimize text length delimiter string Column delimiter terminator string Line terminator firstLine string First header line Apple Script 11 7 data import options Sets the options for importing data from text files data import options mode withtitles withouttitles custom Base format headerLines integer Number of header lines titles boolean Read column titles copyInfo boolean Read header lines as info delimiter string Column delimiter terminator string Line terminator delete Removes a function or program from pro Fit s menus delete reference The function or program to delete delete program FitFrontWindow deletes the specified program delete function linear deletes the specified function delete p
69. text Then there is a tool that can be used to pick up a color and apply it to another graphic object and a tool that lets you draw the individual data points such as those used in graphs The rest of the tools palette contains popup menus for setting line styles and fill patterns and for choosing the zooming factor of the current view in the drawing window The drawing window can be viewed at zoom factors from 25 to 400 To learn more about these tools refer to the section Drawing later in this chapter Drawing and Plotting 7 1 Coordinates accuracy and drawing info pro Fit uses floating point numbers to store the size and position of the various drawing objects This provides a positioning precision that is much more accurate than any output device printer or monitor This is important because all drawing objects can also be created by a user program If you write a program that produces graphical output then you are likely to need a high precision coordinate system pro Fit gives you just this Any drawing that you generate from a program is produced at very high resolution and it will give optimal results when printed on any output device or when exported to other applications as a picture or a QuickDraw GX shape The precise coordinates of any drawing objects can also be viewed after it has been created using the pro Fit Drawing Info window which will be described later in this chapter Although all coordinates are precise f
70. text formats are ignored when storing your document as an EPS file Typographical formatting styles like Bold Face or Italic are nearly always available in all common PostScript fonts Drawing and Plotting 7 13 There is another point involved in keeping the size of EPS files small and it is again connected to fonts pro Fit does include information on the fonts used in your document but does not include the fonts themselves So make sure that you use fonts that are available to the application to which the pro Fit EPS files are imported An alternative way to generate an EPS file is to choose Print from the File menu and select File as destination If you do this the created EPS file will be much larger but it includes the whole definition of the fonts you use in your drawing A pro Fit EPS file contains a PostScript representation of the drawing for printing and a picture to display on screen called the template The format of the picture template that is included in EPS files can be selected using the PICT options panel of the Preferences dialog box File menu All PICT options can be used except the embedded PostScript option which will automatically be replaced by normal It is advisable to use the high resolution bitmaps only if the high resolution information is really needed Otherwise use a normal picture or a low resolution bitmap because they require less memory PICT Options are discussed in Chapter 12
71. the current data window Then it calculates the conductivity according to our model o s J exp T T function conductivity begin y a l data x 3 exp a 2 data x 2 end Note that data x 3 is the value of the x th cell of the third column in the data window that was chosen for fitting data x 3 is the intensity and data x 2 is the temperature Now we can fit this function to our data We use the first column as its x value and the conductivity column as its y value Before fitting don t forget to set reasonable starting values for the parameters in this case most positive numbers will do The fit returns a 1 2 2 and a 2 330 The general idea of this method is to replace a function f x x9 Xp by a single valued function F x which takes an index as its x value From this index F can find the cells in the current data window where the values xj Xp are stored Once xj Xp are known F can calculate f x Xp Multiple functions with one x value Another special case that we can easily lead back to the form y f x is the case of multiple functions with one x value These functions can share one or more common parameters yl fi y2 f2 x Fitting 8 21 Yq fq One method to transform this problem into a fittable form is the following Let us assume that we have x values ranging between 0 and 1000 We now define a function f of the form fix if x 0 999 _ 1000 if
72. the current pen position and the current pen position is offset to the end of the text theAngle defines the rotation of the text and can take the values 0 90 180 and 270 If docenter is false the current pen position is offset to the end of the string DrawPICT procedure DrawPICT left top right bottom extended thePict PicHandle External modules only Creates a new picture in the current drawing window using the Mac OS PicHandle thePict left and top give left top corner of the picture right and bottom are used to define the size of the picture if they are larger than left and top respectively Otherwise the size is derived from the information given in thePict A 24 Appendix A Predefined functions procedures and arrays DrawRect procedure DrawRect left top right bottom extended Creates a new rectangle with the given borders in the current drawing window DrawText procedure DrawText theString Str255 theAngle extended docenter Boolean Draws a text in the current drawing window The text appears at the current pen position set with MoveTo If doCenter is true the text is centered on the current pen position and the current pen position remains unchanged If docenter is false the text starts at the current pen position and the current pen position is offset to the end of the text theAngle defines the rotation of the text and can take the values 0 90 180 and 270 If docenter is false
73. the current pen position is offset to the end of the string DrawTextLine procedure DrawTextLine theString Str255 theAngle extended docenter Boolean External module name See DrawText Erf function Erf x extended extended The error function defined by 2 2 erf x e dt T Erfc function Erfc x extended extended The complementary error function erfc x 1 erf x Erf and Erfc are also available as PErf and PErfc for external Pascal modules to avoid ambiguities when using the unit fp p which defines erf and erfc Exit procedure Exit Exits a local function or procedure If called in main body of a program or function exits the program or function See also Halt Extrema procedure Extrema optional parameter list Finds the minima maxima of a function by varying its x value within a given interval Parameters function String The function to be used Omit for current function xMin Real The start of the x interval to be searched for extrema xMax Real The end of the x interval to be searched for extrema subintervals Integer The number of sub intervals to be searched in the x interval When the function s derivative changes its sign over a sub interval the sub interval is searched for a minimum or maximum printResults Boolean Set to true for printing the results to the Results window Omit printResults or set it to false for suppressing this To r
74. the fit The Monte Carlo fit slows down exponentially when the number of parameters to be fitted is increased Using the Linear Regression algorithm To run a Linear Regression fit choose Linear Regression in the algorithm popup menu of the fit dialog box This dialog box appears when selecting Fit from the Calc menu and it was described above As the name indicates this algorithm forces you to select the Polynomial function of degree 1 with both parameters being fitted It assumes a Gaussian distribution of errors X errors and Y errors are possible 8 18 Fitting When finished the parameter values and their standard deviations are printed to the results window Additionally the correlation coefficient r is calculated as well as its significance which is the probability that Irl should be larger than its observed value in the null hypothesis x and y being uncorrelated Using the Polynomial fitting algorithm To run a Polynomial fit choose Polynomial in the algorithm popup menu of the fit dialog box This dialog box appears when selecting Fit from the Calc menu and it was described above As the name indicates this algorithm forces you to select the Polynomial function of any degree It assumes a Gaussian distribution of errors Only Y errors are possible When finished the parameter values and their standard deviations are printed to the results window Fitting multiple functions and x val
75. the function code and as a default parameter name in the parameters window optional these two strings will appear in the parameters window optional the number of parameters max 64 optional the default values for the parameters their default mode parameter window name lower and upper limit see the Chapter 8 Fitting If you do not define the defaults for a parameter it will be 0 inactive and limited by INF and INF If you do not define a parameter window name for a parameter its default name will be used The default name is either the name you define in the function header e g ampl or a i optional the definition of constants as in standard Pascal optional variable declarations as in standard Pascal After this you can optionally define your own local procedures and functions Then follows the body of the function definition between begin and end In this body you must calculate the function s y value from its x value and its parameters For this you can use the following variables The input variable the independent variable of the function The output variable the function s return value It must be set by your function The parameters of the function Up to 64 parameters can be used It is possible to define your own parameter names in the function header and to use your own names instead of thea 1 a n Defining functions and programs 9 21 function foo ampl
76. them into their destination using the Subscribe mechanism Another application can import the picture in the Edition Container by selecting Subscribe to from the Edit menu In this way you can be certain that the publication always contains the latest version of your graphs or drawings Whenever the contents of the Edition Container are changed the subscribing application will be informed of the changes and will load the newest version To create a Publisher 7 14 Drawing and Plotting 1 Select the objects you want to publish 2 Choose Create Publisher from the Edit menu The following dialog box appears Preview PH A nice publisher amp Batchi amp Batch ff BullsEye Pe Calc Menu Screenshot Name of new edition Untitled Edition PICT Options Click the button PICT Options to choose the PICT options for the publisher you are about to create By default the current PICT Options are used Find more information about PICT Options in Chapter 12 Printing 3 Select the appropriate name and location for the Edition Container and click Publish to create it In the drawing window a Publisher is enclosed by a gray rectangle This rectangle can be moved and reshaped like other drawing objects The publisher contains everything inside its rectangle Double click the publisher rectangle to see the Publishers Options dialog box or choose Publisher Options from the Edit menu Apart form the standard item
77. there The next two sections discuss these two possibilities separately Printing from pro Fit Before printing you should choose Page Setup from the File menu You can print the active window by selecting the Print command from the File menu pro Fit offers three different modes of printing printing through QuickDraw GX printing with PostScript and printing at the printer s resolution You can select the desired method by choosing Preferences from the File menu In the dialog box that comes up click the icon Printing in the list at the left The dialog box now looks as follows Preferences CI Use Quickdraw GX bef Print drawings using PostScript ki Use Quickdraw for text Preview ki TH Interface If you check Use QuickDraw GX pro Fit uses the features of Apple s graphics environment QuickDraw GX This option is disabled if you don t have QuickDraw GX installed on your computer and it only works on Operating Systems prior to Mac OS 8 Once you have checked Use QuickDraw Printing 12 1 GX printing with PostScript is disabled Note that you must restart pro Fit when you have changed this option For best results on any printer you should check Use QuickDraw GX if you have QuickDraw GX installed on your computer and you are using an older system software If you check Print drawings using PostScript pro Fit sends PostScript commands to the printer together with a simple picture describ
78. to the 6 predefined styles style values from 7 to 12 correspond to the 6 custom styles which appear in the arrow style menu Set style to 1 for leaving it unchanged size The size in points 1 72 inches Set it to 0 for leaving it unchanged The following program draws a bent arrow as shown on the right program OneArrow begin SetLineStyle 5 1 line thickness SetArrowStyle 1 2 20 start arrow style 1 SetArrowStyle 2 20 end arrow style OpenPoly 1 false draw a smooth polygon MoveTo 100 100 LineTo 150 100 LineTo 150 50 ClosePoly end SetAxisAttributes procedure SetAxisAttributes whichAxis integer flags longint Sets various drawing options of an axis in the current graph whichAxis 1s equal to xAxis or yAxis and defines if you want to change the current x or y axis To set the current axis call SetCurrentAxis flags is 0 or a sum of the following constants equalToMain drawAxisLine drawTicks drawMajorTickLabels drawMinorTickLabels plusSideTicks minusSideTicks plusSideLabels labelsOutsideFrame Example SetAxisAttributes xAxis sameAsMaint drawAxisLinetticksPlusSidetdrawTicks SetAxisPosition procedure SetAxisPosition whichAxis integer position extended Changes the position an axis in the current graph whichAxis 1s equal to xAxis or yAxis and defines if you want to change the current x or y axis To set the current axis call SetCurrentAxis posi
79. type FloatColumnHandle handle to an array of 4 byte floating point values if it is doubleColumn colH is of type DoubleColumnHandle handle to an array of 8 byte floating point values if it is textColumn colH is of type TextColumnHandle handle to a record of type StringData To get a column s type call GetcolType You can find more information in the files proFit_interface p proFit_interface h Once you call SetColHandle the handle becomes property of pro Fit do not dispose it colH can either be e ahandle that you allocated yourself In this case the Handle s size must be 4 nrRows 1 for columns of type floatColumn 8 nrRows 1 for columns of type doubleColumn 14 size of all strings for columns of type text Column e a handle that you obtained from Get ColHandle e nil if you want to clear the given column This routine should be used by experienced programmers only Warning Accessing text columns in this way is not recommended The definition of the data structures may change in the future SetColName procedure SetColName col longint name Str255 Obsolete Use SetColumnPropertties instead Changes the name of a column in the current data window col is the number of the column name its new name SetColName Causes a run time error if there is no data window open or if col is outside the bounds of the data window SetColType procedure SetColType columnNumber longint theType longint Obsolete Use SetCo
80. understands PostScript such as a printer of the LaserWriter family The pictures generated with this option still look nice on screen but they also have PostScript information included When you select Embedded PostScript you can specify if you want to Use QuickDraw for Text For best compatibility with the widest range of printers and printer drivers Use QuickDraw for Text should be checked For more information on printing with PostScript see the section Printing with PostScript earlier in this chapter High resolution PICT This option generates pictures that print well on most printers if the printing application supports printing at the printer s resolution and does not change any in formation in the pictures it imports However few applications presently support these features When generating a high resolution picture you must enter the desired resolution in a text field appearing at the bottom of the dialog box High resolution pictures may not look perfect on screen but they use a minimum amount of memory Enlarged PICT Pictures generated under this option are enlarged by a zoom factor z given by the specified resolution r You can enter the resolution r in an edit field appearing at the bottom of the dialog box The zoom factor is given by the formula z r 72 dots per inch You can obtain high quality prints of an enlarged picture on many printers by choosing a reduction factor 1 z in the Page Setu
81. unit in C you declare them outside your functions or if you declare them inside a function you declare them as static If you are programming for a 68k Macintosh there is no easy compiler independent way for declaring static data Some compilers such as Think C provide support for using global data in code resources Some others don t The record ExtModulesParamBlock provides a method for storing global static data that works on all compilers Each external module has its own record struct of type ExtModulesParamBlock A pointer to this record is passed to your procedures and functions in the parameter pb There are some fields in this record that you can use for your own purposes Data stored there is preserved between individual calls to your functions e One of these fields is the array of extended values pb v 1 30 under C this is an array of double values pb gt v 0 29 You can use this array for your own purposes it is not used by pro Fit e The second such field is the pointer pb globals under C pb gt global1s If your procedure Set Up returns a non zero value in the parameter requiredGlobal1s proFit will initialize pb globals to point to a memory block of corresponding block size for more information see the description of the procedure Set Up given above You need to set requiredGlobals if you want to use the pb gt globals pointer For examples on how to use global or static data please re
82. up another dialog box that lets you store your settings in the preferences file or load previously stored settings Printing 12 5 Saved PICT styles jLaser Writer 320 Save PICT style as Delete The upper part of the box lists all styles saved in the preferences file To load a style double click its name To delete one or more styles select their names shift click for multiple selections and click Delete To save your current picture settings as a PICT style type a name in the edit item and click Save If you save a style with the name Normal it becomes the default style and it is loaded whenever you start pro Fit 12 6 Printing 13 Preferences pro Fit offers many possibilities to customize its features You can choose the format for exporting pictures the preferred method for printing you can save your preferred user interface options etc All of these settings are saved in pro Fit s preferences file During start up pro Fit looks in the Preferences folder of the System folder for its preferences file If the file is there pro Fit reads its standard settings from it If the file is not there pro Fit creates a new preferences file You can switch to another preferences file or create a new preferences file anytime later If you do not want to load the standard preferences file in the system folder hold down the option and the shift key while starting up pro Fit Most of pro Fit s settings are controll
83. use one of pro Fit s predefined functions such as abs phase re im see Appendix A To define complex numbers use the predefined function comp1 or the predifined constant ii which fulfills sqr ii 1 All predefined functions in pro Fit such as sin cos gamma erf etc automatically become complex valued functions if they notice that their argument is a complex number and return complex numbers as a result 3 String and char types Use the type Char for representing simple characters String for representing strings of up to 255 characters Example 9 28 Defining functions and programs program StringAndCharTest var c Char s String begin c i x s hi there writeln c writes c writeln s writes hi there s s Joe s now is hi there Joe c s 2 c now is i end Conversion between Strings and Chars is automatic For conversion between Char ASCII values and Integer use the functions Ord and Chr For conversions between Strings and numbers use NumberToString and StringToNumber To access the n th character in a string s use s n In other words strings are arrays of type char The following is a list of the most important functions for working with strings Length Returns the length of a string Pos Delete Find delete a sub pattern in a string UpperString Convert between upper and lower case strings LowerString See Appendix A for a complete list Arra
84. x the partial derivative of which is y a sinh x Calculating sinh x can take a lot of time especially when you are working on a slow computer To avoid calculating expressions twice you can save temporary results in the main part of the function to use them later in the procedure Derivatives function MySinh var t real procedure Derivatives begin dyda 1l t use t calculated in body end begin the function s body t sinh x save sinh for derivatives y a 1l t end Procedure First This procedure is used for advanced programming It is called whenever the parameters of a function have been changed before the body main part of the function is called The body of a function will never be called without first having been called beforehand The procedure first can use the following variables ali sasn The parameters of the function The procedure First is mainly used for accelerating calculations that do not depend on the input value x This can make a fit considerably faster First should calculate all expressions that appear in a function but that do not depend on x Defining functions and programs 9 25 To calculate the mean deviation 7p during fitting pro Fit calculates the function for each data point xj yi This may involve up to several thousand executions of the body of the function definition If your function definition contains expressions that do not depend on the value
85. x 1000 1999 4 f x 2000 if x 2000 2999 etc Now we can enter the x values of our points in the first column of our data window and all y values in the second column The first N rows where N is the number of data points we have for f contain the values of x in column 1 and the corresponding values of y in column two The next N rows where N gt is the number of data points for f contain x 1000 in the first column and y in the second column and so on In this way we have reduced a set of multiple functions to a single function When fitting multiple functions it is very important to specify the standard deviations of the y values of each function The reason for this lies in the fact that the y values for each function may have a different order of magnitude E g f might return values in the order of 1010 while fo returns values in the order of 1 If you do not specify the error range of the y values the fitting algorithm weights them all equally and a given deviation of a data point from the function f has the same weight as a deviation from f2 For most cases however it would be more reasonable to give a stronger weight to deviations from f2 than to deviations from f1 This can be achieved by specifying percentage errors in the Fitting Setup dialog box Multiple functions with multiple x values This is the general case as described in the equations Y1 f1 1 x2 Xpy y2 f2 1 X2 Xpp Yq fq 1
86. x2 Xpq We have a set of q functions Each function has a certain number of x values which do not need to be the same for all functions The functions share some parameters that you would like to fit The solution to this kind of problem is a combination of the two methods explained above We define a single valued function x that takes an index as its argument returns the value of one of the functions fj Jq for given x values xj Xp q The x value of tells a which function of f Ig should be evaluated b for which x values it should be evaluated The x values are found in certain columns in the current data window Example 8 22 Fitting You have two data sets which are described by two functions One of these functions has only one x value called the other has two x values called u and v f1 fou v The functions have some parameters in common The data set for f consists of nq pairs of values t1 y1 the data set of f consists of n gt triplets of values U Vj Y2 You also have error estimates for all y values Avji In order to fit the parameters of all functions simultaneously you must first choose a method of arranging the data sets in a data window We propose to put the x values into separate columns All y values must be in one column since you will need them for fitting As the x value for fitting you create an index k which is constructed from the formula k 1000
87. you have two graphs or rectangles set their size to be exactly equal and overlap them at 100 view one of their borders might be off by one pixel if their position is not exactly the same This is because roundoff errors must occur when calculating their rounded coordinates at 100 view If you set their position to be exactly equal using the Align command or using the Drawing Info window the roundoff errors are exactly the same for the two objects and they do overlap exactly in the 100 view too If you are concerned with precise positioning e g when drawing overlapping lines or placing arrows on the axes of a graph always go to a larger zoom factor e g 400 or have a look at the underlying floating point coordinates You can do this using pro Fit s Drawing Info window Choose Coords from the Windows menu to see this floating window 7 2 Drawing and Plotting Whenever a single drawing shape is selected the Drawing Info window shows its floating point coordinates i e its size and its position in coordinates that make sense for the particular shape which is currently eft Top em selected 5 362 7 355 The first row of the Drawing Info window gives the absolute coordinates on width Height the paper the second row gives the dimensions of the selected shape and 4 092 0 529 the third row gives the angle of its diagonal and its length The last row Angle Diagonal shows the current coordinates of the
88. 01 compresses its upper end The min and max values for logarithmic axes must both be 3 positive 10 1 The 1 x scaling type can be used to plot a function whose y value is expected to be proportional to 1 x If you plot such a function on a 1 x scaled x axis the function is a 24 straight line The min and max values for 1 x axes must both have the same sign 10 L 7 16 Drawing and Plotting 0 99 The probability scaling type can be used for plotting normally distributed data or to gt 0 90 be more accurate their integral If you have a sample of sand and you determined the S 0 50 percentage of grains having a diameter smaller than x plot this percentage as a function a n of x using probability scaling for the y axis If the size of the grains is normally distributed your data points will lie on a straight line With pro Fit you can plot on any one of the coordinate axes contained in a graph you can add new coordinate axes and you can change their characteristics The next section discusses the general options that are always available when plotting Then we discuss the procedures for plotting functions and data sets and finally we describe how to edit and use existing graphs General plotting options Whenever you plot a function or a data set you can choose if you want to plot it into an existing graph or if you want to create a new one You can also choose if you want to plot into an existing d
89. 2 It depends on the degree of freedom defined as the difference between the number of measured points N and the number of varied parameters M If Q is large e g gt 0 1 the fit seems reasonable If it is small e g lt 0 001 there might be something wrong Literature and suggested reading W H Press B P Flannery S A Teukolsky W T Vetterling Numerical Recipes the Art of Scientific Computing Second Edition University Press Cambridge 1992 P L Jolivette least squares fits when there are errors in X Computer in Physics Vol 7 No 2 1993 8 10 Fitting The fitting process General features With pro Fit fitting is a highly interactive process You can decide which parameters have to be varied set their starting values estimates and choose a fitting method You can inspect the fitting process while it is running and interrupt it if you don t like it You can reiterate the process and change fitting algorithms The fitting process starts from the parameter values given in the parameters window You can change these values click the numbers and edit them The window also shows which parameters are to be fitted Only those whose name is shown in bold face will be fitted for these parameters the check box Use for fitting which appears when you select a parameter is checked The following is the parameters window for the function Polynom All parameters will be fitted except the parameter nam
90. 55 offset 14 size 256 requiredGlobals longint offset 270 size 4 v array 1 30 of extended offset 274 Working with external modules 10 11 size 300 N 360 F 240 P dummy Boolean size 1 hasDerivatives Boolean size 1 descrl descr2 Str255 size 512 numberOfParams integer size 2 a0 DefaultParamInfo size 58 paramNo integer size 2 answer integer size 2 x y extended size 8 a ParamArray size 4 dyda ParamArray size 4 globalScratch GlobalScratchPtr size 4 moduleFile FSSpec size 70 end ExtModulesParamBlockPtr ExtModulesParamBlock size 4 ExtModulesParamBlockH ExtModulesParamBlockPtr size 4 The most important constants and types are the following e versionNumber is the current version of the pro Fit interface e maxNrParams is the maximum allowed number of parameters maxParamNameLength is the maximum length of a parameter name for a function e isFunction isProgramare possible types of a module to be returned by Set Up described above e maxNrInputValues is the maximum number of input variables for the function Input Box described below e inputRec is the parameter to the function InputBox described below e checkPAnswer is the type of the return value of the function check described above e ModeType describes the mode of a parameter as explained in Chapter 9 Defining functions and programs
91. Chapter 7 Drawing section Text objects Printing with PostScript PostScript is a language for defining graphical objects It is used by many high quality printers When an application prints to such a printer it can use the built in graphics language of the Macintosh QuickDraw which is automatically translated to PostScript by the printer driver before it is sent to the printer However some information may be lost during this translation To get better results an application can generate the PostScript directly and send it to the printer obviating the need for any translation Check Print drawings using PostScript after choosing the Printing panel of the preferences dialog box to let pro Fit generate PostScript during printing To print drawings with PostScript you must disable QuickDraw GX by unchecking the option Use QuickDraw GX When printing with PostScript you should usually check the option Use QuickDraw for text for best compatibility with most printer drivers and printers If Use QuickDraw for text is checked pro Fit first creates PostScript code for all items of the drawing window except text items and sends this code to the 12 2 Printing printer Then it draws the texts without using PostScript This ensures the correct setting of the font and supports all text styles If you uncheck Use QuickDraw for text text will be sent as PostScript code this option is not r
92. Curve procedure OpenCurve curveName Str255 Opens a new curve in the current graph After having called opencurve calls to MoveTo LineTo Move Line will add segmets to the curve curveName is the name of the curve in the legend Call closeCurve when you have completed the curve DrawDataPoint is not affected by this procedure It will continue drawing point shapes Don t use AddDataPoint between OpenCurve and CloseCurve Note that the parameters to be passed to MoveTo LineTo Move Line are in the coordinates of the current x and y axes Use SetCurrentAxis to set these axes before calling Opencurve OpenCurve Causes a run time error if no current graph is available OpenData procedure OpenData fileName Str255 Opens the given file as a data file The file must either be a pro Fit data file or a text file with valid data The new window becomes the current data window If fileName contains a simple file name the file is loaded from pro Fit s folder If fileName contains a file path the file is loaded from the folder defined in the file path Set fileName to to bring up a dialog box prompting the user for the name A run time error occurs if the file cannot be opened This procedure cannot be called while a function is running If you want to open a text file with custom format use Set Text FileFormat to set the format OpenDataSet procedure OpenDataSet errors integer connected Boolean name Str255 O
93. Custom format is selected you can specify the file format yourself Loading TEXT File Format gt Function or program file Data file Format Custom LI Contains header lines Copy to Info field C Skip Lf Contains column titles Column delimiter Line terminator a eR 0 oft ofr You can import any file where the data is stored as lines of text each line containing the values of a row You can specify one or more characters Column delimiter that separate individual values in a line C 4 Appendix C File formats and the characters Line terminator that separate the individual lines For both column delimiter and line terminator pro Fit gives you a selection of the most common combinations Furthermore you can check Contains header lines for skipping the first line s of the file or to copy them into the info field of the data window and Contains column titles if the file contains column titles in the first line following the optional header lines Sometimes you do not exactly know how the text file is formatted Therefore you may want to have a look at the starting lines of that file by clicking Show contents Pro Fit will show you the following dialog box TEAT File to be Loaded Line offset O a a first col4tvery opo000oooooongverg ooocooooooongyery HE 1 000000e 0 t 1 000000e Stvery textt 12000 4r 2 000000e 0t 1 000000e 9 tshor tyr 3 000000e 0 t 3 1417392 e 04 tayr
94. Function 2 To Menu C Debug Help SJ Const J I function UserFunction begin g alii sintx it inisi alz end Browse au i ee The new function appears under the name User_Function in the menu Func It is automatically selected and the parameters window shows its parameters a 1 a 2 After adding the function to pro Fit you can change its parameters in the parameters window You can plot the function use it for fitting calculate a table of its values etc To view the function in the preview window make sure that the option Show function is checked The above method is an abbreviated way for entering functions you simply enter the function s expression and pro Fit translates it into a Pascal function definition before compiling it In many situations you will however want to write or edit the function definition directly Therefore let s have a closer look at it function User_Function begin y a l sin x ln x a 2 end The first word of our example is function It tells pro Fit that the definition of a function follows The next word User_Function gives the name under which the function will appear in the Func menu The function s actual definition is given between the keywords begin and end The function s value is calculated and then assigned by the operator to the variable y The variable x contains the function s x value and a 1 a 2 etc are the f
95. Returns the cosine of x cosh function cosh x extended extended Returns the hyperbolic cosine of x cosh is defined by e e cosh x z CovarMatrix function CovarMatrix i j integer extended Returns the values of the covariance matrix obtained in the last fit i and j are the indices corresponding to the parameter numbers CovarMatrix returns an invalid number NAN Not A Numter if i or j corresponds to a parameter that was not active during the last fit You can test the validity of the return value using the function Invalid Causes a run time error if the last fit was not successful or if i j are out of range You can check if the last fit was successful by using the function NumFitParams CreateNewGraph procedure CreateNewGraph xmin xmax ymin ymax extended xScaling yScaling integer Creates a new graph in the current drawing window xmin xmax ymin ymax are the ranges of the graph axes xScaling yScaling must be set to either 0 1 2 or 3 for linear scaling logarithmic scaling 1 x scaling and probability scaling respectively Causes a run time error if there is no drawing window or if the ranges or axes styles are inconsistent CreateTextFile function CreateTextFile fileName Str255 longint Creates a text file with the given name and returns a reference number used to identify this file Call WriteToTextFile to redirect the output from calls to Write Wwriteln WriteNumber into this fi
96. S routines the names used in the external modules interface files proFit_interface h and proFit_interface p can be slightly different from the names used in pro Fit s function windows Unless the difference between the names is very small and obvious external modules names are also found in the alphabetical listing at the end of this chapter Some predefined functions provide advanced features and are only available for external modules Routines only available for external modules are marked with a in the following functional groups descriptions To get a fast look at what you can do in a pro Fit program go through the following functional group descriptions To get details on a certain function see the alphabetical list which follows Functional groups Operators addition subtraction multiplication division xx power O Sah equal not equal larger or equal larger smaller or equal smaller lt lt and or logical and logical or not logical not Note that the power operator is a synonym is evaluated as x y x y exp y in x Therefore x must be positive The evaluation of this expression can be rather slow If you want to calculate simple integer powers e g x2 or x3 use expressions such as sqr x or sqr x x Appendix A Predefined functions procedures and arrays A 1 sin cos tan arcsin arccos arctan sinh cosh tanh arsinh arcosh artanh erf erfc
97. SelectBottom GetSelection SelectCell SelectRow SelectColumn RowSelected CellSelected GetColName SetColName GetColType SetColType SetColWidth ColEmpty GetDefaultData GetColHandle SetColHandle information on the selection area and the size of the current data window set the selection and check if a single cell or a row is part of a possibly discontinuous selection obtain and write titles of single columns and other column characteristics obtain column data in a single step from external modules All the above calls access the current data window By default the current data window is the frontmost data window You can make another data window the current data window by calling SetCurrentWindow windowl window Input and output Input SetBoxTitle Ask Alert Write Writeln CreateTextFile CloseTextFile WriteToTextFile Drawing SetLineStyle SetLineColor SetFillColor SetFillPattern SetDataPointStyle SetBGDataPointStyle SetArrowStyle SetTextStyle MoveTo LineTo Move Line DrawLine OpenPoly ClosePoly D with windowID being the window ID of the desired data displays a dialog for entering numerical values show alert boxes these procedures write into the results window open and close text files and redirect the output of the write writeln functions to a text file set the style of future drawing calls produce line d
98. Str255 Presents a dialog box displaying the string s Example Calling Alert Incomplete data opens the following window Appendix A Predefined functions procedures and arrays A 13 Incomplete data _stop J _ox_ If you click OK the program continues if you click Stop the program will be stopped In external modules this routine is called Alert Box AlertBox function AlertBox s Str255 Boolean External module name See Alert In external modules AlertBox is a function and it returns true if the Stop button was clicked arccos function arccos x extended extended arccos returns the arcus cosine the inverse cosine of x Causes a run time error if Ixl gt 1 arcsin function arcsin x extended extended arcsin returns the arcus sine the inverse sine of x Causes a run time error if x gt 1 arctan function arctan x extended extended arctan returns the arcus tangent of x arcosh function arcosh x extended extended arcosh returns the inverse of the hyperbolic cosine of x Causes a run time error if Ixl lt 1 arcosh is defined by arcosh x In x x 1 arsinh function arsinh x extended extended arsinh returns the inverse of the hyperbolic sine of x arsinh is defined by arsinh x In x y x74 1 artanh function artanh x extended extended artanh returns the inverse of the hyperbolic tangent function of x Causes a run tim
99. The parameters window also displays the default values for the parameters A xo to and const Starting from these parameters pro Fit can find a better set of parameters for describing our data But first you must define which parameters you want to fit i e which parameters you want to vary in order to approximate the data with the Exponential function As mentioned above the starting time xo is arbitrary Let us set it to 1940 2 Click the number beside xO in the parameters window and enter 1940 This defines the parameter s value Since xg is arbitrary we do not want to fit it 3 Uncheck Use for fitting The check box Use for fitting can be found in the lower right area of the window The parameter name changes from bold face to plain text This indicates that this parameter is constant and will not be fitted Shortcut You can also toggle the option Use for fitting by simply clicking on a parameter s name 4 Click the parameter name const We don t want to fit this parameter either The parameter name is not bold anymore and the option Use for fitting is unchecked now Before fitting it is a good idea to assign starting values to the parameters that are going to be fitted in our case A and fg This increases the speed of the fit and the probability of finding the best set of parameters 3 8 Getting started Reasonable starting values for our problem can be estimated easily
100. a a aa a a a 3 SLAM PIING Pr Oral sass tact side Satan ES E cats cuales AS T EE E E ST 3 Entenng tedata We memmenpner ager mar ior a apm ate earner e aren aN rr creeper Se eR Reyer oer nr 3 Plotting TVG Gl eae arayana a ceva aa Vane ca atic ran as AE A acre dass a Ra aE steals 5 A function to fit our data arrest cttencstectates cath aeanseas obs anteavane aa aan ease ne 7 Intermission Previewing the data and the fUNCTION ccseeeceeeesteeeesseeeesseteeeesees 9 e setae E T A irea eae tga aaa 10 Defining YOUR OWI TUNG GINS oe yh certo tecirecetatiastatalctaserttce uel a a a a N 12 Writing programs issia telah eg ate he ga tact BGR a tated cela aie 15 Working WH ata i wicste iis stainat tdawicccuu atu vind tants rdanetabevedduvadeuanreretsneeitancunten 1 BEIER A E E A m re 1 The data WIN OW Sacha tecttarebatinns sscch teaduttutedeteoviaetiu bedsnvhuuctcin divas theses anesthe futons taut Auesiutte 1 SSIS CHIC Cheat choise Sash Santer T aula esa sa EE A east a E SEE 2 EY NSS aeina a a ed ctl ate Noa 2 EVI Ko E i re acer EE E E E E E 3 Data transtormation wean an nA AA AA a a on a a aataid 4 Algebraic transformations ouceatisccatehs neha ae cmdaaner i Conaten adialemateeniuealenm ancy Gens 4 Userprogra mS ereenn a ern niet ne Een nee a pe NORTE a NOG Aine rr errr 6 PATER KES LULANTA EAEE E wt ced bc accu cls eames eandois A gu vet ec ate T 6 SOMME A eA S ale Be nc E AE alae ddan iad ach abba basta ecebtbustt 6 Transposing datata maes
101. ach row in the table there must be a one to one relationship between the values in the x y columns and the values in the error columns The Distribution popup menu which appears when you define errors gives the error probability distribution that will be assumed for the fit This popup menu is dimmed if the Levenberg Marquardt algorithm is used because this algorithm only works with Gaussian error distributions The check box Use last choice tells pro Fit to use the data window and error settings of the previous fit This feature is rarely used but it makes fitting easier when you have to fit the same data columns several times but want to work with other data windows before and after a fit The results of the fit are shown in the results window Check Print active parameters only if you only want to see the values of the parameters that were fitted Use this option if your function has many parameters that you do not fit and you do not want all the values of inactive or constant parameters to clutter the results window Check Print full description to get for each fit a header that describes the settings that were used for fitting Check Error Analysis if you want to obtain more information on the accuracy of the fitted parameters Confidence intervals for each fitted parameter will be determined by a Monte Carlo method that simulates a large number of fits with a series of synthetic data sets More about this in the Error Analysis section b
102. acters Use this option if the corresponding variable is to be entered by means of a pop up menu or a check box If the title starts with SW orel VS Cie aug i SPxxxxS si Come Example a pop up menu with a list of all data windows is used Initialize the variable for the window to 0 or the reference ID of a data window before passing it to Input On return it contains the reference ID of the selected window a pop up menu with a list of a columns in a data window is used If there is a popup menu with data windows in the same dialog box then the columns of the selected data window are shown otherwise the columns of the current data window are shown a pop up menu with user defined items is used The items are defined by string xxxx terminated by xxxx recognizes the metachars defined for the Mac OS routine AppendMenu e g use semicolons to separate the items in xxxx a check box is used It is unchecked if the variable is 0 checked otherwise The returned value will be 0 unchecked or 1 checked Input SWwindow w SCdata column col SPyes no maybeSdo it fuzzy brings up the following dialog box Window Data 122 3 data column Limitations You can only specify one data window pop up If you have a data window pop up as well as one or more column pop up menus the data window pop up must appear before the column pop up InputBox function InputBox nrArgs integer var r In
103. ad Runs a statistical analysis on the numbers in the current data window The results of the calculations can be accessed using the routines GetBasics GetMedian and GetSkew CalcStat returns false if an error occurred true if the calculation completed correctly Set column to 0 to include all columns set it to 1 to use the current selection Set selRowsOnly to true if you only want to analyze the currently selected rows Appendix A Predefined functions procedures and arrays A 15 If you consequently want to use the results of GetBasics set withBasics to true If you want to use the results of GetMedian set withMedian to true If you want to use the results of GetSkew set withSkewAndkKurt to true CallFunction function CallFunction name Str255 x extended extended Calls a function from the Func menu name is the name of the function as it appears in the menu This parameter is case sensitive Pass an empty string to call the currently selected function x is the x value passed to the function CallFunction causes a run time error if the specified function does not exist Example k CallFunction Polynom 1 23 m CallFunction 0 k is set to the value of the built in function Polynom at x 1 23 using the parameters as given in Polynom s parameters window m is set to the value returned by the currently selected functions at x 0 If you want to set a parameter of the function before calling it use SetFu
104. agrees to secure and protect the pro Fit software package the documentation and copies thereof from copying except as permitted above or from modification and shall ensure that its employees or consultants do not copy or modify the product 5 Ownership The Publisher represents that it has the right to grant the licences herein granted 6 Limited Warranty Whilst all reasonable efforts have been made to test the software and user manual prior to first publication the authors and Publisher welcome corrections being brought to their attention The liability of the Publisher in respect of any defect error or omission in the disk user manual or software defective material and in respect of any breach of warranty or condition is limited to the purchase price paid by the customer The Publisher shall have no liability whatsoever arising out of any defect error or omission or breach of warranty or condition unless the customer shall have returned the defective material to the Publisher within 90 days of the date of purchase In that event the Publisher shall as requested by the customer either replace the defective material without charge or refund the purchase price paid by the customer in respect of the defective material The Publisher or the authors or copyright holders shall have no further or other liability including without limitation in respect of damage to other property or in respect of any economic or consequential loss of w
105. ain axes coordinate system Use this field to change the position of a horizontal or vertical axis with respect to the vertical horizontal main axis coordinates The position is set by default to the minimum and maximum bounds of a plot when it is first created 1 0 1 0 0 1 0 0 0 2 0 4 0 6 0 0 0 2 0 4 0 6 0 Two graphs with different vertical positions of the horizontal axis If the dialog box does not show the main axis X1 and Y1 are the main axes an additional check box is present It is called Same as X1 or Same as Y1 X 2 kvi Same as Xi If Same as X1 is checked most settings of the selected axis such as the range scaling color line thickness tick positions are taken from the main X1 axis 7 24 Drawing and Plotting If you want to use two different axes for the top and for the bottom of your plot you have to uncheck this box before making any changes The radio buttons General Labels and Lines let you switch between different sub panels that are used to edit the general appearance of an axis the appearance of its labels and the kind of lines that are used to draw the axis and its tick marks If you check General you can set the following options General Labels Prefix Lines First fo Last o m 3 Draw Ticks L custom Mf ticks Distance ki minor The Draw check boxes determine which parts of an axis are drawn The First Last fields and the popup menu to their ri
106. ains positive and negative numbers You are only interested in the positive numbers and you want to delete all rows which have a negative number in the first column Here is the program 9 14 Defining functions and programs Clearl program EliminateNegatives var i integer procedure DeleteRow r integer deletes the row r and shifts up all following rows var m n integer begin for n 1 to 2 do begin for m r to nrRows 1 do if DataOK m 1 n then data m n data m l n else ClearData m n ClearData nrRows n clear last row end of for loop end of deleteRow begin main part of program i 1 while i lt nrRows do begin if DataOK i 1 then if data i 1 lt 0 then begin DeleteRow i i i 1 end i i 1 end of while loop end of main part while condition do statement nrRows If a data cell in column 1 and row i contains a negative number the procedure is called which deletes the row i by shifting all following rows up This program tests all numerical values in column 1 This is done in a while loop with general form Its statement is executed as long as its condition is true If you have more than one statement in a while loop they must be enclosed by begin and end Our example program executes the while loop for all rows in the data window while i lt DeleteRow The procedure DeleteRow calls ClearData r c which is a built in procedure of pro Fit
107. ame of a parameter name is the name of the function the parameter belongs to This parameter is case sensitive Use an empty string to specify the function currently selected in the Func menu i is the parameter index GetGlobalData function GetGlobalData index integer real Returns the value stored under the given index in a global data array This data array is shared between all functions and programs It can be used for communication between programs functions scripts and modules The index must between 0 and 99 See also GetGlobalData GetGraphCoordinates procedure GetGraphCoordinates var xmin xmax ymin ymax extended Returns the minimum and maximum values of the main x and y coordinate axes of the current graph in xmin xmax ymin ymax 1 0 If the current graph looks like the one to the right 0 0 GetGraphCoordinates returns xmin 0 xmax 6 ymin 1 ymax 1 Za 1 0 0 0 2 0 4 0 6 0 GetGraphFrame procedure GetGraphFrame var left top right bottom extended Returns the enclosing rectangle of the current graph GetMarkedCoord procedure GetMarkedCoord i integer var x y extended Returns the coordinates of the preview window marker with index i in x y Pass i 0 for the reference marker A 32 Appendix A Predefined functions procedures and arrays GetMedian procedure GetMedian var count longint var mean median minimum maximum extended Obsolete Use Statis
108. ample Ry y can be the negative logarithm of the corresponding probability distribution for the distances d and dyi Minimization of 7p as defined in Eq 2 adjusts the function f x in order to maximize the probability that the measured data set corresponds to an underlying reality described by the adjusted f x This is true as long as the following assumption is fulfilled the measurement errors for each data point must be uncorrelated and described by probability distributions centered around the true values X fE The above assumption might appear harmless but it is in fact more stringent than one would causally expect For example in most cases one tends to assume that the probability distribution is Gaussian but the actual probability distribution for the measurement errors might be different with a sizable proba bility of finding larger errors from time to time i e points that are clearly outside the expected trend outliers To allow for an analysis of such cases pro Fit provides a set of deviation functions R which correspond to various error probability distributions 8 2 Fitting The most common deviation function provided by pro Fit is the squared deviation R d a 3 When using this deviation function Eq 2 becomes the mean square deviation between data points and function Eq 2 then corresponds to the negative logarithm of the probability of obtaining the data set in the presence of no
109. and functions using the standard Pascal syntax For example you write DrawRect 10 10 50 100 In other words you pass a value for each parameter and separate the parameters by commas However some of pro Fit s predefined procedures use an optional parameter list for passing values for instance CloseWindow window Data 1 saveOption dontSave In the above example window and saveOption are the names and Data 1 and dontSave the values of the parameters that are passed to the procedure Close Window In other words each parameter has a name that must be passed in front of its value The advantage of this calling convention is that you can omit some parameters if you want to use their default values For example you can call Defining functions and programs 9 17 CloseWindow saveOption ask In this example we have omitted the parameter window and use its default value the front window instead The pro Fit Programming Guide and Appendix A of this manual state which of pro Fit s predefined procedures use optional parameter lists Aborting procedures functions and programs Use the keyword Halt to immediately end the execution of a function or program Use the keyword Exit for exiting from a local function or procedure to the caller The following is an example of a program calculating the sum of the presently selected cells in a data window The program aborts when the selection contains empt
110. and variables you can optionally define local procedures and functions The general form of their definition is for a procedure procedure MyProc m n real i integer variable and constant definitions begin statements separated by semicolons end for a function function MyFunc m n real i integer real variable and constant definitions begin statements separated by semicolons myFunc return value end In this case MyProc or MyFunc is the name of the procedure function The name is followed by a list of arguments in brackets If the procedure or function has no arguments this list including the brackets is omitted In our examples we have three arguments m n and i together with their type definitions If you define a function the declaration of its return type follows after the argument list Then follows a semicolon 9 12 Defining functions and programs After the line defining the name of the function or procedure you can define constants or variables using the same syntax as described for the program see above These items are only known within this procedure or function The statements of the procedure or function follow enclosed by begin and end You can call a procedure or function anywhere after its declaration like this MyProc 1 72 3 13 20 r MyFunc 1 71 3 14 10 Local functions and procedures can also have var parameters When you change a var paramter you ch
111. ange the value of the corresponding variable of the calling function Example program Test procedure Increase var a Real increase value of a by 1 begin a atl end begin k 1 Increase k increases k by 1 Writeln k writes 2 end If you define a procedure having the name Initialize it is called automatically whenever the program is added to the menu Within Initialize you may want to initialize any variables or print some information into the Results window Here is an example Defining functions and programs 9 13 program DoMyStuff var inputColumn integer where our data comes from procedure Initialize prints a description of the program and sets the default value of inputColumn begin Writeln This program converts a data column Writeln into normalized units inputColumn 3 inititialization end of initialize begin main part of program ask for an input column default is the one that was set in initialize Input which column inputColumn transform data end of main part The above program uses the predefined function Writ en to output text to the results window and the function Input to ask the user for a column number All predefined functions are described in Appendix A Example Let us look at an example of a fully functional program You have a data window that contains data in the first two columns The first column cont
112. anged 1 64 in Pascal 0 63 in C e a0 This is a record in C a pointer to a struct that defines the default values modes names and limits of your parameters as they appear in the parameters window The values that you can access or change in this data structure are listed under the routine InitializeFunc above Check should return one of the following values good if the new parameter is to be accepted update if the new parameter is to be accepted but the parameters window must be redrawn because Check changed some values in a0 bad if the new parameter cannot be accepted Last procedure Last pb ExtModulesParamBlockPtr This routine is called whenever an operation that has used your function such as a command for fitting is done In most cases you can leave this procedure empty Applications of Last are given in Chapter 9 Defining functions and Programs Working with external modules 10 9 Predefined constants and types When writing an external module you can and must use several predefined constants types and procedures or functions In Pascal they are defined in the interface of the file proFit_interface p In C they are defined in proFit_interface h and proFit_paramBlk h This section describes some of the most important things defined in these files The definitions in these files should not be changed Doing so might cause incompatibilities with the present or future versions of pro Fit G
113. arameter set Deletes a saved parameter set delete parameter set string the name of the parameter set Omit to delete all parameter sets of the given function for string the name of the function the parameter set belongs to omit for global sets in alias the file in which to save the object fromMenu boolean set to true to delete the parameter set from the alternate parameter sets menu default true fromFile boolean set to true to delete the parameter set from the file specified in the file parameter default true do script Compile and execute one or more Pascal statements do script reference the window or the statements to execute Examples do script Writeln Hello world executes the pascal statement FFT Fourier transform from real to complex numbers see also inverse FFT FFT window the data window inputCol integer input column data in time domain outputColl integer output column 1 real part or amplitude in frequeny domain outputCol2 integer output column 2 imaginary part or phase in frequeny domain reallmaginary boolean true if output columns contain real and imaginary parts false if amplitude and phase outFreqencyCol integer frequency output column calculated from timeInterval timelnterval real time interval between input data points print results boolean true if comments are to be printed in Results window find extrema of finds maxima an
114. aries of the interval where the minimum must be found This function starts looking for a minimum only if the slope of the function is negative at x min and positive at x max If no minimum is found the function returns NAN Not A Number Use the function invalid to test if the result is an NAN Move procedure Move dx dy extended Offsets the current pen position from its current position by dx dy MoveTo procedure MoveTo x y extended Moves the current pen position to x y without drawing anything NewDataWindow procedure NewDataWindow optional parameter list Opens a new data window Parameters nrRows Longint The number of rows Omit for default 200 nrCols Longint The number of columns Omit for default 10 name String The name of the new window Omit for using a default name boundsLeft boundsTop boundsBottom boundsRight Integer The bounds of the window in global screen coordinates omit for default position and size info String The info text attributed to the window Omit for leaving it empty fontName String The font to be used for the new window fontSize Integer The font size to be used for the new window NewDrawing Window procedure NewDrawingWindow optional parameter list Opens a new drawing window Parameters name String The name of the new window Omit for using a default name boundsLeft boundsTop boundsBottom boundsRight Integer The bounds of the window in global scre
115. arrays GetGraphCoordinates returns the ranges of the main axes in the current graph SetRange MakeTicks change the range ticks position labels format and various drawing SetLabelsFormat options for the current axis SetAxisPosition SetAxisAttributes MakeNewAxis create kill coordinate axes in the current graph and change the GetCurrentAxis current axis used to define a new curve or data set SetCurrentAxis DeleteAxis ClearTicks ClearLables define a custom list of tick marks and or labels AddTick SetLabel SetLabelText All the above calls access the current graph To make a graph the current graph double click it while holding the command key down From a program you can use the call Set Current Graph to make a graph the current graph Some of the above routines use or change the axes of a graph They access the current x axis or the current y axis To make an axis the current x axis call Set CurrentAxis xAxis i where i is the number of the axis Set CurrentAxis xAxis 2 sets the current x axis to X2 To make an axis the current y axis call Set CurrentAxis yAxis i Calls that work on the current axes are SetAxisPosition SetLabelsFormat etc The following code changes the position of the X2 axis of the current graph SetCurrentAxis xAxis 2 2nd x axis SetAxisPosition xAxis 0 5 Setting default parameters SetParameterProperties Sets the value name limit and mode of a parameter
116. ave called setColHandle if you want to call other pro Fit routines first make a copy of the data by using HandToHand once you have made all modifications to the data call SetColHandle GetColName procedure GetColName var name Str255 col longint Returns the title of the column col GetColType function GetColType columnNumber longint longint Returns the type of the data of the given column in the current data window Return values are text Column for text columns floatColumn for numeric columns having a range of 1e30 1e30 i e 4 byte floating point values or doubleColumn for numeric columns having a range of 1e300 1e300 i e 8 byte floating point values GetCurrentAxis function GetCurrentAxis whichAxis integer integer returns the ID number of the current x or y axis whichAxis is either xAxis or yAxis GetCurrentGraph function GetCurrentGraph longint Returns a unique number identifying the current graph as long as it exists Returns 0 if no current graph exists A 30 Appendix A Predefined functions procedures and arrays GetCurrentWindow function GetCurrentWindow windowType longint longint Returns the ID of the current window with type windowType windowType can be dataType drawingType Or text Type specifying data windows drawing windows and function windows GetData function GetData row column longint extended External modules only Retu
117. aw GX installed you can use kerning when printing and exporting graphics for this you must check Use QuickDraw GX in the Drawing General command of the Preferences submenu and enable the export of QuickDraw GX shapes in the PICT Options panel of the Preferences submenu For more details see Chapter 12 Printing Rectangles and ellipses Rectangles and ellipses are created using the corresponding tools of the palette Select the Sm appropriate tool click the desired position of one corner of the rectangle or the enclosing rectangle for an ellipse and then drag the mouse to the opposite corner Lines and polygons Crating lines and polygons is easy as well Select the appropriate tool click the start of the line and drag to its end For polygons click at the positions corresponding to the corner points of the polygon release the mouse when moving from one point to the next Double click when finished Drawing and Plotting 7 7 By holding down the mouse button for a while when you select the polygon tool you can change the tool to the one for closed polygons Hold down the shift key to constrain lines or polygon sections to horizontal vertical or diagonal directions When drawing a polygon hold down the command key and double click to create a corner that remains a corner even when the polygon is smoothed Lines and polygons can have arrows To define at which ends of the line polygon arrows must be drawn
118. awDataPoint i 1 DrawDataPoint i 2 CloseDataSet end end OpenFile procedure OpenFile optional parameter list Opens a file Parameters file String The file to open Use a simple name or a file path type Integer The type of the window to be opened textType dataType Omit for default type Use FrontWindow if you need the window ID of the new window To import data from text files call DataImport Options before calling OpenFile See also GetFileDirectory SetDefaultDirectory SaveWindow There is also an obsolete definition of OpenFile supported for compatibility with earlier versions of pro Fit procedure OpenFile fileName Str255 Opens a data drawing or function file in a new window The new opened window becomes the current window If the given file is a text file the user will be asked if the file should be loaded into a data or a function window To automatically load a text file into a data window use OpenData to automatically open a text file into a function window use OpenText Appendix A Predefined functions procedures and arrays A 45 If fileName contains a simple file name the file is loaded from the pro Fit folder If fileName contains a file path the file is loaded from the folder defined in the file path If you pass for fileName the user will be asked to locate the file If the specified file is a pro Fit module or a compiled AppleScript it is added to the Misc o
119. ax Let us have a quick look at a small program that fills the first column of a data window with the powers of two 2 4 8 16 etc To define this program again open a new function window choose New Function from the File menu and enter for i 1 to nrRows do data i 1 2 i SetColumnName 1 Powers Then click the To Menu button This time pro Fit recognizes that you are defining a program not a function It adds the program to the Prog menu and replaces your text with the syntactically correct version program User_Program var i integer begin for i 1 to nrRows do data i 1 2 i SetColumnName 1 Powers end Note that this program starts with the keyword program and not function The rest of it follows the same syntax as a function definition with the exception that no parameters are used To run the program open a new data window and choose User_Program from the Prog menu The first column of the data window will be filled with the desired values In this chapter you have seen some of the most important features of pro Fit For in depth information consult the following chapters of this manual Getting started 3 15 4 Working with data Data editing The data window The data window is organized in horizontal rows and vertical columns It can hold up to 16 millions columns with up to 16 millions rows if enough memory is available ULE data SS info hook resize field
120. be used 1 yAxis small integer y axis to be used 1 selected only boolean true if plotting selected rows only error bars boolean true if drawing error bars connected boolean data points connected with lines point type small integer index of point style in point menu point size real size of point background point type small integer index of background point type background point size real size of background point point thickness real line thickness for drawing points curve thickness real if connected thickness of line curve dash small integer if connected line dash id curve red integer color red component curve green integer color green component Apple Script 11 11 curve blue integer color blue component plot Plots a function plot reference the function to plot omit for current function xFrom real x range beginning xTo real x range end new window boolean true if plotting into new window new graph boolean true if creating new graph yFrom real y range beginning yTo real y range end autoY boolean true if automatic y range xScaling lin log reciprocal probability x scaling yScaling lin log reciprocal probability y scaling xAxis small integer x axis to be used 1 yAxis small integer y axis to be used 1 step real step width or number of steps 0 for automatic subrange start
121. bject instead of simply moving it option or shift to get a square bounding box General features 14 5 Drawing lines in drawing windows Drawing polygons in drawing windows Resizing objects in drawing windows Resizing lines in drawing windows Clicking objects in drawing windows Clicking graphs in drawing windows Reshaping polygons in drawing windows shift to make the line horizontal vertical or diagonal at 45 option to make a diagonal line option shift same as for lines command double click to produce a corner that remains a corner even when the polygon is smoothed option to keep the bounding box of the object square height width shift to maintain the horizontal and vertical proportions of the object its height or its width command to resize the size of texts in a group option to get a line constrained to 45 directions shift to maintain the direction of the original line or to make the line vertical or horizontal shift to select an object without de selecting other already selected objects option amp command click to see the plot coordinates of the point you are indicating with the cursor option amp command click and then press shift to select an area of the graph to be enlarged command double click to make a graph the current graph command amp shift double click to remove the current graph setting option click a connecting line
122. bjects The floating point coordinates of drawing objects can be edited graphically and numerically e Customizable graphical elements Dash patterns line thicknesses arrows error bars and data point symbols can be customized New arrows and data point symbols can be designed with a graphical editor and added to the standard drawing menus e Extensive graphical output possibilities Support for PostScript PICT format high resolution bitmaps and QuickDraw GX Export of drawings with Copy amp Paste Drag amp Drop Publish amp Subscribe and EPS files e Spreadsheet data management Spreadsheets for editing and transforming data Predefined and user defined algorithms Single precision as well as double precision data columns and text columns are supported e Scriptability and Recordability Automatically record all your actions as a Pascal program or Apple Script for replaying them later e Function and data preview Real time automatic display of the current function and data Interactive graphical editing tools for function parameters and data points e Externally compiled code Import functions algorithms and other programs written in your favorite programming language or in Apple Script e On line evaluation of mathematical expressions Wherever pro Fit expects numerical input such as in spreadsheets or dialog boxes any mathematical expression can by entered e Drawing from a program pro Fit programs can directly draw in p
123. ble If you hold down the option key while dragging the object is duplicated i e a copy of the original is created at the destination instead of simply moving the original You can drag one object from one drawing window to another If you do this a copy of the object is created in the destination window You can drag objects to any other application supporting drag and drop or to the Finder s desktop In the latter case the Finder will produce a small picture clipping which you will be able to use later on either by dragging it back to a pro Fit window or by using it in another application You can drag objects into the Trash to delete them To change the size resize of an object 1 Select the object 2 Click into one of the four black selection handles at its corners and drag While dragging the new outline of the object is shown If you hold down the shift key when resizing the proportions of the object are maintained or the height or width remains constant If you hold down the option key when resizing the horizontal and vertical dimensions of the object become equal If the object is a group of different objects hold down the command key to tell pro Fit to resize all of the objects of the group regardless of their type normally pro Fit would not automatically resize texts or data points To rotate an object 1 Select the object 2 Choose the desired rotation from the Rotate submenu in the Draw menu Obj
124. bounds bounding rectangle the boundary rectangle for the window floating boolean r o Does the window float info string the info text font string the name of the default font for text size fixed the default size for text style tsty the default text style for text lt Inheritance gt base class properties r o Apple Script 11 19 Note You cannot access floating windows You cannot change the name of the parameter window or the results windows To specify a window you can either use its name or its index The index ranges from 1 to the number of windows where 1 designates the front window Class base class properties Properties inherited by all objects Properties properties record a record containing all properties of the element 11 20 Apple Script 12 Printing There is a wide range of different printers that can be connected to a Mac OS machine and each of these printers have different capabilities resolutions and command languages pro Fit allows you to get the best out of most of the commonly used printers if you follow the guidelines described in this chapter Basically there are two possibilities for printing pro Fit drawings You can print from pro Fit directly using the Print command from the File menu or you can export a drawing to another application such as a word processor using the Copy or the Create Publisher commands or by dragging it to the other application and print it from
125. bsequently created markers are auxiliary markers and are numbered starting from 1 Their number appears when they are active when they are flashing To set the color of the reference marker and of the auxiliary markers choose Preferences from the File menu If the reference marker cannot be distinguished by its color pro Fit automatically draws it larger Marker coordinates are displayed in the bottom left corner of the preview window If there is more than one marker there can be two other coordinates displayed to the right of the marker coordinates They correspond to the distance between the reference marker and one of the other markers 6 4 Preview Window What the coordinates mean x y are the coordinates of Ax Ax are the distances from No active markers around the reference marker the other marker if there is only one the active marker the reference marker If a marker is active its coordinates are displayed in editable fields Edit any of these fields to set the coordinate of the marker If the marker is a data marker and the preview window is big the data window row number that corresponds to the marked data point is also displayed It is found above the x coordinates and is labeled CoP 089 1 The behavior when changing the text in the edit fields containing the marked coordinates varies depending if the marker is on a data point or if it is on a function curve e If the marker is on a data point the coo
126. case Since the sinc function is used twice in our example it makes sense to put it into a local function 9 22 Defining functions and programs function DoubleSinc defaults a l 1 active al a 2 20 active xl1 a 3 1 active a2 a 4 20 active x2 function Sinc u real real sin u u begin if u 0 then sinc 1 0 0 is illegal else sinc sin u u end begin body y a 1l sinc x a 2 a 3 sinc x a 4 end Alternative function syntax pro Fit 5 0 provides an alternative method for defining the parameters of a function that allows you to use any desired legal name for your parameters In this syntax you add the parameters in parenthesis after the name of the function Example function MySine amplitdue frequency begin y amplitdue sin frequency x end The first parameter in the list will correspond to parameter a 1 the second one to a 2 etc You can then refer to each parameter either by using its name amplitude frequency or by using a i where i is its number in the parameter list ie a 1 for amplitude a 2 for frequency Special procedures in a function definition As in a program the procedures that you define within a function definition can have any valid name you want However there are some reserved names for special procedures Initialize Check First Derivatives Last that you can define to customize and optimize your function def
127. cation of the best parameter set The Monte Carlo algorithm minimizes 2 with any definition of R by randomly varying the parameters and if the x errors are not zero the set of x coordinates and looking for the smallest value of 2 This algorithm is often useful to scan parameter space and find good initial values for a Levenberg Marquardt or Robust fit Fitting 8 5 The Levenberg Marquardt algorithm minimizes the mean square deviations using 8 It finds at the same time the set of x coordinates x and the function parameters that minimize the mean square deviations between the data points x y and the function values x f x When the x errors are zero the Levenberg Marquardt algorithm minimizes 9 The Robust fitting algorithm minimizes 2 with any definition of R by continually moving downhill in parameter space until the bottom of a valley is found The Linear Regression and the Polynomial fitting algorithms are specialized for polynoms of 1st and nth degree While the Linear Regression allows for x errors we use a straight forward algorithm if there are no x errors the Polynomial fitting algorithm is restricted to y errors only The mathematics used by the various algorithms to perform their job is outlined in the next sections The Monte Carlo algorithm This method randomly varies the parameters of a function within given intervals When x errors are defined the algorithm also varies randomly the set o
128. containing a standard PostScript representation of the drawing This representation is used by other applications that understand and work with PostScript In addition to the PostScript text a PICT representation of the drawing is included The file type of EPS files is EPSF Hold down the option key while saving the file to produce a file type of TEXT To save a drawing as a EPS file bring the drawing window to the front and choose Save as from the File menu In the dialog box that comes up check the option EPS File Appendix C File formats C 7
129. ction curve varies in correspondence to the fitted parameters See Chapter 8 Fitting for more details on the fitting process and the Error Analysis algorithm Choosing initial values of function parameters You can display the data you want to fit together with the fit function in the preview window You can then use the fitting tool to drag the function in such a way that it follows the data points as closely as possible Try using the fitting tool with the various parameters you want to fit This is a kind of hand fitting that can be a very useful and fast way to set up a reasonable set of starting parameters for a fit For special applications you can also mark certain features of your data set using coordinate markers and write a small program which reads the coordinates of these markers and uses them to calculate the optimal initial values for the parameters of the current function 6 6 Preview Window 7 Drawing and Plotting Drawing and plotting takes place in a drawing window This window supports most features of commonly used drawing applications We will first describe the drawing window and its general features The section Drawing discusses standard drawing objects and editing techniques The section Plotting is devoted to the plotting commands used to produce graphical representations of your data and functions It discusses how to manage graphs and how to edit them The drawing window A drawi
130. ction returns nan Not A Number Use the function Invalid to test if the result is an NAN Minimize function Minimize theFunction Str255 precision extended varyX Boolean var x y extended Boolean Obsolete Use Optimize instead Finds the parameter set that gives a minimum value for the given function theFunction is the name of the function as it appears in the Func menu This parameter is case sensitive Use an empty string to specify the currently selected function in the Func menu precision defines accuracy of the calculation Minimize will run repeated iterations until the function s value changes by less than precision in consecutive iterations If varyx is true Minimize varies the active A 40 Appendix A Predefined functions procedures and arrays parameters as well as the x value of the function if false only the active parameters are varied and the x value is not changed The variables x and y return the x and y values where the maximum is found The algorithm used is the Simplex method Minimum function Minimum name Str255 min max extended extended Obsolete Use Extrema instead Returns the minimum of a function that is the x value where the function value is the smallest name is the name of the function as it appears in the Func menu This parameter is case sensitive Use an empty string to specify the currently selected function i is the parameter index min and max are the bound
131. d Returns the base 10 logarithm of x Causes a run time error for x lt 0 Returns INF for x 0 LowerString procedure LowerString var s String Converts all characters of s to lower case See also UpperSt ring MakeNewAxis procedure MakeNewAxis whichAxis integer min max extended scaling integer position extended Creates a new x whichAxis xAxis or y whichAxis yAxis axis in the current graph The newly created axis becomes the current axis Use Get CurrentAxis to find the ID of the newly created axis position gives the coordinate of the new axis in the coordinate system of the main axes X1 Y1 scaling can take the values 0 linear scaling 1 logarithmic scaling 2 1 x scaling 3 probability scaling Appendix A Predefined functions procedures and arrays A 39 MakeTicks procedure MakeTicks whichAxis integer firstMaj distance extended nrMinTicks integer Creates a new set of ticks for the given axis whichAxis S xAxis Of yAxis firstMaj and distance give the position of the first major tick and the distance between major ticks nrMinTicks defines the number of minors ticks between consecutive major ticks MarkedX function MarkedX i integer extended MarkedY function MarkedY i integer extended Return the x coordinate and y coordinate of the preview window marker with index i Pass i 0 for the reference marker Returns a NAN if no marker with index i exists
132. d O 7 correspond to the standard deviations of the Gaussian distributions The denomination chi squared has become so common that it is often used to indicate the result of 2 and not only to indicate the particular case 8 For the sake of simplicity pro Fit follows this somewhat dirty convention and uses the denomination chi squared when referring to the result of 2 even if deviation functions other than square deviations are used The same is true for the predefined function ChiSquared which can be used in pro Fit programs to retrieve the value of 2 obtained d in the last fit Zero X errors In most experiments it is possible to determine the x coordinate much more precisely than the y coordinate In such a case the x errors can be assumed to be very small The only way to minimize the mean deviation 2 is then to have x The mean deviation function becomes much simpler Xr Ex f 9 Oi The function is evaluated at the x coordinates of the measured points The function value and measured y coordinate directly give the normalized distance when weighted with the measurement error The usual case Chi squared and zero x errors In many experiments it is not only possible to make the x errors so small that they can be considered zero It is also common to have or hope for Gaussian distributed measurement errors In this case we have to minimize a particularly simple expression for chi squa
133. d Think C are registered trademarks of Symantec Corp Metrowerks is a registered trademark of Metrowerks Inc CodeWarrior is a trademark of Metrowerks Inc MacDraw and ClarisDraw are registered trademarks of Claris Corporation pro Fit is a trademark of QuantumSoft Ziirich For information and customer support contact QuantumSoft at the following address QuantumSoft Postfach 6613 8023 Z rich Switzerland Fax 41 1 481 69 51 e mail profit quansoft com web http www quansoft com If you need to contact QuantumSoft for support it would help if you have the following information to hand e your serial number e the version of the software you are using e A detailed description of what you were doing when the problem occurred e any special information e g the type of printer if it is a printing problem Table of Contents VEO GUCTION aiiin eaaa aaa aiea a ea a aidia i aa 1 How t read thismanu aliis a tea 2 Basi CONC IOS nsanra a Ss oie a a a iiaa a a aS 3 Changes between versions 5 0 and 5 1 ccsssscssesscsseseceseeeceeeeseseeceecaesaeeaesaeeeseeseessatenees 4 lnstallatio mi iiini ara a aaa a a aa a na auaa A 1 The installatlonproCcequiress sc shoes wees ete each leo en a ae ee 1 DEOPIL VGNGIONS oisexcces Gaeta Ne ee eet ae MI cat te idea eit Ces NAT 1 G tting started crine iaaea suuinedud danseuiduusbvudsuaveduadiueluidancbneans 3 PRIESTS CS SOU ccs cachet ada alc a AE E E E AA 3 QCA arnt ones stain tac octet
134. d from data and data can be recovered from a graph the two documents lead separate lifes After it has been created the graph does not know anymore about the origin of the data used to create it and if you modify that data the graph remains untouched pro Fit uses the second approach There are data documents and there are drawing documents From the data you can create graphs From the graphs you can recover the data used to plot them Drawing and Data documents can be stored and maintained separately and don t affect each other In Chapter 7 Drawing you will see how you can use the Draw menu to plot a function and a data set obtain graphical representations of your data and functions and edit the graphs to obtain the precise graph style you are looking for There is an ongoing discussion between the supporters of the first approach outlined above and the supporters of the second approach used by pro Fit A link between data and its graphical representation is in fact also useful pro Fit s answer to this dilemma is the Preview Window The preview window is a graphical representation of the current function and or the current data set It gives you a graphical view of the function and the data set Any change in the data set or in the function is reflected in the preview window You can even use the preview window to graphically edit the function parameters or the data set Use the preview window to have a quick look a
135. d functions procedures and arrays Gamma function Gamma x real complex real complex Gamma function x must be larger than 0 for real valued results Real value accuracy gt 12 digits Gammal function GammaI a x real complex real complex Incomplete gamma function x and a must be larger than 0 if they are both real valued Real value accuracy approximately 8 digits Complex value accuracy up to 12 digits GammaLn function GammaLn x real complex real complex Natural logarithm of the gamma function Real value accuracy gt 12 digits GammaP function GammaP a x real complex real complex Incomplete gamma function P GammaP a x 1 GammalI a x Gamma a x and a must be larger than 0 when they are both real valued Real value accuracy approximately 8 digits Complex value accuracy up to 12 digits GetAndSetStatus function GetAndSetStatus newStatus integer var s Str255 integer External modules only For advanced programming Returns the present execution status then sets it to newStatus The status can be O if normal operation 1 if the user interrupted operation 2 if a warning has been posted 3 if a run time error has been posted Set newStatus to 1 if you don t want to change the current status If you set a status 2 or 3 pass a suitable error or warning message in s it will be shown once your module is finished On return s holds the current message if status was 2 o
136. d minima of the given function find extrema of reference the function to be used xMin real lower bound of the interfal where extrema must be found xMax real upper bound of the interval where extrema must be found subintervals integer number of subdivisions where to look for a result print results boolean true if comments are to be printed in Results window 11 8 Apple Script find roots of finds the solutions of the equation f x yVal find roots of reference the function to be used xMin real lower bound of the interval where roots must be found xMax real upper bound of the interval where roots must be found subintervals integer number of subdivisions where to look for a result value real the function value yVal in the equation f x yVal default is zero print results boolean true if comments are to be printed in Results window fit fits the given function to the given data fit reference the function to use for fitting algorithm levenberg monte carlo robust linear polynomial fit algorithm to be used using reference the data window with the data to be used for the fit xColumn integer the x coordinates of the data to be used for the fit yColumn integer the y coordinates of the data to be used for the fit xErrorKind individualErr constantErr percentErr unknownErr zeroErr how the x errors are specified yErrorKind individualErr constantErr percentErr unknownErr zeroErr how the y err
137. d taeeet eee telaete agate tien enedes 7 The Robust minimization AlQOritnim ccecccecececeeeeeeeeeeeeeeeeeeeeeeaeseaeeeeeeeeeseeeteeeeaeees 8 The Linear Regression algorithms ccccceccecsceseesceeeeeeeceeeseeeceeeeeseeeeeeseteateeseeeaeeees 9 The Polynomial fitting algorithm s sesesesesesnsnnnnsnennerererernrnrnnsnsnsnerennrnnnnnrenerennnne 10 Goodness of Ui a een a ee etal cede E A E E S 10 Literature and suggested reading ceceececeeceeeeeceseeeeeceseeeeseeseeesseeseeeseatseeseeaneetaees 10 The fitting pProCeSS ssc aaa aah eal a ae ta dle ed cent Uc ceed ea 11 General SAU SS gots crs a r cee teat ace eee acetate 11 Parameter limits css ss cc de das car wa tanctel occas cat ot dete amen caadeetas wee te caeeadade wacnetiemtendast ate nnne 11 FEU MUNG chs cate ste ota td cheat elas ee cere si Nec A eee A E 12 Inspecting the progress Of a fit 2 ee ceeeeecceeeeeeeeeeeeeeeeeeeeceeeesecaeeaeeesaeeaeeeseeeaeeeteataes 14 Error analysis and Confidence intervals cccecccceseesceceeeeeeeeeeeeseeeeeeeseeeeeeeteetees 14 PILING TOSUING E seen de scien ae es ie E E 16 Using the various fitting algorithms eee eeeeeeeesceceeeeeceseeeeeeeseeeseeseeeseateeseeaneeeaees 16 Using the Levenberg Marquardt algorithm c cecccceseeceeceseeeeeeeteeeeeeeteeeeeeeees 17 Using the Robust minimization algorithm cccceceseececeeeeeceeeeeeeeeeeeeeseeeeeeeseetees 17 Using the Monte Carlo algorithim
138. data window to create an info field of the desired size See Chapter 4 Working with data for more information on data windows Data 122 These points were recorded using Finac s correction Columns 3 and 4 give the temperatures at the end points 3 5 96 KS General features 14 3 Note that the info comments are in general only saved in files that have pro Fit s standard formats If you save a function definition as normal text files TEXT format or if you save a drawing window as a picture or EPS file PICT format EPSF format the info comments are not saved If you save a data file as TEXT you have the option of placing the info comments right at the beginning of the text file as a header To set this option you have to choose Custom format in the dialog box that comes up when saving text files Find and Replace pro Fit provides Find amp Replace features to help you navigate through text This feature is available for the results window and all function windows You will find it most useful when you are editing the definition of a function or a program inside a function window The Find amp Replace commands are found in the Edit menu Find 4 SEF Find Again lt gt 366 Enter Selection 4 EE Replace DER Replace amp Find Again 36H Replace All When you choose Find the Find Replace dialog box appears Find Replace Find al3 ki Ignore case Forward O Whole words only d Backward
139. defines the command to be executed To execute a command from a normal not hierarchical menu theMenuItem has the format menu name item name To execute a command from a hierarchical menu theMenuItem has the format menu name submenu name item name Instead of specifying an item name you can also specify the number of the item in the menu preceded by This procedure cannot be called while a function is running Examples DoMenu Edit Copy DoMenu Calc Nonlinear Fit DoMenu Calc Fourier Transform FFT OK DoMenu Draw Rotate 1 If the command that you select in this way brings up a dialog box and if you want to automatically click the OK button of this dialog box add sox to the end of the string Adding sox to the end of the string has the same effect as immediately clicking OK when the dialog box comes up but the dialog box will not appear Appendix A Predefined functions procedures and arrays A 23 DoScript procedure DoScript window integer Runs the script in the given window window is its window ID Equivalent to selecting Run or Run Selection from the menu Misc DoNewWindow procedure DoNewWindow windowType OSType External modules name See NewWindow DrawArc procedure DrawArc left top right bottom start length extended Creates an arc inside the specified bounds in the current drawing window It is a part of an e
140. der with prompt Then it goes through all the files in this folder and uses the command open file name as table for opening the file as a data window It also uses the command write line text for writing a text into the results window Then it closes the file The open file and close window commands are enclosed by the statements try and on error If any of these commands fails and returns an error the write line statement between on error and end try is executed Note that we are setting a property called error alert to false before opening the files This tells pro Fit that it should not show any error alerts of its own when it cannot open a file The above example simply opens each file in the folder and closes it again In practice you may e g want to run a program on each opened file For this purpose simply insert run program MyProg analyze it after the command open file where MyProg is the name of the program you want to run The following is a more complete version of the above script It not only runs a program on each opened file it also defines the program adds it to pro Fit s Prog menu and then exchanges data with it the following defines the pro Fit program run for each data file set scriptProgram to program ScriptProgram var sum i begin sum 0 for i 1 to nrRows do if DataOK i 1 then sum sum datafi 1 globalData 1 sum store result end bring up a dialog for selecti
141. dix A Predefined functions procedures and arrays A 5 program Lissajous va be en r xmin xmax ymin ymax centerH centerV center of the figure radiusH radiusV and its radius angle gin xmin 1 xmax 3 ymin 2 ymax 5 CreateNewGraph xmin xmax ymin ymax false false centerH xmintxmax 2 50 centerV ymintymax 2 radiusH xmax xmin 0 4 radiusV ymax ymin 0 4 4 0 SetLineStyle 1 2 OpenCurve Circle 3 0 MoveTo radiusHtcenterH centerV angle 0 20 while angle lt 2 pi do 1 00 1 50 2 00 2 50 3 00 begin LineTo radiusH cos 3 angle centerH radiusV sin 2 angle centervV angle angle pi 40 end CloseCurve SetLineStyle 1 1 d Creating and accessing graphs Se CY Ge Se Ge Editing Se Se Ge Se tNewGraphRect sets the default size and position of graphs created with CreateNewGraph eateNewGraph creates a new graph in a drawing window tCurrentGraph obtain a unique identification number for a graph and use it to tCurrentGraph access different graphs tNextGraph the current graph tGraphAttributes set various options that determine the appearance of the current graph tLegendProperties set visibility position and size of the legend of the current graph tGraphFrame get set the position and size of the current graph tGraphFrame A 6 Appendix A Predefined functions procedures and
142. dles the little circles or squares at the edges of the polygon To make your work easier pro Fit lets you define a rotational symmetry and mirror symmetries Choosing 5 from the Symmetry popup menu like in the above example tells pro Fit to draw the definition points at 5 positions 360 5 degree apart before connecting them with lines Use the Pts popup menu to set the number of definition points Checking the H or V check boxes tells pro Fit to draw the definition points at the 2 positions obtained by mirroring them at a horizontal or vertical axis respectively You can achieve quite astonishing effects by combining these symmetry settings and using only one or two definition points Hold down the shift key while dragging a polygon handle to constrain the dragging along radial directions Hold down the command key while dragging a polygon handle to resize and rotate the whole polygon in one single move Choose a Symmetry of 1 and no mirror symmetries to draw a polygon free hand 7 10 Drawing and Plotting Note that if you do this you can draw a polygon that is not centered inside the preview area This means that if you use such symbols for plotting the symbols will not be centered on the mathematical coordinates of the data points Click the Copy to Menu button to add the point symbol you just defined to the point symbols menu for later use The data point symbols you define are normally used when plotting see the section
143. dvanced programmers GetFileDirectory function GetFileDirectory ID longint s string boolean Returns the directory where the document displayed in the given window is stored ID is the windowID The path name of the directory is returned in the string s This function returns false if the path name had to be truncated GetFrontWindow function GetFrontWindow longint External module name See FrontWindow GetFunctionName function GetFunctionName Str255 Returns the name of the current function Appendix A Predefined functions procedures and arrays A 31 GetFunctionParam function GetFunctionParam name Str255 i integer extended Returns the default value of a parameter name is the name of the function This parameter is case sensitive Use an empty string to specify the function currently selected in the Func menu i is the parameter index Example GetFunctionParam Polynom 1 returns the degree of the built in function Polynom GetFunctionParamMode function GetFunctionParamMode name Str255 i integer integer Returns the fitting mode active inactive constant of a parameter name is the name of the function This parameter is case sensitive Use an empty string to specify the function currently selected in the Func menu i is the parameter index GetFunctionParamName function GetFunctionParamName name Str255 i integer integer Returns the n
144. e Get Info command from the File menu For data windows it is the text that appears when you drag down the info hook windowID is the window ID of the window such as it is returned by Get WindowID or FrontWindow A 64 Appendix A Predefined functions procedures and arrays Set WindowlInfo procedure SetWindowlInfo windowID longint length longint info Ptr External Modules only Sets the info field of a window to the given text info is a pointer to the new info text and length is its length in bytes Call SetWindow windowID 0 nil to clear the info text windowID is the window ID of the window such as it is returned by Get WindowID or FrontWindow SetWindowProp_ procedure SetWindowProperties optional parameter list Sets the properties of a window Parameters window String or Longint The name or windowID of the window to be affected name String The title of the window Omit for leaving it unchanged boundsLeft boundsRight boundsTop boundsBottom Integer The bounds of the window in global screen coordinates Omit for leaving them unchanged info String The info text attributed to the window Omit for leaving it unchanged fontName String The font to be used in the window Omit for leaving it unchanged fontStyle Integer The font style to be used in the window plain bold italic underline outline extended condensed or any sum of these values Omit for leaving it unchanged fontSize In
145. e Voice 6 SUING STALL DAFAMGIEIS serin ana nia aea a aaea ae ud amie eatin maaan 7 Using other functions or Programs scotch webiste etek eae 8 Numerics On fUNCHIONS eee eae ht cee cate te ane ane diet eat atta clen ine 9 e get ce E AE E E E E E E ANE 9 Using Windows and DOCUMOENIS ii ctvcccasac tes seetceleed cael dealiecles tages niveniouadveniecaivelsevetvante 10 String and character manipulation cacseee scott cds teste ete tied ene eect ete Sen 11 Miscellaneous auxiliary routines eee eceeceeeeeeeeeeeeeceeesececeaneeeseeaeeetseeaeeeseetseeeceaees 12 Advanced routines for external modules ONY ecceecceceeeeeeeeeeceeeeeereeeeseeeeeeeeeeeees 12 Alphabetical NIST ct tesa tte a le eaeets coin as weh eda eee cit drenien denetik ie via yet atrentendet the 13 Appendix B About NUMDECIS iiicsivnseicintervatiewdiecsceaed vedas vahiwnedins ieaheebedcubnnndaves 1 Appendix Gr File f rmats siviscseeismaciuicwecrcuavancewnduwasteccubracndenusdvndswaauowtevaarexnae tu 3 Be fe Petraes Ren ea eT Ra Rr SN PM Pa aN EEE gS NOD RP PP ro aE OT ee ea 3 The default text TOM MAL setae tackle eracet aetna actaless Aine cheats tate ites chal Mee Ratha aehas 3 Loading text TINS fale elec iene Poel faecal e cee Seca ee hes a akaa aaa eae aaa ada pacha ts cede cd 4 STC WATS Bp P M Lo eae ee acm gm Rn Prem eer 5 The native data tOrmMat 2 c6 in vel ok Ger eet oe KE Ga eee eet Ree 6 OWLS ah li ete te a Nace ect le Ca E aa lonsata al ae eas cet ee aa cet 6
146. e arrow keys When you have markers on the function and you uncheck the show function checkbox all of them are deleted The same applies to markers on data points when you uncheck the show data checkbox Preview Window 6 5 Uncheck and check the show function and or show data checkboxes if you have many markers around and want to get rid of all of them in one rapid move Data markers store their position as the number of the data point they mark If you have data markers around and you delete or add points to the data set the data markers might move to a new data point If no new point corresponding to the old index is found for a given marker that data marker is destroyed If you have function markers and you change the ranges of the display in such a way that their x coordinates are not visible anymore those markers are destroyed Tips and tricks Using the preview window during a fit If Show function is checked during a fit the function is redrawn from time to time to show how it changes during the fit This lets you monitor how well the fit converges However drawing the function takes time You should close the preview window or uncheck Show Function to obtain the fastest fitting The same thing happens when you use the Error Analysis feature To perform error analysis pro Fit generates random sets of synthetic data points and fits the function to it If Show Function is checked in the preview window you will see how the fun
147. e background part of the point Boolean True if the data points are to be connected by lines false otherwise Default false Real Thickness of the lines connecting the data points Omit for using default thickness Integer Line dash number corresponding to the dash menu if points are connected Pass the position of the dash pattern in the dash popup menu The values between 1 and 8 always correspond to A 48 Appendix A Predefined functions procedures and arrays curveRed curveGreen curveBlue Integer The colour of the lines connecting data points Pass values between 0 dark and 65535 bright Omit to use the default color function xFirst xLast yFirst yLast autoY from to xScaling yScaling xAxis yAxis new Window newGraph xStep fittedParams curveThickness curveDash curveRed curveGreen curveBlue PlotFunction procedure PlotFunction optional parameter list Plots a function into a graph Parameters String The name of the function to plot Default current function real The start and end of the x axis real The start and end of the y axis Specify these values if you set autoY to false Boolean True if the limits of the y axis of the graph are to be selected automatically to contain the whole plot false if explicit limits are given in parameters yFirst yLast Default is false Real The x coordinates where the plot begins ends Default equal to xFirst xLast Inte
148. e box you can enter the parameter you want to make the table for its range and the step width for tabulating Note that if you have more than one root for a given parameter value only the first root will be found and entered in the table for every value of the parameter you vary Finding minima and maxima To find the extrema of a function i e the x values where f x becomes largest or smallest choose Extrema from the Analyze submenu menu Calc A dialog box similar to the one for the Roots command appears You enter the x range within which extrema must be found and a number of sub intervals pro Fit tries to find one local extremum minimum maximum within each sub interval To tabulate the extrema of a function 1 e the x values where f x becomes largest or smallest for different values of one of its parameters you choose Table of Extrema from the Analyze submenu The dialog box displayed by this command is again the same as for the roots command see above Note If you want to find the extrema of a function by varying not only its x value but also its parameters multi dimensional optimization use choose Optimize from the menu Calc This command is described above Integration To calculate the numerical integral of a function choose Integral from the Analyze submenu menu Calc In the dialog box that appears you can enter the limits of the integral as well as the number of iterations 5 6 Working wit
149. e center of the plot or the dot in the legend You can also double click any text in the drawing to change it Or you can choose any of the drawing tools to add lines polygons text etc A function to fit our data The growth of a population can often be described by an exponential function of the type 3 1 ty where p t is the population at time t p xg the population at an arbitrary start time xg and fg its growth constant P t p x x eof Let us try to investigate the validity of this formula for the world s population We want to find the set of parameters for which equation 3 1 fits our data best 1 Choose Exp from the Func menu Getting started 3 7 This brings the parameters window of the Exponential function to the front It gives a description of the built in exponential function and its parameters parameters 4 amp 1 0000000 x0 O 0000000 t0 1 0000000 const 0 0000000 selected parameter 4 Cmultiplicative factor lower limit none Euse for fitting y expl ix x0 t0 const exponential function The window is divided into three regions The top region displays the function parameters and lets you edit their value The bottom right region displays information on the selected parameter the bottom left region gives a short description of the function The function looks like this X Xo y Axen J const 3 2 0 which is essentially identical to equation 3 1
150. e click a plot symbol in the legend The Graph Settings dialog box now displays the curves editing panel Graph Settings Experieme nt Points C connected Thickness CF MIS to axis XT T2 Gi Coordinate Axes A Appears in legend Cc z pa a w T Edit Text Delete D E Here you can select and change or delete all curves and data sets of a graph To change the drawing order of the plots select a plot by clicking it in the list and click Forward To Front Backward or To Back to move it one position backward or forward or to move it to the back or front of all plots The first plot symbol at the top of the list is drawn first so back means top of the list and front means bottom of the list Change the drawing order if you have white data points behind a curve Pai and you do not want the curve to go through the points To change the text describing a curve or a data set click Edit Text po Instead of doing this you can also double click the text The pop up menus titled Line style let you edit the line that draws a curve or connects the data points The pop up menu Points lets you select the symbol for data points Check connected to draw lines between successive data points The menu Thickness defines the line thickness used to draw the data point symbols It can be set to auto in which case the line thickness will be chosen depending on the size of the data points Drawing and Plotting 7
151. e coordinate range to be displayed You can edit the values to change the x or y range Between these edit items there are check boxes labeled auto and log Check them to let pro Fit automatically recalculate the ranges based on the ranges of current function and data set or to use logarithmic scaling There is a permanent link between the preview window and the data or function it displays The preview window always displays an up to date representation of the current function and data set 6 2 Preview Window Change a coordinate in the data window or add a data point and the corresponding point will automatically appear in the preview window Change a function parameter and the representation of the function in the preview window will be updated automatically Modify a function definition and add it to the menu once again and the preview window will automatically display the new function If you select data points in the preview window the corresponding rows are selected in the data window If you select some rows in the data window the corresponding selection is shown in the preview window There is even the possibility of clicking and dragging data points in the preview window Doing so changes their coordinates in the data window Preview Window Tools To the right of the preview window there is a palette of five different tools You can use them to select data points and change their coordinates graphically to change the ranges of
152. e error if Ixl gt 1 artanh is defined by 1 artanh x In ds xl A 14 Appendix A Predefined functions procedures and arrays Ask function Ask s Str255 Boolean Presents a dialog box displaying the string s The box has a Yes and a No button If the user clicks Yes ask returns true if he clicks No ask returns false Example Calling Ask Continue transformation displays the following window n Continue transformation In external modules this routine is called AskBox AskBox function AskBox var retval integer s Str255 Boolean External Module name See Ask The return values depend on the button that was clicked e Yes button retval is and AskBox returns false e No button retval is 0 and AskBox returns false e Stop button retval is undefined and AskBox returns t rue If AskBox returns true you should stop executing your function or program Beep procedure Beep produces an alert sound BringWindowToFront procedure BringWindowToFront windowID longint Obsolete UseSelectWindow instead Moves the specified window in front of all other windows windowID is a window id such as it is e g returned by GetWindowID or GetCurrentWindow Button function Button Boolean Returns true if the mouse button is pressed CalcStat function CalcStat column longint selRowsOnly withBasics withSkewAndKurt withMedian Boolean Boolean Obsolete Use Statistics inste
153. e function and the data The window shows the current data set and the current function If you change any function parameter the curve will change to reflect the new value try it The window always shows a plot corresponding to the current set of function parameters and data points As you see our first guess for the function parameters was not altogether bad but the function doesn t grow as fast as the actual data The parameter set corresponding to the actual data set can be found by fitting Getting started 3 9 Fitting 1 Choose Fit from the Calc menu You can choose the data columns you want to fit Fitting Setup Algorithm Levenberg Marquardt Data ARA9_a_a Us last choice Window population data examp gt examp population data examp gt O Selected rows only Xcolumn year J veer __ Y column population Mio 4 X errors Column Distribution Distribution Error analysis ef Print full description O Print active parameters only The data column settings are already ok This box gives you also the possibility of specifying errors for the data points For the moment we don t need to do this 2 Click OK to start fitting Fitting is very fast When it is completed the fitted parameters are printed in the results window 3 10 Getting started Results Fit Algorithm Levenberg Margquardt Function Exp g A expe Cx xOastOo const exponential func
154. e function f x was at the coordinates x f x When the x coordinate was determined an inevitable experimental x y error occurred and x was measured instead of x When the y ra coordinate was determined another inevitable experimental error occurred and the measurement gave y instead of f lt GF In real life the true parameter set is not known One has to measure it by measuring many data points at different coordinates and fit f x to the complete data set This is the way we usually find a parameter set which best describes the measurement The parameter set obtained in this way is not the true unknown parameter set but it should be a good approximation for it See the section on Error Analysis to find out how to estimate the errors of the fitted parameters Fitting 8 1 The fitted parameter set corresponds to a function f x which maximizes the probability that the measured data set came from the system described by f x To maximize this probability we have to minimize the deviations between the measured data points and the function curve This deviation can be defined in different ways depending on the way in which the experimental errors are distributed but it is usually a function of the weighted distances d la Oi f y yet 1b oO yi O and O give the magnitude of the errors expected when measuring the x and y respectively The role of these x and y errors is to define t
155. e gt base class properties r o Examples get value of cells 1 thru 8 of columns 4 thru 12 of front window returns a list of lists set value of cell 2 of column 2 to 22 set value of cells 1 thru 5 of column 1 to 2 4 6 8 10 set value of cell 5 of column 8 to there cell in a text column set value of every cell of column 1 to O set all cells of column 1 to 0 Note You can access cells by giving an index or a range of indices If you get the value of an empty cell a so called NAN value is returned Note that the present version of Apple Script will cause an error when being forced to display such a value Class column A column in a data window access by index Properties name string the name of the column default type type class string real single decimals integer the number of decimals 1 for automatic format scientificForm floatingForm display format for numbers width integer the width of the column 0 for default width lt Inheritance gt base class properties r o Note e You can access columns by giving an index or a range of indices e You can set the type of a column by setting default type to string text column real double precision column with approximate range of 1e300 or single single precision column with approximate range of 1e30 Apple Script 11 17 Class function A function access by name or index Elements parameter Properties name string r o the name o
156. e routines only used in external programs then the routines only used in external functions Note for Pascal programmers In ProgramTemplate p and FunctionTemplate p you will find a procedure with the name main Leave this procedure unchanged it provides the glue between pro Fit and your routines Note for C programmers The following function definitions are given in Pascal If you are programming in C you should keep in mind that wherever a var parameter is passed in Pascal the corresponding pointer is passed in C If the description text e g says that a value of 1 0 must be returned in the variable y the C code should assign 1 0 to y i e y 1 0 Further differences between the definitions in C and Pascal will be highlighted along the way All the following routines have a parameter called pb It is a pointer to a record struct in C of type ExtModulesParamBlock Most users won t need the information stored in it Advanced programmers can refer to the section Global variables for more information about data to be accessed through pb 10 6 Working with external modules Routines to be defined in functions and programs SetUp procedure SetUp var moduleKind integer var name Str255 var requiredGlobals longint pb ExtModulesParamBlockPtr This routine is called when your module is linked to pro Fit It must return the following values e moduleKind must be set to the constant isProgram if your module
157. e they are part of a group You don t have to ungroup them If the objects are text objects and you aligned them with the Align command before grouping them their alignment will be maintained when they are edited Choose Ungroup from the Draw menu to ungroup a group If you resize a group containing text objects or data point symbols the proportions and size of the text and data points remain the same If you want to resize them proportionally with the group hold down the command key while resizing the group Objects created with the tools palette The upper part of the tools palette contains the drawing tools needed to create some of the Al FA om more simple drawing objects The lower part contains pop up menus to select background patterns line widths and oh dashing and arrows Their use is explained in the section Editing drawing objects Eir Drawing and Plotting 7 5 Text objects A Use the text tool to create text objects 1 Select the text tool from the tools palette 2 Click inside the drawing window The text dialog box appears Text Settings Helvetica kf Plain L Bold 6 Subscript C Italic 1 O Underline Superscript L Outline O Shadow LI Condense C Extend Here you can enter your text and specify font font size text styles and the vertical position of each character pro Fit uses the command key equivalents H T and S for the fonts Helvetica Times and Symbol
158. e to your definition after compilation will not affect the function or program as it was added to pro Fit s menus To update your changes you must choose Add to Menu again Debugging pro Fit offers a special debugging facility which helps you track down run time errors in your code If you check Debug in the function menu or click the small check box in the header of the function window and compile your definition Add to Menu special instructions are added to its code They allow to identify the position where a run time error such as sqrt 1 occurred These additional instructions make the execution of your program or function slower so you should uncheck Debug when you have finished correcting the function If you check debug and recompile your definition Add to Menu from the Prog menu the next time the error occurs its position in your definition will be highlighted Note that a function compiled with debug option on appears outlined in the Func menu Comparison to standard Pascal The programming language used to define functions and programs in pro Fit is closely related to the Pascal programming language However to keep it simple and to allow the generation of fast code some restrictions are present The most important differences to standard Pascal are e You cannot define your own data types 9 30 Defining functions and programs e All numeric types except complex are interpreted as floating point numbers B
159. eTo x0 radius 1 1 y0 MoveTo x0 y0 radius 1 1 LineTo x0 y0 radius 1 1 GroupEnd end The drawing routines accept floating point numbers as parameters pro Fit uses a precise floating point coordinate system for drawings and drawings created from a program will print at the highest resolution on all output devices A 4 Appendix A Predefined functions procedures and arrays Plotting in a graph PlotData PlotFunction plot a data set or a function SetLineStyle set the line style line thickness color of future line plots and the SetLineColor style of future data points SetFillColor SetFillPattern SetDataPointStyle SetBGDataPointStyle SetCurveFill set the filling options of plots and the appearance of error bars for SetEBarStyle the next curve or data set added to the current graph OpenCurve start end the definition of curves or data sets for the current graph CloseCurve OpenDataSet CloseDataSet AddDataPoint add a data point possibly including error bars to the current data DrawDataPoint set MoveTo LineTo Move define a curve in the current graph Line All the above calls access the current graph To make a graph the current graph double click it while holding the command key down From a program you can use the call Set Current Graph to make a graph the current graph The following is a small example program drawing a Lissajous figure in the drawing window Appen
160. ea Ea e Aaaa aaa 1 Help palloon e eas east e e celts Sages a aeaea ace Be ae a aS 1 Mhe pro FIt GUJE asama a a a a En Waa aaa ale ee ed sete ah Aia ee 1 On line evaluation of mathematical ExPreSSiONS ccceceseecceeeeeeeeeeeeeeeeeeeceeeaeeeeeeeaeeees 1 VS MMLC ta ec E E tek E en e Nee a s 3 Pind Ko Mnie IE E A A E E A te eset 4 Shortcuts and other Options eseseseseseseseseseseseerererersrsnsnsnnnsnsnnnnnntnnnnnnnnnnnnnnnnnn nnmnnn teens cole 5 Table of Contents ix Appendix A Predefined functions procedures and arrayS c sseeseeee 1 PUNIGUIONAl OMOUDS 3 c ta tt r tats totes e ta A aa atte Ge Latee ae cab i Salat las tales acince ats gh Mate oN 1 Operators reece A a a Re aaa aaa Ea Saras Aaa arr ee ee ee 1 Mathematical functions and CONStANS eccceceeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeaeseeeseeeeseteaeeeeeee 2 DatarprocessinNg onna a a aa 2 Accessing the data window ced desk sou le sddeuts ces se sates cute tex tatoencdee onsen seeas eaueseeucids etter ads 2 a ets aCe lao B o B creme area te se oe naire st errr re ae a a Co nee eee 3 Been AS A eee meer a ene enter sere Cee Net Nee Ee ane eee Re eee erm et ee etree eet er ee ern ee 3 Plotting N a orap eea a r ae a re tbat e Gait heals nth Ue cak a kd esa Atala da 5 Creating ANd ACCESSING Graphs eeeeecceceeeececeeeeeceseeeeseeseeeeseeseeeceeseeeceaneetseeaneeeaees 6 Editing the current CEA eos Ves cans heat edt cee cee cE a deeta et dea gen Vena e hs t
161. ea dates ea ede cele a e raa vant cab aaraa aana aUa teed Cearsats Gatideteany 7 Statistical analysis of a data Sele uwensan insane ra waa amma eee eieaees 7 Fourier transi rMS aieiaiee anad kidari nae oia ar aAa i aN aeaa 8 Defining a data set to work Onin eae ee eee eu nn anneanne nenene 11 Working with functions sisssisiiisisisisir iniaiaiai waaar aaa 1 Introd ctoN ninnan a AN N An E 1 FAN AVS TUS E E TEE EE E ca T O easing E E T E 1 Setting one of the parameters of a function to be equal to the value of x 2 Table of Contents V Using UN CEN NS e ect cst ea te tae hat a Sine ree aa i Daie endear eet acum Taaa aeia adea 3 Calc lating f nction VANICS 2c sce cs taec a seles oe lease csneci even a cst tem ani 3 Optimization of functions 5 acect soca cetsd obec en dchebedeerchinsenscs Seba mtebde nance hoenbaa apie beheernaread 4 Finding roots siea ana tartare aaan aaar aAa a eet rer ere Serr E a ret are 4 Finding minima and Maxima s c chee Seiad tena eerie atid 6 Integration Side eek a Kile Ce AN ave h de Ute Katee aes ede iee 6 TIMI SS MIS TAT NG EU Nc che tc each terete acerca icles id tga data a a hae nsce cattle 7 6 The Preview WindoW sssssussussunnnnnnnnnnnnnnnunnunnnnnnnnnnnnnnnnnnnnn mnnn nnna 1 Preview Window TOoOlS ssesessesesesnesesnesesnsnnrnsnnrnstnrnrntnntntnttnnnnnnnnnnnnnnnnnnnnnnnnnnnene ennnen ennet 3 Selecting data points with the arrow tool e e eseseseseseseseseensnnenensnsnsnsnsnnnsn
162. ecify the file where the window is to by saved after in If you do not specify the file where to save the window and the window has never been saved before you are prompted 11 12 Apple Script to enter a file name If you don t specify the file where to save the window and the window has been saved before the window is saved to the same file as before If the specified window is a data window it is saved as a regular pro Fit file by default this is equivalent to specifying as table If you want the data window to be saved as text file for exporting it specify as text Examples save window 1 to file HD data saves front window to file save window data to file data txt as text saves as a text file save parameter set Saves a parameter set save parameter set string the name of the parameter set Omit to save all parameter sets of the given function for string the name of the function the parameter set belongs to omit for global sets in alias the file in which to save the parameter set Omit to save as permanent set select Select the specified object select reference the object to select window function row column cell options add discontinuously add continuously deselect forget old omit for deleting the old selection select all Selects everything within the front window select all set data Set the data of an object set data reference the object to set to anything
163. eck the active parameters the algorithm will vary all parameters that are presently marked as active i e which in the parameters window have a bold face name and use for fitting checked The parameters are only varied within their limits if such limits are specified If you check X the algorithm will vary the function s x value Otherwise the x value is kept fixed at the given value The settings under precision affect the accuracy and speed of the calculation If your function is slow you should first choose a low precision and once you are satisfied with the results choose a higher precision Print full description controls the amount of information to appear in the results window Note that the command Optimize is designed for multi dimensional optimization If you only want to vary the function s x value but not its parameters you should use the faster command Extrema described below Finding roots The Analyze submenu in the Calc menu allows you to calculate the roots the extrema and the integral of a function 5 4 Working with functions Fit klonte Carlo Fit hd Optimize Calculate Polynombcd K Tabulate Polynomgx T Analyze Polynom x gt Roots Extrema Integral Data Transform Data Reduction Sort Table of Roots Transpose Table of Extrema Statistics Table of Integral la Ss aa k Roots The roots of a functio
164. ecommended as it can lead to compatibility problems with some printer drivers Not all printers support PostScript Don t use the Print drawings using PostScript option on non PostScript printers A non PostScript printer will ignore the PostScript commands and will print a non optimized picture with the resolution of the screen Switch off the option Print drawings using PostScript to get optimal results on a non PostScript printer see the next section below Drawings will generally look better when printed with PostScript than when they are printed at the printer s resolution However there are some minor problems when using special patterns or characters e When using patterns only the gray patterns will print All other patterns will be replaced by a 50 gray pattern e If Use QuickDraw for text is not checked outlined shadowed and underlined fonts are not supported e If Use QuickDraw for text is checked text is printed above all other items in a drawing Printing at full printer resolution If your printer does not support PostScript do not check Print drawings using PostScript In this case pro Fit determines the resolution the number of distinguishable dots per inch that can be printed of your printer when it is printing a drawing window Using this information pro Fit can optimize the picture it sends to the printer in order to take full advantage of the resolution available on your printer
165. ects can be rotated by angles multiple of 90 7 4 Drawing and Plotting To flip an object i e to exchange its left and right sides or its top and bottom 1 Select the objects to be flipped 2 Choose the desired operation from the Flip submenu in the Draw menu Flip Horizontal exchanges the left and right side of the objects Flip Vertical turns it upside down Note that you can only flip lines and polygons It is not possible to flip graphs legends imported pictures or text Flip has no effect on rectangles and ovals To change the order in which several objects overlap 1 Select the appropriate objects 2 Choose the desired operation from the Send submenu in the Draw menu You can move objects one position forward or backward commands Forward and Backward or you can bring them to the front or to the back of all other objects in the window To Front To Back To align objects 1 Select the objects to be aligned 2 Choose the desired operation from the Align submenu Using this menu you can align objects to each other or distribute them regularly If the objects are a group of text objects then every object retains its alignment when you edit it To group objects 1 Select all objects to be grouped 2 Choose Group from the Draw menu Objects that can be double clicked to change them e g text objects a graph or its legend can also be double clicked and changed whil
166. ed deg Polynom parameters deg 3 0000000 const 0 00 al 0 0000000 a2 1 0000000 a3 0 0000000 selected parameter const Cy offset lower limit none Be Use for fitting fix const al x aZexZ deg degree of the polynomial To change the fitting mode of a parameter e g from fit to not fit click its name It will switch from bold to normal or from normal to bold Alternatively you can click the check box Use for fitting in the selected parameter field Some parameters can never be fitted For example it does not make sense to fit the degree of a polynomial The name of such a permanently fixed parameter cannot be made bold by clicking it The Use for fitting check box is disabled Parameters that can never be fitted are called constant parameters those that are currently not fitted are called inactive parameters and those that are currently fitted are called active parameters Parameter limits The value of a parameter can be limited to any specified interval by entering the boundaries of the allowed interval in the corresponding edit fields The edit fields appear in the active parameter field once you select a parameter A parameter is not allowed to leave the specified interval during fitting optimization of the function or when you enter a new value in the parameters window See Chapter 5 Working with functions and programs and Chapter 8 Defining funct
167. ed by choosing Preferences from the File menu Doing so brings up a dialog box with several panels Each panel controls a set of options To choose a panel select its icon from the list in the left of the dialog box The panels Printing and PICT Options are discussed in Chapter 12 Printing In the following we discuss the panels General Drawing Preview Interface and Prefs File Panel General This panel controls some general options for output scrolling and data windows Preferences digits after the decimal point in numerical results L Results Window to front after output Default data window range 1e30 1e30 1e300 16300 Help ki Show hints Interface 7 The first item in this panel defines the digits after the decimal point used when displaying numerical results Enter a negative number if you want to set the total number of digits a positive number for setting the number of digits after the decimal points Preferences 13 1 The radio buttons under the title Default data window range control the default range and precision of the numeric columns in new data windows See the section Data Types of Chapter 4 for details Show hints controls if pro Fit should show some hints to guide an unexperienced user Uncheck this option if you don t want any hints to be shown Note that each hint also has an individual checkbox that can be used to diable it If you uncheck and late
168. ed eee aeem enclave nenene 31 Using pro FIt Mod leS ni nann anette eects piace ec dea aloe hence Geen eas 31 Saving functions and programS acccc veces faecal ee ote ete deed ee eae tte 31 Loading functions and Programs s secs ccc cpekercs kes eceptaeede heen ecpehes ta heesseepaerede meet 31 Removing functions and programs from the MENUG ccceeeeeeeeeeteeeeeeeeeteneeeees 32 Loading modules automatically ON StartUp ccecescececeeeeeeeeeeeeeeeeeeeceeeateeseeeeeeeeeees 32 Loading a set of modules together with a new preferences fil ccceeeeees 32 10 Working with external MOdUIES ccccceeeee cece cece seen eee eeeeeeeeeseeeeeeeees 1 Loading an external Module d n0ave cin ie eae alien le ee ea 1 Creating an external module eect eseeceeeeeeeeeseeeceetseeeceaeseeaceaeeesseeseeesseeseeeseaneesseeateees 1 Metrowerks Code Warrior Pro for Power Macintosh ccccesceeeeeeeeeeeeeeeeeeeeeees 3 Metrowerks Code Warrior Pro for 68K ecceceececeeceeeeeceeeeeceeeeeeseeeateesaeeaeeeseeeeeeees 3 viii Table of contents Think C or Symantec C for BK cisectccaveccaccessccteveyestden cote astenseibarastesbivebentevteees 4 Thnk Fascal for KY deel cts ote A a E a 4 MPW C C or Pascal for 68K cccceceeceeeeceeeeeeeeeeeaeceeceaeeeeseeseeesaeseeesaeeaeseaeeaeseaseaes 5 MPW C C for Power Macintosh cececcecceceseeeceeeeeeeeeeeeeceeeaesecaeeareesaeeaeeeseeease
169. edure SetColWidth columnNumber longint width integer Obsolete Use SetColumnPropertties instead Sets the width of the column specified in columnNumber to the value in pixels passed in width width must be an even number between 14 and 510 SetCurrentAxis procedure SetCurrentAxis whichAxis integer axisID integer Sets the current x or y axis The current axis is used for plotting as well as in various other calls such as SetAxisAttributes whichAxis is either xAxis or yAxis axisID designates the number of the axis Example Set CurrentAxis xAxis 2 makes X2 the current x axis SetCurrentGraph procedure SetCurrentGraph graphID longint Sets the current graph to the graph identified by graphip To make no graph the current graph set graphID to 0 SetCurrentWindow procedure SetCurrentWindow windowID longint This routine makes a window the current window of its kind There is a current data window a current drawing window and a current text window These are the windows used by the output routines such as LineTo and SetData When a new window is opened it automatically becomes the current window of its kind windowID is the window ID of the window such as it is returned by Get WindowID or FrontWindow Appendix A Predefined functions procedures and arrays A 57 SetCurveFill procedure SetCurveFill whichAxis integer axisID integer
170. ell of column 1 and enter the first year 1940 We fill the first column with the years and the second column with the population The first year is 1940 3 Click into the first cell of column 2 and enter the population in millions 2200 4 Repeat steps 2 and 3 to enter the other years and population figures in the following rows Enter the values given in Table 3 1 Note that you can use the arrow keys the tab and the return or enter key to move from one cell to another 5 Enter the column titles year and population in millions Click into the titles Column 1 or Column 2 and enter the new names Move the mouse to the vertical separation line to the right of the second column title click and drag the separation line a little bit to the right so that you see the complete title Your window should now look like this 3 4 Getting started data 6 Save the data by choosing Save As from the File menu You are prompted to enter a name for your file Plotting the data Now that we have entered the data we can display it graphically 1 Choose Plot Data from the Draw menu A dialog box appears SSS Plot Data Plot into current graph J Open new window X axis Y axis Data window population data X Column year Y columns O Selected rows only year population in millions Getting started 3 5 Here you can enter the ranges of the plot
171. elow To start fitting click OK Fitting can run for fractions of a second or for hours depending on the execution speed of the function you selected the number of parameters to fit and the number of data points The results of the fit appear in the result window You might want to choose its name from the windows menu and position it in a comfortable place before running a fit You can let proFit always bring the results window to the front after a fit by using the Preferences command To speed up fitting when you are using one of your functions you should define the function s partial derivatives with respect to its parameters The section The role of the partial derivatives below gives more information on this topic You can interrupt fitting by holding down the command key 88 and the period key simultaneously Note that pro Fit can run any fit in the background this means that you can work with another application while pro Fit is fitting You may want to place pro Fit s progress window in a corner of your screen to watch what is going on Fitting 8 13 Inspecting the progress of a fit During lengthy fits you can inspect what is going on and see if the fitting algorithm is behaving correctly pro Fit displays information on the current fit in its progress window Fitting iteration 4 chi squared D 24ES597Te 2 ampl 0 332209 delay 1 109223 type to interrupt This window lists the total number
172. em manually Check the custom check box This changes the contents of the ticks field ki major A list appears that contains all the ticks of the axis To add a tick click a free space in the list there is always a free space at the bottom of the list and enter the desired coordinate To remove a tick select it in the list and press the delete key To change the position of a tick click it and enter a new value Check major to create a major tick Major ticks are written in bold face in the ticks list Click the Standard button to automatically re calculate the tick positions according to the present axis settings To set the label of a tick mark to some general text instead of a number double click the label in the drawing window The text edit dialog box appears and you can then enter any kind of text you want Click Labels in the axis dialog box to edit the format of the labels The inner part of the dialog box now looks like this General Labels Prefix Lines Font Format Digits o Size fiz JG color MS ie Location below axis py 3 pt Use the Format field to set the format of the numbers Use Decimal to suppress exponential representation Auto exponent to have all labels Decimal in exponential format with varying exponent Fixed exponent to have Auto exponent all labels in exponential format with a common exponent The Digits field defines the number of digits to be shown after the
173. en coordinates omit for default position and size Appendix A Predefined functions procedures and arrays A 41 info String The info text attributed to the window Omit for leaving it empty fontName String The font to be used for the new window fontStyle Integer The font style to be used for the new window bold italic fontSize Integer The font size to be used for the new window NewFunctionWindow procedure NewFunctionWindow optional parameter list Opens a new text window Parameters name String The name of the new window Omit for using a default name boundsLeft boundsTop boundsBottom boundsRight Integer The bounds of the window in global screen coordinates omit for default position and size info String The info text attributed to the window Omit for leaving it empty fontName String The font to be used for the new window fontStyle Integer The font style to be used for the new window bold italic fontSize Integer The font size to be used for the new window NewWindow procedure NewWindow windowType longint Obsolete Use NewDataWindow NewDrawing Window or NewFunctionWindow instead Creates a new window of the given type windowType is drawingType for drawing windows dataType for data window or textType for function windows The new window becomes the current window of its type This procedure cannot be called while a function is running NextWindow
174. endix A Predefined functions procedures and arrays A 53 options Integer Controls what happens with the previous selection Pass addContinuously add to previous selection or forgetOld forget previous selection default SelectFunction procedure SelectFunction myFunc Selects the given function in the Func menu and makes it the current function func is the name of the function A call to SelectFunction myFunc is quivalent to SetOptions currentFunction myFunc SelectLeft function SelectLeft longint Returns the column number of the leftmost selected cells of the current data window or 0 if no cells are selected Causes a run time error if no data window is open External modules must use Get Selection SelectRight function SelectRight longint Returns the column number of the rightmost selected cells of the current data window or 0 if no cells are selected Causes a run time error if no data window is open External modules must use Get Selection SelectRow procedure SelectRow optional parameter list Selects a row or a range of rows in the current data window Parameters row Longint The row to select Omit if you use fromRow toRow fromRow toRow Longint The range of rows to select if you want to select several columns Omit if you use the parameter row options Integer Controls what happens with the previous selection Pass forgetOld forget present selection default
175. eneral remarks e Strings passed between pro Fit and an external module are always Pascal strings and not C strings If you are programming in Pascal you won t have any problems with this If you are programming in C you must remember that a Pascal string must be introduced by p example pMyString For assignments you can use the function Set PascalString described earlier in this chapter e Records structs passed between pro Fit and an external module always use 68k alignment Therefore for compatibility with Power Macintosh compilers definitions for C structs are always preceded by and if defined powerc defined __powerc pragma options align mac68k endif followed by if defined powerc defined __powerc pragma options align reset endif e Parameter indices under Pascal always run from 1 to maxNrParams in C they run from 0 to maxNrParams l The following lists the most important constants and types The numbers in curly brackets give the offset and size of some records and their components Pascal or C programmers won t need this information It is provided for porting the records to another programming language Numbers followed by N give the length for the non FPU 68k version numbers followed by F for the FPU 68k version and numbers followed by P for the PowerPC version const versionNumber 1 maxNrParams 64 maxParamNameLength 31 maxNrinputValues 6 isF
176. erent formats for representing floating point numbers or float e Real or float This format has smallest accuracy but requires minimum size It is used in data windows if you set the range of a column to 1E30 1E30 e Double This format has better accuracy but requires more size It is used in data windows if you set the range of a column to 1E300 1E300 e Extended or native double This is the format used for internal calculations It has the same or better accuracy as the double format The following list summarizes the features of each data type for the Power Macintosh and the 68k version of pro Fit real double extended native double Power Mac 68k minimum negative number f 1 8E308 1 8E308 1 1E4932 maximum negative number 2E 2 2E 308 2 2E 308 1 7E 4932 minimum positive number 2E 2 2E308 2 2E308 1 7E 4932 maximum positive number 1 8E308 1 8E308 1 1E4932 decimal 15 16 15 16 19 20 f The FPU version uses 12 bytes the non FPU version 10 Apart from the values in the list above pro Fit knows four other numbers 0 INF infinity INF infinity NAN The first three of them will do what you expect them to do E g 1 0 INF INF 3 INF etc NAN Not A Number is the result of any computation that cannot be carried out such as sqrt 1 The occurrence of NAN values in computations is reported as a run time error Appendix C File formats C 1 Appendix C File for
177. esees 5 Other compilefS 5c eae aie aea ha te a aE cela Gta tote a 5 Writing an external module oak cae cats cetera cane cea re cc cateins Seance ese eee eh acieaedene emcees cccter eneasbocenedts 6 Routines TOs OCI each cea a eae laa dene are cs alec estates 6 Routines to be defined in functions and Programs cccccecececeeeeseteeeeeeeeeeeeeeeeees 7 Routines to be modified in external programs OnI cceecceeeeeeeeeeeeeeereeeeeeeeees 7 Routines to be modified in external functions ON ceeeceeeeeeteeeeteeeeeeeeeeeteneeees 7 Predefined constants and YO OS eae des Gdecles yarn bcca ee endorsed daly galVersbdet le coed ea de eeusn teres 10 Global VAM ADIGS sannan cates eet eae terete eit acy octet eters 12 Procedures provided by pro FilsnvnttG cieek este ae et ate ote 13 11 Apple Scripte deiei einna adieu eae a aa a aie a vavadenuaewuradeangacie 1 guide te tC p Reeeememre erect emer ay rier eesnr sete mere Per R A rine er pert rrr eener tren ory peters 1 Example Simaia aa hae tates St os adr a aes Oe oe cael Add ch ren 1 Opening and closing a Single file ee ete teeeeseeeeeceeeeeeeceaeeeeseeaeeeeseeseeeseeeseeeeaees 1 Batch PrOCeSS AG sacs 52rtss staat tactic ah sake el oie eae eect cette te ce et 2 When to program when to script iin ccc escreeck eel nln aeteeenetieine cies 4 Apple Script commands and ClasSOS 3 cose seoccs hws deeeen ee ceidosuentyecwetey eeeud hee eis eae 5 Required Suite Events that every app
178. etrieve the results of a call to procedure Ext rema call the function GetResult selector Use one of the following selectors Appendix A Predefined functions procedures and arrays A 25 extremaCount the number of extrema found lt 100 extremaXValue x value of each extremal point extremaYValue y value of each extremal point extremaSign specifies if given point is minimum extremaSign has value 1 or maximum value 1 pass an index 1 extremaCount as second parameter to GetResult The following example finds the maxima of the current function between 1 and 1 then prints them program MaximaFinder var i nrPoints Longint begin Extrema xMin 1 xMax 1 subIntervals 50 nrPoints GetResult extremaCount for i 1 to nrPoints do if GetResult extremaSign i gt 0 then if max Writeln GetResult extremaxXValue i end Exp function Exp x extended extended The exponential function exp x e false const false 0 This constant stands for the logical value of false Fit procedure Fit optional parameter list Runs a fit Parameters function String Function to be fitted Omit for current function algorithm Integer Algorithm to be used levenberg montecarlo robust linear polynomial window String or Longint The data window s name or window ID Omit for fitting the front window xColumn yColumn Longint The columns contain
179. f no data window is open External modules must use Get Selection SelectCell procedure SelectCell optional parameter list Selects one or more cells in the current data window Parameters row Longint A row index if you want to select data in a single row Omit if you use fromRow toRow fromRow toRow Longint The range of rows if you want to select data in several rows Omit if you use the parameter row col Longint A column index if you want to select data in a single column Omit if you use fromCol toCol fromCol toCol Longint The range of columns if you want to select data in several columns Omit if you use the parameter col options Integer Controls what happens with the previous selection Pass addContinuously add to present selection forgetOld forget present selection default SelectCells procedure SelectCells left top right bottom longint Obsolete Use SelectCel1 instead Removes the current selection from the current data window and selects all cells within the given rectangle Call with all arguments 0 to deselect all cells SelectColumn procedure SelectColumn optional parameter list Selects a column or a range of columns in the current data window Parameters col Longint The column to select Omit if you use fromCol toCol fromCol toCol Longint The range of columns to select if you want to select several columns Omit if you use the parameter col App
180. f rows held by this column presently always equal to nrRows forWriting must be set to true if you intend to change the contents of the column set to false otherwise If you change the data in the returned handle you must subsequently call SetColHandle colType is the type of the column textColumn floatColumn doubleColumn Do not call DisposeHandle colH colHis allocated and deallocated by pro Fit The organization of the data in co1H depends on the data type of the column as returned by colType if colType floatColumn colH is a handle of type FloatColumnHandle handle to an array of 4 byte floating point values if colType doubleColumn colH is of type DoubleColumnHandle handle to an array of 8 byte floating point values if colType textColumn colH is of type TextColumnHandle handle to a record of type St ringData Note For columns of type floatColumn and doubleColumn the first entry of the array is reserved The value of the first cell is found in the array element having index 1 Warning 1 This routine should by used by experienced programmers only Warning 2 Accessing text columns in this way is not recommended The definition of the data structure may change in the future While you are working on the data in col you should not call any other routines accessing the data window except GetColumnHandle and SetColumnHandle When you modify the data in colH you should avoid calling any pro Fit routines until you h
181. f the column nrParams integer r o The number of parameters shown boolean r o True if the function is shown in the preview window lt Inheritance gt base class properties r o Class globalData an array of double values access by index 0 99 Elements real Note The entries in the list globalData can be acessed by index 0 to 99 but not by range globalData can also be accessed by functions and programs It provides a mechanism for exchanging data between scripts and pro Fit programs Example set myProg to program SumOneColumn calculates the sum of a column var i j Sum begin sum 0 j globalData 1 for i 1 to nrRows do if dataOK i j then sum sum dataji j globalData 2 sum end tell application pro Fit compile myProg compiles the above definition set globalData 1 to 2 the column we want to sum run program SumOneColumn runs the program delete program SumOneColumn clean up pro Fit s menus get globalData 2 get the result end tell Class single a real value with small accuracy Class table a data window access by index or name Elements column Properties name string the title of the window nrCols integer the number of columns nrRows integer the number of rows lt Inheritance gt base class properties r o Note In most cases you can use the classes window or table equivalently you can write 11 18 Apple Script set
182. f x coordinates X while observing the given errors and error distributions For each random guess 7p is calculated according to Eq 2 and the parameter sets corresponding to the smallest values of 7p are remembered The strength of this method is also its biggest disadvantage It looks for the best parameter set by shooting blindly inside the given region of parameter space Although there is an option of letting this parameter space region follow the position of the currently best parameter set this algorithm can only converge very slowly towards the best parameter set Its main use is to scan parameter space in order to find good parameter starting values for one of the deterministic fit algorithms or to try to jump out of a local minimum where a deterministic fitting algorithm is stuck Since the algorithm is normally used for a first estimate of fitted parameters it is not recommended to run it with non zero x errors this merely slows down the algorithm without substantially increasing the accuracy of the estimates The Levenberg Marquardt algorithm The Levenberg Marquardt algorithm is derived directly from the mean square deviation expressions 8 or 10 and cannot be used with deviation functions R other then the square deviation R d The Levenberg Marquardt algorithm is in principle the fastest fitting algorithm available in pro Fit Its performance however depends strongly on the behavior of the function
183. fer to the sample code provided on your distribution disks Procedures provided by pro Fit pro Fit offers a list of functions and procedures that can be called by your external modules If you are programming in Pascal they are defined in the interface of the file proFit_interface p If you are programming in C they are defined in the header file pro Fit_interface h Their implementation can be found in the files pro Fit_interface p or proFit_interface c respectively Most of the functions and procedures provided by pro Fit for external modules are the 1 1 equivalents of the ones that can be used when defining a function or program with pro Fit s definition language Refer to Appendix A Predefined Functions Procedures and Arrays for more information on the individual routines Working with external modules 10 13 11 Apple Script Introduction Apple Script is a language for scripting applications on the Macintosh It provides a common technique for automating tasks exchanging data and process remote control You can use Apple Script with pro Fit Note however that pro Fit cannot create i e compile an Apple Script To use Apple Script with pro Fit you need an Apple Script compiler such as Apple s Script Editor installed together with your system software You enter the script in the script editor and compile it there can save it in its compiled form When using Apple s Script Editor choose Save As f
184. g options Once you are satisfied with them click OK and fitting will start You can switch from one fitting algorithm to the other using the Algorithm popup menu More details about particular options for each algorithm are given below The Window menu lets you select a data window by default the foremost data window 8 12 Fitting The X column and Y column menus define the data set coordinates xj and yj If Selected rows only is checked only rows intersecting the current selection are used for fitting Otherwise all data in the X and Y columns will be used The popup menus X Errors and Y Errors let you specify the errors of your data In the X Errors menu choose zero to use zero x errors the usual case In the Y Errors menu choose unknown if you don t want to specify y errors in this case a value of 1 0 will be used as the error for all data points regardless of the order of magnitude of the y values and all points will have the same weight in the calculation of yg which is calculated with O 1 Choose Constant to set the standard deviation of all points to a given absolute value Choose Percent if you want to enter the error as a fraction of the data value in If you have the errors stored in a column of your data window then select Individual and choose the appropriate column in the pop up menu that appears Make sure that the columns you select contain the correct error values in the correct positions For e
185. ger The scaling of the x and y axes Values can be linScaling logScaling recSclaing for 1 x scaling probScaling probability scaling Omit this parameter s to use the current default scaling Integer The axis to be used as x and y axis Omit these parameters to use the default axes Boolean True if graph is to appear in a new window false if it is to appear in the current drawing window Boolean True if plot is to appear in a new graph false if it is to appear in the current graph Real Step width for plotting Set to 0 for using automatic step width selection Boolean True if last fitted parameters are to be used for the function false if the parameters in the Parameter window are to be used Real Thickness of the curve Omit for using default thickness Integer Line dash number corresponding to the dash menu of the curve Pass the position of the dash pattern in the dash popup menu The values between 1 and 8 always correspond to 1 2 3 4 5 6 ae 8 Integer The colour of the curve Pass values between 0 dark and 65535 bright Omit to use the default color Appendix A Predefined functions procedures and arrays A 49 Pos function Pos pattern s String integer Returns the position of the given pattern in string s Returns 0 if the pattern is not found in string s Example Pos hi hi there returns 1 Pos there hi there returns 4 Pos glue hi there returns 0 PRandom
186. ght are used to edit the range of the axis and its scaling type See the beginning of this section for a discussion of scaling types Note that First can be larger than Last if you want to reverse the axis The Ticks field to the right of the Draw check boxes is used to edit the tick marks Enter the first major tick the distance between major ticks and the number of minor ticks between two consecutive major ones The edit field 1st major gives the coordinate of the first major tick on the axis For a linear axis the Distance field defines the distance between the major ticks For a logarithmic axis this field changes its name to Decades and defines the number of decades between major ticks For a 1 x scaling the edit fields work in the same way as for linear scaling For probability scaling you can edit the list of tick marks directly using the Custom check box For a linear axis the minor field gives the number of minor ticks that are drawn between two major ones For a logarithmic axis this field is replaced by a check box called small ticks which must be checked to draw the minor ticks If major ticks are drawn for each decade the minor ticks are drawn for each multiple of ten If there is more than one decade between major ticks the minor ticks are drawn at all the powers of ten between the positions of the major ticks Drawing and Plotting 7 25 Instead of automatically calculating the positions of individual ticks you can set th
187. h functions Integral of Polynom x Between 1400 Iterations 5 15 The number of iterations affects the accuracy of the results A larger number of iterations yields a more accurate result but more time is needed for the calculation To tabulate the integrals by varying a parameter of the function or one of the integral s limits choose Tabulate Integral from the Analysis submenu The Spline function There is one special function in the list of predefined functions the Spline function You can use this function only when you have a set of data points xj yj in a data window the xj column and the yj column are identified by small x or y labels in column head Change the default x and y columns by clicking the header of a column while holding down the command key The Spline function is defined as a smooth cubic Spline curve going through all your data points The Spline function is useful for interpolation especially when you do not have a mathematical model for your data This is a simple data set together with its Spline function 10 0 Spline 50 data points eb lt a gt o0 5 0 1 0 0 0 1 0 x Value To use the Spline function for a given data set 1 Choose the Spline function from the Func menu 2 Bring its parameters window to the front and click the Select Data button A dialog box appears Working with functions 5 7 Spline Data Data Window U
188. hatever nature arising out of or in connection with the product or any part thereof or its use or application Should you have any questions concerning this licence or this limited warranty or if you want to contact QuantumSoft for any reason please write to QuantumSoft Postfach 6613 8023 Z rich Switzerland e mail profit quansoft com www _ http www quansoft com Copyright Developer Trademarks Customer Support pro Fit QuantumSoft 1991 1998 All rights reserved No part of this publication or the program pro Fit may be reproduced transmitted transcribed stored in a retrieval system or translated into any language or computer language in any form or by any means electronic mechanical magnetic optical chemical manual biological or otherwise without prior written permission of the publisher The information in this user s guide is subject to change without notice This guide refers to version 5 1 of pro Fit QuantumSoft Postfach 6613 CH 8023 Ziirich Switzerland http www quansoft com Macintosh LaserWriter Classic are registered trademarks of Apple Computer Inc Finder MultiFinder System 7 Mac OS 8 PowerBook Macintosh Duo Macintosh Quadra PowerBook Duo MacWorkStation Quickdraw Quickdraw GX Balloon Help Power Macintosh and Macintosh Programmers Workshop MPW are trademarks of Apple Computer Inc PostScript is a registered trademark of Adobe Systems Incorporated Think Pascal an
189. he Power Macintosh from the RISC SDK you will find an example for a make file on your distribution disks Other compilers The distribution disks contain several examples of external modules for other compilers Working with external modules 10 5 Writing an external module The following comments apply to Power Macintosh as well as 68k modules Note once again that the size of the floating point type extended or double in C must be the correct one for the version of pro Fit you are working with For the FPU version it is 12 bytes for the non FPU version 10 bytes and for the Power Macintosh version 8 bytes To write your external modules start from a stationery file ProgramTemplate or FunctionTemplate as shown above These files contain some routines that you will have to modify Routines to be modified The following table lists the routines defined in ProgramTemplate c p and FunctionTemplate c p that can or should be modified by the user Functions or procedures that are only used by advanced programmers are marked with a tT function name modify if defining a SetUp program or function CleanUp program or function InitializeProg program Run program InitializeFunc function Func function Derivatives function First Tt function Check function Last Tt function In the following section we will first describe the routines Set Up and CleanUp that are used for both types of modules Then we discuss th
190. he built in function Polynom to 6 A 60 Appendix A Predefined functions procedures and arrays SetFunctionProp_ procedure SetFunctionProperties optional parameter list Sets the properties of a function in the Func menu Parameters function String The function omit for currently selected function shown Boolean True if the function is shown in the Preview window false if not Omit to leave unchanged nrParams Integer The number of parameters Omit to leave unchanged Do not change the number of parameters while a function is being used e g for fitting SetGlobalData procedure SetGlobalData value real index integer Sets the value under the given index in a global data array This data array is shared between all functions and programs It can be used for communication between programs functions scripts and modules The index must between 0 and 99 See also GetGlobalData SetGraphAttributes procedure SetGraphAttributes flags longint Sets various attributes of the current graph flags is 0 ora sum of the following constants drawFrame draw the frame drawMajorGridx grid lines at major x ticks drawMinorGridx grid lines at minor x ticks drawMajorGridy grid lines at major y ticks drawMinorGridy grid lines at minor y ticks plotBehindAxes first draw curves then axes gridInFront first draw the rest then the grid gridInMiddle draw grid between axes and curves The last two consta
191. he correct scaling of the x and y deviations between a measured data point and the function that should describe it The errors normalize the deviations introducing dimension less numbers d and d Data points are weighted differently given more or less importance depending on their errors A small error will magnify the importance of a given difference a large error will make the normalized difference less important The distances d and d give the difference between measured coordinates and true coordinates Obviously we don t know the true coordinates otherwise there wouldn t be any need for a fitting program in the first place But we can estimate the true coordinates by minimizing some function of the distances d and dyj This function describes the difference between the model function and the set of data points and it is chosen in such a way that its minimization corresponds to the situation with the highest probability of producing the measured data set If the x and y errors are independent a fitting algorithm must generally minimize a mean deviation XR of the type Xr LR Rd 2 where the functions Ry y are deviation functions that tell us in a quantitative way how bad it is that a certain normalized distance d is found for a data point They are normally related to the error probability distribution This is the function that gives the probability that a certain measurement error occurs For ex
192. he menu to the right of the d dx popup field in respect to the x column The result is stored in the y column according to the formula l di d Yi Xia T XG The integral is calculated as the discrete integral of a column d over the x column d is again selected from the menu to the right of the Jax popup field The result is stored in the y column according to the formula y 5 da di Xi Xj i l Sometimes you may want to integrate over a single column d or you may want to differentiate over a single column d according to one of the following equations j 1 Y Xa or y d dj i l You can do this by creating a column containing the numbers 1 2 3 use the fill n command described under Various functions below and using this column as your x column e Various functions Here you can select various simple transformation functions such as sin x exp x In x etc Among them you can also find the currently selected function of the Func menu as well as the special functions fill O fill 1 and fill n which let you fill a column with the values 0 or or with ascending values 1 2 3 respectively e Formula If you select this sort of transformation you are free to define any transformation statement you like Columns are labeled by the character c followed by their column number You can use columns constants mathematical functions or calls to user defined functions in the Func menu Yo
193. he parameters and x value that maximize or minimize a function optimize reference the function to maximize or minimize xValue real the x value passed to the function the starting value if vary x is true precision real precision use 0 for maximal precision minimum boolean must be set to true to look for a mimium instead of a maximum vary parameters boolean set to true to find the values of the active parameters which optimize the function vary x boolean set to true to find the x value which optimizes the function full description boolean true to print a full description of the optimized parameters and results in the results window print results boolean true if comments are to be printed in Results window paste Pastes the clipboard into the front window paste plot data Plot one or more data columns plot data xColumn integer the x column yColumn integer a list of y columns of window the window to take our data from new window boolean true if plotting into new window new graph boolean true if creating new graph xFrom real x range beginning xTo real x range end yFrom real y range beginning yTo real y range end autoX boolean true if automatic x range autoY boolean true if automatic y range xScaling lin log reciprocal probability x scaling yScaling lin log reciprocal probability y scaling xAxis small integer x axis to
194. heck must return one of the values ok bad or update in the variable check to tell pro Fit if it should accept the new parameter and what it should do with the parameters window e If check ok pro Fit accepts the new parameter If check bad pro Fit refuses the new parameter and shows the old one in the parameters window e If check update pro Fit accepts the new parameter and redraws updates the whole parameters window Use this feature whenever you have changed a parameter other than a PNumber in the function check so that the user can see these changes For example your function can have two parameters that represent the same value in two different units of measurement Check can be used to update the value of one parameter when the other parameter is changed Note for advanced users Check is not called during fitting It is called once when fitting is complete Don t use Check for calculating intermediate results for later use in the evaluation of the function You won t notice anything wrong as long as you modify the parameters in the results window but your function will not work when fitting Always use the procedure First see below for calculating intermediate results Procedure Initialize This procedure is used for advanced programming It is called exactly once after compilation of your function or program You can use this procedure to initialize the value of variables or to write some in structions into the Results
195. hematical functions such as sin log are not part of the standard C function set In order to use them use lt fp h gt and lt fenv h gt the header files for the Power Macintosh numerics environment Note If you cannot find some of the libraries such as MSL C 68k 21 F A4 Lib you can rebuild them using the application Build MSL Libraries which you will find in the folder Build Scripts of the Metrowerks Standard Library In the target settings 68K Target of your project you must set the Project Type to Code Resource Creator to NLft Type to ftCD ResType to NLft ResID to any value larger than 127 Leave SegType empty Check Extended Resource Set Header Type to Standard In the target settings 68K Processor you must uncheck 4 Byte Ints and 8 Byte Doubles Set Floating Point to SANE if you are building a non FPU module or to 68881 if you are building an FPU module Think C or Symantec C for 68k If you are using Think C or Symantec C Version 7 0 x for 68k create a project containing the files MacTraps Glue for many Macintosh system routines proFit_interface c Glue for interfacing pro Fit XXX C your code MacTraps came with your copy of Think C and proFit_interface c can be found in your distribution package xxx c is your source code created from ProgramTemplate c or FunctionTemplate c Make sure
196. ich 7 p decreases and moves that way Then it samples again the surroundings by varying the parameters It stops when a minimum is reached When the x errors are not zero the X necessary for calculating the minimal distance between a data Re and the function curve are calculated for each data point by an explicit minimization of the term R d R d in Eq 2 Minimization is performed with limited precision in order to save processing time The will be determined to an accuracy which is a fraction of the x error specified for each point pro Fit will also count the number of function calls it is using to determine one X and will stop after a maximum of 50 8 8 Fitting function calls normally much less function calls lt 10 are needed to find the minimum This procedure introduces a small uncertainty in the determination of 7p However the statistical significance of such an uncertainty will be limited because the precision with which the x are determined is in any case much better then the errors of the data points A robust fit with x errors larger than zero will be considerably slower than the same fit performed with zero x errors When for zero x errors evaluation of 9 requires a number of function calls equal to the number of data points evaluation of 8 will require more or less ten times more function calls when x errors are defined The Linear Regression algorithm In this case we assume a straight li
197. idence interval will converge slowly and randomly towards some stable values If you want to see what happens during error analysis and your function draws itself fast enough open the Preview Window and make sure Show function is checked pro Fit will redraw the function periodically during error analysis and you will be able to see how the fitted function changes depending on the simulated data sets which are generated randomly However doing so will waste time for drawing the function and slow down the error analysis procedure Hide the Preview Window or uncheck Show function to make the error analysis procedure as fast as possible Fitting results When fitting is completed a summary of the results of the fit is displayed in the results window Depending on which fitting algorithm you used the data printed to the results window can vary slightly You may often want to transfer the values of the fitted parameters to the parameters window to use them as starting values for a further fit Choosing Params gt gt from the Calc menu transfers the best set of parameters to the parameters window The results of a fit are made available to custom functions and programs through a set of predefined functions used for accessing the fitted parameters the confidence intervals the value of chi squared and for the Levenberg Marquardt algorithm the full covariance matrix See Appendix A for more details If you want to save the parameter
198. if no data window is open NumberInvalid function NumberInvalid val extended Boolean External modules name See Invalid NumberToStr255 procedure NumberToStr255 x extended var s Str255 format digits integer External modules only Converts the number x into a string format digits control the conversion process format 0 normal conversion Appendix A Predefined functions procedures and arrays A 43 if digits gt 0 the number of digits after the if digits lt 0 the total number of digits approx format 1 optimized conversion removes unnecessary trailing zeros after the decimal point unnecessary signs decimals points etc digits the number of digits NumberToString procedure NumberToString x real var s String minimize Boolean digits integer Converts x to a string and returns it in s If digits is positive or 0 it specifies the number of digits after the decimal point otherwise the total number of digits of the resulting string If minimize is true trailing zeroes and any trailing decimal point are is removed NumFitParams function NumFitParams integer Returns the number of parameters of the last fitted function This is the total number of parameters including constant and inactive parameters Returns 0 if the last fit was not successful Use this function to check the validity of the last fit before using such functions as CovarMatrix Or ParamSD Open
199. ing the x and y data Pass 99 for using the row index as x column xErrKind Integer Errors of the x data individualError if the x errors are found in a column passed in parameter xErrColumn constantError if the x errors are constant passed in parameter xError percentError if the x errors are in percent passed in parameter xError zeroError if the x errors are assumed to be zero Omit if x errors are unknown xErrColumn Longint The column containing the x errors if xErrKind is individualError A 26 Appendix A Predefined functions procedures and arrays xError xErrDistribution yErrKind yErrColumn yError yErrDistribution fullDescription onlyActiveParameters Real The x error if xErrKind is constantError or percentError Integer The distribution of the x errors gaussianDistribution lorentzDistribution expDistribution tukeyDistribution andrewDistribution Integer Errors of the y data individualError if the y errors are found in a column passed in parameter yErrColumn constantError if the y errors are constant passed in parameter yError percentError if the y errors are in percent passed in parameter vError unknownError if the y errors are unknown Omit if the y errors are unknown Longint The column containing the y errors if yErrKind is individualError Real The y error if vErrKind is constantError or
200. ing your drawing You should check this option if you are printing to a PostScript printer When you check Print drawings using PostScript you should also check Use QuickDraw for text More information on this option is given below If neither Use QuickDraw GX nor Print drawings using PostScript are checked pro Fit prints the drawing at the printer s resolution No PostScript commands are sent in this case You should use this setting if you are printing to a non PostScript printer The default setting on a fresh installation of pro Fit is the last one I e no PostScript is sent to the printer The reason for this is that this default setting gives good results on most printers PostScript or not PostScript If you have a PostScript printer you will get better results if you check the Print Drawings using PostScript option 1 Printing with QuickDraw GX QuickDraw GX is Apple s improved printing and graphics environment shipping with System version 7 5 Note however that Quickdraw GX printing is not supported anymore under MacOS 8 You must check the Use QuickDraw GX option in the Printing preference panel if you want to export QuickDraw GX shapes through the clipboard or by drag and drop see next chapter Printing a drawing from another application When printing with QuickDraw GX texts will be kerned and ligatures will be used For more information on kerning and ligatures see
201. inition These procedures are called to perform special actions For example one of them Derivatives is called to calculate your function s partial derivatives Another Check can check a value that was entered into the parameters window The following describes these special procedures A summary is provided at the end of the section Function Check This procedure is only used to include some advanced features in your function It can make function definitions more user friendly Check is called each time the user changes a parameter in the parameters Defining functions and programs 9 23 window It can check the parameter that was changed and act accordingly For example it can refuse a parameter if its value is not acceptable It can also recalculate some other parameters and cause the parameters window to be redrawn Check can use the following predefined variables and constants pNumber The number of the modified parameter a l a n The parameters as they appear in the parameters window They can be checked and or changed mode 1 The mode of each parameter which can be active mode n inactive or constant You can check and or change the modes active inactive These three constants can be used to be compared to or constant assigned to mode i check The function must store its return value in this variable ok bad update One of these three constants must be returned in the vari able check C
202. int Output column for real part or amplitude in the frequency domain outputCol2 Longint Output column for imaginary part or phase in the frequency domain outFrequencyCol Longint Output column to hold the frequency values Hertz of the data in outputColl and outputCol2 Calulated from parameter timeInterval Omit if no frequency column is to be calculated timeInterval Real The time interval Seconds between consecutive data points in the input column Used for calculcating the frequency column Omit if no frequency column is to be calculated reallmaginary Boolean True if the output columns are to hold the real and imaginary values in the time domain false if they are to hold their amplitude and phase printResults Boolean True if statistical information on the processed data is to be printed in the Results window See also InverseFFT FrontmostWindow function FrontmostWindow windowType OSType longint Returns the ID of the front most window of the given type returns 0 if no window of the given type exists windowType can either be dataType textType or drawingType for specifying data windows function windows and drawing windows respectively FrontWindow function FrontWindow longint Returns the window ID of the front window The ID will be valid as long as the window exists For more information about window IDs see the section Windows and Documents above A 28 Appendix A Predefine
203. ion captureOff now output to the file is temporarily suspended Capture option captureOn now output to the file is again turned on A 16 Appendix A Predefined functions procedures and arrays Capture option captureClose now output to the file is turned off and the file is closed CellSelected function CellSelected row column longint Boolean Returns true if the given cell in the current data window is selected ChiSquared function ChiSquared extended Returns the value of the mean deviation function Yp obtained in the last fit yp is the mean square deviation y if the last fit was performed using Gaussian distributed errors Otherwise it is the value obtained by applying whatever deviation function must be applied for the given error specifications See chapter 8 Fitting for more details Causes a run time error if the last fit was not successful You can check if the last fit was good using the function numFitParams Chr function Chr i integer char Converts the given extended ASCII code i to a character Clear procedure Clear Equivalent to selecting Clear from the Edit menu ClearData procedure ClearData row col longint Removes any numerical value in the given cell row column of the current data window and leaves an empty cell Causes a run time error if no data window is open or if the given cell lies outside the bounds of the list ClearLabels
204. ion curve goes through the point indicated by the mouse pro Fit does this by numerically solving the function f a x y where a is the selected parameter and x y is the point indicated by the fitting tool If it is mathematically not possible for the function to go through that point no matter what the value of the selected parameter is then you will not be able to drag the function curve to that point The same applies if pro Fit fails to find numerically the correct value for the parameter If you use the fitting tool with a slow function pro Fit will automatically reduce the resolution with which the function is drawn so the function will not appear to be smooth anymore The resolution will be increased again once you are finished dragging Click the Redraw button to achieve the maximum resolution Inspecting and editing coordinates The last tool in the tools palette can be used to place coordinate markers on a given data point or on the function curve Select the marker tool and click the curve or a data point pro Fit creates a new marker at the indicated position While you move the marker tool around inside the viewport of the drawing window the corresponding coordinates are displayed in the bottom left corner of the preview window When you create a new marker it becomes the active marker The active marker is always flashing on and off You can create any number of markers The first marker you create is the reference marker Su
205. ion to your data Fine But what do you do if your model is described by some mathematical equation that does not appear among the built in functions in the Func menu Define your own function pro Fit can work with virtually all functions you can think of Let us look at an example Imagine you want to analyze a function of the form 3 12 Getting started y asin x xX In x b 3 3 with the parameters a and b To define this function e Choose New Function from the File menu This opens a new empty function window Untitled Function 1 e Er to Menu E een E debug Herp E Const E 2 Help o EEN a gt tig e Enter the definition of your function in the new window Just enter a 1 sin x ln x a 2 on the first line e Click the To Menu button in the function window or choose Compile amp Add To Menu from the Customize menu This translates your function into computer code pro Fit looks at what you wrote and sees that you used the variable x and the standard function parameters a 1 a 2 It therefore assumes that you want to define a new function and interprets your text accordingly The new function is added to the Func menu and the parameter window shows its default parameters Your simple expression is replaced by a complete syntactically correct function definition function User_Function begin y a 1l sin x 1ln x a 2 end The first line defines the name of the fu
206. ions and programs for more information on how to set parameter limits in user defined functions If no limits are specified the default values are and Inf Inf Fitting 8 11 During fitting each parameter is constrained to the interval specified by the parameter limits Running a fit Running a fit consists basically of three simple steps 1 Choose the function to fit in the Func menu Add your own function to the Func menu if it is not already there 2 Define which parameters you want to fit and their starting values You can do this in the parameters window as described above Look at the function and the data set in the Preview Window to see how good your starting values are Use the Fitting tool in the Preview Window to push the function towards the data points The importance of good starting values depends on the function to be fitted Some functions like the Gauss function are more difficult to fit A polynomial can be fitted with almost any starting parameter set 3 Choose Fit from the Calc menu The Fitting Setup dialog box appears Fitting Setup Algorithm Polynomial Data 9 _ ee OS fs 2 last choice Window Untitled Data 1 Z O Selected rows only X errors Zero Column Column Distribution Distribution L Error analysis ff Print full description Print active parameters only Using this dialog box you can set a number of fittin
207. is an external program and to isFunction if your module is an external function e name must be set to the name of your module If you are programming in Pascal you can simply assign a string to it name myName If you are programming in C you must make sure that you return a Pascal string For this purpose you can use the function SetPascalStr that is defined in proFit_interface c SetPascalStr name pmyName 255 The last parameter is the maximum length of the resulting string e requiredGlobals should usually be set to 0 Advanced programmers can set it to the size in bytes of a global data buffer they want to have allocated If requiredGlobals is returned with a value gt 0 pro Fit allocates a block with the corresponding number of bytes and stores a pointer to it inpb globals in C pb gt globals pb is a pointer to a record called ExtModulesParamBlock and is passed to all routines called by pro Fit Note that memory allocated in this way is deallocated automatically when your module is unlinked from pro Fit you must not deallocate this memory yourself CleanUp procedure CleanUp pb ExtModulesParamBlockPtr CleanUp is called when pro Fit is quitting or when your module is removed from pro Fit In most cases you won t have to do anything here Advanced programmers may wish to deallocate some special memory to close a port or to clean up other stuff here Routines to be modified in external programs on
208. is checked the resulting parameters of the last data fit are used for calculating otherwise the parameters displayed in the parameters window are used Choosing Tabulate Function x allows you to create a table of the function s values in a data window You are prompted for the first and last value of the table and its step width Table of Polynom x Tabulate by varying hae Min 1400 Max 2100 Step 0 5 auto points CI Use fitted parameters If you enter a numerical value for Step the function is calculated at equidistant x values If you enter auto in the field Step pro Fit chooses the x values at which the function is calculated by using a special algorithm that decreases the distance between calculated points wherever the function is strongly Working with functions 5 3 bent To tabulate the function at the values of the x column of the current data window enter points in the field Step Instead of auto or points you can enter a single a or p Optimization of functions The command Optimize from the Calc menu lets you find the maximum or minimum of a function by varying the function parameters and or its x value Optimize Polynom x Find the maximum of the function Find the minimum of the function by varying 4 the active parameters KIX Starting value for X bD Precision of calculation Print full description If you ch
209. ism for defining programs For example you can simply enter the following lines in an empty text window NewDataWindow for i 1 to nrRows do data i 1l 2 i When you click the button To Menu or choose Add to Menu from the Customize menu pro Fit finds that you have entered the body of a program and that you have used the variable 1 It therefore adds the necessary Pascal syntax and then compiles your program Your complete program will look like this Defining functions and programs 9 7 Untitled Function 2 ay eE to Menu C debug Help SJ Const program UserProgream wor i begin Hew tahk indow for i 1 to meRows do datali 1 2 i Gd Browse au Ye On line help for programming The help menus When defining functions and programs you can use a series of predefined names functions and procedures To help you use them pro Fit provides a popup menu Help in the header of all function windows Untitled Function 2 Te Menu 2 program User_Program a war i The Help popup menu lists all predefined routines names and syntax elements that you can use The items are organized hierarchically It is easy to find an item by moving the mouse over all the different headings In addition to this the function window provides a popup menu called Const that provides a list of some of the most important nature constants in science and engineering
210. it External modules are documents containing the computer code for a function or program pro Fit comes with a number of ready to run external modules containing useful functions or programs The next section tells you how you add them to pro Fit See the sections Creating an external module and Writing an external module for a detailed explanation of how to create your own external module Loading an external module To add an external module to pro Fit 1 Select Load Module from the Misc menu You are asked to locate your module 2 Choose the external module you want to load and click Open pro Fit checks if an external module can be found in the file you have selected If yes it is loaded If the module is a function it is added to the Func menu If it is a program it is added to the Misc menu Instead of loading a module by choosing Load Module you can double click its file For this the file type and creator of the file must be ftCD and NLft respectively An important note for Power Macintosh users If you have loaded a module and you subsequently change it e g by recompiling it you must remove the loaded module from pro Fit before loading its new version To load your modules automatically at start up put them into a folder called pro Fit Modules located in the same folder as the application itself or in the Preferences folder of the System folder See the end of Cha
211. ites the integer number n to the results window WriteString procedure WriteString s Str255 External modules only Writes the string s to the results window WriteToTextFile procedure WriteToTextFile fileRefNum longint Re directs the output of Write writeln WriteNumber etc to a file fileRefNum is the number returned by CreateTextFile or 0 if you want to direct output to the results window Call closeTextFile to close the file when you are through XColumn function XColumn longint Returns the column number of the x column in the current data window It returns zero if no x column was set and produces a run time error if no data window is available XErrColumn function XErrColumn longint Returns the column number of the Ax column in the current data window It returns zero if no Ax column was set and produces a run time error if no data window is available YColumn function YColumn longint Returns the column number of the y column in the current data window It returns zero if no y column was set and produces a run time error if no data window is available YErrColumn function YErrColumn longint Returns the column number of the Ay column in the current data window It returns zero if no Ay column was set and produces a run time error if no data window is available Appendix A Predefined functions procedures and arrays A 71 Appendix B About numbers pro Fit uses three diff
212. ive If there were negative numbers in the input column the procedure Alert is called Alert takes one argument a string i e a text between quotes It displays an alert box that shows this string Here is the alert box that appears in case negative numbers are found when the above program is executed Some data was negative lt This alert box has two buttons Stop and OK If you click Stop the execution of your program is immediately aborted If you press OK the execution of your program continues For our sample program it will not make any difference if you press Stop or OK when the program calls Alert it is at its end anyway You can now add the sample program MakeRoot to the Prog menu click Add in the function window Then prepare a data window with some data in its first column and run MakeRoot by choosing MakeRoot from the Prog menu A shortcut As mentioned at the beginning of this chapter you can abbreviate the definition of a function by simply entering its expression using x and the parameters a 1 a 2 etc in a function window When you click the button To Menu or choose Compile amp Add to Menu from the Customize menu pro Fit scans the contents of the text window Compile amp Add to Menu If it encounters a simple expression using x it assumes that you want to define a function and adds the corresponding Pascal syntax around your expression You can use the same mechan
213. k The thickness of the caps and of the bar lines in pixels 0 001 50 SetErrorAnalysis procedure SetErrorAnalysis confidence extended iterations longint Sets the options for the error analysis to be used in the next call to Fit confidence is the confidence interval probability in percent iterations is the number of simulated data sets to be analyzed Set FillColor procedure SetFillColor red green blue longint Sets the default RGB color used for filling shapes Used for drawing or filling curves red green blue are integers between 0 and 65535 Appendix A Predefined functions procedures and arrays A 59 SetFillPattern procedure SetFillPattern pattern integer Sets the default fill pattern used for filling drawing objects Set pattern to 0 for making the shapes ks The ares coe shows a list of all eae and their pattern number we eee ET Ee FH ed ES ES SE SetFitDefaults procedure SetFitDefaults algorithm integer yErrDistribution xErrDistribution integer xErrColumn longint xErrValue extended stopTime extended Sets advanced fitting options It sets the x error column and type the algorithm and the stopping criteria to be used in all subsequent calls to Fit algorithm the algorithm to be used 1 Levenberg Marquardt 2 Montecarlo 3 Robust 4 linear regression 5 polynomial yErrDistribution xErrDistribution the distribution of the x and y error
214. late frequency Select the column that contains your time domain data and the columns for the real and imaginary parts of your frequency domain data If you check the box Calculate frequency you must enter the time interval between two points of the time domain Data interval and a column Frequency for the frequency values of the frequency domain data Working with data 4 9 Instead of calculating the real and imaginary parts in the frequency domain you can also calculate their absolute value and complex argument check Amplitude and phase instead of Real and imaginary parts To calculate the inverse Fourier transform select Inverse FFT from the Fourier transform submenu The dialog box that appears for this command is very similar to the dialog box we have just seen Inverse Fourier Transformation Input Real and imaginary parts Amplitude and phase Real part Imaginary part Data interval L Je Output Data column Time Mf Calculate time Your input data are the complex values in the frequency domain You select the columns for the real and the imaginary parts or alternatively when you select Amplitude and phase instead of Real and imaginary parts you select the columns for the absolute value and the complex argument of your data The output column contains the real valued data points of the time domain If you want to calculate the time range in seconds for your output data check Calculate time e
215. later in this chapter for details E x lt x On the right you see a selection of the data point styles offered by pro Fit Choose Other from the point style menu to create your own data point symbols using the Custom Points dialog box Her Omddpro 0 Drawing and Plotting 7 9 Custom Points Background 400 view Fy mep A OOA E D pPts mE 1 Fill symm 3 kf Frame Mirror L H Foreground SMD Size 20 5 OCAVE P pts 2 4 Fill white symm ki Frame Mirror L L H Point line thickness pro Fit defines a data point symbol as a background shape and a foreground shape With this dialog box you can design both of them pro Fit offers some predefined simple shapes and lets you edit any closed polygon to define a new data point symbol In the above example both foreground and background shapes are defined using a closed polygon You can use this dialog box simply to change the size of an existing point symbol or to design more complicated point symbols Draw the foreground and background shapes in the preview area at the right of the dialog box Use the popup menu above it to set the magnification of the preview The center of the preview area defines the hot spot of the data point symbol When plotting the hot spots of data point symbols are positioned on the correct mathematical coordinate Draw a closed polygon by dragging the polygon han
216. le and use CloseTextFile to close the file when you are through Cut procedure Cut Equivalent to selecting Cut from the Edit menu data array data row col longint of extended This array holds the data of the current data window Assigning a value to data row col sets the value of a cell in this window Reading the cell data row col returns the value of a cell Causes run time errors if the data cell is not within window if the cell is empty if the cell is part of a text column or if no data window is open Always call Dat aK row col before using the value of data row col The array data does not exist for external modules External modules must use the routines SetData and GetData for numeric cells and GetCe11 and Setce1l1 for text cells In addition to this the routines GetDefaultData GetColHandle and SetColHandle provide some fast low level access DataExportOptions function DataExportOptions optional parameter list Sets the options for exporting data windows as text files Appendix A Predefined functions procedures and arrays A 19 Parameters mode Specifies the basic format Pass withTitles for standard format with column titles withoutTitles for standard format without column titles or customFormat for a customized format as specified in the following parameters withTitles Boolean Add the text from the info field to the beginning of the file copyInfo Boolean Write
217. lect several rows or columns click and drag over the row or column numbers you wish to select e To select all cells in a column starting from a certain row hold down the option key while clicking the topmost cell of the desired selection or click the column number field and then drag the mouse down to the first row to be selected e To select all cells choose Select All from the Edit menu You can create a discontinuous selection e To extend or modify a current selection to a discontinuous selection of rows click and drag into the rows to be selected or deselected while holding down the command key e Note that a discontinuous selection can also be created by selecting data in the Preview window See also Chapter 6 Preview Window Data types By default each column of a data window contains numerical data i e real valued numbers The precision and range of these numbers can be 4 2 Working with data 10 to 10 with approximately 12 significant digits double precision 10 to 10 8 with approximately 6 significant digits single precision See Appendix B for details on numeric representations By default a new data window opens with either single or double precision columns The default type can be selected by choosing the command Preferences from the File menu In the dialog box that comes up click the General icon See Chapter 13 for details A column can also contain text up to 255 arbitra
218. lement of the covariance matrix C The full covariance matrix of the parameters used in the fit is the inverse of a matrix A C A The matrix A is also called curvature matrix and it is defined by the errors standard deviations of the data points and by the partial derivatives of the function with respect to the parameters When x errors are specified the derivative of the function with respect to x must also be calculated and the curvature matrix A is given by Fitting 8 7 1 Of x Of x cay mes 2 13 z o 03 2 a a 3 ox If the x errors can be considered to be zero the curvature matrix A has the simpler form 1 Of x Of x A E 14 L o a da S Loosely speaking this matrix describes the propagation of the errors from the data points to the parameters We refer to the specialized literature for more details If the x errors can be regarded as zero pro Fit lets you specify unknown y errors In this case the y are assumed to be normally distributed all with the same standard deviation o For fitting o i is taken to be 1 for all i The real o is then estimated from o v where v is the number of degrees of freedom i e the number of data points minus the number of parameters and 07 is calculated from the expressions given above It is interesting to consider the case where a parameter reaches one of its limits during a fit As you know pro Fit lets you specify for each fu
219. lication should support eeeeee 5 pro Fit suite Special commands for pro Fit 22 0 2 ececeeeeeeseeeceeeeeeeceeeeeeeceeeeeeeseeeeeeeees 6 Classes of the pro Fit SUNG tinea tee ves tte a ecier ed ea arate ilaee hs 15 12 SPRUE GQ ie n cic aeecueina ca tuna tau a aa ctannatuawadevendun oiey bin EEEa anaE aina Ean E hia 1 Printing from pro F ita ernega eee ere ener mene mt nor ne aan ef Renee pe ioe ee eee nO 1 Printing With QuickDraw Ga sosses ste otetes ciate arate tacees catia a a a sociale atone a tea 2 Printing with POSUSGNPE lesctecectee lone ead eheleek maces tasers een lacie lade alan ee 2 Printing at full printer resolution feeemeremer arent error truer emy sere cern rr Brera orn aera reane ta 3 Printing a pro Fit drawing from another application ccccceeseeeeeeeeeeeeeeseeeeeeeeeeeeeeee 3 13 Preferentes diiin e eiaa a Aunannee aun euaddiiwd cuuinauaiaeloaturawebnwtels 1 EAEE E E E E E 1 Panel Priming ste erence 0 ohn ere ete eee ea a a a a ia oleae dts e 2 Panel PIC E Options inm inair aa a a ree aaa a a aa a 2 Panels Drawing anana A SN 2 Panel PROWIOW anin tencueeaed aldo ches menla i atadai aap eaea aa A tant an eaaa Hee cte dence cap uelataeieaceee ge 3 eaa aieiai e E A ar eels dA tn ct des ead 4 Panel Prefs TM Stes teh age Ba alate See Sates etcetera ec needed hres tet ate atatenet Ato ennnen 4 14 General featUreS residents pa a td a epa aaa eaa a oianetan eia 1 Getting Nelss e aE peA aa a aer aa
220. ling labels style and range than the X1 axis A typical application for this is a graph that displays its x 0 0 values on its horizontal bottom axis and the reciprocal x values on its top axis 1 0 0 0 2 0 4 0 6 0 A graph with a different coordinate axis as the X2 axis As an example imagine that you have a set of data that was measured for different light wavelengths between 400 and 1000 nm You would like to plot your data as a function of wavelength but you would also like to have a reading for the light energy in eV on the top axis The energy of the light is inversely proportional to the wavelength so you have to use 1 x scaling for the top axis To create such a graph 1 Create a graph with an x axis from 400 to 1000 Simply plot your data between these limits Choose Plot Data from the Draw menu Make sure that you create a new graph by unchecking Plot into current graph in the dialog box that comes up 2 Double click the upper x axis X2 axis The axis dialog box see above for the top axis appears 3 Uncheck Same as X1 Do this to make sure you only change the top x axis leaving the bottom x axis alone 4 Change the axis scaling to 1 x Be sure that the General radio button is selected and use the scaling popup menu found to the right of the edit fields for the axes ranges 5 Enter 1 2398 for First and 3 0996 for Last Drawing and Plotting 7 27 A wavelength of
221. list of real r o fitting standard deviations of the parameters optimizedX real r o optimization x value optimizedY real r o optimization y value rootsCount integer r o roots number of roots rootsX Values a list of real r o roots x values 11 16 Apple Script rootsY Values a list of real r o roots y values extremaCount integer r o extrema number of extrema extremaX Values a list of real r o extrema x values extremaY Values a list of real r o extrema y values extremaSigns a list of real r o extrema signs 1 for maxima 1 for minima integralValue a list of real r o integral value of the integral integralAccuracy a list of real r o integral last correction statCount integer r o statistics the number of evaluated values statSum integer r o statistics the sum of all values statMean real r o statistics mean statMedian real r o statistics median statStdDeviation real r o statistics standard deviation statMeanAbsDeviation real r o statistics mean absolute deviation statMinimum real r o statistics minimum statMaximum real r o statistics maximum statVariance real r o statistics variance statSkewness real r o statistics skewness statKurtosis real r o statistics kurtosis Class cell A cell in a data window access by index Properties value real the value of the cell lt Inheritanc
222. lization of global variables can be done here statements end bsan the main body of the program where execution starts Note the after the end statements end After the title of the program you can define constants and variables The definition of constants is preceded by the keyword const which is followed by the name of each constant the operator not and the value of the constant Example Defining functions and programs 9 11 const c 3e8 startValue 22 Once you have defined the value of a constant you cannot change it anymore The definition of variables is preceded by the keyword var which is followed by a list of variables var u v real done boolean Note that you can specify the type of each variable such as real boolean If you omit the type specification it is assumed that the variable is of type real Variables and constants that you define in the head of a program can be accessed by all statements within the program and the program s procedures and functions You can use any name you like for a constant or variable as long as it is not yet used for any other purpose It can contain letters and digits but must start with a letter Examples for names are myFunc xx JO legal names 2TOX illegal starts with a digit then illegal reserved keyword The same rules apply to the names of procedures and functions see below Following the definition of constants
223. llipse The arc extends from the angle start to the angle start length DrawDataPoint procedure DrawDataPoint x y extended Creates a data point at the coordinates x y in the current drawing window It uses the point style set by SetDataPointStyle SetBGDataPointStyle If OpenDataSet has been called before calling DrawDataPoint then DrawDataPoint creates a new data point in the current graph instead of drawing in the drawing window In this case DrawDataPoint adds a point with zero error bars a call to DrawDataPoint x y is then equivalent to a call to AddDataPoint x y 0 0 0 0 DrawEllipse procedure DrawEllipse left top right bottom extended Creates an ellipse inside the specified bounds in the current drawing window DrawLine procedure DrawLine start_h start_v end_h end_v extended Creates a line in the current drawing window extending between the given start and end points start_h start_v end_h end_vy DrawNumber procedure DrawNumber theNum extended decs integer theAngle extended docenter Boolean Converts theNum to a string and draws it in the current drawing window decs defines the number of digits after the decimal point that must be displayed The text appears at the current pen position set with MoveTo If docenter is true the number is centered on the current pen position and the current pen position remains unchanged If doCenter is false the text starts at
224. lly anywhere in a drawing window This is useful for creating your own legends or for exporting single point symbols to other applications e g for figure captions Since the point symbols can assume a quite large size they can also be used as parts of standard drawings Data point symbols can be edited using a particular set of tools that let you achieve effects not easily achieved with other drawing objects below you will find more details about editing data point symbols To create a point object 1 Choose the point tool from the tools palette Keep the mouse button down for a little while to select the symbol that you want to use A pop up menu with a choice of data points appears Its top part contains a set of standard predefined point symbols The last line contains user defined symbols and the Other field lets you define new point symbols jot Ome ob N s 7 x a o o ay co a Tu i 2 Click the desired position within the drawing A new point symbol drawing object is created 1 Choose the point tool from the tools palette To change the plot symbol of a point object select it and choose the desired symbol from the point style pop up menu in the tools palette or double click it to go directly to the custom points dialog box If the selected object is a graph or a legend the new point style is applied to the data plots contained in the graph See the section Graphs and legends
225. ln log exp tento sqr sqrt Gamma Gammal GammalLn GammaP m or pi true false INF INF invalidNum Data processing Statistics Sort ReduceData FFT InverseFFT DataTransform Transpose Accessing the data window data i jl DataOK ClearData TestData SetData GetData GetCell SetCell SetDefaultCols SetDataWindowProperties xColumn yColumn xErrColumn yErrColumn Mathematical functions and constants trigonometric functions arguments or results in rad hyperbolic functions error function erfc is the complementary error function erfc 1 erf natural logarithm base 10 logarithm exponential function eX power of ten 10X square square root x2 Vx Gamma function and incomplete gamma function constants an invalid number Used to mark empty data cells in a data window run statistical analysis get results sort smooth or reduce data FFT and inverse FFT general data transfomations transposing rows and columns an array and some routines for accessing the data in the current data window setting and reading cell contents including text cells set the default x y Ax and Ay columns and the number of columns and rows in the current drawing window the column numbers of the x y Ax and Ay columns in the current data window Appendix A Predefined functions procedures and arrays NrCols NrRows SelectLeft SelectTop SelectRight
226. loating point numbers apparent accuracy will obviously suffer when drawing on a low resolution device such as a normal monitor In order to represent your drawing at a certain resolution determined by the zoom popup menu pro Fit must round the floating point coor dinates describing a drawing object When you draw something at a low resolution pro Fit must figure out reasonable floating point coordinates It does this by extrapolating from the low resolution appearance in such a way that a high resolution view would give the same symmetry For example at the 100 view you can draw three overlapping lines with thicknesses of 0 25 0 5 and 1 0 pts All three lines have exactly the same appearance e g they appear 1 pt thick pro Fit sets up the floating point coordinates of the lines in such a way that the thinner lines are centered on the 1 pt thick line Thanks to this interpretation you get the same result at 100 view if you draw a pt line and then make it 0 25 pt thick or if you draw a 0 25 thick line directly On the other hand if you draw a 0 25 pt thick line at 400 view go to 100 view and draw another 0 25 pt thick line on top of it the two lines will not overlap This is because the first line was positioned with a much larger precision than the first line Use the Align submenu in the Draw menu to make sure that such lines really overlap or look at their coordinates using the Drawing Info window see later Likewise if
227. lt check box when saving a style or if you define a style with the name Normal this style becomes pro Fit s default style The next time you start up pro Fit the first graph you create will use this style When you load a style a dialog box appears asking you to choose which parts of the style you want to apply to your graph Drawing and Plotting 7 33 Apply Style Select the characteristics you wantto use ki Bounds Xmin Xmax 3 A Axes and grids styles thickness color Lf Curve styles thickness color k Text styles font size hf Label styles number of digits ki Tick styles number of minor ticks G hsi The characteristics of a style are Bounds The ranges of the graph i e the minimum and maximum of all the axes the positions of the first ticks the distance between major ticks the number of minor ticks Axes and grid styles The line thickness dash and color of the axes the frame and the grid the distance of the labels from the axes the location of the ticks inside or outside Curve styles The line style of all plots i e curves and data points Text styles The font size and text style of the labels Label styles The number format of the labels The number of digits after the decimal point and the representation exponential auto decimal of the labels Tick styles The number of minor ticks the axes scaling logarithmic or linear and whether the labels
228. lumnProperties instead Changes the type of the column specified by columnNumber to theType theType can have the values textColumn for text columns floatColumn for numeric columns having a range of 1e30 1e30 A 56 Appendix A Predefined functions procedures and arrays i e 4 byte floating point values or doubleColumn for numeric columns having a range of 1e300 1e300 i e 8 byte floating point values SetColumnPr _ procedure SetColumnProperties optional parameter list Sets the properties of one or more columns in the current data window Parameters col Longint The index of the column to change Omit if passing values for a column range in parameters firstCol lastCol firstCol lastCol Longint The range of columns to change Omit if passing a single column in parameter col name String The title of the column s Omit for leaving it unchanged nrDecimals Integer The number of decimals for numeric columns Omit for leaving it unchanged format Integer The format for numeric columns scientificFormat or floatingFormat Omit for leaving it unchanged width Integer The width of the column s in pixels Omit for leaving it unchanged type Integer The type of the column s floatColumn 4 byte floating point having a range of 1e30 le30 doubleColumn 8 byte floating point having a range of 1e300 le300 text Column Omit for leaving it unchanged SetColWidth proc
229. ly InitializeProg procedure InitializeProg pb ExtModulesParamBlockPtr This routine is called before a program is run for the first time Most users can leave it empty Advanced programmers may wish to allocate some memory open a port initialize global static variables etc here Run procedure Run pb ExtModulesParamBlockPtr This routine is called when your program is executed It should hold your program s main code Routines to be modified in external functions only An important note about parameter indices When accessing arrays that hold values names etc of the parameters such as a i aQO names i mode il dyda i the index i ranges from 1 to 64 in Pascal but from 0 to 63 in C Working with external modules 10 7 InitializeFunc procedure InitializeFunc var hasDerivatives boolean var descristLine descr2ndLine Str255 var numberOfParams integer var a0 DefaultParamInfo pb ExtModulesParamBlockPtr This routine is called once after your external function has been linked to pro Fit It must return some default values and information about the function Advanced programmers may also use it for initialization of global static variables memory allocation etc InitializeFunc should return the following data in its parameters e hasDerivates must be set to true if you want to calculate some derivatives of your function with respect to its parameters yourself in the function Derivatives desc
230. m of the Calc menu Parameters window String or Longint The name or window ID of the data window operation Integer The operation to be performed Use one of the constants sumOp multOp subOp divisionOp powerOp DIVOp MODOp integrateOp derivativeOp formulaOp functionOp sqrOp sqrtOp invertOp absOp expOp lnOp tentoOp logOp fill_O fill_l fill_N sinOp arcsinOp cosOp arccosOp tanOp arctanOp sinOp arcsinOp cosOp arccosOp tanOp arctanoOp selectionOnly Boolean True if operating on current selection false if operating on x and y column selRowsOnly Boolean True if operating on the selected rows only xColumn Longint The x column omit if you pass true for selectionOnly yColumn Longint The y column omit if you pass true for selectionOnly function String The function to be used if operation is funct ionOp formula String The formula if operation is set to formula argumentColumn Longint The column to be used as argument if the operation works on a column argument argument Value Real The value to be used if the operation works on a value argument To use this command you best choose Start Recording from the Misc menu then choose Data Transform from the Calc menu and set the desired options Hit ok The correct call is then recorded in your function window DataOK function DataOK row col longint Boolean Returns t rue if the given cell of the
231. mally expect a macro to do such as complicated calculations and data transformations Here is a small list of what functions or programs can do e Calculate any kind of numerical value even if it cannot be expressed in a closed mathematical formula e Access the data in a data window write results into the results window use dialog boxes and alert boxes e Execute any command from pro Fit s menus open and save files create and close windows e Run fitting operations and predefined numerical algorithms and retrieve their results e Create graphs and other drawings in a drawing window using a precise floating point coordinate system Note All the above can also be done from an external module a piece of code generated by your fa vorite compiler If you are used to programming your own code for data or function analysis you can consider proFit as a big library offering routines for numeric analysis data input output and high resolution graphics Information on how to define external modules is found in Chapter 10 Working with External Modules When you are defining your functions and programs within pro Fit they are translated compiled into native computer code when they are added to pro Fit s menus This code can be executed very quickly by your Macintosh Simple programs and functions can be defined very easily and quickly Even very complicated programs can be defined without much work by simply recording y
232. mats This appendix describes the file formats used by pro Fit for transferring data or drawings to and from other applications Data The default text format To exchange data between pro Fit and other applications text files are used Usually such files hold one or more lines of text Each line contains all values of a row separated by tabs The lines are separated by carriage returns It is possible to use other characters instead of tabs and carriage returns see below There are two standard formats of data text files produced by pro Fit The standard format with titles is defined as follows 1St line namel gt name2 gt name3 J 2nd Jine 0 123 gt 1 732 1 122 31d Jine 2 233 gt 2 125 gt 2 126 J The standard format without titles is very similar but without the column titles line There is an interesting exception for data text files to be loaded into pro Fit If the first line is a single star pro Fit reads the second line as the column titles even if the file is loaded as being standard format without titles Lines are separated by carriage returns char 13 or r for C programmers chr 13 for Pascal programmers The first line with the column titles is optional These names are separated by tabs character code 9 here denoted as gt char 9 or t for C programmers chr 9 for Pascal programmers If pro Fit reads a file without column titles it sets the c
233. mber An invalid number a NAN A 38 Appendix A Predefined functions procedures and arrays KeyPressed function KeyPressed key integer Boolean Returns true if the given key of the keyboard is currently held down key can be optionkey commandKey shiftKey controlKey Length function Ord s String integer Returns the length of the given string s Line procedure Line dx dy extended Draws a line from the current pen position x y to the position x dx y dy Offsets the current pen position by dx dy LineTo procedure LineTo x y extended LineTo draws a line from the current pen position to x y Sets the current pen position to x y Ln function Ln x extended extended Returns the natural logarithm base e of x Causes a run time error for x lt 0 Returns INF for x 0 LoadParameterSet procedure LoadParameterSet optional parameter list Loads a given parameter set previously saved with SaveParameterSet The loaded parameters appear in the Parameter window Parameters name String The name of the set ofFunction String The function the parameter set belongs to Omit if the parameter set was available to all functions file String The file from where the parameter set must be loaded Omit to load from permanent sets See also AddParameterSet UseParameterSet Sav ParameterSet DeleteParameterSet Log function Log x extended extende
234. mined from the current parameter set doesn t decrease appreciably anymore from one iteration to the next When finished the parameter values and their standard deviations are printed to the results window If you need to access the complete covariance matrix you can define a program that uses the predefined function CovarMatrix See Appendix A for more details on how to use this function Using the Robust minimization algorithm To run a Robust fit choose Robust in the algorithm popup menu of the fit dialog box This dialog box appears when selecting Fit from the Calc menu and it was described above Using the Distribution popup menu which appears when you define errors you can select the error distribution that best describes your experiment Robust fitting will deserve its name if you select a distribution that diminishes the importance of outliers like Andrew s sine or Tuckey s biweight When finished the resulting parameter values are printed to the results window This algorithm does not determine a standard deviation for each parameter like the Levenberg Marquardt algorithm does To obtain error estimations you have to run a Levenberg Marquardt fit after the Robust fit converged or you have to check the Error Analysis check box and perform a Monte Carlo analysis See the corresponding section for more details Using the Monte Carlo algorithm To run a Monte Carlo fit choose Monte Carlo Fit from the Calc me
235. mns Changing the ranges of the preview You can change the ranges of the preview either by editing them manually or by using the drag tool or the zoom tool a Click in the viewport area with the drag tool and drag the area of the data set or function curve displayed by the preview The ranges of the preview will change accordingly You start dragging inside the viewport but you can go on dragging also outside thus changing the coordinates by a large amount Preview Window 6 3 Click in the viewport area with the zoom tool the lens to zoom in and magnify the clicked area Hold down the option key while clicking to zoom out If you hold down the command key you can click and drag with the zoom tool thus selecting the precise area that will be displayed in the viewport after zooming Dragging the function curve Select the fitting tool and click in the viewport Hold down the mouse button while you move the mouse The curve of the function follows the position of the mouse while the selected function parameter is adjusted accordingly When using the fitting tool you must specify which parameter you want to vary You can do this either by clicking it in the parameter window or by choosing its name from the small popup menu that appears below the tools palette in the preview window You can only vary one parameter at a time When you select the fitting tool and click into the preview the selected parameter is varied until the funct
236. mouse The units used to display the 4 126 coordinates can be chosen using the Preferences command f f f f Mouse Lens All the coordinate fields are editable Simply click a coordinate and entera 14358 10089 different number to change the size or the position of the selected shape For example you can set the precise length and orientation of a line by entering the corresponding coordinates in the edit fields in the third row The Lens check box lets you open a small viewport with an enlarged version of the region around the mouse Drawing objects A drawing contains different objects There are four different classes of objects in a drawing window e Objects that are created by choosing Plot Function or Plot Data from the Draw menu such as a graph and its associated legend e Objects that are created using the tools in the upper part of the tools palette such as texts lines and rectangles e Objects that were created in another application and that are imported as pictures to pro Fit by choosing Paste or Subscribe To in the Edit Menu or by dropping them in a drawing window e Publishers created by Create Publisher in the Edit menu Everything within a Publisher s rectangle is part of the picture that is made available to other applications The first class of this list graphs and legends is discussed in the section Plotting The other classes objects created by using the tools palette imported pictures
237. mplementing this note that texts between curly brackets and are used as comments and are ignored function Myfunction description text to appear in parameters window Ys gt D y A sin x In x B x lt 0 y B defaults names and defaults for the parameters a l 1 active A a 2 0 inactive B begin if x lt 0 then a 2 else y a 1 sin x 1In x a 2 K ll end When you add this function to pro Fit its parameters window looks like this SS dS rr Function mm parameters A 1 0000000 B 0 0000000 lected t x 0 y A sinisi Inisi B selected parameter x 0 y B B lower limit none Use for fitting In the last version of our sample function two additional elements have been added 9 4 Defining functions and programs e A keyword description followed by two texts between quotes which appear at the bottom left of the parameters window e A keyword defaults which is followed by additional information for each parameter and takes the form a i value mode name lowLimit highLimit where value is the default value of a parameter mode its default fitting mode it can be act ive i e the parameter will be fitted inactive will not be fitted or constant cannot be fitted and name its name between quotes used in the parameters window Using the keyword defaults you can also define a range of acceptable values for a
238. ms is found under program definition syntax Information on how to define functions is found under program definition syntax and under function definition syntax You need to look under both headings because the function definition syntax is based on the program definition syntax Read the sections devoted to programs to obtain an explanation of all the general features that are available to programs as well as functions Program definition syntax The structure of a program definition is basically identical to that of a program in standard Pascal It starts with the keyword program followed by the name of the program and a semicolon Then you can optionally define some variables constants procedures or functions for your own use The main part of the program where the execution starts is placed between begin and end at the end of the program the name of the program myProg will appear in the Prog rogram myProg prog y g menu iiss ogei optional definition of constants and variables var u v real done boolean optional definition of a local procedure or function used by l the program begin Note that you can call local procedures recursively statements procedure MyProc end more definitions of functions or procedures can follow here optional the procedure Initialize that is called once when rocedure Initialize P 5 the program is compiled and added to the function menu begin Any initia
239. n GetResult rootsXValue i end Note There s also an obsolete version of Roots function Root name Str255 min max extended extended which is supported for compatibility with older versions of pro Fit Don t use it for new developments Round function Round x extended extended Rounds x to the closest integer and returns its value RowSelected function RowSelected rowNumber longint Boolean Returns true if anything in the given row of the current data window is selected SaveDataAsText procedure SaveDataAsText windowID longint fileName Str255 Saves a data window as a text file windowID is the window ID of the window such as it is e g returned by GetWindowID or FrontWindow Appendix A Predefined functions procedures and arrays A 51 fileName is the name of the file If fileName contains a simple file name the file is placed in pro Fit s folder If fileName contains a file path e g HD MyFolder file the file is placed in the folder defined in the file path Pass for fileName to bring up a dialog box asking the user where to save the file Use Set TextFileFormat if you want to specify how the text file must be formatted SaveDrawingAs procedure SaveDrawingAs windowID longint fileName Str255 format longint Saves a drawing window as a pro Fit file if format defaultFormat a PICT file if format pictFormat or a EPS file if format epsFormat
240. n s derivative changes its sign over a sub interval the sub interval is searched for a minimum or maximum See also Extrema Optimize procedure TabulateIntegral optional parameter list TabulateInt_ Calculates the integral of a function over a given x range Creates a table of the integral for different values of a parameter of the function or for different values of a limit of the x range Parameters function String The function to be used Omit for current function xMin xMax Real The start and end of the x range to be integrated parameter Integer The parameter to be varied Pass 2 for varying xMin 1 for varying xMax from to Real The start and end value of the parameter or xMin xMax to be varied step Value Integer The step for increasing the parameter or xMin xMax iterations Integer The number of iterations 5 15 The more iterations you use the more accurate the result becomes See also Integrate procedure TabulateRoots optional parameter list TabulateRoots Finds the root s of a function or finds the x value of a function where its y value is equal to a given value within a given x range Varies a parameter and tabulates the roots for different values of this parameter in a data window Parameters function String The function to be used Omit for current function xMin xMax Real Start and end of the x range parameter Integer The parameter to
241. n s main part can use the general predefined variables constants functions and procedures listed in Appendix A General comments about programming Types The pro Fit definition language supports the following types for variables Defining functions and programs 9 27 1 Simple numeric types real extended integer longint or boolean These types are not distinguished by pro Fit and are implemented as floating point numbers The boolean value true is represented by the real value 1 0 and false by 0 0 All non zero values are interpreted as true in a boolean expression Most Pascal compilers on the Macintosh distinguish between the floating point types extended double and real which have different accuracy All simple number types of the pro Fit definition lan guage have extended accuracy The accuracy and range of numerical values in pro Fit is given in Appendix C 2 Complex type The Complex data type is used to represent complex floating point values having a real and an imaginary part Example program ComplexTest var c Complex begin cose 1 writeln sqrt c end The above program recognizes that sqrt is called with a complex argument Therefore a complex version of the square root function is used which can handle sqrt 1 The output of the above program is 0 000 i 1 000 Type conversion from real or other simple numeric types to complex is automatic For converting complex numbers to real
242. n Apple Script from a program first add it to the Prog menu choose Load Module from the Customize menu then call it with CallProgram To call a program from an Apple Script compile it and use the command run program Apple Script commands and classes The following is a list of the Apple Script commands and classes objects supported by pro Fit Keywords are shown in bold arguments are listed in italics optional arguments and keywords are enclosed in square brackets alternatives are separated by Required Suite Events that every application should support open Open the specified object s open file list of objects to open as data window drawing window funcProg window text window If the file is a file of type text you can indicate if it is to be opened as text i e in a new function window or as table i e in a new data window Examples open file HD myData opens the file myData on the disk HD open file data as table opens the text file data as data file open file Drawingi opens the file called Drawing in pro Fit folder print Print the specified object s print reference object s to print dialog boolean indicates if we should show print dialog default is true quit Quit an application program quit Apple Script 11 5 run Sent to an application when it is double clicked run pro Fit suite Special commands for pro Fit add parameter set Adds the cur
243. n f x are those values of x for which f x takes a given value such as 0 To calculate the roots of a function choose Roots from the Analyze submenu menu Calc Roots of Polynomix Between 1400 and 2200 Sumber of subintervals Look for ffx Here you can select the range within which to look for roots This range is divided into a given number of sub intervals Example If you look for the roots f x 0 of a function between x 0 and x 1 and specify ten sub intervals pro Fit looks for roots in the intervals 0 0 1 0 1 0 2 etc In each interval a b it checks if the sign of f a is opposite to the sign of f b or if one of these values is undefined and the other de fined If this is the case the corresponding interval is searched for a root Enter a value Y in the field Look for f x to find the roots of the equation f x Y 0 Per default this value is 0 For example you can use this feature to find all x values where a function becomes equal to 1 0 Table of roots By choosing Table of Roots from the Analyze submenu you can create a table of the roots of your function for different values of one of the function s parameters Working with functions 5 5 Table of Roots of PolynomoOc Between 1400 Sumber of subintervals Look for fix Tabulate by varying const The top part of the box contains the same entries as the Roots dialog box see above In the lower part of th
244. n should be 0 If a cell in the first column is empty the corresponding cell in the second column should be empty too If any cell in the first column was empty the program should give the user a warning when it has finished The program which does this task looks like this program MakeRoot var i integer the row counter doAlert boolean true if a cell was empty begin doAlert false for i 1 to nrRows do if DataOK i 1 then if cell not empty if data i 1 gt 0 then data i 2 sqrt data i 1 else begin datai i 2 i 0 doAlert true end if doAlert then Alert Some data was negative end This program shows some additional features of the definition syntax An additional variable of type boolean has been introduced A boolean variable can take the values true or false which can be used in if statements 9 6 Defining functions and programs e Before accessing the data in a cell we test if there is really a number in this cell This is done with the function Dat aOK r c which returns true if the cell in row r and column c contains a valid number If the cell is empty or if it contains text it Dat aOK returns false e The innermost if statement if data i 2 gt 0 has two statements in its else branch They are grouped by the keywords begin and end to make it clear that they both belong to the else statement e At the end of the program an if condition checks whether any data was negat
245. nction as it appears in the Func menu User_Function is the default proposed by pro Fit You can change it to something like LogSine Then enclosed between begin and end there follows the definition of the function In the third line the function is calculated from the variable x and the parameters a 1 and a 2 and it is assigned to the variable y Note An alternative way to define the same function is Getting started 3 13 function logSine ampl offset real begin y ampl sin x 1ln x offset end In this definition the parameters of the function are defined in the function header The names used in the header are then used in the function body This is the syntax used for standard PASCAL functions pro Fit uses the parameter names defined in the function header for displaying the parameters in the parameters window After adding the function to pro Fit you can change its parameters in the parameters window You can plot the function use it for fitting calculations etc To plot it you should first set its parameters to reasonable values e g 1 and 0 5 Enter these values in the Parameter window and choose Plot Function from the Draw menu In the dialog box that comes up select the plotting range e g the x axis from 0 to 5 If you already have an open drawing window you should check the option Open New Window otherwise your curve will be drawn into the existing graph Our sample f
246. nction parameter an interval of allowed parameter values If a parameter is at one of the boundaries of this interval after a fit its standard deviation cannot be calcu lated The parameter is then considered to be constant i e it is not a free parameter anymore The standard deviations of the other parameters and 7 are calculated using the effective number of active parameters at the end of the fit The results obtained are the same as those that would have been obtained by fitting with the parameter fixed at its limit from the start The standard deviations of the parameters and the covariance matrix that are obtained in a Levenberg Marquardt fit have a clear quantitative interpretation only if the errors of the data are normally distributed If the data errors are not given the calculations for evaluating the standard deviations of the parameters assume that the y are normally d distributed and that the function is the correct description of reality Interpret the results carefully An alternative more general way to estimate the errors of the fitted parameters is described in the section Error analysis and confidence intervals The Robust minimization algorithm This method minimizes Yr 2 with any definition of R by continually moving downhill in parameter space Starting from some initial value the parameters are varied and the resulting value of 7p is calculated From this the algorithm finds the direction in wh
247. nctionParam In external modules after you call callFunction you should call Test Stop to check if the called function has interrupted execution CallProgram procedure CallProgram name Str255 Calls a program module or AppleScript name is its name as it appears in the Misc menu i programs 1 macros 1 scripts causes a run time error if the specified program or script does not exist Note that name is case sensitive In external modules after calling callProgram you should call Test Stop to check if the called program has interrupted execution CancelEvent function CancelEvent var theEvent EventRecord Boolean External modules only For advanced programming Returns true if the given event is a key down event for the escape key or for command and lt Capture procedure Capture optional parameter list Controls redirection of results window to a text file Parameters file String The file to capture the window into Use a simple name or a file path If you pass this parameter a new capture file is opened and capturing starts Omit this parameter when passing the parameter option option Integer captureOn start capturing into the file captureoff stop capturing but leave capture file open captureClose stop capturing and close capture file Omit this parameter when passing the parameter file Example Capture file myFile now output is redirced to the given file Capture opt
248. ndow Choose this window from the Window pop up menu Choose the column that holds your error values from the pop up menu Column The numbers found in the chosen column are assigned to each point in the plot sequentially If you don t check skip empty data fields an error of zero is used for each empty data cell Otherwise pro Fit only uses data cells that contain a valid number Make sure that the column you select contains the correct number of error values and in the right order i e the same order as the data which was plotted originally In general you can add error bars months after you plotted the original data set and proFit does not know the origin of the data set anymore It will simply take the error column you specify and apply the data values sequentially to all data points Therefore the order in your error column must be the same as the order of the original data points when they were plotted e Choose Constant if each data point has the same error Enter the error value in the edit field that appears e Choose Percent if the errors are a percentage of the x or y values of the data points Enter the error value in percent in the edit field that appears e Choose None to remove the errors from you data set Drawing and Plotting 7 31 e Choose Unchanged if you don t want to change the error bars in a given direction Frame A frame is a rectangular box around your graph 0 40 0 40 0 20 0 20 0 00 0 00 2 0 1 0 0
249. ne model for the measured data with normally distributed errors ywx a bx 15 A If there are no x errors and the y errors are assumed to be known 0 is the uncertainty of yj equation 9 can easily be simplified At its minimum the derivatives after the two parameters a and b vanish This leads to a set of linear equations that are solved analytically _ 555 T 8 5 ps S Siy Wey sdn to ee 16 a using the following definitions N 1 N Xi N y sah seb sh i l i i 1 i i l i N x xi s Soe ys a7 i 1 Oi i l i A SS s From these we are also able to calculate the variances of a and b and the correlation coefficient between them O2 Smu A o5 S A Sy 18 Tab SS S B If the measurement shows errors in the xj the minimization of 8 becomes more difficult i e the set of equations derived for a and b are not linear any more However they are solved with numerical means i e with a standard root finding algorithm Together with the fitting parameters and their variances the correlation coefficient r is calculated Pearson s r It takes a value between 1 and 1 depending on how much the x values and the corresponding y values are correlated r 1 if there is a complete correlation with a positive slope r 1 if there is a complete correlation with a negative slope and r 0 if there is no correlation at all Fitting 8 9 The significance of the correlation is the probability
250. ng the folder of the files to analyze set myFolder to choose folder with prompt Choose a folder with data files create a list with all files in the folder set myFiles to list folder myFolder a list of files in myFolder set myFileCount to count myFiles the number of files in myFolder now start working with pro Fit tell application pro Fit ppc set oldErrorAlerts to error alerts save error alert status set error alerts to false pro Fit should not show alerts activate bring pro Fit to front compile scriptProgram add the above program to Prog menu set myTable to make new table open new data window set k to 1 a counter for opened files repeat with i from 1 to myFileCount set theFile to item i of myFiles get the i th file try open file myFolder as string amp theFile as table open the file write line processing amp theFile run program ScriptProgram run the program in pro Fit close window theFile saving no close without saving set sum to globalData 1 get result Apple Script 11 3 set cell k of column 1 of myTable to sum store it in the table set kto k 1 on error errText write line cannot process amp theFile amp amp errText amp end try end repeat delete program ScriptProgram remove the program from Prog menu set error alerts to oldErrorAlerts restore end tell The above script starts with the definition of the program to be run by pro Fit Then i
251. ng window always contains one single page You can select its size and orientation by choosing Page Setup from the File menu Before choosing Page Setup make sure that you have selected a printer in the Chooser or if you are running QuickDraw GX that you have selected your preferred desktop printer in the Finder A dotted rectangle frames the printable area of the page Objects that lie outside this rectangle do not print See your printer s manual for more information on printers and paper sizes You can view the page in a drawing window using various zoom factors which you can set using a popup menu in the drawing window tools palette Drawing tools pro Fit provides various tools for editing drawings These tools are collected in a tool box which is either placed in the left margin of a drawing window or in a separate floating window To place the tools in a separate drawing window choose Drawing Tools from the Windows menu The floating tools palette appears To move the tools back to the drawing window simply close the floating window Oga edzd i m7 _ If you will never want to have drawing tools inside the drawing windows you can disable this option Choose Preferences from the Files menu and check Always use floating toolbox in the Drawing panel Ee The upper part of the tools palette contains tools that are used to select move or create simple objects such as rectangles and
252. ns true if val is an invalid number a NAN Not A Number Use this function to test the results of Root Maximum and Minimun or of other functions that can return a NAN in some cases InverseFFT procedure InverseFFT optional parameter list Performs an inverse Fourier transform on a data window Input are two columns of of real imaginary or amplitude phase in the frequency domain Output is a column of real values in the time domain Parameters window String or Longint Data window specified by name or window ID inputColl Longint Input column for real part or amplitude in the frequency domain inputCol2 Longint Input column for imaginary part or phase in the frequency domain outputCol Longint Output column outTimeCol Longint Output column to hold the time values Seconds of the data in outputCol Calulated from para meter frequencyInterval Omit if no time column is to be calculated frequencyInterval Real The frequency interval in Hertz between consecutive data points in the input columns Used for calculcating the time column Omit if no time column is to be calculated reallmaginary Boolean True if the input columns hold the real and imaginary values in the time domain false if they hold their amplitude and phase printResults Boolean True if statistical information on the processed data is to be printed in the Results window See also FFT invalidNum const invalidNum not a nu
253. nter the frequency interval between consecutive data points of the frequency domain and select a column for the time values Note that if you have N points in the time domain you obtain N 2 1 complex points in the frequency domain and vice versa The FFT algorithm works only for N 2m where m is a positive integer i e for N 2 4 8 16 If the number of input data points is not a power of two then the missing values to the next power of two are assumed to be 0 For further information on the subject of discrete Fourier transformations see e g W H Press et al Numerical Recipes Cambridge University Press Cambridge 1989 4 10 Working with data Defining a data set to work on Some of pro Fit s commands access data in the data windows If you have several data windows open at the same time pro Fit uses some rules for selecting the data window it works on e The transformation commands in the Calc menu work on the active data window the window in front of all other windows If the active window is not a data window these commands cannot be used Example the Data Transformation command is only enabled when the front most window is a data window e Some other commands use the front most of all data windows It does not matter if windows of other kinds are in front If the active window is not a data window these commands look at all the windows behind the active window and work on the first data window they find
254. ntitled Data 1 2 H column Column 1 Y column amp Column 2 Use the popup menus to select the data set to be used by the Spline function If you do not use the Select Data button in the pararameters window then the Spline function will use the data in the frontmost data window Select the appropriate x and y column by clicking the desired column number while holding down the command key If you did use the Select Data button but you close the data with the data set used by Spline then the Spline functions reverts back to using the data set in the frontmost data window 5 8 Working with functions 6 The Preview Window There are generally two different approaches that are used by plotting applications for managing graphs and the data used to generate them e The first one consists in maintaining a permanent link between the data you plot and the result of the operation the graph In this approach whenever you edit the data you used for creating the plot the plot automatically changes to reflect the new values of the data set Since the link between data and plot needs to be maintained it is in generally not possible to save data and graphs separately and they must be saved in the same document In applications using this approach the graph is only a different view of the data but does not lead an independent life e In the second approach graphs and data are independent Although a graph can be create
255. nts cannot be used at the same time SetGraphFrame procedure SetGraphFrame left top right bottom extended Changes the position and size of the current graph to match the new values Use SetNewGraphRect for setting the default size of future graphs SetLabel procedure SetLabel whichAxis integer tickNum integer labelNumber extended Sets the label of tick mark having number tickNum to correspond to the given value Accesses the current x or y axis use whichAxis xAxis Or whichAxis yAxis SetLabelsFormat procedure SetLabelsFormat whichAxis integer format integer decimals integer Sets the number format of the labels of the current x or y axis whichAxis is either xAxis or yAxis format 1 0 1 for auto decimal and exponential respectively A format parameter equal to any other number sets the labels format to fixed exponential and uses format as the number in the exponent Appendix A Predefined functions procedures and arrays A 61 SetLegendProperties procedure SetLegendProperties optional parameter list Sets the visibility position and size of the legend of the current function Parameters are visible Boolean Show or hide the legend offsetx offsety Real Offset between topleft of legend and topright of graph width height Real Size of an entry in the legend left part SetLabelText procedure SetLabelText whichAxis integer tickNum integer labelText Str255
256. nu or chose Monte Carlo in the Algorithm popup menu of the Fitting Setup dialog box When you do this two more items appear to the right of the Algorithm popup menu Please refer to the beginning of this section for a basic discussion of the Fitting Setup dialog box Fitting Setup Algorithm Monte Carlo Auto search Data N Use last choice fi 7 Clicking Ranges presents another dialog box where you can define the ranges within which the pa rameters can be varied Fitting 8 17 Fitting Ranges for Monte Carlo Fit Parameter Yalue From By default these ranges are the ten percent deviations of the starting value of the parameter or 1 and 1 if the starting value is 0 Checking Auto search tells pro Fit to make a more flexible search for the best set of parameters The Auto search check box determines whether the limits within which the parameters are varied will be kept fixed auto search unchecked or if they will be adapted during the fit auto search checked In the latter case the limits will be shifted after every iteration to keep them around the best parameter set Note that the parameters are never allowed to leave the parameter limits defined in the parameters window The Monte Carlo Fit runs until you interrupt it by pressing 6 If you don t stop the fit yourself the Monte Carlo Fit runs for ever The three best sets of parameters are displayed in the results window after you interrupt
257. number assigned to each window You can obtain a window ID by calling GetWindowID FrontWindow FrontmostWindow GetCurrentWindow The following example sets the name of the frontmost data window to favourite data program SetWindowName var windowID longint begin windowID FrontmostWindow dataType SetWindowProperties window windowID name favourite data end Note The Results Parameter and Preview windows always have the same window ID Results window ID 1 Parameters window ID 2 Preview window ID 4 The window IDs of data text and drawing windows are always larger than 0 String and character manipulation Ord Chr convert between extended ASCII codes and characters Length returns the length of a string Delete deletes parts of a string Pos finds a pattern in a string UpperString LowerString converts between upper and lower case strings NumberToString convert between numbers and strings StringToNumber Appendix A Predefined functions procedures and arrays A 11 Miscellaneous auxiliary routines Random Invalid TickCount DataString TimeString Beep SpeakString Button KeyPressed GetClickedCoord MarkedX MarkedY GetMarkedCoord Undo Cut Copy SelectAll Paste Clear DoMenu Capture SetWaitTitle SetWaitText NumberToStr255 Str255ToNumber GetModuleFile DeactivateProFitWindows ActivateProFitWindows GetDefaultData
258. o Code Resource to create a code resource of type NLft with an ID gt 128 Set the file type to ftCD the creator to NLft If you are creating a module for the non FPU version of pro Fit you must set your compile options so that they do not create code for the FPU If you are creating a module for the FPU version of pro Fit set your compile options to create code calling the FPU and to generate 12 byte extended or double in C variables MPW C C or Pascal for 68k If you are using the Macintosh Programmers Workshop MPW for compilation on a 68k CPU you must make sure that the function main which is defined in proFit_interface c for C modules and in your own file xxx p for Pascal modules is the first function in your build order This is important because when calling your code pro Fit starts executing your code resource from its beginning Therefore your code resource should start with the function main or with a jump to this function Most development environments add such a jump automatically MPW doesn t Therefore e If you are writing an external module in C make sure that proFit_interface o is the first file being linked e If you are writing an external module in Pascal make sure that your own file xxx o which you have created from ProgramTemplate p or FunctionTemplate p is the first file to be linked because it defines main MPW C C for Power Macintosh If you are using the MPW compiler for t
259. o copy the whole text contained in the info field of the data window as the header of the file If Write column titles is checked the next line contains the column names separated by the column delimiter Check Optimize size to write the numbers with as few characters as possible without loosing precision The native data format If you want to exchange binary data with pro Fit you can use pro Fit s native file format A description of this format is given in the technical note pro Fit binary data file format that comes with the pro Fit package Drawings pro Fit drawings can be saved as PICT files file type PICT or EPS files file type EPSF These formats are used for export to other applications only and cannot be read by pro Fit To save a drawing as a PICT file bring the drawing window to the front and choose Save as from the File menu In the dialog box that comes up check the option PICT C 6 Appendix C File formats PICT files contain standard Macintosh PICT information and can be read by most drawing applications The exact format of the PICT files created by pro Fit depends on the current PICT settings See Chapter 13 Preferences for more information on the different PICT settings Note that PICT files cannot contain QuickDraw GX shapes Do not use the option QuickDraw GX shape when saving PICT files EPS files are Encapsulated PostScript Files They are essentially text files
260. o create such a curve the function has to be calculated at a much larger number of points If you are working with a slow function you may prefer to use a fixed step to obtain faster plotting and to go over to auto step only when you want to produce a final graph Plotting a data set To plot data 1 Open a data window with the data you want to plot 2 Choose Plot Data from the Draw menu The following dialog box appears Drawing and Plotting 7 19 Flot Data e Plot into current graph Open new window x axis K e s E D Auto range C71 e n 30 trom i tef trom o to Data window population data X column columns Selected rows only year a Point Pe L Connected population in millions i uine Z The upper part of this dialog box was discussed above Special attention must be paid to the Auto range check boxes because they also influence which parts of the complete data set are transferred to the graph If you do not use Auto range but define your own ranges in min and max all data points outside these ranges are ignored only data points within the ranges of the graph are plotted and stored together with the graph If you always want the complete data set to be e stored with the graph check Auto range and resize your graph after plotting Use the Data window pop up menu to select the data window that contains the data to be plotted Use the X
261. oFit_interface c can be found in your distribution package xxx c is your source code created from ProgramTemplate c or FunctionTemplate c Make sure that the files proFit_interface h and proFit_paramBlk h reside in the same folder as your project Many mathematical functions such as sin log are not part of the standard C function set In order to use them use lt fp h gt and lt fenv h gt the header files for the Power Macintosh numerics environment Metrowerks Code Warrior Pro for 68k If you are using Metrowerks Code Warrior Pro for 68k create a project with the files MathLib68K A4 Lib Mathematical routines MSL C 68K A4 Lib Metrowerks standard library MSL Runtime68K A4 Lib runtime library for Metrowerks projects MacOS lib system routines proFit_interface c glue for interfacing with pro Fit XXX C Declaration needed to define a pro Fit function stands for 21 if you are building a module for pro Fit 68k 2i_F if you are building a module for pro Fit fpu Working with external modules 10 3 The library files came with your copy of the Metrowerks C C compiler proFit_interface c can be found in your distribution package xxx c is your source code created from ProgramTemplate c or FunctionTemplate c Make sure that the files proFit_interface h and proFit_paramBlk h reside in the same folder as your project Many mat
262. of a fit often depends critically on the choice of a good set of starting parameters Bad starting parameters can cause convergence to a false i e local minimum of the mean deviation 7p It is good practice to always try to figure out reasonable values for starting parameters Redundancy of parameters Sometimes a fit converges slowly or is even stopped with the cryptic error message A singularity occurred This can be caused by badly chosen starting values for fitting However this error is often a consequence of poorly defined or redundant parameters For example consider the exponential function x x A xex p Jie This function has four parameters A XQ t0 and const However the parameters A t0 and XQ are not independent as it is easily seen when writing 5 in factors Ax 0 x A t y exp 10 exp w const The first two factors A and exp xg to both have the same influence on y A change of xq can be compensated by a change of A These parameters are redundant When trying to fit them simultaneously the fit fails Another problem often encountered during fitting is caused by the poor definition of a parameter Example If you are trying to fit the data points x 1 y 2 01 2 3 99 3 6 00 4 8 02 5 9 98 6 12 00 to a polynomial of second or higher degree y ag ajx aox a3x you will get a very poor estimation of the parameters a5 a2 because your data point
263. of the data points and the resulting mean deviation value by a constant factor Each term in the sum 2 describes a deviation between the measured data point x y and the nearest point on the function curve 2 f The coordinate must be chosen in such a way that each term in the sum 7 is minimized for each data point Fitting 8 3 When the deviation function R is the squared deviation R d d then each term in 2 gives the square of the Euclidean distance between x y and x f The term is minimized when the line connecting the data point to the function curve is perpendicular to the function x y curve A fit algorithm must thus adjust the function until the sum 2 of the squared perpendicular distances between data points and function curve reaches a minimum E fR We refer to the literature for more detailed discussions of the above deviation functions A short description is also found in the classical book by W H Press B P Flannery S A Teukolsky W T Vetterling Numerical Recipes the Art of Scientific Computing The mean square deviation Chi Squared When squared deviation functions are used 2 gives the mean square deviation which is often called 2 xX Oo Oo A 2 A 2 2 x x E y x 5 8 i XI yi The mean square deviation chi squared is used when the measurement errors are described by a Gaussian probability distribution and in this case the errors O an
264. olumns names to Column 1 Column 2 etc A typical Pascal program for writing such a file would be var out text rewrite text filename writeln text x chr 9 y writeln text 1 234 chr 9 2 341 Ln text 1 244 penr 9 3 412 gt writel close text Some applications produce data text files using other formats or read data text files only when they are in special formats pro Fit provides options to read and write text files in other formats as well The details are given in the next section Appendix C File formats C 3 Loading text files For reading text files choose Open from the File menu choose Text Files from the View pop up and select the file to be read You will be prompted for the following information Loading TEXT File Format Function or program file Data file Format With Titles 2 If you select Function or program file the file is opened as a non data text file and loaded into a new function window If you select Data file the file is opened as a data file and loaded into a data window In this case you can select either one of the standard formats or the custom format If Custom format is not selected pro Fit uses an intelligent translation algorithm which recognizes most data file formats automatically By selecting the With Titles format pro Fit interprets the first line in the text file as the column titles If
265. on or variable See Chapter 9 Defining functions and programs for more information about all the predefined keywords and functions you can use in mathematical expressions Working with data 4 3 You can also import data from text files See the Appendix C File Formats for detailed information Data transformation pro Fit offers various methods for transforming data Numerical transformations data reduction sorting trans posing and Fourier transforms In addition you can write programs that edit manage or create data in any conceivable way for more information on writing such programs see Chapter 9 Defining functions and programs All the commands for transforming data are found in the Calc menu and they work on the data window which is in front of all other windows Algebraic transformations To make simple numerical transformations on your data choose Data Transform from the Calc menu The transformations you can carry out with this command are of the form y func x You can define where the x value co mes from and where y has to be stored You can also choose what function you want to use note that some of these functions do not need an x value Data Transformations Fit klonte Carlo Fit Optimize Params gt gt Calculate Exp x Tabulate Exp x Analyze Exp tc Data Transform Data Reduction Sort Transpose Statistics Fourier Transfo
266. on to the first column of the current data window It also calls a function called ChangeUnit to calculate new parameter values that it stores in the second column Before using ChangeUnit it sets the value of its first parameter to zero A 8 Appendix A Predefined functions procedures and arrays program CopyParams var i integer pa extended begin SetFunctionParam changeUnit 1 0 0 for i 1 to GetNumFunctionParams do if GetFunctionParamMode i active then begin pa GetFunctionParam i data i 1 pa data i 2 CallFunction ChangeUnit pa end end Numerics on functions Integrate TabulatelIntegral Derivative Root TabulateRoots Fit Optimize Extrema TabulateExtrema Tabulate Fitting Fit GetResult The following example runs a calculate the integral and the derivative of a function calculate roots set fitting below find extrema of a function by varying its x value and or its parameters tabulate functions runs a fit retrieves the results fit and prints some of the results Appendix A Predefined functions procedures and arrays A 9 program DoFit var i nrParams Longint begin Fit function Sin yColumn 2 Writeln chi squared algorithm levenberg xColumn 1 GetResult chiSquared nrParams GetResult chiSquared Writeln number of parameters nrParams for i 1 to nrParams do writeln
267. onductivity K mW cm 10 8 a tcm 1 200 0 0 00 200 20 8 45 200 40 16 90 200 60 25 35 300 0 0 00 300 20 14 64 300 40 29 29 300 60 43 93 400 0 0 00 400 20 19 28 400 40 38 56 400 60 57 84 Here is a graphical representation of this data set 60 o o T 200 T Oo T 300 o o 40 T 400 o 20 6 0 20 40 60 mW cm2 In order to fit these points with our function we must define the function and the data set in such a way that the function can obtain its two x values from the current data window We enter the temperature T which is our x value into column 2 of a data window the intensity 7 which is our x value into column 3 and the conductivity which is our y value into column 4 We fill column 1 with numbers from 1 to 12 thus numbering all our measured points 8 20 Fitting cond data A eee E 1 000 200 000 0 000 0 000 40 COCICICE 26 56468 Conductivity data entered into a data window Note the auxiliary column 1 providing a unique number for each data point Now we define a function y F x that returns the conductivity as its y value see Chapter 9 Defining functions and programs on how to define your own function and takes the number of the data point in column 1 as x value When this function is called with a given value of x it looks up the values of temperature and intensity i e the values for y and y2 from columns 2 and 3 of
268. oolean expressions are evaluated as floating point numbers a 0 0 representing false any non zero value representing true No records structures or pointers are supported e Arrays are one dimensional e Case statements are not supported e Nested declarations of functions or procedures are not supported External functions and programs Even though pro Fit s definition language is very powerful it does not offer the full versatility of a special purpose programming language It only supports one dimensional arrays except data i j records pointers etc In addition it does not support access to the Macintosh toolbox routines If you do need any of these features or if you want to write a large program or function for pro Fit where execution speed is crucial you should write your definition in any compiler of your choice and add the generated code to pro Fit This process is called writing an external module See Chapter 10 Working with external modules for details Using pro Fit Modules After you have added a function or program to the menus you can save its compiled code as a separate file for later use This file is called a module because it is a self contained unit that can be used to customize pro Fit s menus You can also create modules in an external compiler These modules are called external modules pro Fit comes with a set of external modules for different tasks You can use them to add functionality to yo
269. oop Its general form is repeat statement until condition In contrast to the while loop the statement of a repeat loop is always executed at least once After the execution of the statement the condition is tested If the condition is true the loop is terminated else the loop statement is executed again until the condition becomes true Loop control statements cycle and leave You can place the keyword leave into a for while or repeat loop to exit the loop even if its end condition is not yet reached Example 9 16 Defining functions and programs for i 1 to NrRows do begin if not DataOK i 1 then begin Writeln Empty cell loop aborted leave exits the for loop end end The above example loops through the first column of a data window and does some calculations indicated by If however an empty cell is found the loop is aborted You can place the keyword cycle into a for while or repeat loop to immediately start a new iteration of the loop Example for i 1 to NrRows do begin if not DataOK i 1 then begin Writeln Empty cell skipped cycle goes to next value of i end end The above example loops through the first column of a data window and does some calculations indicated by If an empty cell is found the calculations are skipped and the loop is continued with the next value of i Optional parameter lists Usually you pass parameters to procedures
270. orm for variable startValue to endValue do statement A for loop executes its statement for all integer values of its variable between startValue and endValue If startValue equals endValue the for loop is executed only once If startValue is larger than endValue the for loop is never executed Defining functions and programs 9 5 The end value in our for loop is nrRows nrRows is always equal to the number of rows in the current data window The statement in our for loop is an assignment to the array element data i 1 that corresponds to the ith data cell in the first column of the current data window The expression 2 i stands for 2 you can also use 2 i instead of 2 i Click Add in the function window or choose Compile amp Add To Menu from the Prog menu The program is transformed into computer executable code it is compiled and its name appears in the at the end of the menu Prog Choose PowersOf2 from the menu Prog The program is executed It opens a new data window and fills its first column with the desired values Our next example program is somewhat more complex Imagine you have a data window with some data in the first column You want to write a program that fills the second column with the square root of the values of the first column You want to take some special cases into account If a cell in the first column is negative the corresponding cell in the second colum
271. orrespond to the underlying reality and on the measurement errors that were specified A short description of this error analysis technique is found in W H Press B P Flannery S A Teukolsky W T Vetterling Numerical Recipes the Art of Scientific Computing For each of the synthetic data sets a fit is performed Once that all synthetic data sets have been fitted the confidence intervals are calculated by analyzing the values obtained for each parameter The confidence interval thereby corresponds to the range enclosing a given percentage of the values When error analysis is complete the results are printed in the Results window and a list of the fitted parameters for each synthetic data set appears in a new data window You can use the set of simulated parameters for further statistical analysis Fitting algorithms In the previous section we gave a short overview of the most important mathematical tools used to establish criteria distinguishing a good fit from a bad one Once these criteria are established one can use them to analyze parameter sets and to find out in which direction the best parameter set can be found The search for the best parameter set is the responsibility of a fitting algorithm and pro Fit lets you choose between three different ones The Monte Carlo Levenberg Marquardt and Robust algorithms The algorithms differ by the method they use to orient themselves in parameter space and to find the lo
272. ors are specified xErrorColumn integer the column with the x errors if xErrorKind is individual yErrorColumn integer the column with the y errors if xErrorKind is individual xError real the magnitude of the x error interpretation depends on xErrorKind yError real the magnitude of the y error interpretation depends on yErrorKind xDistribution gaussianDistribution lorentzianDistribution exponentialDistribution tukeyDistribution andrewDistribution the error distribution for the x errors yDistribution gaussianDistribution lorentzianDistribution exponentialDistribution tukeyDistribution andrewDistribution the error distribution for the y errors auto search boolean used when algorithm is montecarlo selected only boolean true if fitting using selected rows only full description boolean true to print a full description of the fit parameters active parameters boolean true to print only the active parameters error analysis boolean true to perform an error analysis after the fit stopCounter integer tells Monte Carlo fitting when it must stop iterations integer the number of iterations to be used for error analysis confidence interval real confidence interval in to be used for error analysis print results boolean true if comments are to be printed in Results window get data Gets the data of an object get data reference the object Result anything the data of the object
273. ostfix Axes can be inverted i e an axis can extend from 1 to 1 The new user interface style and contextual menus introduced with MacOS 8 are supported Some of the menus have been rearranged for better accessability 1 4 Introduction 2 Installation The installation procedure Installation of pro Fit is very easy Just double click the self unstuffing archive to copy all required files onto your hard disk Before installing pro Fit read the read me file if any such file came with the package pro Fit versions pro Fit 5 1 comes in three versions pro Fit 5 1 ppc A version of the application running native on PowerPC machines This is by far the fastest version but it runs only on PowerPC machines pro Fit 5 1 68k A version of the application optimized for a Macintosh with a Motorola 680x0 68k CPU without floating point unit FPU This version runs on all Macintosh models but is not optimized for the Power Macintosh or for 68k models equipped with a floating point unit pro Fit 5 1 fpu A version of the application optimized for a Macintosh with 68k CPU and floating point unit FPU This version is faster than the non FPU version but does not run on Macintosh models without a floating point unit Neither will it run on Power Macintosh models Installation 2 1 3 Getting started A first session This chapter describes a typical pro Fit session It shows how to enter new data plot it and how to fit a
274. our activities using pro Fit s automatic macro recording feature This chapter first gives a short overview on the principles of programming in pro Fit It then explaines the automatic macro recording feature and finally it lists the features of pro Fit s built in compiler in detail At the end it explains how to save programs and functions as modules for later use Defining functions and programs 9 1 Simple examples Defining functions Imagine you want to analyze a function of the form y asin x X In x b 8 1 with the parameters a and b To define it in pro Fit 1 Choose New Function from the File menu This opens a new empty function window Untitled Function 2 To Menu C Debug Help SJ Const 5 E Browse au Ye 2 Enter the formula of your function in the new window The formula looks as follows a 1 sin x ln x a 2 Use a 1 a 2 for the parameters a and b 3 Click To Menu in the function window or choose Compile amp Add To Menu from the Customize menu pro Fit analyses the contents of the window Since you have entered a simple mathematical expression using the value x pro Fit assumes that you want to define a function Your formula is translated into a Pascal like function definition it is compiled and added to the menu Func The function window now shows the Pascal definition of your function 9 2 Defining functions and programs Untitled
275. ower Macintosh Set your compiler linker to build a code resource of type NLft with a resource ID greater or equal to 128 The entry point to your code must be at the beginning of the code resource 10 2 Working with external modules If you are creating a module for the FPU version of pro Fit set your compile options to create code using the FPU with 12 byte extended Pascal or double C variables If you are creating a module for the non FPU option of pro Fit you must set your compile options to not create code for calling the FPU and to use 10 byte extended Pascal or double C variables 4 Link the module to pro Fit To do this either double click the file you have built or load it from pro Fit by choosing Load Module from the Misc menu The following gives some hints for creating modules with some of the most common compilers Note that there are sample project and make included with the pro Fit package Metrowerks Code Warrior Pro for Power Macintosh If you are using Metrowerks Code Warrior Pro or the Power Macintosh create a project with the files MathLib Mathematical routines MSL RuntimePPC lib runtime library for Metrowerks projects InterfaceLib system routines proFit_interface c glue for interfacing with pro Fit XXX C Declaration needed to define a pro Fit function MathLib MSL RuntimePPC lib and Interface lib came with your copy of the Metrowerks C C compiler pr
276. p dialog box before printing Bitmap This is presently the recommended picture format for printing on any high resolution printer that does not support PostScript if you don t have QuickDraw GX installed In a bitmap every pixel of the picture is stored at the printer s resolution You can enter the desired resolution in a text field appearing at the bottom of the dialog box 12 4 Printing Bitmaps print well on most high resolution printers However a bitmap uses a large amount of memory and often looks unsatisfactory on screen Also printing a bitmap can be very slow especially when printing to a PostScript device When you select Bitmap you can specify if your bitmap should be black and white or if it should contain color information Don t check with Color unless you really need a color bitmap black and white bitmaps use considerably less memory e QuickDraw GX shape This option is only available if you have QuickDraw GX installed and if you have checked Use QuickDraw GX in the Printing panel of the Preferences dialog box If QuickDraw GX shape is checked pictures are exported as shapes the data exchange format of QuickDraw GX Shapes print fine from all applications that allow importing them If you are unable to paste a shape into an application then this application does not yet fully support QuickDraw GX Note You can also append a QuickDraw GX shape to normal pictures using the Add Q
277. pecify the function currently selected in the Func menu min and max are the lower and upper limits of the integral iterations is the number of iterations for calculating the integral must be in the range 5 15 A small number of iterations makes execution faster but decreases accuracy a large value slows down execution but yields a more accurate result Integrate procedure Integrate optional parameter list Calculates the integral of a function over a given x range Parameters function String The function to be used Omit for current function xMin Real The start of the x range xMax Real The end of the x range Appendix A Predefined functions procedures and arrays A 37 iterations Integer The number of iterations 5 15 The more iterations you use the more accurate the result becomes printResults Boolean Set to true for printing the results to the Results window Omit printResults or set it to false for suppressing this To retrieve the results use the function GetResult selector with one of the following selectors integralValue the integral integralAccuracy the correction in the last iteration The following piece of code calculates the integral of the current function between 1 and 1 then prints it Integrate xMin 1 xMax 1 iterations 10 Writeln GetResult integralValue See also TabulateIntegral Invalid function Invalid val extended Boolean Retur
278. pens a new data set in the current graph Once you have called OopenDataSet call AddDataPoint or DrawDataPoint to add data points Once you have added all data points call cCloseDataSet Parameters A 44 Appendix A Predefined functions procedures and arrays errors This parameter is 0 if the data points should not have error bars or a sum of the constants eBarx symmetric error bars in X eBarY symmetric error bars in y asymEBarX asymmetric error bars in X asymEBarY asymmetric error bars in Y connected Set this to true if the data points should be connected name The name associated with the curve It appears in the legend of the graph By passing the appropriate value in errors you tell pro Fit if it should allocate space for holding error values or not If you want to use error bars you have to call the routine AddDataPoint to add data points and their error bar lengths in the currently open data set If you are not interested in error bars simply call DrawDataPoint AddDataPoint ignores its xErr parameter if errors is noErrorBars OF errorBarsy It ignores the yErr parameter if errors is noErrorBars Or errorBarsX OpenDataSet causes a run time error if no current graph is available Example The following program draws a graph with all types of data points program test var i j begin CreateNewGraph 0 18 0 3 0 0 for i 1 to 17 do begin SetDataPointStyle i 9 0 5 OpenDataSet 0 false name Dr
279. percentError Integer The distribution of the y errors gaussianDistribution lorentzDistribution expDistribution tukeyDistribution andrewDistribution Boolean True if a complete protocol of the fit is to be printed in the results window false if a shortened protocol is to be printed Boolean True if all parameters are to be printed in the results window false if only the fitted parameters are to be printed stopCounter Longint Defines the number of iterations if algorithm is montecarlo Set to 0 if you want the fit to continue until it is interrupted manually Omit for all other fitting algorithms doErrorAnalysis Boolean True for running a statistical error analysis after the fit slow false if errors are to be derived from the covariance matrix Levenberg Marquardt algorithm only Default false confidence Real The desired confidence interval for statistical error analysis Omit if doErrorAnalysis is false printResults Boolean Set to true for printing the results to the Results window Omit printResults or set it to false for suppressing this To retrieve the results of the fit use the function GetResult selector Use one of the following selectors chiSquared chi squared nrFittedParameters number of fitted parameters fittedParameter fitted parameters covariance elements of the covariance matrix confidenceMin confidenceMax lower and upper limits of the fitted
280. ples get name of front window returns the name of the front window if nrRows of window 2 lt 10 then error get is not necessary Apple Script 11 15 set myVar to cell 1 of column 2 of window Table set name of front window to myData sets front window name set nrRows of window Table to 200 resize a data window set default type of column 2 of front window to string set col type set myvar to value of every cell of column 4 of front window myvar becomes an list of numbers Note a list of the properties and elements that can be accessed is given below The following lists the properties and elements of pro Fit s classes and gives some examples on their use If a property or element is marked as r o it is read only and cannot be changed Class application The pro Fit application Properties default column type type class real single current function function the currently selected function clipboard a list of record r o contains elements of type PICT and TEXT decimals integer the number of decimals for numeric output error alerts boolean true if alert is to be shown when Apple Event failed results calculation results r o Results of preceding calculations script debugging boolean true if script debugging enabled false if disabled version version r o the version of the application lt Inheritance gt base class properties r o Notes error alerts indicates if
281. pro Fit 5 1 User s Manual QuantumSoft Postfach 6613 8023 Z rich Switzerland http www quansoft com End User Licence Agreement proFit 1991 1998 QuantumSoft All rights in this product are reserved This end user licence agreement describes the rights and warranty granted to its customers by QuantumSoft the Publisher By using the pro Fit Software package you the customer are agreeing to be bound by the terms of this agreement which includes the software licence software limited warranty and hardware limited warranty 1 Licence The Publisher grants the customer and the customer accepts a perpetual non exclusive and non transferable licence to use the proFit software software so long as the customer complies with the terms of this Agreement 2 Copies The Publisher grants the customer the right to make copies of the software for back up purposes only The customer agrees to reproduce and incorporate the author s copyright notice on any copies It is expressly understood that such copies will not be used for any purpose except to substitute for the initial copy in the event that it is unusable 3 Use In addition the licence granted herein includes the right to move the software from one computer to another provided that 1 user versions of the software are used on only one computer at a time and that two people will not use the program at the same time on different computers 4 Security The customer
282. pro Fit should show alerts when handling Apple Events i e when executing an Apple Script By default this property is true When your script does its own error handling you should set it to false If you do so reset it at the end of your script if you don t pro Fit will not show any errors when handling Apple Events from the Finder later Setting script debugging to true causes pro Fit to write a list of all Apple Events it receives to the results window This feature does not work for scripts started from within pro Fit Class calculation results The result of the last calculations Properties chiSquared real r o fitting chi squared fittedParameters a list of real r o fitting optimization the fitted parameters nrFittedParameters integer r o fitting the number of fitted parameters sumOfDeviations real r o fitting sum of the error deviations Robust algorithm correlation real r o fitting linear correlation between x and y values linear regression probCorrelation real r o fitting significance of correlation linear regression covariance a list of real r o fitting covariance matrix nrIterations integer r o fitting number of iterations goodnessOfFit real r o fitting goodness of fit confidenceMin a list of real r o fitting low boundaries of confidence intervals confidenceMax a list of real r o fitting high boundaries of confidence intervals standardDeviations a
283. procedure ClearLabels whichAxis integer Kills all labels in the current axis whichAxis is either xAxis Or yAxis ClearTicks procedure ClearTicks whichAxis integer Kills all ticks in the current axis Call before using AddTick whichAxis is either xAxis Or yAxis CloseCurve procedure CloseCurve Stops data collection for the current curve CloseDataSet procedure CloseDataSet Stops data collection for the current data set ClosePoly procedure ClosePoly Stops data collection for the current polygon opened by calling openPoly Appendix A Predefined functions procedures and arrays A 17 CloseTextFile procedure CloseTextFile fileRefNumber longint Closes the given text file fileRefNumber is the reference number returned by CreateTextFile CloseWindow procedure CloseWindow optional parameter list Closes a window Parameters window Longint or String The name or window ID of the window Default Front window saveOption Integer saveToFile always save into its file dontSave never save askUser if window has been changed ask user if it should be saved Default is askUser There is also an obsolete version of CloseWindow which is supported for compatibility with older versions Do not use it in new programs procedure CloseWindow windowID longint saveIt Boolean Set saveIt to false if you do not want to save the window even if it was changed windowID specifies the
284. programs which can access directly the data in the spreadsheet window pro Fit translates these programs into computer code which can be executed directly by the central processing unit of your computer You can automate many operations using such programs or Apple Events and Apple Script Functions can be used for plotting analysis and fitting There are a number of built in functions such as log cos exp etc You can define your own functions using the same simple yet powerful definition language used to define other programs and macros Functions and programs can also be defined using an external compiler external modules You can plot your functions and data sets in a drawing window pro Fit offers most standard features of a drawing program and the appearance of all graphical elements is customizable pro Fit generates high resolution printer information for direct printing or for exporting data via the clipboard Drag amp Drop or Publish amp Subscribe Introduction 1 3 Changes between versions 5 0 and 5 1 pro Fit 5 1 brings various new features This is a list of the most important ones Recording Programming Functions Fit algortithms Data Windows Print Preview Graphing User Interface pro Fit 5 1 is fully scriptable and recordable pro Fit 5 1 can automatically record your actions into a program or an Apple Script The program or script can then be run to repeat your actions To record
285. pter 9 Defining functions and programs for a more detailed discussion of how to work with pro Fit modules The rest of this chapter explains how you can write external modules using your own compiler Creating an external module You need the following to write an external module e Some experience in programming e A compiler such as Think Pascal Think C Symantech C Metrowerks Pascal Metrowerks C C or the Macintosh Programmer Workshop MPW Your compiler must support the generation of code resources for 68k computers or shared libraries for Power Macintosh Working with external modules 10 1 To create an external module proceed as follows 1 Choose a stationery file to start from and save it under a name of your choice In your pro Fit distribution package you will find a number of stationery template files that contain empty functions or programs ProgramTemplate c for creating an external program in C FunctionTemplate c for creating an external function in C ProgramTemplate p for creating an external program in Pascal FunctionTemplate p for creating an external function in Pascal Open the stationery from your programming environment and save it under a name of your own e g XXX C Note you should never modify the files ProgramTemplate c p or FunctionTemplate c p directly always work on a copy 2 Complete the code Since the stationery files only contain empty rou
286. putRec Boolean External Modules Only Replaces the routine Input The parameter nrArgs gives the number of elements of the record r The record r has the type inputRec A 36 Appendix A Predefined functions procedures and arrays type ExtendedPtr extended InputRec packed array 1l maxNriInputValues of record x ExtendedPtr St str255 end Strings and values are set according to the explanations given for the routine Input In addition to the meta commands recognized by Input InputBox also understands the meta command S which specifies that the parameter is a string pointer The following is an abbreviated example showing how to call Input Box in Pascal var dl extended sl ss2 Str255 r InputRec Str255 gt S begin di s dnl default values s default text sl datal and names s2 SSdata2 r l x dl set entries of r r 2 x ExtendedPtr s r l s sl r 2 s s2 if InputBox 2 r then If you are programming in C is Pascal s address operator corresponding to in C For C the indices of the InputRec range from 0 to 5 Integral function Integral name Str255 min max extended iterations integer extended Obsolete Use Integrate instead Returns the integral of a function name is the name of the function as it appears in the Func menu This parameter is case sensitive Use an empty string to s
287. r sin x sinDiff end 9 26 Defining functions and programs The above example uses the procedure Last Procedure Last This is also a procedure used for advanced programming It is called when all calculations fitting etc are completed It is the last piece of function code called by pro Fit before returning control to the user Last can be used to clean up to make final calculations or to re initialize some variables to their starting values as is shown in the example above Last can also be used to print some special messages or results in the results window or to alert the user of some event For example you can let your machine beep when fitting is finished procedure Last begin beep end Summary The following table summarizes the special procedures listed above name called when predefined variables and constants Check whenever parameters are pNumber changed by user alij si Ati mode 1 mode n active inactive constant check ok bad update Initialize once after compilation a l aln First whenever parameters are afl a n changed e g during calculations Derivatives during fitting after calling x all a n the function s main part dyda 1 dyda n kast when calculations are aft ate set through function s main during fitting and other x y a l a n part calculations Note that in addition to the specially predefined variables and constants all procedures as well as the functio
288. r check again Show hints in the Preferences dialog all hints also those that have been disabled individually will be shown again Panel Printing This panel is discussed in Chapter 12 Printing Panel PICT Options This panel is discussed in Chapter 12 Printing Panel Drawing This panel controls some options used by the drawing window Preferences Format of labels in graph axes L Typographical minus L Comma instead of decimal point Printing Exponentials 9 109 e109 8E9 Default units em FIC D T Options Be Mf Automatic grouping of new graphs rawing i O Always use floating toolbox Pre iew Interface Check Typographical minus if you want to use a longer dash instead of the hyphen as a minus sign for numbers in the labels of a graph Note that the typographical minus may not be available on non roman fonts Check Comma instead of decimal point to use a comma as the decimal marker 12 345 instead of a point 12 345 Exponentials controls the style for drawing exponential labels 13 2 Preferences Note that changing the settings under Format of labels in graph axes does not affect the labels of existing graphs When you have changed the settings and want to use them for an existing graph redraw the axis e g by double clicking it and clicking the button Apply Default units controls the default units used for measuring and entering di
289. r 3 Note Calling st opExecution is equivalent to setting error status to and Test Stop returns true if error status is 1 or 3 GetBasics procedure GetBasics var count longint var sum mean variance stdDev meanAbsDev extended Obsolete Use Statistics and GetResult instead Returns some of the results obtained in the last statistics evaluation performed with the routine CalcStat CalcStat must have been called with the withBasics parameter set to true if GetBasics is to be useed be used GetCell procedure GetCell var s String row column longint Returns the string in the given cell of the current data window If the cell is in a number column it converts the number to a string and returns the string GetClickedCoord procedure GetClickedCoord var x y extended Returns the window coordinates where the last mouse click took place in the current drawing window Appendix A Predefined functions procedures and arrays A 29 GetColHandle procedure GetColHandle col longint var colH Handle var length longint var colType longint forWriting Boolean External modules only For advanced programming This routine returns a Mac OS handle to the data of the given column You can read and or modify the data in the handle This is much faster than accessing a column s data through GetData SetData and GetCell SetCell colH can be nil if the corresponding column is empty length is the number o
290. r Func menu Causes a run time error if the file could not be opened This procedure cannot be called while a function is running OpenPoly procedure OpenPoly smoothing integer closed Boolean Starts the creation of a polygon After having called OpenPoly use multiple calls to Line or LineTo to draw it then call ClosePoly when you are through Set closed to true if the polygon should be closed at the end smoothing 0 of no smoothing smoothing 1 for normal smoothing smoothing 2 for B zier smoothing with the curve going through the polygon definition points OpenText procedure OpenText fileName Str255 Opens the given file as a function file The file must either be a pro Fit function file or a text file The new window becomes the current text window If fileName contains a simple file name the file is loaded from the pro Fit folder If fileName contains a file path the file is loaded from the folder defined in the file path If you pass for fileName the user will be asked to locate the file This procedure cannot be called while a function is running Optimize procedure Optimize optional parameter list Finds a maximum or minimum of a function by varying its x value and or its parameters Parameters function String The function to be used Omit for current function getMinimum Boolean true if you want to find the function s minimum false for its maximum varyParams Boolean true if
291. r the Help menus in function windows They show helpful information on the keyword currently selected in the menu The proFit Guide The proFit on line help system comes in a separate files called pro Fit Guide and pro Fit Programming These files are found on your distribution disks and must reside in the same folder as pro Fit If pro Fit cannot find one of these file then the corresponding on line help is not available The main pro Fit Guide can be accessed using the Help menu to the right of the menu bar As an alternative to this there are lots of question marks everywhere in proFit dialog boxes and windows Click any of these question marks if you need help in a particular situation pro Fit will immediately display a floating window that can guide you through the operation at hand The pro Fit Programming guide provides help on all features of pro Fit s function and program definition language This Guide contains a detailed description of every predefined function or keyword The programming Guide can be opened directly at the page describing a given keyword by selecting that keyword in the function window Help menu or by option double clicking a keyword in the text of a function definition On line evaluation of mathematical expressions Wherever pro Fit expects a numerical input such as in spreadsheets or dialog boxes you can enter a mathematical expression For example instead of typing a number directly you can use a mathema
292. rage over This option decreases the number of rows by a factor of n For example if n 3 the values in the rows 1 2 and 3 are averaged and the result is stored in row 1 The average of rows 4 5 and 6 is then stored in row 2 etc e To replace every data value with the average of itself and its n 1 neighboring values in its column select Smooth over Again the average of n values is calculated In contrast to Average over the number of rows is not reduced For example if n 3 the value in row i is replaced by the average over the values in rows i l i and i 1 To transform only the selected cells check Selection only In this case only the currently selected cells highlighted in the data window are affected If the selection is discontinuous whole rows only the above algorithms are applied to each continuous block of the selection one after the other The various discontinuous blocks are treated separately and do not interact with each other To keep only the rows that are presently selected check Keep selected rows To remove all the presently selected rows check Remove selected rows Sorting data To sort data choose Sort from the Calc menu 4 6 Working with data Data Sorting Sort column year Order ascending id descending O Selection only Use the pop up menu to select the column to be used as a reference for sorting You can sort by ascending or by descending values All the rows
293. rawing window or to open a new one And finally you can choose which coordinates axes you want to use for plotting their ranges and their scaling To plot a function or a data set choose Plot Function or Plot Data from the Draw menu The options outlined above are common to function and data plotting and can be set in both the plot function dialog box and the plot data dialog box Therefore the upper part of both dialog boxes looks the same Flot Data e Plot into current graph O Open new window x axis Y axis Check Plot into current graph to plot into the current graph The current graph is usually the one where the last plotting took place However you can define any graph to be the current graph by double clicking it and checking Current Graph in the dialog box that appears Read more about this dialog box later in this chapter As a shortcut you can hold down the command key and double click the graph Check Open new window to create a new graph in a new drawing window If both Draw into current graph and Open new window are unchecked a new graph is drawn in the frontmost drawing window The fields labeled X axis and Y axis determine which axes will be used their ranges and their scaling The two popup menus in the top left corner of the fields X axis and Y axis are used to choose the axis to be used for plotting and to determine its range The second popup menu determines the scaling type
294. rawings in the drawing window collect line drawing calls to define a polygon Appendix A Predefined functions procedures and arrays A 3 DrawLine DrawDataPoint create single drawing objects in the current drawing window DrawPICT DrawRect DrawEllipse DrawArc DrawText DrawNumber group drawing objects GroupBegin GroupEnd DisableDrawingUpdates inhibit updates in the current drawing window until a program is finished GApselaseioanounas find the rectangle corresponding to the boundaries of the current selection in the current drawing window Cetelickedcoor find the last clicked point in the current drawing window All the above calls access the current drawing window By default the current drawing window is the frontmost drawing window You can make another drawing window the current drawing window by calling Set CurrentWindow windowID with windowID being the window ID of the desired drawing window The drawing routines work on a coordinate system that has its origin on the top left of the paper Units are 1 72 inch The following program creates a bull s eye at the point where you last clicked in the drawing window program BullsEye const radius 40 step 8 var x0 yO t real begin GetClickedCoord x0 y0 GroupBegin te 7S step while t lt radius do begin DrawEllipse x0 t y0 t x0 t yOtt E c3 ESE epy end r MoveTo x0 radius 1 1 y0 Lin
295. rd ch char integer Returns the extended ASCII code of character ch PageSetup procedure PageSetup optional parameter list Shows the Page Setup dialog box for a given window Parameters window Longint or String The name or window ID of the window Default Front window See also Print ParamSD function ParamSD i integer extended Returns the standard deviation calculated for parameter i in the last Levenberg Marquardt fit Returns an invalid number NAN if the index i corresponds to a parameter that was not active during the last fit You can test if the return value is a NAN using the function Invalid Causes a run time error if the last fit was not successful or if i is out or range Use NumFitParams to check if the last fit was successful Paste procedure Paste Equivalent to selecting Paste from the Edit menu Phase function Phase z complex extended Returns the argument of the complex number z i e the angle between the vector pointing to the complex point and the positive real axis The function Abs gives the amplitude of the number abs c exp ii phase c c pi 7 const pi 3 1415926535897932 m 3 1415926535897932 Approximation of the ratio between the circumference and the diameter of a circle t 3 1415926535897932384626433832795028841971 First approximations for this peculiar number were already known by 2000 B C the Babylonians found T 3 1 8 the Egyptians m 4
296. rdinates displayed in the edit field correspond to the coordinates of that data point in the data window Editing them changes the values in the data window e Ifthe marker is on a function curve editing the coordinates sets the position of the marker If you edit the y coordinates pro Fit numerically inverts the function to find the corresponding x value You can use this feature also as a shortcut to calculate the inverse of a function or its root Coordinate markers can be accessed from proFit programs using the predefined functions GetMarkedx GetMarkedy and GetMarkedCoords Managing coordinate markers We already saw above how to create markers and look at their coordinates There are a few other simple operations that can be applied to markers e Click a marker to make it active e Click a marker while holding down the option key to transform it into the reference marker e Hit the delete key backspace while a marker is active to delete it e Click and drag a marker to move it to a new position e Move a function marker to the right or left border of the viewport to delete it To move a marker click and drag it or use the left and right arrow keys A data marker jumps to the next point to its left or its right a function marker will move along the function curve pro Fit makes sure that you don t move a marker outside the ranges of the viewport You can override this by holding down the option key while moving the marker with th
297. real start of subrange to plot subrange end real end of subrange to plot fitted parameters boolean true if using fitted parameters curve thickness real if connected thickness of line curve dash small integer if connected line dash id curve red integer color red component curve green integer color green component curve blue integer color blue component reduce data applies various data reduction algorithm do the data reduce data reference the window containing the data to be reduced using keep remove average smooth keepSelected removeSelected algorithm points integer number of points over which to average etc selection only boolean true if reduction is applied only to the current selection run program Run a program from the User submenu run program string The name of the program Example run program FitFrontWindow run the specified program For a more elaborate example see the command compile above save Save a window save reference the window to save in alias the file in which to save the object as data file drawing file EPS file function file PICT file text file file type for data export Windows can be specified by name or index 1 is the frontmost window 2 is the window behind it etc Note that Apple Script allows you to specify indexed objects in various ways such as window 1 front window 3rd window last window Optionally you can sp
298. red 8 4 Fitting Swe l 10 Oi Since this case is easy to handle from an algebraic and numerical point of view many common fitting algorithms and applications work under the assumption that the mean deviation is the mean square deviation given by Eq 10 A classical fitting algorithm that works on this basis is the Levenberg Marquardt algorithm in its unmodified original form see below Error analysis and confidence intervals Although some fitting algorithms most notably the Levenberg Marquardt fitting algorithm do provide estimates for the error of the parameters these estimates are often not sufficient or too imprecise pro Fit provides a general way for estimating the confidence intervals within which the true value of a fitted parameter can be assumed to lie with a certain probability level The influence of variations in the data points on the fitted parameters is analyzed with the help of a Monte Carlo simulation For this purpose synthetic data sets are generated starting from the points 2 f X that were obtained in the fit see above For each of the original data points a simulated data point is generated by random variation around f x within the specified errors and using the specified error distributions This produces a synthetic data set that effectively simulates a measurement The simulation of the measurement is based on the function that was determined in the last fit which is assumed to c
299. red Set withColTitles true to save the titles of the columns false if you don t want to save the titles Pass true for copyinfo to save the info field of the data window at the beginning of the text file noHeaderLines specifies the number of lines that must be skipped at the beginning of a text file when loading it into pro Fit Set inout 1 to modify the settings for importing text files set inout 0 to modify the settings for exporting text files SetTextStyle procedure SetTextStyle fontName Str255 size extended style integer Sets the default font font size and style for subsequent text drawing Text color can set using the Set LineColor routine SetWaitText procedure SetWaitText sl1 s2 s3 s4 s85 s6 Str255 Writes the strings s1 s6 into proFit s progress window which is displayed during lengthy operations The strings are arranged in a two columns by three rows arrangement sl s2 s3 s4 s5 s6 Use an empty string if you don t want to change it See also SetWaitTitle SetWaitTitle procedure SetWaitTitle s Str255 Writes the string s as a title into pro Fit s progress window which is displayed during lengthy operations See also SetWaitText Set WindowInfo procedure SetWindowInfo windowID longint info Str255 Obsolete UseSetWindowPropertties instead Sets the info field of a window to the given string The info field of a window can be viewed by choosing th
300. refore you might save a temporary result in Func for later use in Derivatives See also Chapter 9 Defining functions and Programs Parameters e x The function s independent variable e a The function s parameters a i Note that the index i ranges from 1 in Pascal but from 0 in C e dyda i The partial derivatives to be returned First procedure First a ParamArray pb ExtModulesParamBlockPtr This routine is called whenever the parameters a have changed before Func is called In most cases you can leave it empty Advanced programmers can use First for speeding up your function by evaluating temporary results that only depend on your function s parameters but not on its x value for more information see the description of First in Chapter 9 Defining functions and Programs Parameters e a The function s parameters a i Note that the index i ranges from 1 in Pascal but from 0 in C Check function Check ParamNo integer var a0 DefaultParamInfo pb ExtModulesParamBlockPtr CheckPAnswer Check is called whenever the user has entered a value in the Parameters window In most cases you can leave Check empty returning the value good Advanced programmers can use it for improving the parameters window s user interface Applications of Check are described in Chapter 9 Defining functions and Programs Parameters e paramNo This is the index of the parameter that the user has ch
301. rent parameters to the parameter set menu add parameter set as string the name for the set option for all boolean true if added set should be available for all functions calculate statistics performs statistical calculations on the given window calculate statistics reference the data window for the statistical analysis column integer the column for the statistical analysis 0 to use all columns median boolean set to true to calculate median minimum maximum basic boolean set to true to calculate basic statistical information skewness boolean set to true to calculate Skewness and Kurtosis selected cells boolean true if statistical analysis of the current selection selected rows boolean true if statistical analysis must be applied only to the data contained in the selected rows To retrieve the results use e g get statMean of results returns the mean value Available selectors of results are listed for class calculation results below capture Switches capturing on and off capture constant to file enabled disabled done to alias the file to capture into not used for options on off done Example tell application pro Fit PPC capture to file HD logFile start capturing to logFile write line hi there will be captured capture disabled disable capturing temporarily write line some text will not be captured capture enabled enable capturing write line add this
302. ribed below Any derivative you don t calculate will have to be calculated numerically by pro Fit If you set hasDerivates to false all derivatives will be calculated numerically and the function Derivatives will be ignored The derivatives are used for nonlinear fitting e descristLine descr2ndLine These two strings are displayed in the parameters window and should give a short description of your function C programmers should use the function SetPascalStr described under Set Up above for setting these strings e numberOfParams Here you should return the number of parameters of your function up to 64 e a0 This is a record in C a pointer to a struct that defines the default values modes names and limits of your parameters You can leave this record unchanged if you want to use the default values The following table lists the values that can be set in a0 for each parameter i Pascal notation C notation 2 contains a0 value i a0 gt value i Default value ad mode i a0 gt mode i Default mode set to active varied during fitting inactive not varied during fitting or constant cannot be fitted ad name i a0 gt name i Parameter name a Pascal string of length maxParamLength 3 ad lowest i a0 gt lowest i The lower limit for a parameter By default this value is INF a0 highest i a0 gt highest i The upper limit for a parameter By default this value is INF
303. ring The window to take the data from You can either pass a window ID or the window s name Boolean True if the limits of the x axis y axis of the graph are to be selected automatically to contain all data points false if explicit limits are given in parameters xFirst xLast yFirst yLast Default is false real The start and end of the x axis Specify these values if you set autoX to false real The start and end of the y axis Specify these values if you set autoY to false Integer The scaling of the x and y axes Values can be linScaling logScaling recSclaing for 1 x scaling probScaling probability scaling Omit this parameter s to use the current default scaling Integer The axis to be used as x and y axis Omit these parameters to use the default axes Boolean True if graph is to appear in a new window false if it is to appear in the current drawing window Boolean True if plot is to appear in a new graph false if it is to appear in the current graph Boolean True if only the currently selected rows are to be plotted false if all rows are to be plotted Boolean True if error bars are to be plotted false otherwise Integer Index of point type in the point style menu Real Size of point between 2 and 128 Real Thickness of lines for drawing points 0 auto 0 25 0 5 1 0 Integer The same as pointType but for the background part of the point Real The same as pointT ype but for th
304. ript for opening and closing a single file tell application pro Fit open file measured data open a file run program Analyze analyze it close window measured data close it end tell The script starts with the statement tell application pro Fit which indicates that all subsequent statements until end tell are to be sent to pro Fit The following lines tell pro Fit to open a file called measured data run the program Analyze from the Prog menu and then close the file again Apple Script 11 1 To use this script you must enter it in a script editor such as Apple s Script Editor untitled gt Description ad Mamon f Record Stop Fun Check Syntax tell application pro Fit open file measured data open a file run program Analyze anakyze it close window measured data close the File end tell AppleScript a When you click Run the script is compiled and then executed When compiling the script the statements are converted into Apple Events data packets that can be exchanged between applications When running the script they are sent to pro Fit As mentioned above you can save the script as a Compiled Script and then load the compiled script from pro Fit by choosing Load Module from the Customize menu The script is added to the Prog menu from where it can be run Batch processing Imagine you have a large number of data file
305. rm P Colum n Form at msout Xx eyear e Y couma T selected rows only Selected cells cell X cell Simple arithmetics d Column arithmetics d Differential Integral C Various functions d Formula The transformation is either by columns or on the current selection Check Selected Rows only to only include selected rows in the calculation Choose Selected cells to work on the current selection 4 4 Working with data In calculations on the current selection each cell x in the selection is replaced by its transformed value y In transformations by column the cells of the x column are transformed and stored in the cells of the y column You can select the x and y columns from the pop up menus In these menus empty columns are marked with gt columns already containing data with and text columns with f Five different groups of transformations are available e Simple arithmetics All these transformations are of the type y x op val where op is one of the operators multiplication division power div integer division mod modulus e Column arithmetics These transformations are of the type y x op col Again op can be any of the operators mentioned above Differential Integral These transformations return the discrete derivative or integral The derivative is calculated as the discrete derivative of a column d that is selected from t
306. rmally distributed measurement errors The deviation function 3 corresponds to a Gaussian error distribution In this case the probability density that a certain error occurs when measuring x or y is given by a Gaussian distribution or normal distribution The next deviation function provided by pro Fit is R d d 4 and corresponds to a two sided exponential error distribution exp d It leads to the calculation of a mean absolute deviation instead of a mean square deviation The deviation function R d log 1 ia 5 corresponds to a Lorentzian error distribution 1 1 d 2 The last deviation functions available in pro Fit are a ch cos d c d lt cm d gt cm with c 2 1 and ay ef1 1 2 i ld lt c R d 4 7 ld gt c 6 with c 6 These deviation functions are called Andrew s sine the derivative of 6 is sin z c and Tuckey s biweight respectively They don t correspond to a particular probability distribution for the errors They are designed to decrease the weighting of data points with very big errors outliers in order to allow a robust fitting through the more reasonable data points It should be obvious that this procedure should only be used if you know your experiment and data set well enough and we repeat the usual calls for caution Note that using the deviation functions 6 and 7 with another constant c is equivalent to changing all errors
307. rns results for Fit Optimize Statistics Root Extrema Integral See the definitions of the respective commands for the selectors to be passed to Get Result GetSelection function GetSelection Rect External modules only Returns the coordinates of the contiguous selection in the current drawing window The rectangle s coordinates correspond to SelectLeft SelectTop SelectRight SelectBottom GetSelectionBounds function GetSelectionBounds var left right top bottom extended Returns the boundaries of the current selection in the current drawing window GetSkew procedure GetSkew var count longint var mean variance skewness kurtosis extended Obsolete Use Statistics and GetResult instead Returns some results of the last call to calcStat CalcStat must have been called with the withSkewAndCurt parameter set to true before this function can be used Appendix A Predefined functions procedures and arrays A 33 GetWindowID function GetWindowID windowName Str255 longint Returns the window ID of the window having the given title Returns 0 if there is no window with this title GetWindowTitle procedure GetWindowTitle windowID longint var name Str255 Returns the title of the given window windowID is the window ID of the window such as it is e g returned by GetWindowID or FrontWindow GetWindowType function GetWindowType windowID longint longint Ret
308. rns the numerical value of the given cell in the current drawing window GetData replaces the predefined matrix data i j used from functions within pro Fit GetDefaultData procedure GetDefaultData xColH yColH xErrColH yErrColH ExtendedArrayHandlePtr indecesH LongArrayHandlePtr var arraySize longint selectedRowsOnly Boolean info DataInfoPtr type DataInfo record xMin xMax xPosMin xNegMax extended yMin yMax yPosMin yNegMax extended ordered Boolean zeroYErrors invalidYErrors zeroxXErrors invalidXErrors Boolean end DataInfoPtr DatalInfo This routine provides a copy of the default x y data in the current data window It allocates memory for the x y arrays for the x y Error arrays and for the array that gives the corresponding row numbers in the data window Then it fills them with the data It copies only the data where both the x and the y cell contain valid numbers The arrays are returned in xColH yColH xErrColH yErrColH Pass nil for one of these arrays if you are not interested in it The record info holds some more information about the returned data The arrays returned by GetDefaultData contain valid data starting from the element with index 1 The value of the element with index 0 is undefined The last element has index arraySize arraySize is Set to zero in case of out of memory situations or other problems Warning This routine should only be used by a
309. ro expression string the pascal expression to be used as a transformation function selected cells boolean true if the transformation must be applied only to the current selection selected rows boolean true if fitting using selected rows only transpose Exchanges columns and rows in a data window transpose reference the data window to transpose use parameter set Moves a parameter set found in the alternate parameter set menu to the parameters window use parameter set string the name of the parameter set or fitted parameters for string name of the function the parameter set belongs to omit for the current function option for all boolean true to use one of the sets available for all functions write Write a text into the results window write string the text to be written write line Write a text into the results window and advance to a new line write line string the text to be written Classes of the pro Fit suite Many of the classes windows columns etc that can be accessed within pro Fit have properties or elements For instance each window has a property called name each column has the properties name and default type A data window table has columns as elements each column has cells as elements You can access properties and elements by using the following standard Apple Script commands get mom data or set data Abbreviated they are used as get set and copy Exam
310. ro Fit s drawing windows to create drawings with high precision coordinates These drawings are available for copying and pasting into other applications and for high resolution printing Introduction 1 1 e Macro programming Write complete macros to perform common tasks such as opening and closing document windows fitting importing and exporting files etc e Extensive on line help Balloons and Apple Guide provide answers and explanations A dedicated on line help is available for function and program definition e Powerful plug ins Various external modules further increase pro Fit s power e g for contour plotting and 3D plotting of functions and data sets 3D plotting requires a Power Macintosh with QuickDraw 3D e And much more Such as Drag amp Drop Publish amp Subscribe Numerics algorithms customizable data file import etc What you need to run pro Fit pro Fit runs on Mac OS with System version 7 5 or later pro Fit requires at least 2 MByte suggested 4 MByte of free memory if virtual memory is off the Power Macintosh native version requires at least 3 MByte suggested 5 MByte The QuickDraw GX features are available when running with the QuickDraw GX extension installed The QuickDraw 3D modules run only on a PowerPC machine with the QuickDraw 3D extension installed How to read this manual This manual gives a full description of pro Fit 5 1 If you do not want to read it you will still be able
311. rom the File menu choose the type Compiled script and save the script Such a compiled script can be loaded into pro Fit Choose Load Module from the Customize menu and select the compiled script It is added to the Prog menu Once the script is compiled you can either run it from your script editor or you gt compiled script In the following we give some examples for scripting pro Fit through Apple Script Then we discuss the differences between programs and scripts Finally we give a list of the Apple Script commands and objects that you can use with pro Fit Apple Script is a very powerful programming language However it may be confusing for the beginner The easiest way to get started is using Apple Script s recording capabilities Just open the Script Editor and click the Record button Now go into pro Fit and do by hand what your script is supposed to do Script Editor records all your e actions as Apple Script commands Once you are through go back to Script Editor and click the Stop button Your script is now complete Note that this chapter is not intended to give a beginner s introduction to the Apple Script language We will however explain some its aspects as we use them To learn more about Apple Script consult the dedicated literature such as the Apple Script Language Guide distributed by Apple Examples Opening and closing a single file The following is a very simple Apple Sc
312. rors in the y coordinates The probability of incurring in a given measurement error can decrease in some known way when the magnitude of the error increases There are also various possible methods of looking for the best parameter set pro Fit provides a choice of different ways for measuring the distance of the data points from the function as well as a choice of different methods to reach the best parameter sets The first part of this chapter deals with the definition and mathematical description of deviation functions and fitting algorithms the second part shows you how to select these options in pro Fit and how to run a successful fit Mathematical background In order to find the best parameter set describing a given measurement it is necessary to establish a quantitative method to measure the distance between a data set and the function that should describe it This requires the introduction of weights for the data points and of probability distribution functions They are described in the next sections Distribution functions and data weights Consider a function f d a x f x we won t write explicitly the function parameters every time and a measured data set sy eel ENAT Let s assume that the function with its true parameter set correctly describes the quantity that was measured We further assume that when the data point x y was determined the true system the one described by th
313. round symbols To set the background symbol separately call SetBGDataPointStyle SetDataSize procedure SetDataSize numberOfRows numberOfColumns longint Obsolete Use SetDatawindowProperties instead Sets the number of columns and rows of the current data window The number of rows and columns must be between 1 and 30000 Set numberOfRows to 0 if you only want to change the number of columns Set numberOfColums to 0 if you only want to change the number of rows To get the current size of a data window use the functions NrRows and NrCols SetDataWindow procedure SetDataWindowProperties optional parameter list Sets the properties of a data window Parameters window String or Longint The name or windowID of the window to be affected name String The title of the window Omit for leaving it unchanged boundsLeft boundsRight boundsTop A 58 Appendix A Predefined functions procedures and arrays boundsBottom Integer The bounds of the window in global screen coordinates Omit for leaving them unchanged info String The info text attributed to the window Omit for leaving it unchanged fontName String The font to be used in the window Omit for leaving it unchanged fontStyle Integer The font style to be used in the window plain bold italic underline outline extended condensed or any sum of these values Omit for leaving it unchanged
314. rtant predefined constants T or pi 3 141592 true 1 false 0 INF infinity 1 INF 0 The operators are identical to those that are defined in standard Pascal In addition the power operator or has been added The operators in ascending order of precedence are Defining functions and programs 9 19 SES Pe 2E comparison returning true 1 or false 0 PISTON add subtract logical or and multiply divide logical and k k A r power x y x y X not logical not You can change the order of precedence of the operators in the above list by using brackets and Y Note that there are two ways for using the power operator x y and x y They are equivalent Use whichever you prefer On some machines x y x y is calculated as exp y In x As a consequence of this the x y may not work for negative x and may be slow Therefore you should not use this notation for calculating small integer powers for example use sqr x instead of KEEA Note for Pascal programmers is used for the power operator pro Fit does not know anything about pointers and is not used for dereferencing The order of precedence for the operators is the same as in standard Pascal But since the pro Fit definition language does not distinguish between boolean and real expressions refer to the next chapter this order of precedence provides a dangerous pitfall a gt x and b gt y will be
315. rwise it will be kept fixed The fitting mode of a parameter determines the style of its name in the Parameter window Parameters with names displayed in bold face will be varied during a fit Parameters displayed in normal type face are kept fixed during a fit As an alternative to using the Use for fitting checkbox simply click the name of the parameter to toggle its fitting mode Setting one of the parameters of a function to be equal to the value of x You can enter the expression x when changing the value of a parameter in the parameters window Polynom parameters deg 3 0000000 const 4 al 0 0000000 a2 10000000 a3 00000000 The selected parameter is forced to be equal to the current x value of the function If you want to study the dependence of a function upon various parameters you can define your function as a function of parameters only without explicitly using the variable x You then designate the parameter treated as the x value by entering x for its value in the parameters window If you explicitly use the variable x inside a function and also define a parameter to be equal to x both will have the value of x A function like y a 1 sin x becomes the function y x sin x if a 1 is set to be equal to x in the parameters window If you define your own function you cannot use this feature for parameters that you use in the procedure first because x is not defined in the procedure first If
316. ry characters in each cell To switch between text and number formats first select the column or columns you want to change and then choose Column Format from the Calc menu Alternatively you can also double click the column number of a column you want to change After either of these actions the Column format dialog box appears Column Format Format of column 1 J Text Column width default Numbers Range Format 1e30 1e30 Decimals auto 1e300 1e300 O Scientific Check Text if you want the selected columns to contain text check Numbers for numerical data In the latter case you can specify their Range single or double precision and define the format for displaying numbers select the number of digits to be displaced after the decimal point decimals from the Decimals pop up menu If you check the scientific option all numbers will be shown in exponential representation i e 1 34e 3 for 1340 You can also enter the column width in pixels in the corresponding edit field A second way for changing the width of a column is to click on the boundary line between column titles the mouse cursor will change to 4 and drag it to the desired position Entering data You can type data in the data window copy and paste it or drag it and drop it everywhere you want Instead of entering a number directly you can enter a mathematical expression e g exp 1 or 6 sin 7 4 or any predefined functi
317. s If the selected object is a graph the line styles of the axes ticks grid and frame will be changed The color also applies to the labels More complex options are available for the graph See section Graphs and legends in this chapter If the selected object is a legend you can change the appearance of the curves and data sets displayed in the legend and the corresponding graph See the section Graphs and legends later in this chapter for details Drawing and Plotting 7 11 Arrows of various size and shape can be added to polygons and lines using the Arrows pop up menu Arrows can be added to all lines and polygons smoothed as well as unsmoothed Choose Other from the Arrows menu to design your own arrows and add your personal arrow styles to the Arrow menu Custom Arrows Edit arrow atline end start Arrow size Lf Equal arrows at both ends og STSTSISI ES Voor k Half sided amp Left Right You can define a different arrow to be used for the start and the end of a line use half sided arrows define various other types of line caps etc Fill colors and line colors are set using the corresponding popup menus To copy the line color from one object to another 1 2 3 Click the color measuring tool Zin the tool palette Click the color you want to copy to pick it up The shape of the cursor changes and becomes a paint bucket Click the drawing object to
318. s They can be gaussDistr doubleExpDistr lorentzDistr andrewDistr OrtukeyDistr xErrColumn tells if x errors should be used set it to 0 if x errors are unknown to 1 if they are constant pass the value in xErrValue to 2 if they are given in percent pass the percentage in xErrValue or to the number of an x error column stopTime tells when to stop Monte Carlo fitting pass a value gt 0 to give the maximum number of iterations a value lt 0 to give a negative maximum time in seconds 0 for continuing fitting until manual interruption SetFitParamRange procedure SetFitParamRange paramNr integer rangeMin extended rangeMax extended asPercent Boolean Sets the fitting range for parameter paramNr as it is used for Monte Carlo fits If asPercent is true the range values can be given as a percentage offset from the parameter value The fitting ranges set by this command stay valid until the next fit command has been executed SetFunctionParam procedure SetFunctionParam name Str255 i integer value extended Sets the default value of a function parameter as it appears in the parameters window name is the name of the function as it appears in the Func menu Use an empty string to specify the function currently selected in the Func menu This parameter is case sensitive i is the parameter index value its new value Example setFunctionParam Polynom 1 6 sets the degree a i of t
319. s are nearly on a straight line and are sufficiently described by the parameters aq and a1 The standard deviations of the coefficients a9 a3 will be accordingly large The errors of the data set When using errors standard deviations for your data it is useful to keep some points in mind 8 24 Fitting e Multiplying all errors of your data points with a common factor does not affect the results of fitting but changes the estimate of the standard deviations or the confidence intervals of the fitted parameters e Changing the relative errors of your data points affects the numerical weight of the data points Example If you have a large number of points in one area e g between x and 2 and just one or two points far out e g at x 50 it is necessary to decrease the error for these lonely points if you want to force the function to come close to them e When plotting a curve in a graph with a logarithmic y axis a deviation of the curve from a small y value appears much larger than the same deviation from a larger y value If this astonishes you it is probably because your measurement errors are proportional to the measured value When plotting a fit on a graph with a logarithmic y axis the errors of the y are often given in percent This results in smaller deviations from points with small y values Here is an example of logarithmically plotted data with fits using percentage errors and constant errors 106
320. s this dialog box also contains a PICT Options button in the bottom left corner Use it to change the picture format used by the publisher Importing pictures Every picture in the standard PICT format can be imported into a drawing window Note that you cannot paste QuickDraw GX shapes into pro Fit 5 0 There are two ways of importing pictures over the clipboard by choosing Paste in the Edit menu or via an Edition Container by choosing Subscribe to in the Edit menu Importing pictures over the clipboard or using Drag amp Drop When you create a picture in any application you can transfer it via the clipboard by copying and pasting it or by directly dragging and dropping it into a pro Fit drawing window Note that pro Fit imports pictures as a whole and does not take them apart If you use a drawing application to create a line and a rectangle and paste these objects together into pro Fit they are interpreted as one picture not as a line and a rectangle Drawing and Plotting 7 15 An imported picture can be resized or rotated but it cannot be edited in any other way Rotating and resizing may not work with imported pictures if they contain any non standard information such as PostScript commands Importing pictures by subscribing Another method to import pictures is to subscribe to an Edition Container by choosing Subscribe To from the Edit menu To open the application that created the Edition container Click Open
321. s file In multi user environments different users might want to use the multi preferences file mechanism provided by pro Fit The pro Fit preferences file holds the default settings and other information for many pro Fit s options Different users may want to use different preferences files pro Fit normally uses the preferences file found in the Preferences folder inside your System folder It is possible however to start pro Fit by double clicking another preferences file or to switch to a new preferences file while pro Fit is in use by choosing Preferences from the File menu This allows each user to use his own set of preferences See Chapter 13 Preferences to learn how to use preferences files pro Fit provides a mechanism that allows users to load their favorite modules together with their preferences file whenever a preferences file is opened pro Fit looks for a folder named pro Fit modules in the same folder as the preferences file and loads all the modules it contains To take advantage of this mechanism simply put your preferences file and pro Fit Modules folder inside a common folder 9 32 Defining functions and programs Charles Zitems 197 3 MB in disk Whenever pro Fit opens the preferences file it also loads all the modules found in the pro Fit modules folder Defining functions and programs 9 33 10 Working with external modules This chapter explains how to add external modules to pro F
322. s given by the following parameters headerLines Integer The number of lines to be skipped at the beginning of the file copyInfo Boolean Copy the header lines specified with parameter headerLines into the info field of the data window withTitles Boolean Read the column titles delimiter String Column delimiter at least 1 character Typical values are t which defines a tabulator decimal 8 which is a simple space which is a simple comma s stands for 1 or more spaces w stands for 1 or more spaces and or tabulators in any sequence Any combination of characters and t A 20 Appendix A Predefined functions procedures and arrays terminator String Line terminator after each row with at least 1 character Typical values are r which defines a carriage return decimal 13 n which defines a line feed decimal 13 Any combination of characters and r n Note that the line terminator must not be equal to the column delimiter To import data from a text file fist call DatalmportOptions for setting the desired file format Then call OpenFile and pass textType for loading the file into a function window or dataType for loading the file into a data window for the parameter type DataTransform procedure DataTransform optional parameter list Performs various data transformations on a data window Corresponds to the command Data Transfor
323. s in a folder You want to open each of these files from pro Fit and analyze its data Without scripting you would have to open each file by hand run your analysis then close it again boring work if you have to do it often The following script does it all for you bring up a dialog for selecting the folder of the files to analyze set myFolder to choose folder with prompt Choose a folder with data files create a list with all files in the folder set myFiles to list folder myFolder a list of files in myFolder set myFileCount to count myFiles the number of files in myFolder now start working with pro Fit tell application pro Fit set oldErrorAlerts to error alerts save error alert status set error alerts to false pro Fit should not show alerts activate bring pro Fit to front repeat with i from 1 to myFileCount go through all files set theFile to item i of myFiles get the i th file try open the file for processing as data file open file myFolder as string amp theFile as table write line found amp theFile write comment to Results window close window theFile saving no close without saving on error errText write line cannot open amp theFile amp amp errText amp end try end repeat set error alerts to oldErrorAlerts restore end tell 11 2 Apple Script This script first brings up a dialog box for selecting a folder by using the Apple Script extension choose fol
324. s quickly pointsStep tabulate for all values of the x column in the current data window Default if omitted numericStep parameter Integer Omit or set to 0 if tabulating the function by varying its x value Set to the number of a parameter for tabulating the function by varying this parameter xValue Real defines the function s x value if you pass a non zero value for parameter Omit otherwise fittedParams Real true for tabulating the function with the parameters obtained in the last fit false default if tabulating the function with the parameters given in the Parameter window Appendix A Predefined functions procedures and arrays A 67 procedure TabulateExtrema optional parameter list TabulateExt_ Finds the minima maxima of a function by varying its x value in a given interval Calculates a table of the extrema for different values of a parameter of the function Parameters function String The function to be used Omit for current function xMin xMax Real The start and end of the x interval parameter Integer The parameter to be varied for tabulating Pass 2 for varying xMin 1 for varying xMax however these two options do not make much sense from to Real The start and end value of the parameter to be varied step Value Integer The step for increasing the parameter subintervals Integer The number of sub intervals to be searched in the x interval When the functio
325. s the given axis axisID corresponds to the number used in the axis popup menu in the dialog box that appears when double clicking an axis e g axis D 2 for axis X2 whichAxis is either xAxis or yAxis DeleteFunction procedure DeleteFunction func String Removes the given function from the Func menu func is the name of the function See also DeleteProgram DeleteParameterSet procedure DeleteParameterSet optional parameter list Deletes a parameter set previously saved with SaveParameterSet Does nothing if the parameter set is not found Parameters name String The name of the set Omit to delete all the sets belonging to the given function ofFunction String The function the parameter set belongs to Omit if the parameter set was available to all functions file String The file from which the parameter set must be deleted Omit to delete from permanent set fromMenu Boolean True if the param set must be deleted from the parameter set menu Default true fromFile Boolean True if the param set must be deleted from the file Default true See also AddParameterSet UseParameterSet SaveParameterSet LoadParameterSet A 22 Appendix A Predefined functions procedures and arrays DeleteProgram procedure DeleteProgram prog String Removes the given program module or script in the Misc menu prog is its name See also DeleteFunction Derivative function Derivati
326. s when there are errors in X Computer in Physics Vol 7 No 2 1993 Partial derivatives To fit a function of the type y f a a x the Levenberg Marquardt algorithm needs the partial derivatives of the function with respect to its parameters It uses the partial derivatives when it estimates the influence of the parameter set aj on y The partial derivatives fj are given by K df as X f iQ Oa 1 i and they are calculated for all x coordinates X during every iteration When you define your own function for fitting and you find that the fitting process is too slow then you should define these derivatives explicitly in the procedure called derivatives If you do not define the derivatives yourself pro Fit must calculate them numerically This makes fitting considerably slower More information on how to define functions and their derivatives is given in Chapter 9 Defining functions and programs Estimation of parameter errors The Levenberg Marquardt algorithm allows the determination of the standard deviations of the parameters These are the values that are printed in the results window after a successful fit under the heading standard deviations The standard deviation defines the region that contains 68 3 of the total integral of a Gaussian distribution The standard deviation uj of the parameter value a Lj obtained after a successful fit is found from aj is 12 where C is the diagonal e
327. sed 7 18 Drawing and Plotting If you are using linear x axis scaling the entry in the field Step determines the distance step width between consecutive calculated x values If you are using any other x axis scaling the field has the name Steps and determines the number of x values that will be calculated to plot the function The default value for step is auto This invokes a specially designed plotting algorithm that automatically selects the x values at which the function is calculated If the curve representing the function is strongly bent in a given interval then the number of points that are required for drawing the function is large On the other hand if the function is a straight line the number of points needed is smaller The following figure illustrates this function caclulated points Note that the number of calculated points is optimized for the range a function is plotted in If you change the axes range of a graph later e g for zooming into a detail the number of calculated points may not be sufficient anymore for representing the curve accurately In this case you should redraw the function to create an optimized plot for the new range Note that plotting with the auto option results in the smallest number of data points stored to represent a function s curve In this way you can create a plot that uses a minimum amount of memory and that is redrawn at maximum speed However t
328. snsnsnsnnnnnne 3 Changing the ranges of the PreviCw ecceccscesseceeceseeseeceeeeeeeeseeeceeeseeeceaneenseeaneeeaees 3 Dragging the function CUVE aot sieniin aiaia aeiaai gaea daie ariaa iiiaae 4 Inspecting and editing coordinates ssi scie oka eed etce oA crcteuicat A eect Mince cece 4 Managing Coordinate markers cccecceceseececeeeeeeeeeeeceeeeeeeceeeaeeeseeeaeeeseeeeeeseeseesaseatenees 5 TpsaAnd iCk a aa a stated abe aar a EAA asc eittadl tee Sasaaiecadt 6 Using the preview window during a fit cess eeeseeeeeceeeeeeeceeeeeeeeeaeeeeseeaeeeseetseeeeeeneeees 6 Choosing initial values of function parameters cece ecceeeeeeeeeeeceeeeeeeceeeateeeeeeeeeeeeees 6 7 Drawing and PlOUTiing iisieicicc ccc ciccsciee cca iesccy ee cate wales anana anap aw eran neha ee 1 Thedrawing WINdOW eer serene eres crear oaa crcl rer errr crn earch pear AEN 1 Drawing TOMS siennes ar aeaa aaa teow cae cet naaa Meee ces a EAN A tera Aaaa aaan aiaa 1 Coordinates accuracy and drawing infO cceceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeseeeeeeeeeeeeeeeees 2 Drawing objects seo c a5 ead cota atc geet tded eect eres delat eaten tata eliedeareh bec deateyeetbeaataed 3 EPR csc a hen 2 ve oe a a oe Ah ae See ee eee cee 3 General drawing commandS sec cre acts each cet ete pies te beerestiees auteceweshM cue be caeeretereeeeas 3 Objects created with the tools palette eceeeeseeceeceeeeeeeeeeeeeeeeeeeeceetseeeseaneeeseeaneeeaees 5 TEXT ODI SCS sic ic
329. st be used as a reference to draw the grid lines The grid lines are drawn at the tick marks of their reference axis By default the ticks of the main axes X1 and Y1 are used Graph Styles The appearance of a graph is defined by many parameters such as its size the ranges of its axes the number of minor ticks the symbols used for plotting etc These settings are called the style of a graph You can save the style of a graph to use it or parts of it later for another graph Styles are saved in the preferences file 7 32 Drawing and Plotting By using styles you can create graphs with equal formats e g graphs having the same size the same length of the ticks the same fonts etc To save the style of a graph you can either double click the graph and click the button Style in the dialog box that comes up or you can choose Styles from the Graph submenu in the Draw menu after having selected your graph Graph Styles SE Saved styles Extra Large Standard Save style as LI Default This box shows a list of the styles that are already saved in the current preferences file You can delete one of these styles by selecting it and clicking Delete To save a new style enter its name and click Save To load a style select its name in the scrolling list and click Load The name of the button changes from Save to Load when you move from the Style name edit field to the Saved styles scrolling list If you click the Defau
330. stances in the drawing window and the Drawing Info window Check Automatic grouping of new graphs if you want to automatically group a graph the names of its axes and its legend when it is created Uncheck this option if these items should not be grouped Check Always use floating toolbox if you never want the drawing tools to appear inside the drawing window Panel Preview This panel controls some options for the preview window Preferences Data points Color im gt selection color im gt Coordinate markers Color fm gt Reference color m Coordinate lines xs yefo O ki Allow dragging of data points Interface The first two pop up menus define the colors of the data points the points used for showing your current data The menu Color sets the color of the data points which are not part of the current selection The menu Selection color sets the color of selected data points The second two pop up menus define the colors of markers for more information on markers see Chapter 6 The menu Color sets the color of all markers except the reference marker the menu Reference color sets the color of the reference marker The Coordinate Lines are drawn in a light grey color in the preview window behind the data points and the function curve They are two perpendicular lines that cross the x and y coordinate axes of the preview at the coordinates given in the two edit fields Preferences 13 3
331. syntax ses k ands dees neobes oh ces ee weseeeetivertceaseeceses eee eeledeas etek ctese 23 Special procedures in a function definition ee eect eseeeteeeeeeeeeeeceeteeteeeateetaees 23 F n tion CHOC 2 lian cached a Mead At od aT a aaa n ee 23 Procedure WINAZGs 5226 cutest ds Boves tact hide Berea sya tater ete cece eee enne 24 Procedure Derivatives ncc55 clic ce cyan tien cea cece ak coal alee uit eaea 24 Proced re FS cha ese cacti te cae eed ea treet aetna eee A AATE 25 PIGCCOUEG BAST saci coc peorccatei nnn oe ot chs a a the Seachem ote ech aa aati 27 ROI TAA tcc EA AE ES hans oat E E AE Acueh sues elias ciate ete ts 27 General comments about programming ccecceesceeeeceeeeeeeeeeeeeeeeeenaeeeaeeeeeeenneneaees 27 be 81 ks eee ee EN a MRE ee ete Pe a rey eT eee eae ee 27 1 Simple numeric tyPOS ee eeeeeeeeseeeeeeeeeeeeeceeteeeeceaeeeeaceaeeesseeseeeseanseneceaneetaees 28 2 COmMmpl x type raitaa atts A Aa etd Mere is A ee ett as tema ty 28 Oe Stringand char LY POS oe dst aces oiaie fee Oe Gas aaia tain Ge bode eee As aaa 28 PRCA Sasa sate a R teh tage Nes es aka aL 29 Bil ale ace 6 60 6 l eaateeee eae renee mere rar esate nr ern ere at a wer enone emer rns meer area Serene ai 30 B 0 fo 0 aye E E A an Ty Sorgen teeta noe ncn E 30 Comparison to standard Pascal c cecceccseeeeeeceeeseeececeeeeeeeeeeeeseeseeseeeaneeseeeaeeeseees 30 External functions and programS suit csecctatcraea cbhecles pi
332. t EE eee a ele te E el a ei ei hee diane aes 6 Rectangles and ellipS s eccceeeccssessecceceeeeeceseeeeeceaeeeeseeseeesneeseeessanseeaseaneesseeaneetaees 7 TINGS and OW OOS sioner i scales cian eal ne Be lace vate Sect eta Aires lees tet a a aaa aa 7 POINTS neea a a E A E A A T E Co eet 9 Editing drawing objects iv nnVie sete ecccereiaes ue neler Viel idicede nae sere te ese 11 Exporting pietu reS xi 2ctt a Aras Lead ual aaar aAa Eara aiaa est cas Soca eel Raia ASi a 13 Saving a drawing as a PICT or EPS file 00 eeeeceececeeeeeeeeeeeeeeeeeeeeseeeeeeeseeteeeaeeaees 13 Exporting pictures over the clipboard s s sssssssssssrsrerersrsrrrnrnrnrnrnrnrnrnrnrnnnenrnennn 14 Exporting pictures using Publishers s sssssssssssnsnsnsnererenerernnnrnnnnnnnrnrnnnrnnnnnrnnnrnennn 14 Importing NCES career de aetna ws Paces eects ete feces ta aaia niaren baaada rat aaan kausai keia 15 Importing pictures over the clipboard or using Drag amp Drop s s s sesesesesesesesesesen 15 Importing pictures by SUDSCIIDING cceccceceeeeeeeceeeeeeeeeeeeeeeeaeeeaeeseneseeeeaeeeaeeeneees 16 POT Enea sd ved Yaa ete vin tee hl Raa Ree Wee E ede ee Ee 16 Ele ale go b6 e11 1 qe emeemmeee errr err ete ter mere arene ern ere eee tyre a 17 Plotting a PUNCH O Pics ee lates ect feed ede nianses nhia adeuda anana uecacontudel raaka daana Kina bade naia 18 Plotting a data set ese sce aces an nc eae aN ee Ae Ste eaten 19 Graphs and legend Sunnen irena e E
333. t a function or a data set without actually plotting it For instance you can let the Preview Window be a floating window and keep it in front while you load many different data files The preview window will automatically display all data contained in the current x and y columns of the front window You can also use the preview window to view functions graphically edit function parameters select a range of data points compare a function to a data set etc Preview Window 6 1 Choose Preview from the Windows menu to see pro Fit s Preview Window This is how the Preview Window looks like when it has its smallest size and is working as a floating window ae 1 2000 selector tool ow data x Show function x Auto drag tool C Fitted params zoom tool T 02000 fitting tool 1 0000 C Auta oaa d marker tool x O7736 y O4225 marker s coordinates On the left side of the Preview Window there are some check boxes that determine how the window behaves and what it shows The main part of the window is a rectangular viewport that shows a graphical representation of the current function and data set On the right of the window there is a tool palette with tools for changing the coordinates displayed by the viewport for graphically editing the function and the data set and for determining precise x and y coordinates Check Floating to make the preview window a floating window which always stays in fron
334. t of all document windows Uncheck this option to transform it into a normal window which you can be hidden by other windows Check or uncheck Show data and Show function to choose what is shown in the window When Show data is checked the window displays the current data set i e the x and y columns of the current data window You can select the data set to be shown in the preview window by clicking the Data button or by directly setting x and y columns in the data window The Fitted params check box appears whenever a fit was successful to give you the option of seeing a plot of the function using the parameters obtained in the last fit instead of seeing the function with the parameters shown in the Parameters window Click the Redraw button if you want to let pro Fit redraw the complete function at maximum resolution pro Fit automatically decreases the resolution at which it draws the function if it notices that the function is too slow You can override this by clicking the Redraw button The Undo button appears only when the Preview Window is floating and it allows you to undo the last operation When the Preview Window is not floating you can undo the last operation as usual by choosing Undo from the Edit menu At the right end of the title bar there is a zoom box Click it if you want to work with a larger window At the edges of the rectangular viewport that displays the function and the data set are four edit fields giving th
335. t opens a new data window and stores its reference in myTable Now it opens each data file in the designated folder calculates the sum of the values in its column 1 and stores these sums in column of the data window myTable The script starts with set scriptProgram to This statement sets the symbol scriptProgram to the text following it The symbol at the end of the line tells the script editor that more lines follow to generate this symbol type the return key while holding the shift key down The statement compile scriptProgram add the above program to Prog menu sends this text to pro Fit and tells pro Fit to compile it i e to add it to the Prog menu Then the script creates a new data window using the command set myTable to make new table open new data window The symbol myTable becomes a reference to the new data window Now the files of the designated folder are opened one by one After a file is opened the ScriptProgram is run and the file is closed again Then the script retrieves the result of the program from globalData 1 The values in the array globalData can be accessed from scripts by using the object globalData and an index such as set sum to globalData 1 get result The result retrieved in this way is transferred to the k th row of column 1 of the data window myTable set cell k of column 1 of myTable to sum store it in the table As you can see scripts can exchange data with pro Fit ei
336. tOptions procedure SetOptions optional parameter list Sets some options of pro Fit Parameters currentFunction String The current function Alternative call to SetOptions currentFunction myFunc iS SelectFunction myFunc Omit for leaving the current function unchanged decimals Integer The number of decimals to be used for writing numbers in the results window Pass a negative value for setting the total number of digits a positive value for setting the number of digits after the decimal point Omit for leaving the setting unchanged A 62 Appendix A Predefined functions procedures and arrays errorAlerts Boolean true if error alerts are to be shown when running into errors during the execution of programs or scripts Omit for leaving this option unchanged scriptDebugging Boolean Set to true if debug info is to be printed while running AppleScripts Omit for leaving this option unchanged SetParamDefaults procedure SetParamDefaults i integer value extended mode integer name Str255 min max extended Obsolete Use SetParameterProperties instead Sets the value fitting mode name and limits of a parameter of the currently running function i is the parameter index value its new value mode its new fitting mode can be constant inactive or active name its new name and min max the lower and upper boundaries of the parameter SetParamDefaultValue procedure SetParamDefaultValue i integer
337. teProFitWindows AddDataPoint procedure AddDataPoint x y xErrl yErrl xErr2 yErr2 extended Adds a new data point to the current data set in the current graph x and y are the coordinates of the new data point xErr1 and yErril xErr2 and yErr2 the lengths of the asymmetric error bars Depending on the parameters passed to OpenDataSet the parameters xErr1 through yErr2 may be ignored Call openDataSet before calling AddDat aPoint The style and size of the data points can be set using the routine SetPointStyle See also DrawDataPoint AddParameterSet procedure AddParameterSet optional parameter list Adds the parameters that currently appear in the Parameter window to the parameter set menu Parameters set String The name of the set forAll Boolean True if the parameter set is to be available for all functions false if the parameter set is only to be available for the current function Default false permanent Boolean true if the parameter set must be added permanently to the menu i e if it will be still available after a quit and restart Default true See also UseParameterSet SaveParameterSet LoadParameterSet DeleteParameterSet AddTick function AddTick whichAxis integer tickPos extended isMajor Boolean integer Adds a tick at the position tickPos to the current axis makes it a major tick if isMajor is true whichAxis is either xAxis Or yAxis Alert procedure Alert s
338. teger The font size to be used in the window Omit for leaving it unchanged SetWindowTitle procedure SetWindowTitle windowID longint name Str255 Obsolete UseSetWindowPropertties instead Sets the title of the given window to the string name windowID is the window ID of the window such as it is e g returned by GetWindowID or FrontWindow Sin function Sin x extended extended Returns the sine of x Sinh function Sinh x extended extended Returns the hyperbolic sine of x sinh is defined by Xx X e e sinh x 2 Sort procedure Sort optional parameter list Sorts rows in a data window Parameters Appendix A Predefined functions procedures and arrays A 65 window String or Longint The window specified by name or window ID Omit for front window referenceCol Longint The column to be used for sorting order Integer sortAscending Or sortDescending the sort order selectionOnly Boolean True if only the rows of the currently selected columns are to be sorted false or omitted if the rows of all columns are to be sorted SpeakString procedure SpeakString s Str255 Lets your hardware read the text contained in the string s If text to speech extensions are not installed on your computer this routine does nothing Sqr function Sqr x extended extended Returns the square of x sqr x x2 Sqrt function Sqrt x extended extended Re
339. that Irl should be larger than its observed value in the null hypothesis x and y being uncorrelated It ranges from 0 good correlation to 100 bad correlation We refer to the specialized literature for more details The Polynomial fitting algorithm Our model is the general linear combination of arbitrary functions SY a 19 The functions Fx can be wildly nonlinear functions of x Linear refers only to the model s dependence on its parameters ak Once again we assume that the measurment errors oj of the ith data point are known By defining the matrix A and the vectors b and a as fe oP pee a 20 Oi Oi it is possible to describe the minimization equations in matrix form A7 A a A b 21 The es ee of the parameters can be found as the square root of the diagonal elements of the inverse matrix To solve equation 21 we use the method of Singular Value Decomposition SVD It is a very robust algorithm for overdetermined as well as for underdetermined systems although it is a little slower and needs more memory resources than solving the normal equations For further details see the literature listed below Goodness of fit It is very important to know the quality of a fit otherwise the minimizing parameters found are in general not meaningful The goodness of fit which is the probability Q that a value of chi square X should occur by chance is calculated by the incomplete Gamma function N M 7 9 2
340. that the files proFit_interface h and proFit_paramBlk h reside in the same folder as your project Many mathematical functions such as sin log are not part of the standard C function set In order to use them add the files math c and errno c that came with Think C C to your project and include the file lt math h gt in your source file xxx c Set the project type to Code Resource to create a code resource of type NLft with an ID 128 Set the file type to ftCD the creator to NLft Think Pascal for 68k If you are using Think Pascal 4 0 create a project with the files DRVRRuntime lib Glue for many Macintosh system routines Interface lib Glue for many Macintosh system routines proFit_interface p Glue for interfacing with pro Fit XxXxX p your code 10 4 Working with external modules DRVRRuntime lib and Interface lib came with your copy of Think Pascal proFit_interface p can be found in your distribution package xxx p is your source code created from ProgramTemplate p or FunctionTemplate p In addition you may want to add the SANE numerical environment because it defines many mathematical functions not available in standard Pascal To do so add the following files to your project SANELib881 1lib or with FPU SANELib 1lib without FPU SANE p Interface for the SANE routines All these files come with your compiler Set the project type t
341. the preview window viewport to graphically change the value of the function parameters and to set coordinate markers Selecting data points with the arrow tool Use the arrow tool to select data points Simply click a data point to select it Click and drag to select a range of points with a selection rectangle Hold down the shift key to add points to the current selection or to remove points from the current selection If you hold down the shift key while dragging a selection rectangle the selection state of the data points contained in the rectangle toggles between selected and not selected Hold down both shift and option keys to always add the points inside the selection rectangle to the current selection You can set the color of the data points and the color used to mark selected data points using the Preferences command in the File menu If you have a monochrome monitor pro Fit will use a dithered pattern to mark the selected points Whenever you select a data point in the preview window the corresponding row is selected in the data window If you then choose Data Transform from the Calc menu you can perform calculations on the data in the selected rows only Selecting a data point in the preview window always selects the whole corresponding row in the data window If you select a range of data points in the preview and then delete them you will delete all data in the selected rows and not only in the current x and y colu
342. the columns to be plotted and more In this introductory session we can use the settings as they are 2 Click OK A drawing window appears showing a graph of the data Untitled Drawing 2 population data example Ej 7 gt E population Miq SO pa nm a HE E pm i 7 E 2 Fe T 5 oo a oe z000 1940 1960 1980 year Hi Ole lis L x 6 068 omy 7 473 om a a You can edit a drawing easily For example you can change most parts of the graph just by double clicking 3 Double click the vertical axis to change its range Double click the vertical axis itself not the numbers to the left of it A dialog box called Graph Settings appears presenting the settings of the left y axis 3 6 Getting started Graph Settings Gi General Labels Prefix Lines First 2000 Last 550 iin 4 Ticks _ custom ae Ist major 2000 minor minor i 3 0 You can change a variety of parameters here Often you will use the edit fields First and Last to set the range of the axis Another important field is the Distance field that defines the distance between major tick marks 4 Enter 0 for First and 6000 for Last then click OK The vertical axis of the graph now starts at 0 and ends at 6000 Double click other parts of the graph or its legend to change other attributes Try double clicking the horizontal axis th
343. the new value set fit range of parameter sets the fitting range of a parameter for Monte Carlo fits set fit range of parameter integer the parameter number minimum real lower range limit maximum real upper range limit percent boolean true if the range is defined as percentage deviation from the parameters value set legend properties sets the visibility position and size of the legend of the current graph set legend properties visible boolean show or hide the legend offsetx real offset between left of legend and right of graph offsety real offset between top of legend and top of graph width real width of legend item left part height real height of a legend item sort Sort the numbers in a data window sort reference the data window to be sorted using column integer the data is sorted with respect to this column order sortAscending sortDescending the sorting order ascending descending selection only boolean true if only the current selection must be sorted Apple Script 11 13 undo Undoes the last action undo tabulate tabulate a functon tabulate reference the function to tabulate parameter integer the parameter to be varied 0 for x from real the starting x value to real the maximum x value step value real the step between successive calculations step numeric auto points stepping option auto points x value real the x value used when tabula
344. the text from the info field optimize Boolean Remove leading spaces and trailing zeros in all numbers delimiter String Column delimiter at least 1 character Typical values are t which defines a tabulator decimal 8 which is a simple space which is a simple comma Any combination of characters and t Usually n line feed or r carriage return should not be used terminator String Line terminator appended after each row at least 1 character Typical values are r which defines a carriage return decimal 13 n which defines a line feed decimal 10 Any combination of characters and r n Note that the line terminator must not be equal to the column delimiter firstLine String A string to be added to the first line of the file To export data into a text file fist call DataExportOptions for setting the desired file format Then call SaveWinow and pass textFileType for the parameter See also DatalmportOptions DataImportOptions function DataImportOptions optional parameter list Sets the options for importing text files Parameters mode Integer Specifies the basic format Pass asFunction for loading text files into a text window withTitles for loading text files as data in standard format with column titles withoutTitles for loading text files as data in standard format without column titles or customFormat for loading text files as data in a customized format a
345. ther through globalData or by accessing values in a data window There are other ways of interaction between scripts and pro Fit They are explained in the last section of this chapter which lists all Apple Script commands and objects supported by pro Fit When to program when to script As you may have realized there are various things you can do through Apple Scripts as well as from a program defined within pro Fit For example you could define the following program for writing the sum of the two first cells of a data window into the results window 11 4 Apple Script program Sum begin Writeln data 1 1 data 1 2 end Alternatively you could do the same from an Apple Script tell application pro Fit set sum to value of cell 1 of column 1 value of cell 1 of column 2 write line sum end tell Even though the above examples do the same you will prefer the program because defining programs is usually more convenient and faster In practice you probably use programs more often than Apple Scripts Programs can be defined within pro Fit they are much faster and they are better suited for numerical applications However there are some things that you simply cannot do from a program such as exchanging data with other applications communicating with the Finder batch processing a large number of files etc For these tasks you can use Apple Scripts You can combine the advantages of Apple Scripts and programs To call a
346. tical expression like exp 1 or 6 sin pi 4 pro Fit reads the mathematical expression you typed or pasted and calculates the numerical result General features 14 1 Text windows such as the result window can be used as a calculator by typing an expression on a new line positioning the insertion point on that line and hitting the Enter key The result is displayed on the next line Results Lfsqrte2 gt O 7O7 1 100 70 7107 You can also use mathematical expressions in all pro Fit dialog boxes As an example if you want to tabulate a function between 0 and two times pi at intervals of pi 5 type command T and enter the following Table of Polynom x Tabulate by varying x jj Klin klax 2 pi Step 1 5 0 5 auto points Use fitted parameters When typing a mathematical expression you use the same syntax elements that are available when writing a function definition In on line mathematical expressions x is equal to the last result that was evaluated and a i is equal to the parameter values shown in the current parameters window You can use all the predefined functions available when writing the definition of a function As an example after a successful fit you can type ChiSquared in a data window cell This tells pro Fit to set the value of that cell to the mean deviation obtained in the last fit see Chapters 9 and 10 together with Appendix A for more information on predefined f
347. tics and GetResult instead Returns some results of the last call to calcStat CalcStat must have been called with the withMedian parameter set to true before this function can be used GetModuleFile function GetModuleFile FSSpecPtr External modules only Returns a pointer to the FSSpec record of the file where the currently running external module was found Returns ni1 if no such file exists GetNextGraph function GetNextGraph graphID longint longint Returns the graph following the one with the given ID returns the first graph if graph1D 0 Returns 0 if graphID points to the last graph Returns 0 if no graph exists with the given ID Called repeatedly GetNextGraph cycles through all graphs and returns their ID Start with GetNextGraph 0 to make sure that all graphs are scanned GetNumFunctionParams function GetNumFunctionParams name Str255 integer Returns the number of parameters used by a function name is the name of the function This parameter is case sensitive Use an empty string to specify the function currently selected in the Func menu GetResult function GetResult selector indexl index2 This function returns the results of various commands The desired result is selected by the resultSelector If the result is an array or matrix you have to add one or two indices index index2 If the result is a simple number omit the indices These are the commands that GetResult retu
348. ties for changing and editing a graph are one of General pro Fit s key features A whole set of specialized options lets you create the W axes graph you need These options are accessed either by double clicking the Y lt axes graph or its legend or by using the Graph submenu in the Draw menu This submenu is only available if a single graph is selected or if a drawing window contains only one graph Curves Frame Grid Styles When you double click a graph or choose General from the Graph submenu the following dialog box appears Graph Settings Draw 4 Legend Lf Current graph O Frame Grid Drawing sequence Grid Axes Frame Curves Graph height 6456cm a c lt i ui Eo 7 22 Drawing and Plotting The icons in the list to the left of this dialog box correspond to the items in the Graph submenu Click the icons to access and edit the various parts of a graph Click the Apply button to see the effects of your changes Check Current graph to make this graph the currently active graph This is the graph where plotting takes place per default The three Draw check boxes indicate if legend frame and grid should be drawn or not If you uncheck the box named legend the legend is deleted If you check it again the legend reappears to the right of the graph The Drawing Sequence popup menu defines the order in which the various parts of a graph curves axes grid are dra
349. tines you must fill in your code The following section Writing external modules tells you how to do this 3 Build your code Note that in addition to the code defined in your file you must also compile the file proFit_interface c or proFit_interface p respectively which contains glue code for calling pro Fit s routines If you are using C please note that proFit_interface c as well as your own source file xxx c include the files proFit_interface h and proFit_paramBlk h Therefore these files must be in the search path of your compiler they could e g reside in the same folder as the c files If you are using Pascal note that your own source file uses the unit proFit_interface defined in proFit_interface p 3 Build the module The module should be created in a file having the type ftCD and the creator NLft If you are building a module for a Power Macintosh Set your compiler linker to build a shared library or import library The entry point of your module is the function main which must be exported from your library Consult your compiler s manual on how to export symbols from a library The example source files contain compiler options for exporting main in one of Metrowerks compilers Note that these compiler options may not work correctly with other compilers If you are building a module for a 68k Macintosh i e an old non P
350. ting by changing a parameter fittedParams boolean true to use fitted parameters instead of the current function parameters tabulate roots of tabulates the roots of a given functon tabulate roots of reference the function to tabulate parameter integer the parameter to be varied 2 for xMin 1 for xMax from real the starting parameter value to real the maximum parameter value step value real the step between successive calculations xMin real lower bound of the interval where roots must be found xMax real upper bound of the interval where roots must be found subintervals integer number of subdivisions where to look for a result value real the function value yVal in the equation f x yVal default is zero tabulate extrema of tabulates the extrema of a given function tabulate extrema of reference the function to tabulate parameter integer the parameter to be varied 2 for xMin 1 for xMax from real the starting parameter value to real the maximum parameter value step value real the step between successive calculations xMin real lower bound of the interval where extrema must be found xMax real upper bound of the interval where extrema must be found subintervals integer number of subdivisions where to look for a result tabulate integral of tabulates the integral of a given function tabulate integral of reference the function to tabulate parameter integer the parameter
351. tion Data gt population data example x column year Ax value 0 0 4x distr Gaussian WY column population Mio g value not speci fied ay distr Gaussian terat ions Chi squared 1 6958644 Farame ters Standard deviations A 2113 2935 AA 30 2618 xO 1940 0000 tO 54 8120 4to 1 0812 const o 0000 The fit yields 54 8 years for t and 2113 millions for A The Preview window automatically shows the function with the new fitted parameters x Floating 5500 0 x Show data x Show function x Auto E Fitted params L Leg a era Auto Log 1990 0 The function now approximates the data points quite well We can plot function 3 2 using the fitted parameters 3 Choose Plot Function from the Draw menu A dialog box appears displaying options for plotting the function Getting started 3 11 SS Plot Function Exp Plot into current graph O Open new window Y axis from o to soo0 M OFrom 1930 __ to 1999 We don t need to change any of these options 4 Click OK to draw the curve The curve is drawn in the graph You can now rearrange the items in the drawing window to obtain a representation of data and theory like this one The world s population since 1940 6000 oO 4000 2 w 3 2000 population Mio 9 theory 0 1940 1960 1980 2000 year Defining your own functions In the previous session you have fitted the built in exponential funct
352. tion is the position in the coordinates of the main axis perpendicular to the specified axis If position is outside the range of this main axis it is set to its minimum maximum SetBGDataPointStyle procedure SetBGDataPointStyle style integer size extended Sets the default background style of data points Appendix A Predefined functions procedures and arrays A 55 style size have the same meaning as for the routine SetDataPointStyle If style designates a composite point only the background of this composite point is used Always call SetDataPointStyle before calling SetBGDataPointStyle For more information see SetDataPointStyle SetBoxTitle procedure SetBoxTitle title Str255 Sets the title of the dialog box invoked with the next call to the predefined function Input or Input Box for external modules SetCell procedure SetCell row column longint s Str255 Sets the string in the given cell of the current data window to s If the given cell is in a numeric column SetCe11 attempts to convert s into a number If this conversion fails the given cell is cleared SetColHandle procedure SetColHandle col longint colH Handle External modules only For advanced programming Sets a given column to the data in colH The organization of the data in colH depends on the data type of the column See also the entry for GetColHandle If the column is of type floatColumn colH is a handle of
353. tion key For example if a function window looks as follows Correlation SIF ie Tete C debug Help S Const Gj 2 datali col 1 meant 2 datali col2 meanz s11 511 sqrctis zsi slz2 ti t S22 s22 sgretza end e i g sgqrtis11ts221 SelecthHindowt Results 39 Hritelna Heitelne set 1 column colds Hr itelnt set 2 column col23 Hritelac number of data points counti Browse au i e and you want to know how SelectWindow is defined double clicking it while holding down the option key brings up its definition in an Apple Guide panel Defining functions and programs 9 9 SelectWindow procedure SelectWindowlwind String or Longint ioves the specified window in front of all other windows wind is the windowID or the name of the window See also Frontwindow Frontmostwirndow Huh Automatic Macro Recording pro Fit 5 1 can record most operations that you perform and generate a Pascal program or an Apple Script therefrom Open Apple s script editor to record your activity as an apple script See chapter 11 Apple Script for more information If you do not know how to program a certain action with pro Fit s definition lagnuage switch on recording perform the action you want to program and look at the recorded commands Each text window has record play and stop buttons SSS Untitled Function 1 gt Ej H The record button
354. to find your way through pro Fit pro Fit was designed to be used without a manual and most of its features are self explanatory Extensive on line help is provided However you will need to read the manual to efficiently work with some of pro Fit s most advanced features Those of you who are already familiar with pro Fit 5 0 are referred to the last section of this chapter Changes between versions 5 0 and 5 1 Then you may go directly to the chapters giving in depth information on the new features Those who prefer a beginner s introduction should continue with Getting started which gives an overview on the most common features of pro Fit A description of the basic concepts of pro Fit is given in the next section 1 2 Introduction Basic concepts pro Fit works with data drawings functions and programs or through Apple Events with other applications or AppleScripts Functions Programs ae bs y a 1 sin x NewWindow for i 1 to 10 data i 1 i AppleScripts Data A o Tas X y tell applicatio 1 00 0 23 open file da 1 10 0 38 run program 1 20 0 13 close windo Drawings You can enter data into spreadsheet windows Data can be transformed by built in transformation algorithms e g sort transpose filter Fourier transform or mathematical operations or by user defined ones Data can be text or numbers You can define your own data transforms by writing
355. to be fitted as well as on the selected starting parameters The classical version of the Levenberg Marquardt algorithm does not allow for x errors and minimizes the mean square deviation 10 The algorithm can be described in words as follows Starting from a given set of parameters the mean square deviation 2 is calculated Then the parameters are varied slightly to observe their influence on y From this the direction in which y2 decreases most rapidly can be evaluated and a new set of parameters is chosen This procedure is reiterated with this new set of parameters When the minimum is near the algorithm goes over to a more deterministic guessing at the position of the minimum and solves some equations to find it The fitting stops when the value of 2 does not decrease anymore between successive steps 8 6 Fitting The algorithm is described in W H Press B P Flannery S A Teukolsky W T Vetterling Numerical Recipes the Art of Scientific Computing Second Edition University Press Cambridge 1992 When x errors are specified the algorithm is modified in such a way that it minimizes 8 It finds at the same time the set of x coordinates x and the function parameters that minimize the mean square deviations between the data points x y and the function values x f The extensions to the Levenberg Marquardt algorithm that allow the interpretation of x errors are described in P L Jolivette least squares fit
356. to be varied 2 for xMin 1 for xMax from real the starting parameter value to real the maximum parameter value step value real the step between successive calculations xMin real lower bound of the interval where extrema must be found xMax real upper bound of the interval where extrema must be found iterations integer number of iterations used for the numerical computation of the integral transform performs data transformations in a data window 11 14 Apple Script transform reference the window containing the data to transform operation sumOp subOp multOp divisionOp powerOp DIV Op MODOp integralOp derivativeOp formulaOp functionOp sqrOp sqrtOp invertOp absOp expOp InOp tentoOp log 100 p fill0 fill 1 fillN sinOp arcsinOp cosOp arccosOp tanOp arctanOp sinhOp arsinhOp coshOp arcoshOp tanhOp the operation used for the transformation calculations using reference the function from the Func Menu to be used xColumn integer the x column to be used in column transformations yColumn integer the y column to be used in column transformations argumentColumn integer the argument column to be used with transformation functions that need another argument besides x Set this parameter to zero to use a constant numeric value argumentValue real the argument value to be used with transformation functions that need another argument besides x Used when the argument column is set to ze
357. to insert a new polygon point option click a point to delete it hold down the command key while dragging a single point to let the selected point coincide with the nearest neighboring point 14 6 General features Using the line style pop up menu in a drawing window to change the line styles in a legend Using the point style pop up menu in a drawing window to change the point styles in a legend Clicking a cell in a data window Clicking the column number cell in a data window Clicking on the larger font size controls in the text edit dialog box Clicking on the subscript superscript position controls in the text edit dialog box Choosing New Function from the file menu Importing text files Saving a drawing as an EPS file Using lists in dialog boxes e g the y column list in the plot data dialog box Clicking with the lens tool in the Preview Window shift to change the line styles of all the lines in the legend option to change the line style and set the attribute points connected for the data plot in the first row of the legend shift amp option to change the line styles of all the lines in the legend and set points connected for all data plots shift to change the point style of all the data plots in the legend option to select the whole column above the clicked cell shift to enlarge a selection command to set the default columns x y Ax A
358. to load the parameter set make Make a new window make new type class the class of the new element table drawingWindow textWindow with properties record the initial values for the properties of the element Result reference to the new object s The keyword new is optional in Apple Script what specifies the type of window to be opened Specify table for a data window drawingWindow for a drawing window textWindow for a function window The with properties parameter specifies the properties of the window in an Apple Script record All types of pro Fit windows have the property name holding the name of the window as a string In addition to this data windows have the properties nrRows and nrCols with the numbers of rows and columns Examples make table with properties name myTable creates a new data window having the name myTable make drawingWindow with properties name lookatthis creates a new drawing window having the name lookatthis make textWindow_ creates a new function window make table with properties name small nrCols 10 nrRows 20 creates a data window with name small 10 columns and 20 rows the following creates a new data window and then closes it using a temporary reference to the window set myRef to make new table close myRef 11 10 Apple Script page setup Brings up the page setup dialog box page setup reference window optimize Find t
359. to log file will be captured capture done close the capture file end tell clear Clears the current selection clear close Close a window close reference the window to close saving yes no ask Specifies whether or not changes should be saved Windows can be specified by name or index 1 is the frontmost window 2 is the window behind the frontmost window 11 6 Apple Script If you append the specification saving yes then all changes are saved if the window has not yet been saved to a file you are asked to specify where you want to save the changes If you append saving no changes are not saved If you append saving ask or if you do not append a saving specification and the window contains unsaved changes pro Fit will ask if you want to save the changes Examples close front window prompts for saving unsaved changes close window Table1 saving no closes the window without saving compile Compile a function or program written in pro Fit s definition language compile reference text or file to compile Examples compile file HD myProg compiles the given file compile function lin begin y a 1 x end compiles a text the following is a more realistic way to define and compile a larger program from a script note that you can create the character by hitting option return this character specifies that the line is continued on the next one set myProg to program test var i
360. tral values for even N e The minimum smallest value and the maximum largest value e The sum of all valid values S ya i 1 1 N e The mean enay N Nix Li ge _ 2 e The variance Var aa x Tiiz e The standard deviation o Var 1 N e The mean absolute deviation ADev oe Keak i 1 N _z 3 e The skewness Skew L E NTL o l 1 amp fx xT e The kurtosis Kurt 5 l 3 NTL o The Skewness characterizes the degree of asymmetry of a distribution around its mean The kurtosis measures the relative peakyness or flatness of a distribution Fourier transforms pro Fit can calculate Fourier transforms of numerical data A Fourier transform is a transformation of numerical data from the time domain into the frequency domain or vice versa If you have a one dimensional set of real valued data points hg k 0 N 1 the discrete Fourier transform Hy of these points is given by N I H 2a Y hye N l 1 k 0 where n goes from N 2 to N 2 N is assumed to be even The inverse Fourier transform is the inverse operation It allows the calculation of data hx in the time domain from data Hx in the frequency domain by N 1 k N n n 0 4 8 Working with data Note that hx as well as Hk can be complex values A classical interpretation of the Fourier transformation is the following A signal h t is sampled at a regular time interval Ar resulting in a set of data points hk h At k The
361. turns the square root of x Causes a run time error for a negative argument Statistics Statistics optional parameter list Performs statistical analysis on a data window Parameters window String or Longint The window s name or window ID of your data Omit for using the frontmost datawindow column Longint The column to work on or O for all columns Omit if selectionOnly is true selRowsOnly Boolean True if only the currently selected rows are to be analyzed Only used when parameter selectionOnly is false selectionOnly Boolean True if the currently selected cells are to be analyzed False if the columns specified in parameter column are to be analyzed withBasic Boolean False for suppressing calculation of the sum mean variance standard deviation and absolute deviation Default true withSkew Boolean False for suppressing calculation of skewness and kurtosis Default true withMedian Boolean False for suppressing calculation of mean median maximum and minimum Default true printResults Boolean True for printing the results to the Results window Omit printResults or set it to false for suppressing this To retrieve the results of this command call GetResult with one of the following selectors statCount number of evaluated values statSum sum statMean mean statMedian median statStdDeviation standard deviation statMeanAbsDeviation mean absolute deviation statMinumum minimum
362. u can use the symbols i or n for the row number and if you have chosen Selection only j or m for the column number Examples x sqrt x an expression tan c10 tangent of values in column 10 CovarMatrix i j the covariance matrix of the last fit The size of such a transformation statement is limited to 255 characters If the result of a calculation is not defined either because a data field used for the calculation is empty or because there was an numerical error the resulting data field is cleared Working with data 4 5 User programs pro Fit lets you define your own data transform programs or macros These programs can perform data transformations in the data window create a graph in the drawing window etc They are found at the end of the Misc menu Chapter 9 Defining functions and programs explains how to define such programs Data reduction The command Data Reduction in the Calc menu offers several possibilities for data reduction e g by averaging over several data points or by skipping part of the points Data Reduction Keep every d Remove every E 2 data Average over E Smooth over O Selection only Keep selected rows d Remove selected rows e To keep every nth row and to remove all other rows select Keep every e To remove every nth row and to keep all other rows select Forget every e To replace groups of n consecutive cells in a column by their average select Ave
363. ubmenu in the Misc menu You also can change the line styles and color of curves and lines in a legend by choosing the appropriate setting from the Pen and Dash pop up menus in the drawing tools palette e To change the line style of the first item in a legend that is drawn using a line either connected data points or a function curve select the legend and choose the line style in the Pen and or Dash pop up menus e To change the line style of all items in a legend select the legend and choose the line style in the Pen and or Dash pop up menus while holding down the shift key Drawing and Plotting 7 21 e To add a connecting line to the first data point in a legend select the legend and choose a line style from the Pen or Dash menu while holding down the option key e To add a connecting line to all data points in a legend select the legend and choose a line style the Pen or Dash menu while holding down the shift key By default a legend lists every plot of the related graph You can however hide one or more plots from a legend by unchecking Appears in legend in the dialog box for editing curve styles This is explained later in this chapter A legend can be ungrouped by selecting the legend and choosing Ungroup from the Draw menu When an legend is ungrouped it is transformed into a set of lines data points and texts Editing graphs The nearly unlimited possibili
364. ues You may sometimes want to fit simultaneously several functions fj fg with one or more common parameters Or you may want to fit a function that does not depend on a single x value but on a set x1 X9 Xp of x values Or you might even encounter a combination of these two cases In the most general case you have q functions each of them depending on one or more x variables Each function has some parameters some functions can share one or more parameters Y1 f1 1 x2 Xpq y2 f2 X1 X2 Xp2 Yq fq 1 x2 Xpq For each function you have a set of data points that should be described by it Now you want to fit all these functions simultaneously There are several methods of tackling this kind of problem with pro Fit Some of them are described in the following section Functions with multiple x values Let us first consider the special case of a single function that depends on more than one x value y fy 1 9 Xp Example The photoconductivity o of some light detectors as a function of the incident light intensity 7 and the operating temperature T obeys a relation of the form o s I eTo where is the intensity of the incident light and T is the absolute temperature in Kelvin s and T are parameters In our example we have a number of measurements of the conductivity o at different temperatures T and different intensities Z The values are given in the table below Fitting 8 19 Temp Intensity c
365. uickDraw GX option described below The options Normal PICT Embedded PostScript Enlarged PICT and Bitmap all generate a classic QuickDraw picture It can be pasted into nearly all applications that support graphics The option QuickDraw GX shape generates a QuickDraw GX shape which can only be pasted into applications that support this data type You also can combine a classic QuickDraw picture and a QuickDraw GX shape to get the best of both worlds If you select one of the types Normal PICT Embedded PostScript Enlarged PICT or Bitmap and if you have QuickDraw GX and QuickTime installed there appears a checkbox and a pop up menu titled Add QuickDraw Gx CJ Add Quickdraw GH BD a for screen amp printer Check this option if you want to add a QuickDraw GX shape to your classic QuickDraw picture When you print such a picture the QuickDraw GX shape is used when printing through a QuickDraw GX printer driver while the classic QuickDraw picture is used otherwise If you choose for printer only from the pop up menu the QuickDraw GX shape is ignored when the picture is drawn on screen If you choose for screen amp printer the QuickDraw GX shape is also used for on screen display when QuickDraw GX is installed At the bottom of the Printing panel in the Preferences dialog box there is a button called Standards Standards Clicking this button brings
366. uilt in functions that you can use as is and gives you the possibility of defining your own functions To do this you can use the built in programming language see Chapter 9 Defining functions and programs or you can write your functions in your own compiler and import them as modules see Chapter 10 Working with external modules A list of the currently available functions can be found in the Func menu Introduction A function in pro Fit has the form y fx a1 a2 an 1 where x is its argument and y its value a1 a2 an are the parameters of the function An example is the polynomial function one of pro Fit s built in functions y aQtajxtazx2 You can select the function you want to work with from the list in the Func menu When you do this a short description of the function and its parameters appears in the Parameters Window As an example the polynomial function has the following parameters window SS EO m parameters deg 3 0000000 const 0 0000000 al 0 0000000 a 1 0000000 a 0 0000000 selected parameter al lower limit none E Use for fitting fix const al x abxc3 deg degree of the polynomial Parameters In the Parameters window you can view and set the parameters of the function The upper part of the window lists all the parameters of the function It also contains a popup menu where you can save parameter sets for later use see below The
367. unction 1 isProgram 2 type 10 10 Working with external modules inputRec packed array 1l maxNriInputValues size 48 of record x extended offset 0 size 4 So Shr 55s offset 4 size 4 end field size 8 offset 8 fields 6 checkPAnswer update good bad size 1 update 0 ok 1 bad 2 ModeType active inactive constant size 1 active 0 inactive 1 constant 2 ParamName string maxParamNameLength size 32 ParamArray array 1l maxNrParams of extended size 640 N 768 F 512 P field size 10 N 12 F 8 P offset 10 N 12 F 8 P fields 64 ParamNameArray array l maxNrParams of ParamName size 2048 field size 32 offset 32 fields 64 ParamModeArray array l maxNrParams of ModeType size 64 field size 1 offset 1 fields 64 DefaultParamInfo record size 58 value ParamArray offset 0 size 4 lowest ParamArray offset 4 size 4 highest ParamArray offset 8 size 4 mode ParamModeArray offset 12 size 4 name ParamNameArray offset 16 size 4 end DefaultParamInfoPtr DefaultParamInfo size 4 type parameters for all functions calling pro Fit ExtModulesParamBlock record size 4 RunTimeProcPtr Ptr offset 0 size 4 globals Ptr offset 4 size 4 versionNumber integer offset 8 size 2 moduleKind integer offset 10 size 2 codeType integer offset 12 size 2 name Str2
368. unction s parameters a is a predefined array that represent the function parameters The parameters can be accessed by their index i e a 1 a 2 etc Instead of using a i for the parameters you can also use parameter names of your own by declaring them as in standard Pascal in the header of the function See the section Alternative function syntax later in this chapter Our sample function is not defined for x lt 0 If you use it in calculations with negative x values a run time error is generated However the function converges to y a 2 for x 0 You may want to expand its definition range by defining y x a 2 for all x lt 0 This can be done easily in a new version of our function Defining functions and programs 9 3 function LogSine begin if x lt 0 then y a 2 else y a 1 sin x In x a 2 end Note that you can insert additional spaces or lines anywhere between keywords The new version of the function which now has the name LogSine shows how you can use the if statement for conditional execution It takes the general form if condition then do this else do that do this is executed if the condition is met do that if it is not met If you work with your function more often you might want to make sure that the Parameter window shows reasonable default values for the parameters and a short description of what the function does Here is a final and more complex definition i
369. unction is not defined for x lt 0 If you were to calculate it for a negative x value an error would occur How ever the function converges to y a 2 for x 0 You may want to expand the definition range of the function by defining y x a 2 for all x lt 0 This can be done easily with the following modification function logSine begin if x lt 0 then y a 2 else y a l1 sin x 1n x a 2 end After having modified a definition in the function window click the To Menu button or choose Compile amp Add to Menu from the Customize menu to add it to pro Fit in its new form Your function could even become much more complicated than this You can define functions that contain more than one statement as well as variables and procedures You can use most elements of the PASCAL programming language for defining functions As we already noted above it is also possible to implement the same function in such a way that it uses arbitrary names for the parameters instead of the predefined array element a 1 a 2 function logSine amplitude offset real begin if x lt 0 then y offset else y amplitude sin x ln x offset end The pro Fit package comes with more examples of function definitions Look them up 3 14 Getting started Writing programs Besides defining functions for fitting and plotting you can also define any data generation and transformation algorithms using the same synt
370. unctions Let s look at a simple example that illustrates how you can use pro Fit s understanding of mathematical expressions when you are pasting into a data window Write the following text and copy it to the clipboard a 2 fittedParams 2 a 2 fittedParams 2 paramSD 2 a 3 fittedParams 3 a 3 fittedParams 3 paramSD 3 a 4 fittedParams 4 a 4 fittedParams 4 gt paramSD 4 14 2 General features Where the stands for a tabulator character and each line is terminated with a carriage return If you paste the above text into a data window after a successful fit you automatically obtain a table containing the parameter values before the fit the values after the fit their difference and the resulting standard deviations File info pro Fit lets you save a comment with every one of its files You can edit this comment with the Get Info command from the File menu Choosing Get Info presents a dialog box with a large field for editing text Infos about Data 122 These points were recorded using Finac s correction Columns 3 and 4 give the temperatures at the end points 2 5 96 KS You can add an info comment to data windows drawing windows and functions or programs The data windows let you view and edit this information directly without using the Get Info command For this you drag down the info hook a black area on top of the right scroll bar of a
371. unctions or for writing intermediate results or status information at regular time intervals to the Results window TimeString function TimeString secs Boolean String Returns a string with the current time Set secs to true for appending seconds See also DateString Transpose procedure Transpose optional parameter list Transposes a data window i e exchanges its rows and columns Parameters window String or Longint The window s name or window ID Omit for transposing the front window true const true 1 This constant stands for the logical value of true Appendix A Predefined functions procedures and arrays A 69 Undo procedure Undo Equivalent to selecting Undo from the Edit menu UpperString procedure UpperString var s String Converts all characters of s to upper case See also LowerSt ring UseParameterSet procedure UseParameterSet optional parameter list Moves a parameter set appearing in the parameter set menu to the parameter window Parameters set String The name of the set forAll Boolean True if the parameter set is one available for all functions Default false ofFunction String The function the parameter set belongs to Omit for the current function See also AddParameterSet SaveParameterSet LoadParameterSet DeleteParameterSet Write procedure Write string or expressions This procedure can have any reasonable number of strings or
372. ur copy of pro Fit according to your needs See Chapter 10 Working with external modules for an explanation on how to build external modules This section explains how to use such modules LintInterpol Slow To save a function or program as a module choose Save User Function Module from the Customize menu to see a submenu with all the functions and programs that can be saved as modules Saving functions and programs test User_Program This sub menu has two sections divided by a horizontal line The first section lists the functions the second section the programs Choose the function or program you want to save as a module and pro Fit will ask you where you want to save it Note that you can only save functions and programs that you compiled in pro Fit you cannot save built in functions or external modules The resulting file is a pro Fit document You can load it by using the Load Module command or by double clicking it from the Finder Loading functions and programs Choose Load Module from the Customize menu to load a module You are asked to locate the module Defining functions and programs 9 31 The command Load Module can also be used to load compiled Apple Scripts See Chapter 11 Apple Script for details Removing functions and programs from the menus To remove a function or a program or an Apple Script from pro Fit s menus choose Remove from Menu
373. urns the type dataType for data windows text Type for function windows drawingType for drawing windows of the given window Returns 0 if the given window is of any other type windowID is the window ID of the window such as it is returned by Get WindowID or FrontWindow globalData globalData array 0 100 of extended Obsolete Not supported in version 5 1 or later Use GetGlobalData and SetGlobalData instead GrLine procedure GrLine x y extended External modules name See Line GrLineTo procedure GrbLineTo x y extended External modules name See LineTo GrMove procedure GrMove x y extended External modules name See Move GrMoveTo procedure GrMoveTo x y extended External modules name See MoveTo GroupBegin procedure GroupBegin Starts the definition of a group All drawing taking place after this call will be part of a group Call GroupEnd when you have finished drawing the parts of the group GroupEnd procedure GroupEnd Ends the definition of a group See GroupBegin Halt procedure Halt Exits the running a program or function See also Exit A 34 Appendix A Predefined functions procedures and arrays HandleEvent procedure HandleEvent var theEvent EventRecord External Modules only For advanced programming Passes theEvent to pro Fit for handling it Use this call to handle update events when creating your own window theEvent is a pointer to the Mac OS e
374. used to draw the plot In this way you can retrieve data points from a drawing when you have lost the original data set or you can obtain a list of the data points that pro Fit calculated to draw a particular function Click Delete to delete the curve or data points from the graph You can use the delete backspace key as a keyboard equivalent for this button Click the Error Bars button to define error bars for the selected data set this button is dimmed for a function 7 30 Drawing and Plotting Error Bars Bar thickness C Error bars as box Cap thickness CE Cap length Ly Read errors from O Selected rows only Window population data M4 Skip empty data fields Yertical O Use asymmetric errors Type Individual Column year Horizontal J Use asymmetric errors Here you can specify if you want to use error bars for your data points and if you do what they should be You can use symmetric or asymmetric errors To use asymmetric errors check Use asymmetric errors for horizontal and or vertical direction otherwise leave this option unchecked If you check the option you can select the errors on the top bottom or left right of the data points individually Using the menus titled Type or Top Bottom Right Left you can select the type of errors to add e Choose Individual if each point should have its own unique non percent error In this case you must have stored the error values in a data wi
375. vadeeneeution 8 The help af ale koeeemeareester meena trate Memrrenrmre ene Mane oe yer fi Person eee Pee ere RCo aaia 8 Browsing functions and PFOGFAMS ccecceceeeececeeeeeeeeeeeceeeaeeeceeeaeeeseeeaeeesseeaeseseetsesaeeates 8 Finding the definition of AS yVIMDOl cticsszeccea tates seeks cal eta tee ee one 9 Automatic Macro Recording eccscecceccsceseeseeceseeeeeeseeeceaeseeecansesaceaneeeaeeaeeeteatseeaseataeeas 10 Syntax of function and program efiNitiOnS cceeeceeeeceeeceeeeceeeeeeeeeeaeeeeeeeeaeseeeeeeeeees 11 Programidetinition Syntax ssi esnidnn ae eae Recah elena elt eet ciel Neat 11 EATS eats foes kl hea aa Fa ote A che ela N 14 DSO Steet ee wt ae ta Re Atte a et hearts gal 16 The while l00p yee renee me ere rane ae ever mn cr ean ee een eee over me 16 SIS TO PIO GD eA E ach cette Sa agiete tates cad teria dice ata Nariel Gough DA ad tec eae 16 Thetepedatloop Reaper rary cree a ar ame eer ares Nn erry a a ae meee rare 16 Loop control statements Cycle ANd lCAVE cecceeeeeeeeeeeeeeeeeeeeeeeeeeteaeeeeeeeeeeeeaes 16 Optiorial parameter lists xcescisacctemaenei need aa a aa 17 Aborting procedures functions and PrOGrAMS cececceceeeeeeeceeeeeeeeeeeeeeeeeeeeeeeeeeees 18 Predefined constants functions procedures and operatOrs ceecceceeeeee 19 FUNCTION definition SYMtAX eececcececeeesceeeeeeeeeeeaeeeaeeseeseeeseeeeeeseeeaesaeeaeeeaseaeeneeeeeeeees 20 Alternative function
376. value A 66 Appendix A Predefined functions procedures and arrays statMaxumum maximum value statVariance variance statKurtosis k urtosis StopExecution procedure StopExecution External modules only Tells pro Fit to interrupt execution of the current module as soon as possible Str255ToNumber function Str255ToNumber s Str255 var x extended integer External modules only Converts the string s to a number x s can be a numeric string or an expression Return values are 0 conversion successful 1 x is infinite 2 s is empty 3 x is an NAN invalid number 4 user aborted or 5 run time error String ToNumber function StringToNumber s String var x real integer Converts the string s to a number x and returns a result code as follows 0 conversion successful 1 x is infinite 2 s is empty 3 x is an NAN not a number 4 user aborted calculation 5 run time error Tabulate procedure Tabulate optional parameter list Tabulates a function to a data window Parameters function String The function to be tabulated omit for current function from to Real The first and lastvalue to be tabulated stepValue Real The step between tabulated points Omit if you pass autoStep or pointsStep for parameter step step Integer numericStep tabulate for equally spaced points as defined in stepValue autoStep choose step width automatically use a larger number of points where the function varie
377. value extended Obsolete Use SetParameterProperties instead Sets the default value of a parameter of the currently running function The default value is the value that appears in the parameters window i is the parameter index value the new value This function is generally used within the predefined function Initialize SetParameterProperties procedure SetParameterProperties optional parameter list Sets some properties of a parameter of the current function Parameters param Integer The index 1 based of the parameter to be changed name String The name of the parameter as it appears in the Parameter window Omit for leaving it unchanged value Real The value of the parameter as it appears in the Parameter window Pass equalx for setting it x Omit for leaving it unchanged min max Real The lower and upper limits of the parameter Omit for leaving the corresponding limit unchanged mode Integer The mode of the parameter Use paramInactive paramActive paramConstant for making the parameter inactive active or constant Omit for leaving the mode unchanged SetParamLimits procedure SetParamLimits i integer min max extended Obsolete Use SetParameterProperties instead Sets the limits of a parameter of the currently running function Parameter limits define the range of values that are admissible for a given parameter for example during a fit i is the parameter index and min
378. ve name Str255 x scale extended extended Returns the derivative of a function name is the name of the function as it appears in the Func menu This parameter is case sensitive Use an empty string for the function that is currently selected in the Func menu x is the x coordinate where the derivative must be calculated scale is the length of a typical interval of x values over which the function s value changes For the parameter scale a rough estimation is good enough scale is typically something like the length of the x axis when you plot your function It must not be too small As an example if your function describes a 20 ns laser pulse and uses time in seconds as its input set scale e g to 10 10 ns Causes a run time error if the function does not exist DisableDrawingUpdates procedure DisableDrawingUpdates By default pro Fit draws a shape immediately after a program created it If you don t want shapes to be drawn immediately call this routine before you start drawing This can accelerate the execution of your program There isn t any EnableDrawingUpdates routine DisableDrawingUpdates inhibits drawing until your program has finished DoCloseWindow procedure DoCloseWindow windowID longint savelIt Boolean External module name see CloseWindow DoMenu procedure DoMenu theMenuItem Str255 Executes a command appearing in pro Fit s menus theMenuItem
379. vent record ii const ii compl 0 1 The imaginary unit Im function Im z complex extended Returns the imaginary part of the complex number z To get the real part call function Re inf const inf 1 0 An infinitely large number Use in for an infinitely large negative number Input procedure Input sl Str255 var vl s2 Str255 var v2 Brings up a dialog box where you can enter new values for v1 v2 Input can set up to 6 variables of type Real or String Each variable can be preceded by a string defining a title to be shown for the variable If you omit this string the variable s name is used The title of the dialog box can be set using the SetBoxTitle Example program test var a extended i integer begin a 0 5 i 10 SetBoxTitle starting parameters Input value of a a value of i i end This program first assigns default values to the variables a and i Then it asks the user to change these variables if she wants to The program displays the following dialog box starting parameters Value ofi The title was set using the routine SetBoxTitle The user can enter new values for the variables If she clicks OK the program continues if she clicks Stop the program is interrupted immediately Appendix A Predefined functions procedures and arrays A 35 Input checks if the title for a parameter starts with s followed by one or more special char
380. w into Use a simple name or a file path Default the file currently attributed to the window type Integer The type of the file if non default type textFileType PICTType EPSFType Omit for default type To control the format for exporting data to a text file call DataExportOptions before calling SaveWindow See also GetFileDirectory SetDefaultDirectory OpenFile A 52 Appendix A Predefined functions procedures and arrays There is also an obsolete version of SaveWindow supported for compatibility with earlier versions Do not use it in new programs SaveWindowAs procedure SaveWindowAs windowID longint fileName Str255 Saves the contents of the given window into a file with the specified file name windowID is the window ID of the window such as it is e g returned by GetWindowID or FrontWindow fileName is the name of the file If fileName contains a simple file name the file is placed in pro Fit s folder If fileName contains a file path e g dD MyFolder file the file is placed in the folder defined in the file path Pass for fileName to bring up a dialog box asking the user where to save the file SelectAll procedure SelectAll Equivalent to selecting SelectAll from the Edit menu SelectBottom function SelectBottom longint Returns the row number of the bottom most selected cells of the current data window or 0 if no cells are selected Causes a run time error i
381. which you want to transfer the color 7 12 Drawing and Plotting The line color of the clicked shape takes the color you picked with the color measuring tool To picked up a fill color for the target shape instead of a line color hold down the shift key while clicking with the color measuring tool pro Fit stores the color that was measured with the color measuring tool inside the standard color popup menu This opens up an other even more flexible I white possibility to copy colors 1 Click the color you want to copy with the color measuring tool 2 Select an object and apply the measured color using the standard Fill or Line color popup menus On black and white monitors pro Fit displays a simpler version of the color menus with a more limited choice of color To see the standard color menu which is displayed on color monitors hold down the option key while clicking the popup menu symbol Exporting pictures There are five ways to export pro Fit drawings e saving the whole drawing as a PICT file e using the Copy or Cut commands in the edit menu e dragging them and dropping them to their destination e choosing Create Publisher from the Edit menu e saving the whole drawing as an EPS file In the first four cases the drawing is converted to a picture a data structure in the so called PICT format or a QuickDraw GX shape A picture can be imported into most other Macintosh applications Use the Preferences
382. window Procedure Derivatives This procedure is optional If defined it is used during fitting with the Levenberg Marquardt algorithm This algorithm uses the partial derivatives of the function with respect to its parameters If you do not define the procedure Derivatives the derivatives are calculated numerically but this slows down 9 24 Defining functions and programs the fitting process considerably If you notice that fitting is particularly slow you should define this function and at least calculate some derivatives pro Fit will still calculate numerically any derivative you don t define The procedure derivatives can use the following predefined variables x The x variable the function s x value allt ss aln The parameters of the function dyda 1 dyda n The partial derivatives Must be set to dyda i of x dal i for all parameters that are not declared as constant Derivatives can set the values dyda i for some or all of your function s parameters If you don t set a value it will be calculated numerically Whenever a function is used by pro Fit a call to the procedure Derivatives is always preceded by a call to the main part of the function Therefore you may use temporary results from the main part of the function by storing them into global variables This decreases the number of calculations your function must perform and makes fitting faster Example You want to fit the function y aj sinh
383. window This procedure cannot be called while a function is running ColEmpty function ColEmpty columnNumber longint Boolean Returns true if the given column of the current data window doesn t contain any data Compile procedure Compile windowID longint Compiles the given text window Equivalent to choosing Add to Menu from the Misc menu Generates a run time error if windowID does not belong to a function window or if a syntax error occurs windowID is a window id such as it is returned by GetWindowID or FrontWindow Compl function Compl r1 r2 extended complex Returns the complex number with rl for real part and r2 for imaginary part ConfidenceInterval procedure ConfidencelInterval i integer var min max extended Returns in min max the confidence interval for parameter i as it was calculated in the last fit Note that this routine does not return meaningful results if the confidence interval for a given value was not determined e g because the given parameter was not active during a fit or because the chosen fitting algorithm did not calculate confidence intervals See also ParamSD Conj function Conj z complex complex Returns the complex conjugate of z Copy procedure Copy Equivalent to selecting Copy from the Edit menu A 18 Appendix A Predefined functions procedures and arrays cos function cos x extended extended
384. wn This is especially important if you use color to highlight your curves or if you use very large data points A grid in front of a curve can then look quite different from a grid behind a curve The Graph width and Graph height edit fields let you enter precise dimensions for the graph You can also do this by selecting the graph in the drawing window and editing its size using the Drawing Info window The button Styles lets you save and load the current settings of a graph A more detailed description of graph styles is given at the end of this chapter In the following sections we discuss the various parts of a graph and how to edit them Axes When you want to edit an axis double click it Alternatively you can choose Axes from the Graph submenu in the Menu Draw or you can reach the axis editing panel using the list of icons in the Graph Settings dialog box The axis editing panel for x axes looks like this Drawing and Plotting 7 23 Graph Settings atve o General Labels Prefix Lines First me Last o fog J Ticks _ custom Lf ticks i ki minor ticks i gq minor a i 3 T 4 3 6 aga E Use the popup menu in the top left corner to navigate between the various axes to create a new axis or to delete the current axis The X1 and the Y1 axes are the main axes and cannot be deleted The edit field in the top right corner gives the position of the selected axes in the m
385. ws A 50 Appendix A Predefined functions procedures and arrays Root procedure Root optional parameter list Finds the root s of a function or finds the x value of a function where its y value is equal to a given value A given x interval is searched Parameters function String The function to be used Omit for current function xMin Real The start of the x interval xMax Real The end of the x interval subintervals Integer The number of sub intervals to be searched in the x interval When the function s sign changes over a sub interval the sub interval is searched for a root y Value Real The desired y value Omit or set to 0 if finding the x value where the function becomes zero roots printResults Boolean Set to true for printing the results to the Results window Omit printResults or set it to false for suppressing this To retrieve the results of a call to procedure Root call the function GetResult Use one of the following selectors rootsCount the number of roots found lt 100 rootsX Value x value of each root rootsY Value y value of each root pass an index 1 rootsCount as second parameter to GetResult The following example finds the roots of the current function between 1 and 1 then prints them program RootFinder var i nrRoots Integer begin Roots xMin 1 xMax 1 subIntervals 50 nrRoots GetResult rootsCount Writeln nrRoots for i 1 to nrRoots do Writel
386. xi j where i is the number of the function and j the index of the data point in the data set of this function This works fine as long as we have less than 1000 points in each data set Note that this scheme of coding can also be used for more than two functions A data list for this problem will be filled up like this col 1 col 2 col 3 col 4 col 5 col 6 1001 y l Ay11 ty ul V1 1002 y12 Ay12 to Un2 Vn2 1000 n Yinl Ayint thi 2001 y21 Ay 2001 n2 y2n2 Ay2n2 The function you define for fitting first converts the index which is its x value to the number of the function it has to call by testing if it is larger or smaller than 2000 then gets the appropriate t or u and v values and calls fj or fz function twoFunctions var u v ireal begin if x lt 2000 then begin x data x 1000 4 now calculate y f1 x end else begin u data x 2000 5 v data x 2000 6 now calculate y fo u Vv end end For fitting you use column 1 as the x value column 2 as the y value and column 3 as the error value Fitting 8 23 If you often have to perform this kind of fitting and for a large number of points it may be convenient to write a small program that starting from separate columns for all data sets creates a data list as shown above by merging all y values and their errors and by creating an appropriate index column General hints for fitting Starting parameters As already pointed out the success
387. y using a pop up menu option to increase the font size by 1 pt only option to change the vertical position of the selected text by 1 pt only option to open a new definition window containing a sample function definition option shift to open a new definition window containing a sample program definition option to tell pro Fit not to ask for information and to open the text files as data files using the current settings option to create a TEXT file containing the PostScript information shift click shift and drag to select more than one item shift click to de select an item command to drag a selection rectangle specifying the region to enlarge option to zoom out instead of zooming in General features 14 7 e Selecting an item from the Help option menu in a Function window to paste the template with a and a carriage return command to enable pasting templates and disable help panels shift to enable help panels and disable pasting templates e Clicking a marker in the option Preview window to transform the clicked marker into the reference marker e Moving a marker with the option arrow keys in the Preview to let the marker go outside the ranges of the preview window e Using the left and right arrow option keys in a data window to move the insertion point by one character within the active data cell e Clicking in the data window command to create a discontinuous selection e Starting pro Fit option
388. y data cells Note that it uses the predefined variables selectLeft selectRight selectTop selectBottom which return the enclosing rectangle of the currently selected data cells program CalcSum var row col integer sum real begin sum 0 for col selectLeft to selectRight do for row selectTop to selectBottom do begin if not DataOK row col then Halt sum sumtdata row col end writeln sum end The following program does basically the same as the one above but the sum is calculated in a local function which is aborted by Exit 9 18 Defining functions and programs program CalcSum function SumSelection real sums the selected data returns l if a selected cell is empty var row col integer sum real begin sum 0 for col selectLeft to selectRight do for row selectTop to selectBottom do begin if not DataOK row col then begin SumSelection 1 Exit end sum sumtdata row col end SumSelection sum end begin Writeln SumSelection end Note Calling Exit from the main body of a function or program has the same effect as calling Halt Predefined constants functions procedures and operators This section lists the operators and the most important predefined constants that are available in the definition syntax An alphabetical list of all predefined functions procedures and constants is found in Appendix A The following are the most impo
389. you seta parameter to be equal to x its value will be undefined in first See Chapter 9 Defining functions and programs for more details If you plan to set a parameter equal e to x never use it in the function first 5 2 Working with functions Using functions The following explains what you can do with functions It does however not describe how to plot or fit functions these topics are covered in Chapter 8 Fitting and Chapter 7 Drawing Calculating function values You can calculate the y value of the currently selected function for a given x value by choosing Calculate Function x from the Calc menu the name of this command changes it always uses the name of the currently selected function You can calculate the y value of the Calculate Polynom x currently selected function for a given x value by choosing Calculate Function x from the Calc menu the name of this command changes it always uses the name of the currently selected function LI Use fitted parameters If you click OK the function is calculated for the given x value its y Cancel oit D 2 Cancel value is printed in the results window 2 Cancel o and the dialog box disappears If you click Do It the function s value is displayed in the dialog box and written to the results window The box does not go away and you can calculate other values of the function immediately If Use fitted params
390. you want to vary the function s parameters to find the minimum maximum Only the active parameters of the function are varied varyX Boolean true if you want to vary the function s x value to find the minimum maximum xValue Real If varyX is false this parameter gives the value of the function s x value If varyX is true it gives the starting value for x precision Real The desired precision Pass 0 for best precision le 7 for medium precision le 2 for low precision fullDescription Boolean true if a complete protocol is to be printed in the results window false if only the resulting parameters x and y values are to be printed printResults Boolean Set to true for printing the results to the Results window Default false To retrieve the results of a call to procedure Optimize call the function GetResult selector Use one of the following selectors optimizedX the optimized x value optimized Y the optimized x value fittedParameter the optimized parameters Pass parameter index 1 based as second argument to GetResult A 46 Appendix A Predefined functions procedures and arrays The following example finds the minimum of the current function by varying its x value and its active parameters then prints the optimized value of the second parameter Optimize xValue 0 precision 0 getMinimum true varyParams true varyX true Writeln GetResult fittedParameter 2 Ord function O
391. ys pro Fit allows the definition of one dimensional arrays The following syntax is used var name array minIndex maxIndex of type Where name is the name of the array minIndex is its minimum index maxIndex is its maximum index type its type Since types are ignored by pro Fit you can omit of type in the declaration To access an array use the syntax name index Example var arrl array 1 10 of real arr2 array 0 100 i for i 1 to 10 do arrl i 0 arr2 33 22 1 Note the maximum size of all variables in a variable list is limited to 32 kBytes This limits the size of an array to about 2700 entries for the FPU version of pro Fit to about 3200 entries for the non FPU version and to about 4000 entries for the Power Macintosh version Multi dimensional arrays are not supported Defining functions and programs 9 29 The compiler When adding a definition to the list of functions or programs of pro Fit the definition text is translated into machine code that can be executed by your computer This results in a very fast execution speed of programs and functions functions programs y a 1 sin x or i 1 to 10 do datali 1 0 compiler code OOFA 2CC3 3008 299S 8001 FF29 The translation of your definitions into machine code is carried out when you choose Add to Menu from the Prog menu or if you click the button Add in the toolbox of the function window Any changes that you mak

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