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Some BASIC programs m j}ay contain instructions in their program listings. LIST to read. -To view DOCumentation files one page at a time, k} press [START], [Return], or the Joystick Trigger to display the highlighted DOC file. Pressing the [Esc] key cau l}ses a return to MENU. -To print out a hard-copy of any DOCumentation file, [Q]uit the MENU, boot DOS, and then from m} DOS, use the (C)Copy command: D:Filename.DOC,P: -To use this great MENU program on your own disks, simply n} copy the file "AUTORUN.SYS". D:Filename.DOC,P: -To use this great MENU program on your own disks, simply ! _____________________ MATHPAD PROGRAM FILES _____________________ NAME EXT SEC DESCRIPTION ---p}- --- --- ----------- MATHPAD1DOC 006 This listing MATHPAD2DOC 017 A Mathpad "walk-thru"q} MATHPAD3DOC 067 Complete set of instructions for MathPad MATHPAD4DOC 022 Matr}hPad program outline MATHPAD BAS 173 MathPad Program DEMDT3 MPD 002 Data type 3 s} demo file DEMDT5 MPD 002 Data type 5 demo file DEMDT2 MPD 005 Data type 2 t} demo file DATASET FMT 002 .MPD dataset format/shell - Textpro file y _____________ USING MathPad _____________ By M.K.O'Neill (c) 1988 The Mv}athpad disk contains sample data files to demonstrate its features and capabilities. The following is a brief 'walk-thw}ru' of the program: 1) Boot the Mathpad disk. Select MATHPAD.BAS from the menu. 2) After the program loads andx} displays the main menu, select the SAVE/LOAD (S/L) option (=3). 3) Select the directory option from thy}e S/L menu to list the Mathpad files (*.MPD) on the disk. There are three demo files: DEMDT2, DEMDT3, DEMDT5z} for data types 2,3 and 5. 4) Back at the S/L menu, select the load option. At the file name prompt, enter D{}EMDT2. After confirming that you want this file, it will be loaded and a file summary will be displayed.|} 5) Return to the Main Menu and select the INPUT DATA option (1). From this menu, select the VIEW DATA opt}}ion (4) to display the data. 6) Return to the Main Menu and select the ANALYZE DATA (A/D) option (2). From ~}the A/D menu, select the STATISTICAL ANALYSIS option. The results of the analysis will be displayed. }7) Go to the INPUT DATA menu and select the DELETE DATA option (1). Delete all the data when prompted. 8) }Load the DEMDT3 file, and VIEW if you care to. 9) From the A/D menu, select the LEAST SQUARES FIT option. }Enter 3 as the order of the polynomial fit. The program will calculate coefficients to provide an optimum fit} to the data. These coefficients are saved for subsequent use. 10) Back at the A/D menu, select the ANALYZE} FUNCTION option. From this menu you may perform a number of operations with the derived polynomial. 11) Ba}ck at the Main Menu, select the PLOT DATA option. Select the the four quadrant plot. Set the x scale at 7.5 a}nd the y scale to 90, then plot (and dump if you wish). 12) The last demo is a solution of simultaneous line}ar equations. Load DEMDT5 and use the SOLVE MATRIX option in the A/D menu. That's about it as far as the demo} files are concerned. Try entering your own data to analyze. The program disk contains a .MPD dataset 'shell', DATASET}.FMT, to assist you if you wish to create a dataset with a text editor. Be sure to read the MATHPAD.DOC file. } Thanks and good luck! eate a dataset with a text editor. Be sure to read the MATHPAD.DOC file. ' _________________________________ MathPad _________________________________ MathPad 8 Bit Numbe}r-Crunching _________________________________ by M.K. O'Neill (c) Jan/88 _________________________________ } INTRODUCTION ____________ Since their first development, digital computers have been used in engi}neering and scientific applications. While Fortran continues to be the principal tool for such applications, most pr}ogramming languages, including Atari Basic, lend themselves easily to the solution of mathematical equations through }either analytical or numerical methods. Mathpad is a Basic program for data analysis which uses standard techniques }found in any numerical analysis subroutine library. It will perform statistical analysis, linear regression, least s}quares(polynomial) fits, funtional analysis on a user-defined polynomial and will solve simultaneous linear equations}. It also features simple screen plots, screen dumps to print (for Epson compatable printers), and disk drive suppor}t. Datasets may be entered and edited in Mathpad or may be prepared using most text editors (e.g. T:EDIT, ANALOG, May,} 1987). USING MATHPAD _____________ Since Mathpad is menu and prompt driven, the best way to} become familiar with its features is to use it. Type in the program listing and SAVE it to disc, then RUN the progr}am. At first, the title screen will appear while the two machine language routines are set up. The main menu will a}ppear and present you with the options outlined below. DATA ENTRY __________ This menu off}ers the choice of entering, editing, deleting or viewing data. There are five kinds of datasets which can be entered:} 1) Single data points - this is a dataset composed of single points (a sample) which can be analyzed stati}stically. 2) Single data points (typed) - this is also a dataset composed of single points, but each poin}t is identified as belonging to a subset by a number (e.g. 1=male, 2=female). Up to ten subsets can be s}pecified and each subset will be analyzed statistically. During data input you will be prompted to enter }both the value and type for each point, separated by a comma. At the end of input, you will be prompted to in}put an identifier for each data type. 3) Paired data points - this is a dataset containing paired data } points (e.g. X versus Y). You will be prompted to enter two values, separated by a comma, for each point. T}his data may be analyzed in a number of ways and/or ploted on the screen. 4) Polynomial function - an Nth } order polynomial is a function expressed as F(x)=a0*x^0 + a1*x^1 + ... + aN*x^N. The a0,a1,..aN are the } coefficients of the polynomial. You will be prompted to enter the order (N) of the polynomial and then } the coeficients in ascending order. 5) Simultaneous equations - a linear equation in N variables is a fu}nction expessed as b*y= a1*x1 + ... + aN*xN. a set of N such equations may be treated as an augmented (N by } N+1) matrix and solved for x1,x2,..xN. You will be prompted for the number of equations(N), and each mat}rix row(N+1 values) is input (a1,a2,..aN,b). After data entry is complete, you will be asked if you wish to }change the labels for the data from the defaults (x data,y data). For data types 1,2,3, individual points may be edi}ted or deleted. Each data point is identified in the delete or edit option by its order in the data array. The view} option will display the data for all dataset types but 4. ANALYSIS ________ There are }several options available for data analysis: 1) The statistical analysis routine work with data types 1 and 2.} It will calculate the mean, variance, standard deviation of the sample, and the unbiased estimator of the } population standard deviation. These values are displayed as MEAN,VAR,SIGS, and SIGP. 2) The linear regressio}n routine will find the best linear (straight line) fit to a set of paired data points (type 3). The slop}e of the line, the Y intercept (Y(x=0)), and the correlation factor (CORR) will be displayed to the screen. } The correlation factor is an indicator of the 'goodness of fit', with a value of 1 corresponding to a perf}ect fit. The coefficients are saved for plotting or functional analysis. 3) The least squares routines } will fit a polynomial of order N (input) to your data (type 3). Again, the coefficients are saved for plott}ing or functional analysis. 4) Selection of functional analysis produces a sub-menu where analysis of eithe}r input or calculated (see 2,3 above) polynomials may be performed. Options include the calculation of d}erivatives, integration, finding real roots and data corelation. 5) The solve matrix routine will find the }solution for a set of simultaneous linear equations in matrix form (data type 5). SAVE/LOAD } _________ Data may be saved to, or loaded from disk. All Mathpad data files use the .MPD extender. Drives 1} or 2 may be selected and a directory function (for *.MPD files) is provided. PLOT DATA _}________ Data (type 3) and functions may be plotted in either the upper right quadrant or over all four quadrants. }The routine will prompt you to specify the scales of the x and y axis. The title of the dataset, and the grid scales} are written to the plot. A beep will sound when the plot is complete. The plot may be dumped to print. ________}_________________________ OTHER FEATURES _________________________________ In addition to the main program } options described above, Mathpad has a number of utility features that are useful: SCREEN DUMPS } ____________ At any point in the program where input or output data are displayed, the option of a screen dum}p is offered. ERROR HANDLING ______________ The program traps most errors and will return you }to the point of error following a trap, so you won't often find yourself hitting the reset key. Following a trap, the} program will beep and display the error code and a prompt. CREATING DATA FILES ___________________} In addition to the data entry routines in Mathpad, datasets may be prepared using most text editors. This may be u}seful with large datasets where a full-featured editor will speed up entry and editing. A Mathpad data file is forme}d from a set of records, each ending with a EOL (CR) character. The format of a file, by record, is as follows: 1) }Dataset title (36 chrs) 2) Data type (1,2,3, or 5) 3) Number of data points or pairs (type 1,2,3) or the number of} equtions/unknowns (if type 5) 4) Data format (field length) - see record 8 5) X data name or column ide}ntifier (10 chrs) 6) Y data name or row identifier (10 chrs) 7) Typed data identifiers (10 chrs) - required o}nly if if data type 2 is being input. An identifier musr be specified for each subset 8) The data to be in}put. The load routine expects a single point per record for type 1, two points per record for type 2 (va}lue,type), two points per record for type 3 (x,y) and N+1 values for a linear equation (type 5). All data } should be formatted using the field length given in record 4. If this seems complicated, just create a small} file with Mathpad, save it to disk, and then look at it with your favourite text editor. You'll quickly become adep}t at creating data files in this way. ABOUT THE PROGRAM _________________ Mathpad uses standard }numerical techniques which are described in detail in any elementary text on the subject. All polynomials are evalua}ted using Horner's method. The real roots of a polynomial are found using the Newton-Rapheson method. Matrices are }solved using Gaussian elimination. While these methods are generally accurate and reliable, it should be recognized }that no numerical method is foolproof . Caution is appropriate. Data arrays are DIMensioned using the variables giv}en in line 9100. The data array is set up to accept 100 points. This may be increased to 1000+, but owing to memory }limitations, the plot option will fail. The program rounds values to three decimal places for display purposes only }(Line 3500). If you require more precision, increase ICON1 (Line 9105) by a factor of 10 for each additional decimal} place required. Mathpad uses two "classic" ML subroutines, both from COMPUTE! books: i) the "49 second second scree}n dump" (Line 9145), and ii) the "Graphics 8 text plotter" (Line 9160). Thanks to David Newcom and Douglas Crockford f}or these two useful routines. A FINAL NOTE ____________ Mathpad was written to demonstrate } how 'number crunching' could be implemented on a small computer. I hope it will be useful to you.en to demonstrate j ___________ MATHPAD 1.0 ___________ By M.K. O'Neill (c) 1988 PROGRA}M STRUCTURE ----------------- MATHPAD is constructed from a set of general-use Atari Basic subroutines. The} following is a top-to-bottom summary of the program structure: UTILITY SUBROUTINES ___________________} Line 30-38: Screen paging prompt. Entry points at lines 30 and 35 Line 40: Trap for keyboard entry error} Line 50-51: General use keyboard input Line 60: Sound routine Line 70: Trap for keyboard entry } error Line 80: Screen header Line 90-91: Exexcution error identification and display } Line 100-120: Graphics 0 screen dump DATA ENTRY MODULE _________________ Line 400-4}35: Main menu Line 450-490: Delete data routine Line 500-590: Data entry routines Line 600-620: Data editing routine} Line 650-723: Data display routines Line 750-753: Data input routines. Called by } edit and entry routines Line 770-790: Data (X,Y) name input. Called by } entry routine Line 800-890: Typed data identifier input. Called by entry } routine Line 900-990: Matrix data input. Called by entry routine DATA ANA}LYSIS MODULE ____________________ Line 1800-1836: Main menu Line 1900-2090: Statistical analy}sis Line 2100-2190: Linear regression routine Line 2200-2290: Least squares polynom}ial fit routine Line 2300-2335: Functional analysis sub-menu Line 2500-2525: Calcul}ate F(x), F'(x), F''(x) for a given value x Line 2600-2730: Find real roots } of F(x) by interval search and then Newton- Rapheson method }Line 2750-2760: Correlate data with F(x) Line 2900-2950: Integrate F(x) over range }Line 3000-3090: Solve Simultaneous linear equations ANALYSIS SUBROUTINES } ____________________ Line 3500: Round value to 3 decimal places for display Line 3700-3725:} Calculate F(x), F'(x), F''(x), and the integral of F(x) using } Horner's method Line 3830-3880: Solve matrix using Gauss' method Line 390}0-3953: Statistical subroutines Line 3960-3970: Initialize arrays PLOT MODULE } ___________ Line 6000-6460: Main plot routine Line 6500-6550: Plot grid, put text on screen Line} 6600-6630: Plot function on screen Line 6700-6750: Plot data on screen Line 6900-6}950: Dump Graphics 8 screen to printer SAVE/LOAD MODULE ________________ Line 7000}-7040: Menu Line 7050-7052: Toggle drive #1, #2 Line 7100-7250: Save data routine Line 7300-7450: }Load data routine Line 7600-7650: Directory routine MAIN MENU _________ Line 8921-8925: I}nitialize data variables Line 9000-9021: Screen setup, title page Line 9100-9135: D}imension arrays, initialize string variables, open K: channel, post } screen message Line 9145-9151: The venerable "49 second" graphics 8 scr}een dump routine Line 9160-9171: A ML routine to put text on a Gr.8 }screen Line 9200-9999: Mathpad main menu and exit routine put text on a Gr.8 Q.UCUSBLINERESEECSDTITLSPRBLDODDNDAAIDTYNDIMNDATINNRECPXNAMYNAMA1DTYPXIYISLDUMFM }AOIINPXXSVARYSNUSIGSXYJAOPFDFDDFDFDDFDFDDFDRTCONCONINTFICONWASIGPNDIMNDIMNDIMXYXSCINC }YSCINCGR08GDROFNNAMEXTNDIMCON@2@$$A@@ $ $ } @ @@Ae@@A@@@A }<  F  A@P dd@P @ !; " #@$@%@&A' (@V)@) }A*\ +AA, -@A. /0A@1@&234@P56@E789 }:;<=A> ?>@>ABAAC DAEF F@G@H@!}IA`J@K@ L?PM@N@O~ P Q R@S) T! 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