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GRAPHICA v2.2 A System for Drawing Scientific Graphs ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ User's Manual by Antonio Montes 3 February 1993 (C) Copyright 1992,1993 Antonio Montes. Portions (C) Copyright 1991 Borland International. ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ If you like this program, you can send a contribution to the address near the end of this file. The version you get is the full and latest version released as of the date above. Contributors to the development of GRAPHICA are entitled to mail support, a copy of the latest version and a printed manual. Please tell me the version number of your copy of GRAPHICA when you send in your contribution. My address can be found near the end of this file. ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ MANUAL SUMMARY ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Chapter 1: INTRODUCTION Contains information concerning installation and hardware requirements. Chapter 2: GETTING STARTED Defines the fundamental elements common to all plots, defines the manual usage and presents a description of the command syntax. Chapter 3: TUTORIAL Takes the user through a series of short lessons to get familiar with GRAPHICA. Chapter 4: COMMAND REFERENCE Gives a list of all the commands understood by GRAPHICA. Chapter 5: ADDITIONAL INFORMATION Provides additional information on program access, reporting bugs, and other concepts useful to run GRAPHICA. CONTRIBUTIONS SHAREWARE DISTRIBUTION TABLE OF CONTENTS ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Chapter 1. INTRODUCTION 1.1 Overview 1.2 Disclaimer 1.3 Files 1.4 Equipment Requirements 1.5 Installation Chapter 2 GETTING STARTED 2.1 Overview 2.2 Document Conventions 2.3 Starting Up and Exiting 2.4 For Beginners 2.5 Errors Chapter 3 TUTORIAL 3.1 Introduction 3.2 Entering Commands 3.3 Plotting Functions 3.4 Plotting Data 3.5 Plotting Data Files 3.6 Plotting Parametric Curves 3.7 Using Script Files 3.8 Multiple Graphs on one Page 3.9 Importing GRAPHICA Plots into WordPerfect Chapter 4 COMMAND REFERENCE Chapter 5 ADDITIONAL INFORMATION 5.1 Mathematical Expressions 5.2 Environment Variables 5.3 Startup File 5.4 Comments 5.5 Text Control Sequences 5.6 User-Defined Functions and Variables 5.7 Bug Reporting Chapter 1 INTRODUCTION ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 1.1 Overview ───────────── GRAPHICA is a command-driven interactive graphics program for making presentation quality graphs on a computer. This two- dimensional data plotting system is designed specifically for scientific and engineering applications. GRAPHICA is SHAREWARE, i.e. it's user-supported. GRAPHICA is easy to use, interactive, and powerful. With GRAPHICA, you can: o plot functions or data files o evaluate and plot mathematical expressions o fit spline or polynomials to data o display and print a graph on hardcopy devices o export graphs in HPGL, PostScript or other formats o draw text in roman, greek and cyrillic fonts o get online help 1.2 Disclaimer ─────────────── The authors have made their best effort in producing this software, but hereby disclaim all warranties. The authors will not be liable for any damages arising from the use or misuse of GRAPHICA. The person using the software bears all risk as to the quality and performance of the software. The program is provided as is. 1.3 Files ────────── GRAPHICA consists of the following files: GRAPHICA.EXE main program GRAPHICA.HLP help file GRAPHICA.DOC user manual (this file) README.1ST quick instructions HISTORY.DOC log of latest changes EXAMPLES.ZIP an archive containing *.PLT sample input files *.DAT data files 1.4 Equipment Requirements ─────────────────────────── GRAPHICA normally detects automatically what graphics monitor hardware is present in order to preview graphs. In general, you basically need the following items: Computer: IBM PC,XT,AT or compatibles Disk Drives: 2 floppy drives or 1 floppy drive/hard drive Memory: 640K Bytes Video Cards: CGA, EGA, VGA or compatible adapter Hercules Monochrome Adapter or compatible Hardcopy: - Plotters HP7475A or HPGL compatible - Printers Epson 80 and 100 series Panasonic 1080i or equivalent Other Output: PIC HPGL PostScript 1.5 Installation ───────────────── There are no special installation requirements. The simplest procedure is to make a new directory on your hard disk, and to copy all of the files there. You may wish to put the GRAPHICA directory on your path, or to copy the files to a RAM disk. Let's suppose you wish to install GRAPHICA into a directory called GRAPH. To create the directory, simply do the following: C:\md graph C:\cd graph If you have changed your system prompt with $P$G (as part of your AUTOEXEC.BAT file, for example), the prompt should show: C:\GRAPH> GRAPHICA should have been distributed as one file, called GRPHCA22.ZIP or GRPH22.ZIP. If so, then all files will have to be extracted. To do this run PKUNZIP or equivalent program on the command line. If you received GRPHCA22.ZIP, do: C:\GRAPH>pkunzip grphca22 All the GRAPHICA files will be put in this directory and you are ready to start graphing. Chapter 2 GETTING STARTED ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 2.1 Overview ───────────── GRAPHICA is an interactive computer program which accepts English sentence specifications of graphs, and, from those specifications, produces publication quality pictures. This manual describes how to use GRAPHICA. The specifications that the user provides are referred to as "commands" or "statements". Final graphs are of publication quality and may be fitted to pages with existing text thereby eliminating costly reproduc- tions (photocopying and reduction). The user operates the program through a set of problem oriented language (POL) commands. Each command consists of keywords and data values separated by blanks or commas. This requires minimum data input and enables simple and efficient graphing. For example, if the user enters: map x 0,10 y 0,100 GRAPHICA determines that the user wants the x-axis range set from 0 to 10 and the y-axis range set from 0 to 100. The user must separate entities in a command with blanks or commas. In this manual, blanks are not explicitly indicated. GRAPHICA capabilities include: - multiple curve plotting and graphs - axis drawing with labels and scaled divisions - log-log, semilog, probability and linear plots - graph titles and legends - lettering in five fonts and different sizes - hardware and software character generation - 3 units of measure (in, cm, mm) 2.2 Document Conventions ───────────────────────── Input to GRAPHICA is in the form of a problem oriented language (POL) designed specifically for graphing purposes. The following is a description of the conventions used within the manual to explain GRAPHICA commands. The appearance within a GRAPHICA command of a descriptor of the form <integer> implies that the user is to enter an item of data within that position in the statement of the class described by the descriptor (in the above example, an integer). The command divisions x <integer>,<integer> implies that the word divisions is to be followed by the word x and two integers such as 2 or 3, and that the statement entered by the user as input data should be of the form divisions x 2,2 The following are definitions of most of the descriptors used within the language. Those not described below are ex- plained when they first occur in the text. <integer> a series of digits optionally preceeded by a plus or a minus sign. Examples are 121, +300, -410. <real> a series of digits with a decimal point included, or a series of digits with a decimal point followed by an exponent indicating a power of 10. Real numbers may be optionally signed. Examples are 1.0, -2.5, 3.6E+10. <value> is either an integer or a real number. 'string' is any textual information enclosed within a pair of apostrophes (') or quotes ("). An example is 'Are you following this so far?' As noted above, input to GRAPHICA is a series of English- like commands. Many of the words or phrases in these commands are optional and are permitted primarily for readability or are used to specify options within a command. The curly braces {} denote these optional items. Each command is entered on a new line. Commands can be entered in lower case, upper case, or both. Only the first significant characters of a command are needed. A line starting with a left square bracket [ or a # will be treated as a comment line. Also, anything after those two characters in a line will be treated as a comment (see section 5.5). Items such as <integer> shown in the command definitions must always be replaced by an integer. Undesignated items such as <minimum>, <maximum>, etc. can be replaced by either an integer or a real. For example, divisions x2 <integer>,<integer> can be specified as div x2 3 2 whereas map x <minimum value> <maximum value> can be entered as map x 20 30 or map x 20.0 30.0 Sometimes keywords in a command line can be entered in any order (except the very first one, of course). For instance, plot add x connect y will plot the X/Y data connecting all points and adding symbols. In many commands, items may be repeated or more than one word is acceptable in a given position within a command. The choices are listed enclosed in curly brackets '{}'. For example, the command definition draw {x} {y} {x2} {y2} {mask} {reflect} indicates that the user may enter commands like draw x reflect y2 reflect draw x y draw y reflect x2 mask. Similarly, paper {size} <horizontal value> {by} <vertical value> can be written as paper size 11.0 by 8.5 pap 11.0 8.5 or paper 11 by 8.5 In order to be more descriptive within the command definitions, actual data items (items enclosed within '<>') are sometimes described in terms of their physical meaning and followed by the type or class of data item which can be used in the command. For example, a command definition of the form input {from} {file} <filename> implies that the data item following the word input is the name of a file. For example, acceptable commands would be input 'myfile.p' input from 'graph.dat' Filenames or labels are not acceptable if they are not enclosed within apostrophes or quotes. Examples of commands with incorrect labels or filenames are input from my data label top you*beast! xlabel honey.pie 2.3 Starting Up and Exiting ──────────────────────────── GRAPHICA can be run from any directory as long as GRAPHICA.EXE is placed in the directory search path. To start the plotting system, simply type graphica at the DOS prompt: C:\graphica GRAPHICA takes a few seconds to load into memory, and when the graphica> prompt is displayed, the program is ready for your input. To exit, type quit or exit at the GRAPHICA command level. graphica>quit and you're back at the DOS prompt. 2.4 For Beginners ────────────────── For a quick demonstration of GRAPHICA's main capabilities, run GRAPHICA and then load some of the sample script files (*.PLT). For example, C:\GRAPH\graphica (press return) graphica>load 'demo' (press return) Alternatively, command-line arguments may be names of files containing GRAPHICA commands. Then, for example, C:\GRAPH\graphica demo is another way of running the demo above. 2.5 Errors ─────────── Error messages are self-explanatory. If an error is detected while parsing a command or a script file, GRAPHICA will inform you with a beep and message. CHAPTER 3 TUTORIAL ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 3.1 Introduction ───────────────── Welcome to the GRAPHICA tutorial. A plot is a graphic image used to present information in a visual manner. The components of a graphic image are: lines, markers, text strings, polygons, etc. The basic ingredients of a plot are: a page, a subplot area and data points. The data points are plotted using symbols, characters or simple dots. Data points and curves are drawn or plotted on a grid space formed by Cartesian coordinate axes. The horizontal line is the x-axis and the vertical line, the y-axis. A graph is made with GRAPHICA by either loading an existing script file from the disk, or by creating a new graph through the command line. This section explains how to create graphs. All commands may be abbreviated, as long as the abbreviation is not ambiguous. Any number of commands may appear on a line, separated by semicolons. A file is loaded with the load command. Commands may extend over several input lines, by ending each line but the last with a backslash (\). The backslash must be the last character on each line. The effect is as if the backslash and newline were not there. Commenting out a continued line comments out the entire command. 3.2 Entering Commands ────────────────────── For help on any topic, type help followed by the name of the topic at the graphica> prompt. Let's get started. Let's assume that you have copied all the GRAPHICA files in a directory called GRAPH. Start GRAPHICA by entering graphica at the DOS prompt and pressing return: C:\GRAPH>graphica The screen will clear, there will be a brief notice and you'll be at the graphica> prompt: graphica> Now you are about to begin making scientific graphs. The plot command is the heart of GRAPHICA. It is used to plot data, functions and datafiles. We will be using it a lot in the next few pages. Anytime you are ready to type in the next GRAPHICA command and your screen shows a plot (in other words, you are in graphics mode), just press any key or start typing the command in. At the graphica> prompt, you can always type show to have a look at what you have plotted on the screen so far. 3.3 Plotting Functions ─────────────────────── To plot a sine wave, enter the following command at the graphica> prompt: graphica>plot sin(x) Within a few seconds, a graph of sin(x) as a function of x will be plotted. Press any key and then enter: graphica>draw x y The x and y axes will be drawn. The x axis will range from -10 to 10, since that is the default range. You can plot functions that have singularities. GRAPHICA will try to choose the appropriate y scale. Enter: graphica>clear to sort of clear your graphics slate. Then enter: graphica>samples 300 graphica>plot tan(x) The samples command simply tells GRAPHICA that we would like to plot more points of the function that the default of 150. After that, the plot command plots the function. To draw the axes, do: graphica>draw x y You can give a list of functions to plot all at once. Go ahead and clear everything by entering: graphica>clear Then, map the x-axis with the following command: graphica>map x 0 2*pi To actually plot the functions, enter: graphica>plot sin(x), sin(2*x), sin(3*x) And to draw the axes: graphica>draw x y GRAPHICA always tries to plot functions as smooth curves. As a result, in places where your function wiggles a lot, you may adapt GRAPHICA's sampling of your function to the form of the function (we did that by giving the samples command at the beginning of this section.) Since GRAPHICA can only sample your function at a limited number of points, it can sometimes miss features of the function. By increasing samples, you can make GRAPHICA sample your function at a larger number of points. Of course, the larger you set samples to be, the longer it will take GRAPHICA to plot any function, even a smooth one. The function sin(1/x) wiggles infinitely often when x is near zero. GRAPHICA can never sample the infinite number that it would need to reproduce the function exactly. As a result, there are slight glitches in the plot. Go ahead and try it: graphica>clear graphica>map x -1,1 graphica>plot sin(1/x) graphica>draw x y Now you have seen how to plot functions. See section 5.1 for a more detailed explanation about mathematical expressions. 3.4 Plotting Data ────────────────── You may combine two GRAPHICA commands, plot and data, to plot data points. For example: graphica>clear graphica>data data>2 3 data>5 4 data>6 4 data>7 5 data>5 3 data>end graphica>plot x y add graphica>draw x y This sequence of commands will result in a simple graph with both axis autoscaled. See the map command for more details on how to change the x-axis scale in the plot. 3.5 Plotting Data Files ──────────────────────── Data may also be plotted by retrieving the information from a data file. There are a couple of ways of doing this. The first is by simply specifying: graphica>clear graphica>data 'bob.dat' where bob.dat contains 3 columns of numbers. To plot the data, you can do: graphica>plot data which will plot the first 2 columns. To draw the axes: graphica>draw x y Using the other method, you can plot a datafile directly: graphica>clear graphica>plot 'bob.dat' and now the axes: graphica>draw x y The first method allows you to read in several columns of data and then choose which one will be plotted (see column in the reference section.) By default, specifying plot data simply plots the first two columns of data as x versus y. 3.6 Plotting Parametric Curves ─────────────────────────────── In a parametric plot, you give both the x and y coordinates of each point as a function of a third parameter, say t. Let us construct a parametric plot. In this example, the parametric curve made by taking the x coordinate of each point to be sin(t) and the y coordinate to be sin(2*t): graphica>clear graphica>parametric plot t 0,2*pi sin(t) sin(2*t) graphica>draw x y 3.7 Using Script Files ─────────────────────── Every graph in this documentation can be readily reproduced from the script files provided in the GRAPHICA package. A script file is simply a text file containing valid GRAPHICA commands. The script file can be executed by the load or input command. The name of the input file must be enclosed in single or double quotes: graphica>clear graphica>load 'torp.plt' 3.8 Multiple Graphs on one Page ──────────────────────────────── With GRAPHICA, you may plot as many graphs on one page as you wish by changing the subplot area. Try this: graphica>clear graphica>load 'rocha.plt' Several axes have been defined, x and y axes with labels, a y2 axis without labels, etc. The data shown is actual experimental data obtained by a doctoral student and the graph is part of his dissertation. You may now quit GRAPHICA by typing exit at the graphica> prompt. 3.9 Importing GRAPHICA Plots into WordPerfect ────────────────────────────────────────────── This document was prepared using WordPerfect 5.1. The plots were produced with GRAPHICA, exported using HPGL output and imported into WordPerfect. Once a graphic has been imported into WordPerfect, you can move it, scale it, rotate it, add captions, etc. Let's create a graph with GRAPHICA and retrieve it into a WordPerfect document step by step. There is a file in your distribution disk called ris108.plt. Start GRAPHICA: C:\GRAPH>graphica and load the script file: graphica>load 'ris108.plt' The screen will clear and a plot will be drawn. In fact, this plot makes use of font 5 (complex cyrillic). The graph was created after one in a russian text dealing with petroleum chemistry (I thought it might draw your attention). Now press any key and enter: graphica>dump hpgl 'ris108.hpg' The dump command will create a file called ris108.hpg containing HPGL commands. You may later send this file to a plotter or pull it into any of the many programs that accept HPGL commands. Now, exit GRAPHICA by typing: graphica>quit and start WordPerfect: C:\GRAPH>wp When the screen clears, do the following: 1) press Alt-F9 (for the graphics menu) 2) type 1 (for figure) 3) select 1 (for create) 4) select 1 (for filename) 5) enter ris108.hpg (to read the file in, no quotes) WordPerfect will retrieve the HPGL information into a graphic box immediately. You can edit the graph further within the graphics menu: 6) press 9 (for edit) or simply view the graph: 7) press F7 (to exit the graphics menu) 8) press shift-F7 (for print) 9) press 6 (for view document) and you have successfully imported a GRAPHICA plot into a WordPerfect document. CHAPTER 4 COMMAND REFERENCE ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ This chapter gives an alphabetical lookup for all the GRAPHICA built-in commands. Here are all the supported commands: ARROW Plot an Arrow at the End of a Line AUDIT Set Command Trace AUTOSCALE Set Axis Autoscaling AXES Draw One or More Axes BACKGROUND Specify Background Color BEEP Turn beep on and off CHARACTER Set Character Attributes CHARACTER FONT Change the Character Font CHARACTER GAP Change the Character Gap CHARACTER RATIO Change the Character Ratio CHARACTER SIZE Change the Character Size CHARACTER SLANT Set the Character Slant CD Change the Working Directory CIRCLE Draw a Circle CLEAR Erase Output Device COLUMN Assign Data Columns to Axes DATA Read Data from Terminal or a File DEL Delete a file DIGITIZE Establish an x-y position DIR List a directory DIVISIONS Set Number of Axis Divisions DRAW Draw an Axis DUMMY Specify Dummy Variable DUMP Generate Hardcopy Output ECHO Echo Typed Commands EXIT Exit GRAPHICA EXPONENT Select Format in Log Labels FORMAT Specify Axis Label Formats FRAME Draw a Frame GRID Draw a Grid HELP Display On-line Help LABEL Draw a Label LEGEND Draw a Legend LINE Draw a Line LOAD, INPUT Specify an Input File LOCATION Specify Type of x/y Position MAP Specify the Limits of an Axis MASK Mask a Rectangular Area MEMORY Give the Amount of Memory Left ORIGIN Specify Axis Origin OUTPUT Specify Output Terminal PAPER SIZE Specify Paper Size PARAMETRIC PLOT Plot a Parametric Curve PAUSE Pause and/or Wait for User Response PEN Specify a Pen Parameter PLOT Plot a Datafile, Curve or Function PLOTTING SEQUENCE Select a Plotting Sequence POLYFIT Generate a Polynomial by Least Squares PRINT Print the Value of an Expression PWD Print Current Working Directory QUIT Exit GRAPHICA RECTANGLE Draw a Rectangle SAMPLES Specify Sampling Rate SHADE Shade a Specified Set of Data SHELL Spawn a DOS Shell SHOW Show a Parameter SPLINE Fit Data to a Spline SUBPLOT AREA Specify Area Where Plot Will Go SUB/SUPERSCRIPT Set the Sub/Superscript Size SYMBOL Select a Plotting Symbol TERMINAL Specify Output Terminal Type TIC Specify Tic Mark Size and Direction TITLE Draw a Centered Axis Label TYPE Type a file UNIT Specify Drawing Units VIEW Move Paper to View Plotter Output X,Y,X2,Y2 Specify Axis Type X,Y,X2,Y2LABEL Draw a Centered Axis Label The file GRAPHICA.HLP (included with this package) is used by the program to give you online help. It is an ASCII file and may be printed. It contains detailed information about each of the above commands, their features and how to use them. CHAPTER 5 ADDITIONAL INFORMATION ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ 5.1 Mathematical Expressions ───────────────────────────── In general, any mathematical expression accepted by C, FORTRAN, Pascal, or BASIC is valid. The precedence of these operators is determined by the specifications of the C programming language. White space (spaces and tabs) is ignored inside expressions. Complex constants may be expressed as the {<real>,<imag>}, where <real> and <imag> must be numerical constants. For example, {3,2} represents 3 + 2i; {0,1} represents `i` itself. The curly braces are explicitly required here. functions ───────── All functions in GRAPHICA accept integer, real, and complex arguments, unless otherwise noted. abs(z) returns the absolute value of the real or complex number z. The returned value is of the same type as the argument. For complex arguments, abs(z) is defined as the length of z in the complex plane [i.e., sqrt(real(z)**2 + imag(z)**2) ]. acos(z) returns the arc cosine (inverse cosine) of z. All results are given in radians. arg(z) returns the phase angle of a complex number z, in radians. The result is always between -π and π. asin(z) returns the arc sine (inverse sine) of z. All results are given in radians. atan(z) returns the arc tangent (inverse tangent) of z. All results are given in radians. besj0(z) returns the j0th Bessel function of z. besj0 expects z to be in radians. besj1(z) returns the j1st Bessel function of z. besj1 expects z to be in radians. besy0(z) returns the y0th Bessel function of z. besy0 expects z to be in radians. besy1(z) returns the y1st Bessel function of z. besy1 expects z to be in radians. ceil(z) returns the smallest integer greater than z. For complex numbers, ceil returns the smallest integer greater than the real part of z. cos(z) returns the cosine of z. cos expects z to be in radians. cosh(z) returns the hyperbolic cosine of z. cosh expects z to be in radians. erf(z) returns the error function of z. erf(z) is the integral of the Gaussian distribution. The error function is central to many calculations in statistics. erfc(z) returns the complementary error function of z. erfc(z) is simply 1.0 - erf(z), where erf(z) is the integral of the Gaussian distribution. exp(z) returns the exponential function of z (e raised to the power of z). floor(z) returns the greatest integer less than or equal to z. For complex numbers, floor returns the largest integer not greater than the real part of z. imag(z) returns the imaginary part of z as a real number. int(z) returns the integer part of z, truncated toward zero. ln(z) returns the natural logarithm (base e) of z. log(z) returns the logarithm (base 10) of z. real(z) returns the real part of z. sgn(z) returns 1 if z is positive, -1 if z is negative, and 0 if z is 0. If z is a complex value, the imaginary component is ignored. sin(z) returns the sine of z. sin expects z to be in radians. sinh(z) returns the hyperbolic sine of z. sinh expects z to be in radians. sqrt(z) returns the square root of z. tan(z) returns the tangent of z. tan expects z to be in radians. tanh(z) returns the hyperbolic tangent of z. tanh expects z to be in radians. operators ───────── All operators in GRAPHICA accept integer, real, and complex arguments, unless otherwise noted. The ** operator (exponentia- tion) is supported, as in FORTRAN. Parentheses may be used to change order of evaluation. The following is a list of all the binary operators and their usage: symbol example explanation ** a**b exponentiation * a*b multiplication / a/b division % a%b * modulo + a+b addition - a-b subtraction == a==b equality != a!=b inequality & a&b * bitwise AND ^ a^b * bitwise exclusive OR | a|b * bitwise inclusive OR && a&&b * logical AND || a||b * logical OR (*) Operator requires integer arguments. Logical AND (&&) and OR (||) short-circuit the way they do in C. That is, the second && operand is not evaluated if the first is false; the second || operand is not evaluated if the first is true. Multiplication must be explicitly noted with the asterisk; adjacent parenthetical terms such as (a+b)(c-4) are not automatically multiplied. symbol example explanation \: a\b:c * ternary operation (*) Operator requires an integer argument. The ternary operator evaluates its first argument (a). If it is true (non-zero) the second argument (b) is evaluated and returned, otherwise the third argument (c) is evaluated and returned. The following is a list of all the unary operators and their usage: symbol example explanation - -a unary minus ~ ~a * one's complement ! !a * logical negation ! a! * factorial (*) Operator requires an integer argument. The factorial operator returns a real number to allow a greater range. 5.2 Environment Variables ────────────────────────── An environment variable is used to specify from DOS certain parameters of program operation. The "environment" is really just a common area of memory that programs can write to and read from. Some programs are geared to look specifically at the environment to find particular data important to their operation. If we were to look at the DOS environment (by typing the SET command at the DOS prompt), we might see a listing similar to the one below: COMSPEC=C:\COMMAND.COM PATH=C:\;C:\DOS;C:\UTIL Other values might be present, like PROMPT=$P$G, and more depending on the types and kinds of software you are running. Some programs ask you to place a variable into the environment equal to a certain value so that they can find support files which could not be found otherwise. Environment variables are specified before running GRAPHICA. They can be specified directly from DOS, from within the AUTOEXEC.BAT file, or from within any batch file. The command for setting an environment variable is: SET PARAMETER=PARAMETER VALUE A number of shell environment variables are understood by GRAPHICA. None of these are required, but may be useful: - GRAPTERM - GRAPDUMP - GRAPHELP - GRAPHICA If GRAPTERM is defined, it is used as the name of the terminal type to be used. This overrides any terminal type sensed by GRAPHICA on start up, but is itself overridden by the GRAPHICA.INI (or equivalent) start-up file, and of course by later explicit changes. GRAPHELP may be defined to be the pathname of the HELP file (GRAPHICA.HLP). GRAPHICA is used as the name of a directory to search for a GRAPHICA.INI file if none is found in the current directory. COMSPEC is used for the SHELL command. Examples: C:\SET GRAPTERM=hpgl (sets the terminal type) C:\SET GRAPHELP=C:\plot (location of the help file) C:\SET GRAPHICA=C:\plot (location of the .INI file) 5.3 Startup File ───────────────── When GRAPHICA is run, it looks for an initialization file to load. This file is called GRAPHICA.INI. If this file is not found in the current directory, the program will look for it in your home directory (the environment variable GRAPHICA should contain the name of this directory). If the initialization file is found, GRAPHICA executes the commands in the file. This is most useful for setting your terminal type and defining any functions or variables which you use often. 5.4 Comments ───────────── Comments are supported as follows: a # or [ may appear in most places in a line and GRAPHICA will ignore the rest of the line. It will not have this effect inside quotes or inside numbers (including complex numbers). Examples: graphica>[ test file ] graphica>echo # echo all commands graphica># map axes graphica>map x 0 10 y 0 10 5.5 Text Control Sequences ─────────────────────────── Description: Text primitives generate a string of characters on a display device in a specific location in the world coordinate system. The character string may comprise letters, numerals, and symbols. Text primitives provide a method for labeling and clarifying a graphical image. This section describes the control sequences which are accessible when specifying a string label. GRAPHICA recognizes \ as a special character used to signal the start of an escape sequence. There are two sorts of escape sequences, those that take an argument and those that do not. Two escape sequences do not take an argument: \U move up half a character size \D move down half a character size The following take an integer argument immediately after the escape sequence and a space after it to delineate the end (the space is not printed): \Cn set color to n \C-1 reset color to the default \Fn set font to n \F-1 reset font to the default \Sn set character size to n \S-1 reset character size to the default \Ln set character slant to n degrees \L-1 reset character slant to the default slant \An print ascii n \rn save current position in register n \Rn restore position from register n Examples: to print greek characters such as in 'beta = x + lambda': label '\F2 b\F1 = x + \F2l' to label the x-axis with 'velocity U sub f': xlabel 'velocity, U\Dsub' to place a top label of 'stress in dynes per cm squared': top label 'stress (dyn\cm\U2\D)' to get 'x squared plus y squared': label 'x\U2\D + y\U2' and finally, an advanced example. To get 'A sub b sup beta': label 'A\r1 \Db\R1 \U\F2 b' This last example is translated as: do A, save this spot, go down half, do b, restore the saved spot, go up half, switch to font 2 (greek simplex), do beta. Notice the use of registers to stack characters on top of each other. To get a backslash, you'll have to use \\. 5.6 User-Defined Functions and Variables ───────────────────────────────────────── User-defined function syntax: <function-name> ( <dummy-var> ) = <expression> show functions where <expression> is defined in terms of <dummy-var>. User-defined variable syntax: <variable-name> = <constant-expression> show variables Description: You may define your own functions and variables. User-defined functions and variables may be used anywhere an expression is called for. Variable and function names are case sensitive; thus "A" is not equivalent to "a". A function refers to a general expression and can take one argument (dummy variable). Examples: graphica>w = 2 graphica>q = floor(tan(pi/2 - 0.1)) graphica>f(x) = sin(w*x) graphica>sinc(x) = sin(pi*x)/(pi*x) graphica>delta(t) = (t == 0) graphica>ramp(t) = (t > 0) ? t : 0 The following variables have already been defined for you: pi = 3.14159 e = 2.71828 gamma = 0.57721 goldr = 1.61803 5.7 Bug Reporting ────────────────── GRAPHICA is under constant revision, updating and being given expanded capabilities. Prior to each release, I strive to verify new features and bug fixes through testing. However, as inevitably happens with any software, some bugs do survive and show up in user runs. Users can aid in the problem fixing process by following the guidelines below: a) Report any unusual messages, computed results, format overflows, etc. even though the program appears to have terminated normally. b) For any abnormal program termination, save the input file and all output obtained by running the program. Reported problems will be fixed as quickly as possible. In most instances, alternate methods or techniques of plot formulation and input are available to permit graphing despite the bug. All problems encountered with GRAPHICA should be reported to the address below. CONTRIBUTIONS ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ If you like the program and find it useful, you can support its continued development by sending me a contribution of HFL 45.- (dutch guilders) or US$25 (US dollars). A contribution will entitle you to mail support, a copy of the latest version and a printed manual. More to the point, though, it'll make you feel good. I've not infested the program with any beg notices, crippled it or had it verbally insult you after a few days. I trust you to support GRAPHICA if you like it. If you want to see additional features in GRAPHICA, please send in a contribution. Feel free to contact me for any reason. My address is: Antonio Montes Postbus 13 2350 AA Leiderdorp The Netherlands e-mail: CompuServe 71031,1162 internet: 71031.1162@compuserve.com EUROPEAN USERS ────────────── In addition to sending me your name, address and size of disk you need, you may contribute in one of three ways: 1) send a eurocheque for HFL 45.00 to my address. 2) wire HFL 45.00 to the Postbank Giro Account 3366191 in my name. 3) send HFL 45.00 in cash in an envelope at your own risk. OTHER USERS ─────────── In addition to sending me your name, address and size of disk you need, you may contribute by please sending a check in US funds for the equivalent of US$25. You can send me a check from any bank in the United States. I have a US account and will have no problem making a deposit. If you send a check drawn on an international bank, make sure that it will be negotiable in the United States. If there's no bank routing number along the bottom of the check, it will not clear. SHAREWARE DISTRIBUTION ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ I don't have the facilities to send out disks in response to all the shareware distributors requesting a disk. If you're a fairly large shareware distributor, I can provide you with a floppy disk. If you'd like to request a disk, please send me a copy of your current catalog. Your catalog must satisfy the following requirements: - It must be commercially printed. I am unable to accept catalogs on disk, catalogs which have been duplicated with a photocopier or mimeograph machine or catalogs which have been created using a dot matrix printer. - It must be comprised of descriptive listings for the shareware it offers. Such a listing should be at least four or five lines describing the software in question. - It must explain in a clear and prominent way that the software being offered in the catalog is user supported software, that paying your company for it does not constitute registering it and that users who buy your disks and use the programs on them are expected to register their software if they continue to use it. - If you don't have a catalog which meets the above description, you can obtain a copy of the shareware disk for $10.00 (US). Please note that I will send you one disk. I can send you updates of the software if you're able to provide me with an account of how many copies of the package you have distributed.