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SHORT INSTRUCTIONS FOR PROGRAM PLOTFIT (VERSION 4.0) ==================================================== This program was written in GFA Basic and will therefore require that you have the GFA Basic interpreter ( GFABASRO.PRG Versiom 2.0). This program may be used with a color or a mono Atari St computer. Once the program is started the appropriate file PLOTFIT.MON or PLOTFIT.COL will be read. After that these files will not be needed anymore. These file must reside in the same folder than the interpreter. This program is fully menu driven. PLOTFIT will allow you to graphically display the X, Y range pair with the optional error checking of the Y range. Different point symbols like lines may be used. There is no pie chart. The X- and Y- axis will automatically be adjusted for the chosen range. You may write to both axis and you may also add text at any place you like. Text may be chosen in different fonts. Logarithmic and linear representations of both axis are posssible. Many pictures can be drawn on the same screen. Lines and symbols may be combined. More than one data set may be created at the same time (<=8). All attributes from the data set (scale range, axis markings) will also be created and may be changed individually. Maximum number range: -2000000 -> 2000000 Minimum number range: -0.01 -> 0.01 Maximum number of points: 250, 500 for the last data set. A second menu includes a fit packet. This allows you to match different functions to the data set: 1)Polynomial (like a parabola) 2)Exponential function (like Y =height*exp(const.*X),or a Gauss-curve. 3)Power function (like Y=const.* x^power) 4) multibles ( <=3) overlaying Gauss-curves. At the most 10 parameters will be matched. The match may consider the error in the Y value or the absolute or relative disgression of the Y value from the curve. The matched data set may then be supplied with specification by one or more X values by using the mouse. A third menu allows you to manipulate the data set: 1)Addition, Subtraction, Division, Multiplication of the Y value. 2)Copy, Combine, Erase data sets 3)Invert Y value, exchange X and Y value, sort, averaging neighboring points, calibration of the X and Y values. 4)Replace, erase, calibrate and averaging ranges of a data set. 5)Transformation of cartesian coordinates (X,Y) to polar coordinates or the reverse, as the rotation and mirroring of the X,Y pair. Examples and possible problems are at the end of this document. Short description of each of the PLOT-MENUES -------------------------------------------- DESK-Menu ========= Return to the desktop by selecting DESK or to Basic by the BASIC option. Before calling accesorries be sure to save the screen by using the BUFFER option from the OUTPUT-Menu and then restore it with the BUFFER option from the INPUT-Menu. INPUT-Menu: =========== The input may be from a file, the keyboard or the mouse. X-values may automatically be produced by the program. If input is by mouse, the X- and Y- scales must have been defined by using the X-RANGE and Y-RANGE or they must been established thru previous input. The option COEFF allows input of the coefficients of a polynomial (see FIT). With the help of those coeffiecents a data set (X-,Y- value pair) may then be created. Errors for the Y value can be input as either absolute or relative ( in %). These are identified by the input of a "%". The option ERROR makes Y-errors possible, that are build tru roots (Y)-statistical error. Later changes are possible by using the option CHANGE from the INPUT menu. While in CHANGE, individual points may be changed by using the mouse or the keyboard. You may also change individual coefficients by selecting COEFF from the INPUT-Menu. It it also possible to append or merge data from another data set. The option CHANGE performs all changes to the data set that was chosen in the DATA SET option (the current data set graphically displayed). The option TEXT makes it possible to include your own text into the picture (maximum of 10 lines). These lines may be changed or deleted thru the CHANGE option within the INPUT menu. ( You may use the backspace to change text or use the mouse to change the position of the text. The option DATA SET allows you to select the data set that will be used for the display (Pick data set number, replace current data set with new data set). OUTPUT-Menu: ------------ Data may be output to the screen, printer or a file. The HARDCOPY routine creates copies which are turned 90 degrees, and are 1.8 times as large as normal hardcopies. The first time HARDCOPY is called the printer type must be selected (IBM or Epson). When using medium resolution the grey will be red and blue. You can always use the ALTERNATE HELP to get a normal hardcopy. The OUTPUT menu also contains an Integration routine. SUM Y adds all Y values within a X range and calculates the mean and the X- median (SUM X(i)*Y(i) / Sum Y(i) ). INTEGRATE is useful to compute the sum Y(i)*Delta-X(i). Through the DATA SET option, the mode of all OUTPUT options of active data sets may be chosen. The option FIT selects the FIT menu (see below). You can use the option BUFFER to store the screens. The actual data fields are not changed only the X- and Y- scales. You may therefore put more graphs into a buffered picure by using the option ADD from the DRAW menu. X-SCALE Menu ============ RANGE allows you to input the axis range by using the keyboard or the mouse. AUTO selects the range according to the data. Once AUTO is deactivated the previous set range goes into effect. If no range was specified than the range will be set automatically. LOG turns on the logarithmic display of the data set. CALIBRATE recomputes the X values (X-new = X-old * slope + Offset. A RETURN without a value makes slope=1 and offset=0. EXPAND allows you to increase the range via the mouse. The X values are not changed and the range selected by AUTO remains intact. MARKER turns vertical help lines on and off. They do not become visible until NEW or FRAME is selected from the DRAW menu. Y-SCALE Menu ============ see X-SCALE Menu. Instead of EXPAND you must use the ZOOM option to enlarge the picture. Select the start and ending positions with the click of the mouse. DRAW-Menu: ========= NEW erases the screen and plots a graph based on the range selected thru the X-SCALE and Y-SCALE Menus. ADD allows you to add more graphs into the same picture. The ranges are not changed. FRAME draws only the X- and Y-axis. The screen is erased. FIT allows you to add the last match to the existing screen. The line form of the fitcurve may selected by using option LINE from the STYLE Menu. DATA SET allows you to pick the data set. Data set is displayed in the top right corner. NEXT switches the the next data set. When the last data set is reached, the first data set will again be chosen. PREVIOUS select the previous data set. This wraps around to the last data set from first. TEXT allows you to turn the display of text on and off during graphic display. ERROR turns the Y-ERROR bars on and off. STYLE-Menu: =========== The selected style from option TEXT is only active for labels, which are inserted somewhere into the screen by using option TEXT from the INPUT Menu. Lines and symbols may be combined by selecting them from the STYLE Menu and adding them thru the option ADD from the DRAW menu. The option COLOR allows you to select different color for text and lines. All other options are self explanatory (maybe). Greek letters and other signs may be added by pressing Control S and any other letter of your choice. (K=Delta, J=Omega, H=Phi, etc). Short description of the FIT Menu: ---------------------------------- FUNCTION ======== Selects the fit functions (match functions) and allows you to select up to ten fit parameters. The default is 2. This fits a polynomial (option LINEAR, EXPONETIAL, POWER LAW ). Thru this the Y values can become logarithmical (option EXPONENTIAL) or the X- and Y- values (option POWER LAW). Errors will always be correctly changed. Attention:In the case of option POWER LAW negative values ((X-X0) < 0) will not be evaluated during the curve fitting. Negative Y-values with option EXPONENTIAL and POWER LAW will be replaced by the maximum of the Y axis/100000 (linear Y axis) or the minimum of the Y axis/10 (logarithmic Y axis)! In the case of a Gauss-curve, the height, position of the maximum,. median and area of the Gauss-curve will be computed from the fit parameters (option EXPONENTIAL,3,coefficient). With the option GAUSS-FUNCT. you may match one or many Gauss curves. a non linear match system is used. This requires the input of starting values (position, height and mean of the Gauss-curve). This method is more complicated but also more accurate. If the start values are to far from the optimal value, the solving process may last forever and the fitting is interrupted. The option TEST-FUNCTION allows you to apply a previous selected function to the data. The function itself can be specified thru input of coefficients by using the INPUT menu or thru another data set. The option X-REFERENCE allows you to select a reference point (X0) for the fit parameters. Attention: The option POWER LAW requires positive values (X-X0) within the fit range (see above). Option FIT performs the selected functions on the data, whereby the mean deviation (CHI**2) is minimized. If the statistical error of the data is taken into account (see: Menu WEIGHT), the probability is computed that will correctly describe the data (values between 5% and 95% are possible). WEIGT ===== Specifies the weight that is assigned to each data point. Y-ERROR: Previously entered errors of the Y values will be used as the weight. ABSOLUTE: The deviation of the data points from the fit curve is minimized. RELATIVE: The relative deviation of the data points from the fit curve are minimized. Attention: With option ERROR and RELATIVE the smallest weight factor is (y-max - Y-min)/10000 with linear or Y-min/1000 with logarithmic Y-axis. Smaller weight factors will be replaced by these values! REGION ====== Specifies the range of the data that will be used to fit the curve: ALL: All data points. DISPLAY: Range of current data displayed. NEW: Select X range with the mouse. APPEND: Add additional X ranges (maximum of 10). SHOW: shows thru markers the X ranges that were selected with NEW or APPEND option. At the same time these ranges are reactivated in case the option ALL or DISPLAY were previously active. DATA SET: Specifies the data set or sets to which the fit curve should be applied to. The currently displayed data set is the default. STORE: ====== Allows you to save the X- and Y- results of the fit as a data set. The option CREATE allows you to pick your own X range. Option SUBTRACT subtracts the fit result from the data set. Option DIVIDE divides the data with the fit result. Option DATA SET selects the data set in which the result is saved. If no data set is specified a new data set is created. DRAW: ===== see main menu. Option Buffer is also present (see INPUT menu in the main menu. OUTPUT: ======= Allows you to print the result of the fit to the printer (option PRINT), the screen (option SCREEN) or the disk drive (option FILE). The mean deviation of the data within a given range can also be specified ( option SUM-ERROR). The option X -> Y calculates the Y value for a give X value. The error of the Y fit value is also calculated. This makes it possible to estimate the values that are past the visible range. Option MAIN MENU returns you to the main menu. Note: ----- The menu STORE and OUTPUT are also active if a set of coeffiecents were previously entered thru the keyboard (option COEFF from the INPUT menu). The errors are set to null in this case. Short description of menus from MENU III. ----------------------------------------- CREATE ====== The currently displayed data set is combined with another data set (see below). The result will be put in a new data set or an old data set will be overwritten (option DATA SET). ADD: Addition or subtraction of the Y values between two data sets. The Y values of the second data set may be multiplied by a factor value. DIVIDE: Division of the Y values between two data sets. MULTIPLY: Multiply the Y values of two data sets. In all three cases will the error of the resulting Y values be calculated from the errors of the output values. If more than one data set is displayed than only the last one will be used. If the X values of the data sets are not identical, the Y values of the second data set will be adjusted. COPY: Copies one or more data sets to a new data set. MERGE: Merges the selected data set into the displayed data set. It is merged by the size of the X value. The relative order of the value pairs of the two data sets remains unchanged. Attention: The number of the new data set should not be identical to the number of either output data set! DELETE: ======= To erase all of the data set or the text of the data set. CHANGE: ======= Changes to contents of a data set. INVERT: Replaces the Y values by 1 / Y value. Y-errors, ranges, text coordinates will also be recalculated. SWAP X, Y: Switches the X and Y values. This option can also be used to display error result for the X values. CALIBRATE X: linear allignment of the X values: X-new = X-old*slope + Offset. CALIBRATE Y: Linear allignment of the Y values. AVERAGE: Creates the average of the two neigboring points. If the Y values are given with error results, a weighted average will be performed so that the errors of the Y average is minimized. If the number of data points is not even, the last value will be taken as is. SMOOTH: Three Y values are averaged. The number of values remains unchanged [ Y(i)=( Y(i-1) + 2*Y(i) + Y(i+1) )/4 ]. Attention: The data points are not statistically independent after a SMOOTH operation! INTEGRATE: Numeric integration thru the X-, Y- value function: Y-new(n) = Sum(Y(i)*delta-X(i)), i=1-n. Attention: depending on the distant between the points on the X axis, large Y values may be created. Calibrating these values by using the option CALIBRATE Y is sinful. REGION ====== Changes a data set only within the selected range. REPLACE: Replaces the data points of the displayed set or sets with the values of another data set with values in the same range. The marked range of the displayed data set is not required to contain points. In this case the points of the second data set will be inserted or added. DELETE: Erases all points of the chosen X range. CALIBRATE X: Calibrates the data points of selected range on the X axis (see X-SCALE). CALIBRATE Y: Same as previous except (Y-SCALE). AVERAGE: Computes the average between the two neighboring points within a selected range. If more than one data set is displayed, then all above operations are performed for all displayed data sets. TRANSFORM: ========== X-Y -> `-R: Transforms cartesian coordinates (X,Y) into polar coordinates (angle, radius). A circle will for example be transformed to a horizontal incline. Angles are given in degrees. `,R -> X-Y: Transforms polar coordinates into cartesian coordinates. A incline with a slope <>0 would for example be transformed into a spiral. Example: input of the smallest radius (example 10) and the increments of the radius per degree (example 0.1) thru the COEFF option. LINEAR from the INPUT menu and a choice for the Theta value X-min=0, X-max=1080 with increment=10. ROTATE: Rotate the value pair clockwise by the given angle. MIRROR: Mirror the X and Y values of the displayed data set or sets thru the X-Y CENTER. X,Y-CENTER: Sets the orgin from which the data is rotated. (Default: X=0, Y=0 ). Errors for the Y values are not taken into account during any of the above functions. File-Structure: =============== The data file must have the extension .DAT. It can reside in a folder as well as a folder within a folder. The data file can contain many different options or comments before the actual data set. Options are identified by key words followed by the option: X-RANGE:X-min,X-max Y-RANGE:Y-min,Y-max X-TEXT:X-axis text Y-TEXT:Y-axis text STYLE:Symbol-flag, Histogram-flag, style-Nr, Line-width, Line-Color LABLE:Lable Text (anywhere on the screen) X-Position, Y-Position, Text-style (1-31), Text-size (4,6,13,32) All lines that do not begin with a keyword will be treated as comments. The first Comment line will be saved and transferred to the Output-File, all others are ignored. The start of the data fields begin with the keyword DATA: Example: DATA:X,Y(,Y-ERROR or X-ERROR) (The optional keyword X-ERROR identifies that Error results ( 3 numbers per line) are for the X values. The following input values will automatically be tested for input error.) X value, Y value, Y-error or X value, Y value or X value, Y value or X value, Y value, X-error No special mark to signify the end of the data set is needed. A empty line after the data set will result in an error message. END: needed to seperate more than one data set within the same file. (It may be the only thing after the data, but further input is then ignored.) Keywords do not have to be capitilized. The option FILE from the OUTPUT menu creates these data files. Changing the default program parameters: ======================================== The file PLOTFIT.MON or PLOTFIT.COL contain the disk drive default and dimension for data fields (size of data sets) in line 1. Line 2 contains the screen coordinates used for graphic. The dimension variables follow along with the keywords for the menus. The Symbol table of the graphic symbols is on the end. Possible Problems!! =================== If the Menu row is frozen after a command, a short click with the mouse will unlock it. Multiple inputs with the mouse are terminated by pressing the right mouse button. If everything else fails try pressing the RETURN key. The old value usually remains in tact when pressing the RETURN with any input; Exception: X- Y- axis marking. In the case of an error it is best to return to the menu. If nothing else works you may save data and start from the beginning. If hardcopy does not work, turn printer of and on. To fit a data set with the EXPONENTIAL or POWER LAW function requires positive X or X and Y values. You may have to expand the range using the EXPAND from the X-SCALE menu. If the program is too much pressure on your nerves, just erase the program. Example Program: 1) Load TEST2.DAT by selecting FILE from the INPUT menu. Plot the yearly taxes of Hans Zahlemann by selecting NEW from the DRAW menu. Compute the yearly average from the years 197801984 by selecting INTEGRATE from the OUTPUT menu. All taxes for this range are automatically computed. Select FIT from the OUTPUT menu. By selecting EXPONENTIAL from the FUNCTION menu (Number of Fit parameters=2) and then picking from FIT, you will receive a adjustment curve that will allow you to inspect the future and the past. (option X -> Y). Select MAIN MENU and then X-SCALE (1930-2030) and then Y-SCALE (0-65000) to see the predicted curve of your taxes. The screen text will also change, but you may discard it it by using the TEXT option from the DRAW menu. The FIT option in the DRAW menu will tell you the predicted taxes to your country. The option MOUSE from the OUTPUT menu will give you more accurate information. The CREATE option in the STORE menu allows you to save the results as a data set. 2) Load TEST1.DAT and fit a Gauss curve in the peak. Then select the range by using the NEW option in the region menu. Then select EXPONENTIAL from the FUNCTION menu and specify the number of fit coefficients (# OF COEFF. = 3. The height, width and position of the gauss curve is obtained by selecting the SCREEN or PRINT option from the OUTPUT menu. Compare the mean deviation CHI with the result by using the GAUSS-FUNCT. Have fun! Wolgang Koenig, am Bruehl 1, 6101 Messel, Tel. 6159-1476, December 86 PS. The internal hardcopy command should work without any problem on Epson and IBM compatible printers. (see your printer documentation for more information). Translated to English by Wilford Niepraschk.