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G r a F USERS MANUAL Version 1.0 Written by Dan L. Kunkel 8 Mansfield Ave Burlington, VT 05401 First Edition, January 1989 {C} Copyright 1989 by Dan L. Kunkel. All Rights Reserved. DISCLAIMER Written by Dan L. Kunkel for the IBM PC,XT,AT or compatibles using DOS 2.0 or later. GraF, GraFDemo and the accompanying documentation is copyrighted by the author. You may make copies of the demo program and documentation files for your own use, and you may copy the files for others. You may not charge for such copies, or in any other way sell the program or otherwise attempt to make money from it or any modified version of it. An exception to the above is granted to RECOGNIZED USER'S GROUPS, which are hereby authorized to charge a small amount (not to exceed $3.00) for media, postage, handling, etc of the demo version. For use by corporations and other institutions, please contact me for a site licensing agreement. The source, customizing, and special licensing are also available upon written request. Purchase orders and invoicing are acceptable. While every precaution has been taken in the preparation of this software and manual, Dan L. Kunkel assumes no responsibility for errors or omissions. Neither is any liability assumed for damages resulting from the use of the information contained in this manual. I do not warrant that the documentation is accurate, or that the program operates as designed. I will not be liable for any damages of any kind sustained through the use of this program. By using this software, you agree to this. Your comments, suggestions, and friendly criticisms are welcome. IBM is a registered trademark of International Business Machines Corporation. HP and HP Laser Jet is a registered trademark of Hewlett Packard Corporation. AT&T and AT&T PC6300 are registered trademarks of American Telegraph and Telephone. EPSON is a registered trademark of Epson America, Inc. If you are using GraF Demo and find it of value, a copy can be purchased for $20. Makes checks payable in U.S. dollars to Dan L. Kunkel. Thank you. {C} Copyright 1989 by Dan L. Kunkel. All Rights Reserved. PREFACE Welcome to GraF. GraF is a complete graphing system which will accurately plot experimental data as well as mathematical functions. GraF is intended for the those people who need to graph data or functions frequently and efficiently. GraF allows you to do the following: Plots graphs with up to 200 data points. View Spline Interpolations of your data. Take both the first and second derivative of your interpolated data. View user specified mathematical expressions. Find the Derivative of mathematical expressions. Integrate mathematical expressions. Performs least squares data modeling to Polynomials, Fourier Series, Exponential, Natural Logarithms, and Power. Store and retrieve data from the disk. Equipment Requirements: One of the following: IBM PC,XT,AT, AT&T PC6300, or any IBM compatible that has at least 312 K of Memory. The following graphic display standards are supported: CGA Graphic Adapter EGA Graphic Adapter VGA Graphic Adapter AT&T PC6300 High Resolution Mode Graphics Adapter. Optional Equipment: Hewlett Packard Laser Jet Printer. Epson/IBM compatible dot matrix printer. TABLE OF CONTENTS 1. INTRODUCTION ............................ 1 2. PROGRAM OVERVIEW ........................ 2 3. GETTING STARTED ......................... 4 4. TUTORIAL ................................ 6 5. REFERENCE ............................... 10 6. APPENDICES .............................. 16 Calculator ............................ 16 Data Editor ........................... 17 Line Editor ........................... 18 Data File Format ...................... 20 File Selector ......................... 21 INTRODUCTION GraF Version 1.0 is a user-oriented graphing software package. It is intended for the college student, and assumes the user has very little computer experience. The pop up menus make the program very easy to learn and use. The software is designed to integrate data plotting with data analysis. It will perform least squares fit, cubic spline interpolations, and mathematical calculations of functions you type in. Using this program will save you valuable time when plotting your data, as well as assisting in the analysis of your data. How to use the manual The manual is intended to familiarize the user with the operation of the program. If you're the type of person who hates to read documentation, try browsing the next section, then run GraF and experiment with the sample data. The tutorial will illustrate most of the functions of the software in a clear, concise manner. Page 1 PROGRAM OVERVIEW Along with the standard graphing options provided with most any graphing program, GraF provides additional support with spline interpolation, least squares data fitting, and the plotting of mathematical expressions. The program has functions which allow you to edit, save or retrieve your data. It automatically plots your data to the screen, and allows you to change the scale, graph title, and axis labels. It is also possible for you to control the existence of data symbols, error bars, and lines connecting the data points. The data fitting section performs a "Least Squares" or best fit of your data to a simple mathematical expression. The mathematical forms include: Fourier (Sines, Cosines), Polynomial (a * x^2 + b * x + c), Exponential ( a*exp(b*x) ), Power (a*x^b) or Logarithmic (a * ln(b*x)). The coefficients will appear on the plot along with the "Standard Deviation" or quality of the fit. Cubic splines are also included in the software. A spline is a "smooth curve" which goes through all of your data points. Included in this section is the ability to see the "Derivative" or slope of the spline (the rate of change of the spline), and the "Second Derivative" which the rate at which the derivative is changing. Finally, the program will allow you to specify a mathematical expression such as "-3 * x^2 + 0.23 * x + 12" and will it compute the value of the function at any x value. The Page 2 program can also perform calculus manipulations with your function such as Differentiation and Integration using numerical methods. GraF will also plot mathematical expression along with your data simultaneously. Page 3 GETTING STARTED What You Need to Get Started - Any IBM PC, XT, AT or IBM true compatible computer. - Must have at least 312K of random access memory (RAM). - At least one 360K Disk Drive. - A CGA, EGA, VGA or AT&T graphics monitor. Invoke AT&T high resolution Graphics by including /a after the name of the program. Example "graf /a". - The GraF Software Diskette. Optional Equipment - A parallel or serial serial printer that is either Epson/IBM compatible, or a HP LaserJet. You will also need one 5 1/4-inch, double density floppy diskette to make a working copy of GraF. Refer to your DOS manual if you have any questions about formating a diskette. Page 4 Preparing a Working Copy Before you start the GraF tutorial, you must first complete some preparatory steps. The first step is to make a working copy of the original GraF program diskette that came with this manual. The working copy diskette should be the one you use at all times. The original should be put away to protect it from being damaged or destroyed. Here's how: Step 1 : Turn on your computer, and place your DOS diskette in the Drive labeled A:. Enter the correct time and date. Step 2 : Put your new Diskette in Drive B:, and format with the system. - See your DOS manual's section on formating a diskette if you need assistance. Step 3 : Take out the DOS disk, and replace it with the GraF program diskette. Step 4 : Type "copy a:*.* b:" and press <RETURN>. Step 5 : Put the GraF program disk in a safe place. You may repeat this process any time you need additional working copies. Page 5 TUTORIAL This section of the GraF manual provides step by step instructions to help you understand and operate GraF. Loading the program. If the computer is off, insert the working copy of GraF in Drive A and turn on the computer. Then, enter the time and date, pressing <RETURN> after each. The A> prompt will appear on the screen. If you are using an AT&T PC6300 type: A>graf /a and press <RETURN> to utilize its high resolution monitor. Otherwise type: A>graf and press <RETURN>. After several seconds the Title and Copyright screen will appear. Hit any key to continue with the tutorial. To Quit: Use the <LEFT> and <RIGHT> arrow keys to select "Quit" on the menu bar on the top of the screen, and press <RETURN>. Page 6 Creating Your First Plot: After the Title and Copyright message disappears, the program will display an empty plot and menu bar. You can select a menu option by pressing the <LEFT> and <RIGHT> arrow keys (Number 4 and 6 on the Numeric keypad). Move to "File/Data" and press <RETURN>. Another menu will appear below the menu bar. Select the top entry "Edit/Create Data" using the <UP> and <DOWN> keys and press <RETURN>. A screen containing titles and lists of numbers will appear. Use the instruction box in the upper right corner. REMEMBER to use the <F9> and <F10> or <TAB> and <Shift TAB> keys when moving from one column of numbers to the next. Position the cursor for each item and type in the following data: X axis Y axis 0.664 0.1 1.08 0.25 1.44 0.3 1.80 0.45 2.37 0.5 Pressing <ESC> will abort editing, and plot the data you just entered. Let's save the data. Hit a key to make the menu bar appear, then press <RETURN> to bring up the "File/Data" menu. Move down to "Save Data" by pressing the <DOWN> arrow key several times, and press <RETURN> again. When the program prompts for a name, type "MYFIRST.DAT" and press <RETURN>. Now we want to change the X axis scale so it starts from Page 7 Zero, and ends at 2.5. Hit a key to make the menu bar pop up, then move to "GraF" and press <RETURN>. Move down to "Change Scale", and type <RETURN>. Enter "0" <RETURN> to make the X axis lower limit zero. Move down to X axis upper limit, and type "2.5" <RETURN>. Now press <ESC> to see the new plot displayed. In order to change the Title and Axis Labels, you must first go to that command under "GraF". Change the Title by typing "Spring Constant", <RETURN>. Then change the X axis to "Time^2 (sec^2)", and the Y axis to "Mass (Kg)". Press <ESC> to quit editing, and see the new lables. Let's perform Linear Regression on the data. Go to "Data Fitting", and pick "Linear Regression" from the menu. A straight line will appear adjacent to the line that is connecting the data points. The equation of the straight line can be found in the upper left corner of the plot with the Regression Coefficient of the fit written just below that. Sometimes lines connecting the Y data points are confusing, so let's just have the computer plot symbols at each of the data points. Go to "GraF", "Line Type", and pick "Hide Y Data" from the menu that appears on the screen. Notice that your data disappeared; don't worry, it's still in the computer. Now pick "Symbols" to see your data points plotted with boxes. <ESC> or "Exit" will make the menu box disappear. Let's interpolate your data by moving into the Spline menu and choosing "Interpolate". A smooth curve, also known as a cubic spline will go through all of your data points. Page 8 We can examine the difference between your data and the equation "Y = x^(5/4)/4+0.1" by using the "Calculator". Pick Calculator, Plot Function, and type in "X^(4/5) / 4" and press <RETURN>. After a moment a plot of the function will appear. Now you can visually compare your data to the function. If you have a printer connected, now is the time to turn it on and correctly position the paper. Choose GraF, Print, and select the type of printer output, and press <RETURN>. The computer will think for a short time, and then start printing your plot. When you're all done, pick "Quit" from the menu bar. If your data has been changed, the computer will ask if you want to save it to the disk before quitting. That's all there is to it. Page 9 REFERENCE This section will help you understand all of GraF's many capabilities. GRAPHING BASICS: GraF requires a two dimensional data point - a point specified by an X and Y coordinate. Traditionally, X is the controlled variable, and Y is the measured variable. Due to the computers internal number representation, some weird things can happen at very large or very small scales. This can be remedied by scaling your data before entering it into GraF. GraF has the ability to plot many different lines on the same graph. In addition to your data, the error data can also be plotted. Data Fitting, Spline, and Calculator can each have one line plotted. The lines are drawn automatically when you choose a command from their sub-menus, and can be removed from the plot by choosing either Clear or Remove Plot. Page 10 MENUS EXPLAINED When you run the program, the first thing you will see is an introductory screen. After hitting any key, the program will display an empty plot on the screen, and produce a pop up menu bar. The Menu options include: File/Data This has everything to do with Editing, Loading, and Saving the data. It also lets you change directories and view text files. GraF This controls all the aspects of plotting your data, such as how your data is printed. Other options include Auto-Scaling your data, as well as changing the scale, sorting your data, and printing. Data Fit This menu allows you to choose what kind of Data Fitting to perform, as well as Auto-Scaling the Fit, and Clearing it from your plots. Splines This option allows you to choose the Spline Interpolation or one of its derivatives, as well as Auto-Scaling the spline, and Removing it from your plots. Calculator This will pop up a sub-menu has all the options dealing with the mathematical expressions you would type in. You can evaluate an expression, as well as Differentiating or Intergrating that expression at any point. The plot function option will graph your function on the screen. Auto-Scale and Remove plot will scale your function, or remove it from the plot. Quit Returns you to DOS. Picking things from the menus is easy. Just move with the arrow keys until the desired item is highlighted (NumLock must be off), then press <RETURN>. A faster way is to just type the first character of the command choosen. To return at any time to your graph, just press the <ESC> key. A help document will appear on the screen when you type <F1>. Page 11 FILE/DATA Edit/Create Data This command found in the File/Data menu is used to edit or enter data into the computer. The commands for operating the Data Editor are found in the Appendix. Load / Save These two commands will let you save the data you entered into the diskette, or read it from the diskette after you've saved it. When you're Loading data into the computer, it will let you pick the name of the file from the Directory chooser. The File Selector and File Format are discussed in the Appendix. New/Erase Data New/Erase Data will erase all of the data that is stored in the computer's memory. Directory Directory will let you examine the files contained on the specified diskette. Change dir Change dir displays the current drive and directory, and allows you to change to a specified drive and/or directory. View ASCII File This routine will let you list ASCII files to the screen. The commands it understands are <UP>, <DOWN>, <PGUP>, <PGDN>, <BEGIN> and <END>. Press <ESC> will return you to the program. Page 12 GraF Line Types Y Data/Hide Y data controls whether lines are used to connect each data point. Symbols/No Symbols controls whether the box symbols are placed on every data point. Valid Error Bars/Invalid Error Bars controls the use of Error Bars on your plot. Error Data/Remove Error Data controls whether the Error data is also plotted. This allows you to display two lines at the same time, but you have no control over the attributes of the Error Data Line. Auto-Scaling The program will automatically scale a plot. Entering this command will scale the data currently being used. For instance, Auto-Scaling in the Calculator menu will automatically scale the current Calculator Function. Changing Scale This option will let you change the limits of the plot. You can also choose to have your data plotted on a logarithmic scales. IMPORTANT Since logarithms aren't defined for numbers less than or equal to zero, make sure your data and plotting limits are all positive numbers larger than zero. Title/Axis Labels This option lets you change your X and Y axis labels and plot title. Sort X axis. This option will sort your data into ascending order. Print Graph This command will print the plot on the screen to either a Dot Matrix printer, or a HP Laser Jet printer. The Large Dot Matrix printout will rotate the printout and make it larger. You can choose to have the output sent to a file, by entering the files name, or to the printer by entering "PRN". When you want to print the file that is generated, just type "copy FileName PRN /b". Page 13 DATA FITTING Each Data Fitting routine prints the formula to the plot in the upper left hand corner, and is followed by the quality factor of the fit. Linear Regression This performs standard Linear Regression on your data. The regression coefficient is displayed along with the data. Polynomial Fit This performs a Least Square Fit with a polynomial of degree N which you specify. Fourier Fit This fits the data to Y = A + B*Sin(x) + C*Cos(x) + ... using the least squares method. You can enter the number of terms you want in the fit. Exponential The data is fitted to the form Y = A * exp(B*X) using the least squares method. Power The data is fitted to the form Y = A * x^(B*X) using the least squares method. Logarithmic The data is fitted to the form Y = A * ln(B*X) using the least squares method. Derivative This can be used instead of Fitting your Data, to compute the change of your data divided by the change in X. Auto-Scale This command will automatically scale the plot so that the entire Data Fit will be visible. Clear This function will stop displaying the data fit text and line plotting. SPLINE Interpolation This routine computes and plots the cubic free spline of your data. This spline is then superimposed on the plot. Differentiation This routine computes and plots the derivative of the cubic spline that was created from your data. Second Derivative This routine computes and plots the second derivative of the spline that interpolates your data. Auto-Scale This command will automatically scale the plot so that the entire Spline will be visible. Edit/Create This routine will let you examine and/or change the Spline data. Clear This function will stop plotting the Spline data. Page 14 CALCULATE Expression This routine will return the numerical value of a function at any point. See the Appendix on the Calculator commands. Integrating This routine computes the Integral of your function over a interval you specify. It uses the Adaptive Simpson method. If you don't know what these are, you can find discussions in your nearest Calculus book. Differentiating This routine computes the Differential of your function a a specified point. Information about this can also be found in your Calculus book. Plot Function This routine will let you enter a function of X and plot it. The routine will use the X axis Limits to choose the input range for the function. Auto-Scale This command will automatically scale the plot so that the entire function is visible. Edit/Create This procedure will let you examine and/or change the function data. Clear This routine will stop plotting the mathematical function. Page 15 APPENDIX CALCULATOR GraF contains a full functioned scientific calculator. All operations are performed according to Algebraic Rules. The legal functions include : Addition (+) Subtraction (-) Division (/) Multiplication (*) Factorial (!) Exponential (exp) Natural Log (ln) X to the Y (^) Logarithms (log) Square (sqr) Square Rt (sqrt) Round (round) Absolute Value (Abs) Random Number (RND) Trigonometric Sine (sin) Cosine (cos) Tangent (tan) Secant (sec) Cosecant (csc) Cotangent (cot) Arcsine (arcsin) Arccosine (arccos) Arctan (arctan) CHANGING CALCULATOR MODES: The calculator is in Radian Mode upon startup. Typing "Deg" instead of a mathematical expression will put it into Degree Mode. "Rad" invokes Radian Mode. Hyperbolic Sine (sinh) Cosine (cosh) Tangent (tanh) Arcsine (arcsinh) Arccosine (arccosh) Arctanh (arctanh) Constants and Variables: The constant "Pi" is defined as 3.1415926... The variables X, and Y are understood, but Y is always evaluated as being 0. Page 16 DATA EDITOR The Data Editor is designed to let you easily input and/or edit data. It is invoked every time you "Edit/Create" data. The data editor commands include the following: <UP> Moves up one line. <DOWN> Moves down one line. <PGUP> Moves up a page. <PGDN> Moves down a page. <F1> Invokes a Help Screen. <F5> Copies the value of the entry that is being edited to the line numbers you specify. <F6> Copies the values of all the lists of numbers to the line numbers you specify. <F7> Inserts a Line for Data. <F8> Deletes a Line of Data. <F9>, Moves which list you are editing to the left <TAB> one position. <F10>, Moves which list you are editing to the right <Shift TAB> one position. <ESC> Returns to the data plot. Page 17 LINE EDITOR Whenever you are asked to input a name, a string, or a number, the following commands are available: <F1> Displays a help document. <F2> Change the case of the letter at the cursor. <ESC> Escape and go back. <RETURN> You're done, that's it. TYPEOVER AND INSERT MODES The GraF editor has two basic modes: the typeover mode and the insert mode. In typeover (normal mode), anything you type will replace the text currently displayed at the cursor. In insert mode, anything you type will be inserted into the text at the current cursor position, displacing any characters to the right of the cursor. The <INS> key toggles between typeover and insert modes. CURSOR MOVEMENT KEYS GraF uses the following keys for cursor movement: <HOME> Moves the cursor to the first position in the line. <END> Moves the cursor to the end position (following the last character displayed). <LEFT> Moves the cursor to the left one character. This does not erase any characters; it simply moves the cursor. Remember that <LEFT> is the left-arrow Page 18 key on the numeric keypad (key 4), not the backspace key (the larger left arrow next to NumLock). <RIGHT> Moves the cursor to the right one character. <Ctrl LEFT> Moves the cursor to the left one word. A "word" is any sequence of characters bounded by one or more spaces; the cursor will be placed on the first character of the previous "word". <Ctrl RIGHT> Moves the cursor to the right one word; it will be placed on the first character of the next word. TEXT DELETION KEYS The following GraF editor keys are used to delete text: <DEL> Deletes the character at the cursor position. <BACKSPACE> Deletes the character to the left of the cursor position. This is known as a destructive backspace; it is exactly equivalent to keying <Left> followed by <Del>. <Ctrl END> Deletes all characters from the cursor position to end of the command. Page 19 DATA FILE FORMAT The File format is a simple ASCII format, which can be edited and changed by any text editor. The format is: Title if the Line is Text. X axis Label if the Line is Text. Y axis Label if the Line is Text. 0,0,0 1,1,0 ... Spaces and many characters can be used instead of commas as delimiters. Page 20 FILE SELECTOR The file selector is designed to make chooseing files easier. The DOS-style mask allows the user control over what files appear in the selector. You can load in a specific file by just typing it's name. After pressing <RETURN>, a box with all of the choices will appear on the screen. File Selector commands: <ESC> Get out without selecting anything. <F1> Displays a help document. <UP> Moves up one line. <DOWN> Moves down one line. <PGUP> Moves up a sceen. <PGDN> Moves down a sceen. <HOME> Moves to the top. <END> Moves to the bottom. <RETURN> Selects a file or directory. Page 21