Shareware Overload Trio 2

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-------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- -- ┌────────────────┐ │╒═══════════════╧╕ ││ Help File ├───────────────────────────────────── ││ └────────────────────────────────────── ││ ││ AstroDataFitter 3 Least-Squares Equation/Data Fitter ││ ││ Help File Version 3.12 03-01-1994 <ASP> ││ L 10 │ (c) Copyright 1981, 1994 PC SuperComputer Capital, Inc. All rights reserved. Read and understand WARRANTY INFORMATION . Type J twice to read. Instructions on using help file are at end of file. Type K to read. L 20 ╒══════════╕ │ CONTENTS └────────────────────────────────────────────────────────── 0.00 Table of Contents * To quickly jump to Sections, position the Section line number * on the │JUMP│ line (line 12) and type J or type Lxxx (enter) * where xxx is line number. For example, to jump to line 139, * type L139 (ent). Type S or R to skip back/forth to Sections. L 30 SECTION TITLE PAGE│LINE 0.00 ... Table of Contents ................................... 1 25 1.01 ... Equations Display, What is it? ...................... 3 101 1.02 ... How to Use the Calculator. .......................... 5 188 1.03 ... How to find Things With Auto-search Function ........ 6 236 1.04 ... Summary of Letter Commands Used in Equations ........ 6 254 Display 1.05 ... F1-F10 Keys, Commands assigned. .................... 18 817 L 40 1.06 ... Command Sequences Used to Perform Special .......... 19 845 Operations 1.07 ... Editing Keys: Functions During Text Entry .......... 19 866 2.01 ... Entering Equations Into the Program ................ 21 965 2.03 ... Writing Equations: Definition of Terms ............. 23 1015 2.10 ... Rules for Writing Algebraic Expressions, ........... 25 1114 ------------------------------------------ 0.00 -- Table of Contents --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 2 -- Formulas and Equations 2.15 ... Rules for Evaluation of Parentheses ................ 27 1214 2.20 ... Rules for Evaluation of Intrinsic Functions ........ 27 1236 2.25 ... Rules for Evaluation of Mathematical Operations .... 28 1259 L 50 2.30 ... Glossary of Intrinsic MATH FUNCTIONS and ........... 29 1298 Function Operators 2.40 ... Numbers: Format-free, Examples of Formats .......... 34 1524 2.42 ... Controlling the Number of Decimal Digits ........... 34 1560 2.45 ... Maximum Number of Equations, Variables and ......... 35 1598 Constants 2.46 ... Maximum Number of Data Points and Data ............. 36 1630 Coordinates 2.50 ... Errors During Equation Evaluation and Elsewhere .... 36 1649 3.01 ... Directory Screen: Commands During Display .......... 37 1669 L 60 3.05 ... Commands Used While Plot Screen is Displayed ....... 39 1767 4.01 ... Commands Unique to this Program AFIT3.EXE. ......... 41 1862 4.02 ... Commands Used to Manipulated Data Points and ....... 43 1955 Their Values. 4.04 ... Introduction to Fitting Equations to Data by ....... 45 2049 Nonlinear Least-Squares Regression. 4.06 ... Finding Best Values of Transistor Parameters ....... 48 2192 from Experimental Data by Nonlinear Least Squares. 4.08 ... Automatic Least-squares Polynomial Regression ...... 54 2461 L 70 (Linear Least Squares) 4.10 ... Advanced Functions using Data and Active ........... 57 2610 Equation 4.12 ... Reading External Files of Data Only ................ 60 2716 5.01 ... Summary of Common WARNINGS During Calculations. .... 61 2774 5.05 ... Summary of ERRORS during evaluation of equations ... 63 2874 6.01 ... Setting Foreground/background Colors of Main ....... 65 2960 Equations Screen and Program 6.05 ... Clock Screen: Commands During Display .............. 66 2992 6.10 ... Apostrophe Commands: What They Do and How to Use ... 67 3055 L 80 Them 6.12 ... Apostrophe Commands Unique to AstroDataFitter. ..... 70 3196 7.01 ... Information After Program Name on DOS Command ...... 70 3217 Line. How the Program Uses It and What It Does. 8.01 ... Product License and Warranty. ...................... 72 3278 8.03 ... User Support. ...................................... 73 3344 8.04 ... Ombudsman/Arbitration Policy. ...................... 74 3365 8.05 ... Product Information and How to Order Complete ...... 74 3387 Package. 8.06 ... Software Included in Astro 3 Registration .......... 76 3477 L 90 8.07 ... Order/Registration Form ............................ 78 3562 8.08 ... Instructions for Manually Installing Package. ...... 79 3627 ------------------------------------------ 0.00 -- Table of Contents --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 3 -- 8.09 ... Interested in Becoming the Author of Your Own ...... 80 3669 Interactive Application File? 9.01 ... Help File: Summary of File Viewing Commands ........ 81 3691 ╒═══════════════╕ │ EQUATIONS ??? └────────────────────────────────────────────────────── L 100 1.01 Equations Display, What is it? ──────────────────────────────────────────────────────────────────────── The equations display is the spreadsheet portion of AstroDataFitter 3. It contains the equations, variable names, variable values and a comment. Most operations are performed while in the equations display through the use of characters, letters, combinations of characters with letters and the "F" keys. The blinking cursor prompt ">" is always positioned between a variable name like TIME and its current L 110 value which might be 2.3. For example: TIME => 2.3. Numbers and math operations are passed to the variable on which the blinking cursor resides. Other characters and combinations serve as commands to activate certain functions such as integration or derivitization. Certain commands require that two characters be typed consecutively. Commands such as "!C" or "@C" mean that the "!" or "@" is typed first and the "C" next. Representations such as "(esc)", "(enter)" and "(space)" represent single keystrokes. L 120 To change the display colors to high-intensity white on blue type Q when the highlight bar is lighted on the EQU below. 'EQU 'COL HWHITE BLUE 'HELP An illustration of the equations display for the equation of a straight line: Y=M*X+B with the blinking cursor on variable X is shown below. A comment which describes the L 130 equation is listed first. The equation and the value of its dependent variable Y (=4) is listed next. The current time and date are listed in the middle of the screen. The three independent variables B, M and X are listed in alphabetical order. Finally, a summary of keys and functions is displayed at the bottom of the screen. The last line scrolls through additional commands and is not shown. ----------------------------- 1.01 -- Equations Display, What is it? --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 4 -- ----------------------------------------------------------------------- --- Comment --> Equation of a straight line. L 140 Y=M*X+B Y = 4 12:23:04 03-07-1981 B = 4 M = -2 X => 0 L 150 F1 hlp, F2 appl hlp, F3 exit, F4 shl, F5 com, F6 equ, F7 dir, F8 get, F9 ----------------------------------------------------------------------- Definitions of terms used to define an equation. ■ EQUATION. A formula, expression or recipe directing the program on how to execute mathematical operations such as Y=M*X+B which is the mathematical representation of a straight line (Y. vs. X) with slope M and y-intercept B. Equations are written in a symbolic language which is identical to how L 160 they would be expressed if written in the popular computer language BASIC. In this equation Y is assigned the value of M multiplied by X and then added to the value of B. ■ DEPENDENT VARIABLE. Unique name associated with every equation and its value is usually the object of a calculation such as Y in Y=M*X+B. ■ INDEPENDENT VARIABLE(S). Name(s) always to the right of the equal sign such as M, X and B in Y=M*X+B. Independent L 170 variables are always used to calculate the values of the dependent variables. ■ STORAGE VARIABLE(S). Names that are generated by simple assignment statements entered in the equations display such as (space) PI=3.1415926 (enter). They are similar to independent variables and can be used in all equations, expressions and calculations. The storage variables and their values are saved and recalled separately from the equations using the "!]" and "![" commands. Their values are usually L 180 hidden unless requested with the "Z" or "Y" commands which toggle through their names or by typing the variable name followed by equal sign: (space) VARNAME= (enter). ----------------------------- 1.01 -- Equations Display, What is it? --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 5 -- ╒════════════════╕ │ CALCULATOR ??? └────────────────────────────────────────────────────── 1.02 How to Use the Calculator. ──────────────────────────────────────────────────────────────────────── L 190 The "blinking cursor" or "=>" is located between a variable name and its value. It begins the AFIT3 command line just like a DOS prompt. Information is passed to the program by typing appropriate characters. Just about any calculation can be performed and stored by assigning its value to a variable name, one that already exists or a new one. Variables that do not appear on the equations display screen are called "storage variables". For example, if the cursor is on variable B, then one can perform a calculation and save it as a storage variable named Q1: L 200 ----------------------------------------------------------------------- --- Comment --> Equation of a straight line. Y=M*X+B Y = 4 12:25:04 03-07-1981 B => q1=23.45+56.78+12.98-34.56-12.78 (enter) X = 0 L 210 F1 hlp, F2 appl hlp, F3 exit, F4 shl, F5 com, F6 equ, F7 dir, F8 get, F9 ----------------------------------------------------------------------- When "(enter) is typed, the program will evaluate the expression, assign its value to Q1 and display the result on the time/date line. Note, because most letters represent commands, it is wise to start such calculations with a space. Expressions can reference any previously defined variable: L 220 dependent, independent or storage. For example (space) x=2*B-y+3*m (enter) or q1=q1+67 (enter). The current values of storage variables can be displayed with the storage toggle commands "Y" and "Z" or by typing their name followed by the equal sign and enter. For example, (space) Q1=(enter). Storage variables can be used in the equations, if previously defined. Multiple assignment can be made with the 'VAR apostrophe command. For example: 'var y=3 b=4 x=-5 (enter) The storage variables are saved independent of the equations with the command "!]". See below for more discussion on L 230 --------------------------------- 1.02 -- How to Use the Calculator. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 6 -- storage variables. ╒═════════════╕ │ AUTO-SEARCH └───────────────────────────────────────────────────────── 1.03 How to find Things With Auto-search Function ──────────────────────────────────────────────────────────────────────── This entire file can be automatically searched for words, phrases and other characters using the auto-search command "A". L 240 Type "A" and then enter the characters. Search is in uppercase and is case-insensitive. To continue the search, type "A" repeatedly as required until wrap around occurs. To perform another search, it may be necessary to first type "(space)" then "A". For example, to find "Help File:", type "A", then (end esc) help file: (enter). However, this will only get you back to this line because the search starts at the top of the screen! Type "A" again to continue and find another "hit". Type "A" a few times to get back to here. L 250 ╒══════════╕ │ COMMANDS └──────────────────────────────────────────────────────────── 1.04 Summary of Letter Commands Used in Equations Display ──────────────────────────────────────────────────────────────────────── The following discussion may assume that the "default" equations or amortization equations are currently being displayed. To load these equations from the main equation display, type (F6) or "!/" and type (end esc) "" (enter) in L 260 response to the "-- ? Equations ->" prompt. **** Commands, keystrokes, functions and explanations follow **** -> Activate variable: A !A @A Use "A" to activate an equation and its dependent variable. Used to mark equations which participate in other commands like the "G" and "D" commands used for integration and differentiation, respectively. Only active equations are L 270 integrated and differentiated. Also used to specify equations set equal to each other in the intersection command "U" or plotted with the plot command "P". Initially, all equations are active. Inactive equations do not have an "=" following variable name. Use !A to activate all dependent or independent variables at once. The location of the cursor determines which ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 7 -- set. Use @A to activate all variables at once. One can also use the apostrophe command 'ACT VARNAME (enter) to perform activation. See below. Use the commands I, !I or @I to inactivate variables and equation(s). L 280 -> Background/foreground colors: !N @N "!N" toggles next foreground color. Use "@N" to toggle next background color. Colors are normal-intensity black, blue, green, cyan, red, magenta, brown and white and the high-intensity shades. For monochrome monitor, default values are recommended. Color settings are saved with equations. If fore/back colors are equal then displayed info becomes invisible. Use "!(esc)" to reset monochrome colors: Fore, L 290 white (green); Back, black. "!(esc)" sets monochr colors: Fore, white (green) #7; Back, black #0. "@ (esc)" sets monochr colors: Fore, black #0; Back, white (green) #7. One can also use the apostrophe command 'COL color1, color2 (enter) to perform this function. 'COL (enter) resets monochrome colors. See below for more details. -> Bottom line command scrolling: J !J @J K !K @K "J" toggles to previous command menu display at bottom of L 300 screen. "!J" turns on auto-scrolling about every 10 seconds. "@J" turns off auto-scrolling. "K" toggles to next command menu display at bottom of screen. "!K" turns on auto-scrolling about every 10 seconds. "@K" turns off auto-scrolling. -> Calculate dependent variables: C (enter) (esc) "C" calculates the values of all dependent variables using the current values of the independent and storage variables. "(enter)" calculates dependent variables if used after a valid L 310 number or allowed expression is entered. "(esc)" recalculates equations and redraws the display. Also, use the apostrophe command 'CALC (enter) to recalculate without entering a variable. -> Chaining calculated values to other equations (overlaying equations) Use "@[" to get a file of equation(s), comment and variable status only. Common variables are assigned existing values and new variables are initialized to 0.0. Allows overlay or chain L 320 operations to other equation(s) with identical variable names. ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 8 -- -> Chaining to other ASTRO3 programs: 'CHAIN The 'CHAIN apostrophe command is used to switch to another ASTRO3 program and pass it the current equations, dependent and independent variables (as file A.EQU) and storage variables (as file A.EQU). CALC or C is used to designate AstroFormulaCalculator 3. SOLVE or S is used to designate AstroEquationSolver 3. FIT or F is used to designate L 330 AstroDataFitter 3. At the blinking cursor, type 'CHAIN C (enter) to chain to AstroFormCalc, type 'CHAIN S (enter) to chain to AstroEquationSolver and 'CHAIN F (enter) to chain to AstroDataFitter. In AUTOEXEC.BAT, be sure to set a PATH to where the ASTRO 3 programs can be found and set the environment variable ASTRO3 to that same path. -> Changing displayed precision of dependent variables: !\ @\ Use "!\" for the single-precision display (default) of L 340 dependent variables of equations with var name displayed before current value: ABC = 1.234567. Use "@\" for the double-precision display of dependent variables of equations without variable name displayed before current value: = 1.234567890123456. To see the full precision of an independent variable, type "\". and then type (enter) to return to the blinking cursor ">". Also, use the apostrophe commands 'PRE SINGLE (enter) or 'PRE DOUBLE (enter). -> Changing number of displayed decimal digits in main equation display L 350 The number of decimal digits displayed in the main equation display can be globally changed with the 'DEC apostrophe command. For example, to set 2 decimal digits, type 'DEC 2 (enter). To set none, type 'DEC 0 (enter). To reset, type 'DEC (enter). The decimal operator attached to a variable name will override the global default. For example, a variable named MONEY.2 will always display 2 decimal digits no matter what the global default. Global defaults also apply to the displayed values of the storage variables and numbers L 360 displayed on the plot. -> Clock display: !C Use "!C" to display full-screen clock/calendar in which the alarm is set. Type $ to exit back to the equation display. See below for a summary of the clock commands. Also, use the apostrophe command 'CLO (enter) to jump to the clock. ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 9 -- -> Copy an equation L 370 Move the cursor to the desired equation, type "@/" and type "(esc) or "(ctrl Q)" to exit to the equation display without any changes. Remember that the immediate calculation buffer (command "|") now contains this equation. Type (F6) or "!/" to edit the displayed equations. Move the cursor to the location where the equation is to be inserted and type "(alt 9)" to insert. Remember to add spaces where needed to separate equations and remove or change the other equations/dependent variables. Also, the name of the dependent variable of each L 380 equation must be unique. Also, see command "!F", "@F", "!M", "@M", "!L" and "@L" for other ways to copy equations. -> Cursor movement: B F L M N arrow keys (tab) (shift tab) (backspace) "B" and (shift tab) move the cursor ">" backwards to preceding variable. Also use (backspace) for the same purpose. "F" moves the cursor ">" to the first dependent variable "L" moves the cursor ">" to the last independent variable. "M" moves the cursor ">" to the middle or first independent variable. "N" L 390 and (tab) move the cursor ">" to the next variable. Also use (enter) and (ctrl enter) for the same purpose. Arrow keys - Use edit keys: (Home) (up arrow) (PgUp) (left arrow) (right arrow) (End) (down arrow) (PgDn) to move blinking cursor. Note: Keys (up arrow) and (down arrow) move cursor vertically through variables Keys: (left arrow) and (right arrow) move cursor through independent variables only. The (tab)/(shift tab) and backspace keys moves the cursor to the next/previous variable. L 400 -> Cut and Paste (copying equations): !F @F !M @M !L @L These commands save equations in the immediate calc text buffer. This buffer is accessed by the | command and its contents are further saved in the immediate calc text stack. The contents of this buffer can be "pasted" into equations and other text fields while in the edit mode using the (alt 9) function. L 410 "!F" adds the immediate calc text buffer to the text stack, clears the immediate calc buffer and inserts all INACTIVE equations into it. Inactive equations have variable names that are not followed by an "=" sign. The immediate calc buffer can ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 10 -- be inserted while in the edit mode using the (alt 9) function. Use A and I commands to activate/inactivate equations before using these commands. "@F" adds the immediate calc text buffer to the text stack, clears the immediate calc buffer and inserts all ACTIVE L 420 equations into it. Active equations have variable names that are followed by an "=" sign. "!M" appends all INACTIVE equations to the immediate calc text buffer without appending to the text stack. "@M" appends all ACTIVE equations to the immediate calc text buffer without appending to the text stack. "!L" clears the immediate calc buffer of all text. The buffer L 430 is displayed with the | command. "@L" clears the immediate calc text stack. This stack is used to save the immediate calc buffer. -> Directories of *.EQU, *.STO and *.HLP: (F7) or * !* @* "(F7)" or "*" gives directory of *.equ in directory of specified path. "!*" gives directory of *.sto in directory of specified path. "@*"gives directory of *.hlp in directory of L 440 specified path. Enter path for desired directory in response to prompt. For example: (end esc) \project1\analysis (enter). A filename can be included in path but it must have a period. For example (end esc) \calc\*.dat (enter) or \calc\beta???. If no extension, then the default extension is used. Use cursor keys to locate file and (enter) to select. Program will always load file as EQU, STO or HLP even if extension differs from default. Use (esc) or (ctrl Q) to exit. Use "(space)" to get information about the current highlighted file. L 450 -> Designate coordinate variable O - Designate an independent variable as the coordinate for the X-axis of a plot. One or more equations can be plotted vs. a single coordinate. A ":" designates a coordinate and will appear in place of the "=". Use A or I to change status to active or inactive as required. -> Display all 16 digits of variables value L 460 ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 11 -- \ - Display the full 16 digit precision and position the cursor for editing the number. Type (enter) to return to the blinking cursor. For example, to subtract 1000 from the current number, type "\", and type (end) -1000 (enter). After typing "\", the cursor is always positioned at beginning of number. Type (end) to move the cursor to the end of the number and (esc) to clear the number. Always type (enter) to perform a calculation or exit. -> Display entire comment: (comma key) L 470 Type the comma from the equations display in order to see the entire text of the comment. If the comment ends in "...", then it was terminated because of a lack available screen space. If the "||" pairs are used within a lengthy comment then only the part enclosed by the || is displayed. If a double single quote '' is used, then only the part before the '' is displayed. In these cases, use the comma command to display the full text. Type any key to return to the main equation display. L 480 -> Display/remove storage variables: Y !Y @Y Z !Z @Z "Y" displays the name and value of storage variable, if any. Repeat "Y" to toggle to previous storage variables and so on. "!Y" displays the current storage variable without toggling. "!Z" has the same functions as "!Z". "@Y" removes all storage variables. Program will prompt "? equations" to check for any references to the erased storage vars. If present, they now become independent vars. "Z" displays the name and value of L 490 storage variable, if any. Repeat "Z" to toggle to next storage variable and so on. Up to 256 storage variables can be entered with user-defined names. For example: =PI=3.1415926 (enter) (spc) DATA1=: (ent) Always start first with "(space)" or "=" because most commands begin with letters. "!Z" like "!Y" displays the current storage variable. Use "@Z" to remove the current storage variable. If a storage variable is removed, the immediate calc buffer (command "|" ) is assigned: VARNAME = value. To restore storage var or assign value to storage var which has become independent var, type "|" (enter). Storage L 500 variables are not displayed like other variables. To display the value of any storage variable, type (space) VARNAME= (enter). The storage-index counters are positioned on this variable. Type "!Z" to check and type "@Z" to remove, if necessary. Type "|" to recall this calc, if it needs to be recovered. ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 12 -- -> DOS shell: !E @E "!E" executes DOS command and then returns control to program. L 510 Type the DOS command in response to the prompt. "@E" shells by exiting to DOS. The program is still memory resident. Enter DOS commands and other operations. Must type EXIT (enter) to return to program. -> Edit an individual equation: @/ "@/" edits a single equation and updates the immediate calc buffer with that equation. Move cursor to dependent var of desired equation and type "@/". To inspect and return to L 520 equation display without changes, type "(esc)" or "(ctrl Q)". To update, type changes followed by "(enter)". To remove equation, type the null string "" (enter). Can also be used to copy and/or move equation. See "Entering Equations", below. "@/" always causes immediate calc ( | ) to be updated. -> Entering comment: (F5) / Use "(F5) or "/" to enter or modify a comment only. Comment can contain up to 1840 characters (23 lines). Use "||" pairs L 530 to designate segment of comment to be displayed. If the text is "first part || second part || third part" then the displayed comment will be "second part". Use the double single-quote "''" to indicate the end for the displayed comment. If the text is "first part''second part" then only "first part" is displayed. A double single-quote "''" or four "|" at beginning of text: "'' rest of text" or "|||| rest of text", suppresses comment. To view entire comment, type (comma key). Type any key to exit. The amount of the displayed comment depends on number of equations/variables. Quotes are not required for L 540 strings but may be needed to prevent string compression or loss of desired spaces. Complete equations and comment are save with screen dump. See command "V" for more details. -> Entering equations: (F6) !/ Type "(F6) or "!/" to enter 1 or more equations. Equations are entered in BASIC symbolism. Leave at least one space between each equation. Read rules discussed below. Total equations can contain up to 1840 characters (23 lines). Current maximum L 550 of 63 equations with up to 66 independent and dependent variables. ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 13 -- -> Entering number without calculating main equations: (ctrl enter) To enter a number into a variable of the main equations without calculating the dependent variables type the number and terminate it with (ctrl enter) instead of (enter). -> Escaping from the "? Enter Equation(s)" prompt. L 560 If the equations contain only constants, then typing (esc) will result in program termination. For example, starting with AFIT3 45.19+56.78+89.34 (enter) and then typing (esc) will get to the "? Enter Equation(s)" prompt. Typing (esc) now will terminate the program. In some situations, the (ctrl Q) or (esc) sequences may not return to the equations display. This event will usually occur when a previously-entered valid equation does not exist. L 570 For example, if the program is started with an improper equation entered on the DOS command line, then one must either correct the equation or type (end esc) then "" (enter) to load the default equations. To exit from the program while in the edit mode, one must use the apostrophe command: 'exit (enter). -> Exit program: E Use "E" to exit from the program. If equations or storage need to be saved, the program will inform you. Save them L 580 immediately because the use of "E" clears the reminders. If necessary type "E" a second time to exit. Type Y (enter) to exit/terminate. or N (enter), "(enter)", "(ctrl Q)" to return to equation display. -> Generate "Definition of variables" template as comment: ! (comma) "! (comma)" will generate a comment which is a template of variable names each followed by the define character "≡". The comment must be empty for this to happen. If the comment L 590 contains text, set it to a null comment by typing (F5) then (end esc) "" (enter) or type the apostrophe command 'com "" (enter). If the equation is y=m*x+b then the comment will look something like: Definition of variables. Y ≡ B ≡ M ≡ X ≡ ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 14 -- Type (F5) to edit the comment and type in the meanings of the variables. L 600 -> Get/save file of equations: (F8) [ (F9) ] "(F8)" or "[" gets a file of equations and the values of variables. Enter the path/filename followed by "(enter)" in response to prompt. "(F9)" or "]" saves a file of the equations and the values of variables. These two commands save equations, dep and ind vars but not storage vars. Filenames can be specified with paths. For example: \data\results.001, \project\z21\analysis.equ, d:\appl\line.equ. Default extension L 610 for equation files is ".EQU". Use "." at end of filename if does not have extension. For get operation, if .HLP is the extension, then program will re-initialize and attempt to read file as application file. The extension .HLP cannot be used with a filename for the save (F9) operation. -> Get/save file of storage variables: ![ !] Use "![" to get a file of storage variables and values only. Note: Use "!*" to generate a directory on the screen from L 620 which the name of an existing file can be located and selected. Use "!]" to save a file of storage variables and values only. Default extension for storage files is ".STO". Use "." at end of filename if does not have extension. If .HLP is the extension, then program will re-initialize and attempt to read file as application file. -> Help files: Using on-line help file, user-manual help file and application help file. L 630 To use the on-line help file, type (F1) or the letter "H". To use the on-line user-manual, type "!H" or type (F2) and enter its name. To use the application help file type "(F2)" or "@H". Type the name followed by "(enter)". After reading the application help file, to get the program to prompt for a new name, first type "@C" to display version number or type "(F1)" to access the on-line help file. Type "(esc)" or "E" to exit and then type "(F2)". Set DOS environment variable ASTRO3 to the path where AFIT3HLP.HLP can be found prior to running this program. L 640 Summary: (F1) or H Read on-line condensed help file AFIT3HLP.HLP. ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 15 -- !H Read on-line user-manual help file AFIT3MAN.HLP. (F2) or @H Read application help file *.HLP. Enter filename in response to prompt. If found, program will not prompt unless (F1), H, !H or @C is typed. L 650 -> Inactivate variable: I !I @I "I" inactivates an equation or variable. The "=" will disappear. Used to indicate dummy eqns for D, G and U. Inactive equations are not plotted. "!I" inactivates all dependent or independent variables at once. The location of the cursor determines which set. "@I" inactivates all variables at once. Also use the apostrophe command 'INA varname (enter) for the same purpose. See below for more L 660 details. Use the commands "A", "!A" or "@A" to activate an equation or variable. -> Inspect a too-long-to-display equation Move the cursor to the desired equation, type "@/" and type "(esc) (enter)" or "(ctrl Q)" to exit to the equation display without any changes. Remember that the immediate calc buffer (command "|") now contains this equation and it can be dumped with the "(alt 9)" command in the edit mode. L 670 -> Modify an equation: @/ Move the cursor to the desired equation, type "@/" and make changes. Type "(enter)". Remember that the immediate calc buffer (command "|") now contains the original equation. -> Multiple calculations: apostrophe command 'IMM The apostrophe command 'IMM allows multiple calculations to be L 680 performed from the main equation display. These calculations can reference any defined variable and if a calculation results in the creation of a new variable it is assigned as a storage variable. The main display equations are not evaluated during/after these calculations. For example the immediate calc: 'IMM y=sqr(2*x)+b z=2*y (enter) would assign variables Y and Z the results of these calculations. The immediate calc buffer is updated following this calculation. The ":" implies the value of the variable the cursor resides on. For example the immediate calc: 'imm sqr(2*:+45) (enter) would use the L 690 ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 16 -- value of the variable the cursor is on and would assign the result to this variable. -> Plot equation: P "P" plots the active equation(s) vs. coordinate. See below for a complete discussion of the additional commands that can be used while the plot screen is displayed. The cursor should reside on the independent variable to be the coordinate of the x-axis, if some var is not already designated. A coordinate L 700 variable has a ":" following its name. -> Printer initialization: !P @P Use "!P" to initialize printer for NLQ (double strike) printing. Use "@P" to reset printer and cancel NLQ printer. -> Program name and version number: @C Use "@C" to recalculate with the program name and version #. L 710 -> Recalling last immediate calculation: | "|" displays the last immediate calculation and position the cursor after an imbedded apostrophe ('). Use edit keys to change a calculation and use (enter) to execute. Use (alt 9) to insert the current immediate calc before the cursor when in the edit mode. Use (alt 4) and (alt 5) to toggle to previous calculations saved on the immediate calc text stack. The "|" command allows a single calculation to be entered and the main L 720 display equations are evaluated after this calculation. On the other hand, the immediate calc apostrophe command 'IMM allows multiple calculations to be entered and the main display equations are not evaluated during/after these calculations. -> Reference to current value of variable in calculations Use ":" to designate the current value of variable on which the cursor resides while entering an immediate calculation. For example, if the cursor is on variable A which currently equals L 730 10, then typing 2*:+6 (enter) will result in A being set to 26. -> Remove an equation: @/ Move the cursor to the desired equation, type "@/" and type (end esc) "" (enter). Remember that the immediate calc buffer ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 17 -- (command "|") now contains the original equation. Should you wish to add it back, type "(F6) or "!/" to edit equations, locate cursor and type "(alt 9)" to insert it before the cursor. L 740 -> Repetitive calculations without variables To perform repetitive calculations without variables such as adding and subtracting numbers, get to the "-- ? Equations(s)" prompt by typing (F6) or "!/". Type (end esc) to clear the field. Enter the calculations such as 23.45+46.78-32.00 (enter). The text of the calculations is now stored on the immediate calc text stack. Use the (alt 4) and (alt 5) keys to toggle back and forth to previous calculations. The (alt 6) L 750 key is used to insert the entire immediate calc text stack into the present calculation and the (alt 7) key is used to replace the current calculation with the entire contents of the immediate calc text stack. To exit the Program, type (end esc) "" (enter) to return to equation display and then type "E". -> Saving equation in immediate calc text buffer: !| "!|" replaces immediate calc buffer with the equation on which cursor resides and updates the immediate calc text stack with L 760 the previous contents. -> Saving comment in immediate calc text stack: @| "@|" replaces immediate calc buffer with comment and updates immediate calc text stack with the previous contents of the buffer. One can use "@|" to transfer equations/values from the comment to the equations and or variables. Once the comment is on the immediate calc text buffer it can be recalled in the edit mode by using (alt 4) and (alt 5) keystrokes. The L 770 text can be edited to select what is desired. -> Screen dump to text file: V "V" dumps the equations display (or the plot) to a text file. Used to save calculations or plots for inclusion in reports, etc. Program name and date/time are appended. The complete equations, comment and values/status of the variables are appended at the end in the 'EQU format. These files can be used to build a user-generated application file. Enter L 780 filename in response to prompt. Note: Filenames ending in numeric extensions from "000" to "999" are automatically ------- 1.04 -- Summary of Letter Commands Used in Equations Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 18 -- incremented each time the command is used. Thus, SCRN.001 --> SCRN.002 --> SCRN.003 and so on. Filenames can be specified with paths. For example: \data\calc.001, \project\p23\screen.056, d:\appl\calc10.new If a file already exists, the program will prompt to "APPEND" or to "REPLACE". -> Set all variables to same value: ? !? @? L 790 "?" sets values of all variables to a constant. Active/inactive status of variables not affected. Use "!?" to set all dependent or independent variables only. The location of the cursor determines which set. Use "@?" to set all variables to a constant and to change status of all variables to active. Constant may be explicitly specified or be the current value of any variable or the result of a simple calculation such as 2*A. -> Turn sound on/off: !B @B L 800 "!B" turns beeping sound "on" at various locations in program. "@B" Turns beeping "off" at most places including warnings. The default is sound "off". -> Universal quit: (ctrl Q) "(ctrl Q)" will cause control to return to the equation display but only if valid equations exist in the program. "The universal quit". Use the (ctrl Q) anywhere to get back to a L 810 familiar part of the program which is usually the main equation display. ╒═══════════════╕ │ F1 - F10 KEYS └─────────────────────────────────────────────────────── 1.05 F1-F10 Keys, Commands assigned. ──────────────────────────────────────────────────────────────────────── Key Command Purpose L 820 F1 help Access on-line help file AFIT3HLP.HLP F2 appl help Access application on-line help file. F3 exit Exit from program F4 shell Shell to DOS, type exit (enter) to return. ---------------------------- 1.05 -- F1-F10 Keys, Commands assigned. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 19 -- F5 comment "? comment" prompt L 830 F6 equation "? equation" prompt. F7 directory "Directory of *.EQU" prompt. F8 get file Get a file of equations (*.equ) F9 save file Save the current equations (*.equ) F10 prod info List product information. L 840 ╒════════════════════╕ │ SPECIAL OPERATIONS └────────────────────────────────────────────────── 1.06 Command Sequences Used to Perform Special Operations ──────────────────────────────────────────────────────────────────────── -> Saving and inserting one or more equations into existing equations. 1) Type @L to clear immediate text stack. L 850 2) Move cursor to each equation. Type !| 3) Type !/ to edit equations. 4) Mover cursor to place for insert, type (alt 6). Remember: all dependent vars must have different and unique names to first 8 characters. Edit as necessary. 5) Type (enter) to load equations and return to main equation L 860 display. ╒══════════════╕ │ EDITING KEYS └──────────────────────────────────────────────────────── 1.07 Editing Keys: Functions During Text Entry ──────────────────────────────────────────────────────────────────────── Editing keys can be used whenever the underscore cursor "_" is flashing on the screen. At these instances, any character L 870 above the cursor will also blink. A summary of the editing keys follows. (esc) - Clear the entire text, line or number. If cursor on ------------------ 1.07 -- Editing Keys: Functions During Text Entry --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 20 -- first position of field, specifies the escape sequence (ctrl Q) discussed below. Note, if the program is started with an improper equation, either correct the equation or type (end esc) then "" (enter) to load the default equations. (backspace) - Delete character directly in front of cursor. L 880 (tab) - Move cursor 5 characters to right. (shift tab) - Move cursor 5 characters to left. (home) - Move cursor to beginning of text. (ctrl) (home) - Delete all before cursor to beginning of text. (ctrl) (PrtSc) - Redraw all lines of the current text. L 890 (arrow up) - Move cursor one line up, if possible. (arrow left) - Move cursor one character to left. (ctrl) (arrow left) - Move cursor 5 characters to left. (arrow right) - Move cursor one character to right. (ctrl) (arrow right) - Move cursor 5 characters to right. L 900 (end) - Move cursor to end of text. (ctrl) (end) - Delete all from cursor to end of text. (arrow down) - Move cursor one line down, if possible (ins) - Insert text before cursor. Toggle on and off. (del) - Delete character at cursor. L 910 In insert mode (large cursor), the cursor character is deleted and the entire remaining text is shifted left. In the replace mode (small cursor), the cursor character is deleted but only text on the current line is shifted left. (enter) - Used to terminate a string of information which is to be entered into the program. (ctrl enter) - Same function as enter but prevents the program from calculating the main equations when appropriate. L 920 ------------------ 1.07 -- Editing Keys: Functions During Text Entry --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 21 -- (ctrl Q) - Quit entry, erase information and return back into the program. Used to return to program if the wrong command was typed. "The universal quit". (alt 1) - Fill current line to end with spaces (if necessary) and move cursor to the next line. Used to provide the "carriage return" function in the text edit mode. (alt 2) - Split line at cursor. L 930 To insert a blank line, position cursor on start of line and type (alt 2). Line is inserted before cursor. (alt -) Join function. Cursor must be on space (blank). The opposite of the split function (alt 2). Removes the cursor blank and all following blanks up to first non-blank character across the entire text. (alt 3) - Add all remaining lines and fill with spaces. This is essentially full-screen edit because information can be L 940 enter anywhere in the allowed field. (alt 4) - Toggle to previous calculation or text stored in the immediate calculation text stack and replace current text. Note: If a mistake occurs, type (ctrl Q) to exit. The imm calc text stack is updated with information from the immediate calculation, command |. (alt 5) - Toggle in opposite direction to that of (alt 4). L 950 (alt 6) - Insert the entire text of the immediate calculation text stack before the cursor. (alt 7) - Replace current text with entire contents of immediate calculation text stack. (alt 8) - Clear all text from immediate calculation text stack. (alt 9) - Insert the text of the last immediate calculation before the cursor. The immediate calculation is command |. L 960 ╒════════════════╕ │ EQUATION ENTRY └────────────────────────────────────────────────────── 2.01 Entering Equations Into the Program ──────────────────────────────────────────────────────────────────────── ------------------------ 2.01 -- Entering Equations Into the Program --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 22 -- An equation or a series of equations is entered into the program in response to the prompt "-- ? Equation(s) -->". While the screen is displaying the equations, type (F6) or L 970 "!/". Use the edit keys, as discussed above, to enter the equations. In particular note that the "(end esc)" key clears the screen. Following a successful evaluation of the equations, the program will prompt "-- ? Comment -->". At this time a comment can be added to describes the equations, their use, meaning of of variables, etc. Double quote marks are required to preserve string spacing. To clear away an old comment type (end esc) "" (enter). The "" signifies an empty or null character string. To enter three equations, one might type (F6) then: L 980 (end esc) y1=a+b+c y2=a-b-c y3=a-b+c (enter) Next, to enter a comment, one might type: (end esc) "Three equations with three unknowns." (enter) Note: The string does not have to be enclosed in quotes, however if quotes are used, make sure that there are 2 -- one at each end! L 990 If one enters equations without any independent variables, then the program will perform the calculations and prompt "? Equation(s)". For example, one can enter a series of equations: (end esc) y1=1+2+3 y2=1-2-3 y3=1-2+3 (enter) The values of y1, y2 and y3 are remember and can be referenced in the next calculation. For example: L 1000 (end esc) y1=y1-10 y2=y2-20 y3=y3-30 (enter) Also, more than one calculation can be performed if expressions are enclosed in parentheses. For example: (end esc) (1-45) (23+45+67) (sqr(4/98)) (enter) Use the (ctrl Q) keys to abruptly and immediately terminate anything! L 1010 ------------------------ 2.01 -- Entering Equations Into the Program --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 23 -- ╒═══════════════════╕ │ WRITING EQUATIONS └─────────────────────────────────────────────────── 2.03 Writing Equations: Definition of Terms ──────────────────────────────────────────────────────────────────────── Before any further discussion of equations and their evaluation, the user should become familiar with the following terms: L 1020 ■ EQUATION: A symbolic recipe for calculating a number associated with a dependent variable. An equation consists of a dependent variable followed by an equal sign and ending with a series of mathematical operations involving constants, independent variables, functions and dependent variables. An INCONSISTENT EQUATION is one in which the final value of the dependent variable depends on its initial value in some way. Counters, such as COUNT=COUNT+1, and summers, such as TOTAL=TOTAL+X, are good examples. L 1030 ■ DEPENDENT VARIABLE: A name, beginning with a letter, which identifies a variable whose value is calculated. The dependent variable usually appears to the left of the equal sign but it may also appear to the right in certain cases. Each equation must have a unique name for its dependent variable. ■ INDEPENDENT VARIABLE: A name, beginning with a letter, which identifies a variable whose value is assigned. The value of an independent variable usually does not change as the result of a L 1040 calculation. An independent variable always appears to the right of the equal sign. ■ STORAGE VARIABLE: A variable which is used similarly to an independent variable and is created as the result of an assignment statement. For example, an assignment statement might be PI=3.1415926 and an equation using PI might be AREA=PI*RADIUS^2. The values of the storage variables are saved independently of the dependent and independent variables. L 1050 ■ CONSTANT: A number whose value is explicitly defined and does not ever change. Numbers may be in the integer format (no decimal point), decimal format or floating (exponential) format. Some examples are: INTEGER: -50, 100, 0 DECIMAL: -49.95, 99.67, 0.0 --------------------- 2.03 -- Writing Equations: Definition of Terms --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 24 -- FLOATING or EXPONENTIAL: -1E-3, 1.674E+6, 0.0E0, 3.2D-3 Note: L 1060 E-3 or D-3 means 10^-3 ■ FUNCTION: A special mathematical recipe that has an argument enclosed in parentheses. A special number is calculated from the value of the argument. See help file for more details. For example: E=M*C^2 AVERAGE=(ITEM1+ITEM2)/ABS(N) Y=3*COS(X)^2-1 Dependent variables: E, AVERAGE, Y L 1070 Constants: 2, 3, 1 Independent variables: M, C, ITEM1, ITEM2, N, X Functions: ABS(...), COS(...) Math operations: * (multiplication), ^ (power), + (addition), / (division) - (subtraction) Note: Parentheses specify the order of the calculation. All equations begin with a dependent variable, whose value is L 1080 calculated by the equation. The dependent variable is followed by an equal sign "=". Following the "=" sign are a collection of constants, independent variables, dependent variables and functions. Pairs of parentheses are used to group terms and to specify the the order of a given calculation, especially when the desired order opposes the default priorities discussed below. More than one equation can be entered in response to the "? Equation(s)" prompt. If you enter more than one equation, you should be careful with the use of spaces! The equations, including spaces, cannot exceed 1840 characters (23 L 1090 lines). An example of a group of equations is: H=1+C*R1*R2/(R1+R2) A=20*LOG(X^(2*Y)) E=P*(A-D)/2 REL_MIN=SQR(1+DMIN^2) EMAX[Q]=-LOG10(SQR(1-Q^2)) L 1100 Dependent variables: H, A, E, REL_MIN, EMAX[Q] Constants: 1, 20, 2 Independent variables: C, R1, R2, X, Y, A, D, DMIN, Q --------------------- 2.03 -- Writing Equations: Definition of Terms --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 25 -- Functions: LOG(...), SQR(...), LOG10(...) Math operations: + (addition), * (multiplication), / (division), ^ (power) - (subtraction), - (negation) L 1110 ╒════════════════╕ │ EQUATION RULES └────────────────────────────────────────────────────── 2.10 Rules for Writing Algebraic Expressions, Formulas and Equations ──────────────────────────────────────────────────────────────────────── Algebraic expressions, formulas and equations are virtually identical mathematically and will all be collectively called "equations" in this Manual. The rules for writing equations L 1120 are fairly universal. Equations are entered using the conventions found in the BASIC computer language. In particular, the user should note that an implied multiplication is not allowed. Thus AB would be interpreted as a variable name and A*B, as multiplication. Also, operations of equal priority always execute from left to right. The rules are: ■ All variable names must begin with either an English capital letter. (Lower case letters will be converted to upper case) or a Greek letter such as α, ß, Γ, π, Σ, σ, µ, τ, Φ, Θ, Ω, or L 1130 δ. To enter these Greek letters use the keypad numbers. Hold down the (alt) key and type the following ASCII codes on the keypad and then release the (alt) key. α 224, ß 225, Γ 226, π 227, Σ 228, σ 229, µ 230, τ 231, Φ 232, Θ 233, Ω 234, δ 235. Variable names such as AMAX, EMIN, TIME_OF_DAY, F[T] are ok but 123ABC is invalid. The remaining characters can be any ASCII characters with values greater than ASCII 32 which is the "(space)". For example, "R║" and "R┴" may be used to define variables where the ║ (ASCII 186) conveys "parallel" and the ┴ (ASCII 193) conveys "perpendicular". If an embedded space is L 1140 desired, use ASCII 255 which is the "alternate" blank. Note, the "normal" space (ASCII 32) is a separator. ■ Variable names can be any length of characters but only the first 8 are significant. Thus variable names such as MINIMUM_, MINIMUM_HEIGHT, MINIMUM_VALUE and MINIMUM_LENGTH are all equivalent. ■ Variable names must be different from the names of the intrinsic functions described above. Thus Y=SINZ+LOGQ would be L 1150 ---------- 2.10 -- Rules for Writing Algebraic Expressions, Formulas --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 26 -- ok but Y=SINH*LOG is invalid because SINH and LOG are the names of intrinsic functions. The names of the intrinsic functions are reserved words. Don't use them for the names of variables! ■ Equations must begin with the name of a single dependent variable. If a group of equations is entered, each equation must have a dependent variable with a unique, different and allowed name. For example, Y1=A+B Y2=A-B not Y=A+B Y=A-B. ■ The dependent variable must be followed by an equal sign and L 1160 the remainder of the equation. Intervening spaces are ok. For example: Y=M*X+B not Y-B=M*X. Operations are not allowed to the left of the equal sign. See other rules below. ■ Spaces and commas are allowed within the equation(s). Most are ignored and removed by the program. Use them in numbers for ease of entry: 1,000,000 or 1 000 000 or 1000000. Y = 2,000 * ( X + 3 0 * Z ) is equivalent to Y=2000*(X+30*Z). If exponential notation is used in a number then the "E" or "D" must immediately follow the last digit of the number. Thus, L 1170 1.45E-2, 1 . 4 5E - 2 and 1.45E -2 are equivalent but 1.45 E-2 signifies two equations: The first contains the number 1.45 and the second, the variable E minus 2. Separate all equations by at least one space. ■ There must be at least one constant, independent variable or dependent variable to the right of the equal sign. For Example: Y=3, Z=X, W=SIN(0.7), A=A+1. A single equation with only constants to the right of the equal sign, such as Y=SQR(4)+ABS(-3), is calculated and then the program prompts L 1180 for a new equation. ■ Parentheses must always be matched. They must always occur in pairs. For example: Y=(3*X)-2 and Y=3*(X-2) not Y=LOG(SQR(1-X^2). ■ An empty pair of parentheses is not allowed. Y=SIN() and Y=3+()-4 are not allowed. ■ Independent variables with the same names, that are used in L 1190 different equations, always share the same memory locations. Their values are always in common to all equations. To make an independent variable unique, it should be given a unique name. ■ If a group of equations is entered, the first equation is the "nearest to start" of the string and the last equation is the ---------- 2.10 -- Rules for Writing Algebraic Expressions, Formulas --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 27 -- "nearest to end". Calculations proceed from the first equation to the last. For example, a group of equations might be: N=N+1 L 1200 YTOTAL=YTOTAL+X YAVE=YTOTAL/N Each time that a calculation is made, the following happens. The current value of N, a counter, will be increased by 1. To the current value of YTOTAL is added the value of X. The average value, YAVE, is calculated as YTOTAL divided by N. "N" and "YTOTAL" are termed inconsistent equations because they do not represent math equalities. L 1210 ╒═════════════╕ │ PARENTHESES └───────────────────────────────────────────────────────── 2.15 Rules for Evaluation of Parentheses ──────────────────────────────────────────────────────────────────────── ■ Nested parentheses, that is, parentheses within parentheses, are evaluated from innermost to outermost matched pairs. For example, if Y=ABS(5+LOG10(3*X+2)-6) then 3*X+2 would be performed first, then 5+LOG10(..)+6, then ABS(...). If L 1220 Y=(((X+1)/2)*3)+4, then X+1 would be performed first, then /2, then *3, then +4. ■ Matched parentheses are always evaluated from left to right. For example: if Y=(3+X)+(4-X)/(X^2-1) then 3+X would be performed first followed by 4-X and X^2-1. Finally, the results of the last two parentheses would be divided and that result added to the first parentheses. ■ The maximum number of pairs of parentheses in any equation is L 1230 128 and parentheses may be nested in any depth up to 128. ╒════════════════════╕ │ BUILT-IN FUNCTIONS └────────────────────────────────────────────────── 2.20 Rules for Evaluation of Intrinsic Functions ──────────────────────────────────────────────────────────────────────── ■ The names of the intrinsic functions are reserved words and these names cannot be used as the names of variables. For L 1240 example, Y=SIN(X) is ok but Y=SIN+X is not allowed. ---------------- 2.20 -- Rules for Evaluation of Intrinsic Functions --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 28 -- ■ Operations within a function are always performed prior to the evaluation of that function. For example if Y=SIN(2*PI*X) then the order of evaluation would be 2*PI*X and then SIN(...). ■ Nested functions are always evaluated from innermost to outermost function. For example if Y=LOG(ABS(SIN(X))) then the order of evaluation would be SIN(...) then ABS(...) then LOG(...). L 1250 ■ Functions are evaluated from left to right. For example, if Y=SIN(X)+COS(X)+LOG(X) then the order of evaluation would be SIN(...) then COS(...) then LOG(...). ╒═════════════════╕ │ MATH OPERATIONS └───────────────────────────────────────────────────── 2.25 Rules for Evaluation of Mathematical Operations ──────────────────────────────────────────────────────────────────────── L 1260 ■ Highest priority: power (exponentiation) Y=X^2 leading negation Y=-X multiplication, division Y=3*X, Y=X/4 lowest priority: addition, subtraction Y=X+10, Y=X-7 ■ Operations of the same priority are evaluated from left to right. For example: Y=2^2^3 (=64, not 256!) L 1270 Y=8+4/4-2*5 (=-1, not 5!) Y=-4^2 (=-16, not 16!) Y=2+4*2^2/4 (=6, not 36!) ■ Parentheses can be used to change the order of mathematical operations. For example: Y=2^(2^3) (=256, not 64!) Y=((8+4)/4-2)*5 (=5, not -1!) Y=(-4)^2 (=16, not -16!) L 1280 Y=((2+4)*2)^2/4 (=36, not 6!) ■ Redundant or superfluous operations will be simplified and/or eliminated from the equations. These operations usually include multiple combinations of the "+" and "-" with themselves or other operators. For example: Y=-+A or Y=+-A --> Y=-A ------------ 2.25 -- Rules for Evaluation of Mathematical Operations --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 29 -- Y=--A or Y=++A --> Y=A Y=A^-+2 or Y=A^+-2 --> Y=A^-2 L 1290 Y=10/+A --> Y=10/A Y=A*+50 --> Y=A*50 Y=-+-+-+A --> Y=-A ╒════════════════╕ │ MATH FUNCTIONS └────────────────────────────────────────────────────── 2.30 Glossary of Intrinsic MATH FUNCTIONS and Function Operators ──────────────────────────────────────────────────────────────────────── L 1300 The program contains intrinsic mathematical functions which perform well-know calculations based on the value of their arguments. All functions have names which start with a letter and contain from 3 to 5 characters. The name is followed by an argument which may be a simple constant, a variable or an expression. The argument is always enclosed in a matched set of parentheses. For example: Y=SIND(45) has a constant, 45, as the argument. Y=ALOG(X) has a variable, X, as the argument. Y=ABS(4*X-6) has an expression, 4*X-6, as the argument. L 1310 Y=SQR(ABS(X)) has another function, ABS(...), as the argument. Functions are "built in" recipes for performing well-known mathematical operations which are described below. The argument of a function may be a number or an expression which is always enclosed in parentheses. Function operators are 2 letter suffixes attached to numbers. Thus SIND(45) and 45SD are equivalent. Function operators can be attached to any number except the constants in equations entered in response to the prompt "-- ? Equation(s) -->". There are one-to-one L 1320 correspondences between functions and operators. The allowed functions and function operators and their uses are: Op Function Purpose AB ABS(X) The absolute value of X. If X > or = 0 then ABS(X)=X, but if X<0 then ABS(X)=-X. op: -5AB 10AB -20AB func: Y=ABS(-5), Y=5. Y=ABS(10), Y=10 L 1330 OC ACOS(X) The inverse cosine of X. The result is in radians. ABS(X) must always be < or = to 1.0. op: 1OS 0OC .5OC func: Y=ACOS(1), Y=0. Y=ACOS(0), Y=1.570796 ---------- 2.30 -- Glossary of Intrinsic MATH FUNCTIONS and Function --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 30 -- DC ACOSD(X) The inverse cosine of X. The result is in degrees. ABS(X) must always be < or = to 1.0. op: 1DC 0DC -.61DC func: Y=ACOSD(1), Y=0. Y=ACOSD(0), Y=90 L 1340 HC ACOSH(X) The inverse hyperbolic cosine of X. X must always be > or = to 1.0. op: 1.54308HC 1HC 2HC func: Y=ACOSH(1.54308), Y=1. Y=ACOSH(1), Y=0 IS ASIN(X) The inverse sine of X. The result is in radians. ABS(X) must always be < or = to 1.0. op: 1IS 0IS .707IS func: Y=ASIN(1), Y=1.570796. Y=ACOS(0), Y=0 L 1350 DS ASIND(X) The inverse sine of X. The result is in degrees. ABS(X) must always be < or = to 1.0. op: 1DS 0DS .707DS func: Y=ASIND(1), Y=90. Y=ASIND(0), Y=0 HS ASINH(X) The inverse hyperbolic sine of X. op: 1.17520HS 0HS 1.5HS func: Y=ASINH(1.17520), Y=1. Y=ASINH(0), Y=0 AT ATAN(X) The inverse tangent of X. The result is in radians. L 1360 op: 1AT 0AT 2AT func: Y=ATAN(1), Y=.7853982. Y=ATAN(0), Y=0. DT ATAND(X) The inverse tangent of X. The result is in degrees. op: 1DT 0DT 2DT func: Y=ATAND(1), Y=45. Y=ATAND(0), Y=0 HT ATANH(X) The inverse hyperbolic tangent of X. X must always be > -1.0 and < 1.0 op: 0.76159HT 0HT -.435HT L 1370 func: Y=ATANH(0.76159), Y=1. Y=ATANH(0), Y=0 CI CINT(X) Convert X to an integer by rounding. The absolute value of X must always be less than 1E16 for this to be a meaningful calculation. op: -5.75CI 12.65CI 4.567CI func: Y=CINT(-5.75), Y=-6. Y=CINT(12.65), Y=13. CO COS(X) The cosine of X. X is in radians. op: 0CO 1.7CO -.567CO L 1380 ---------- 2.30 -- Glossary of Intrinsic MATH FUNCTIONS and Function --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 31 -- func: Y=COS(0), Y=1. Y=COS(1.570796), Y=0. CD COSD(X) The cosine of X. X is in degrees. op: 0CD 90CD 45CD func: Y=COSD(0), Y=1. Y=COSD(90), Y=0 CH COSH(X) The hyperbolic cosine of X. op: 1CH 0CH 0.567CH func: Y=COSH(1), Y=1.54308. Y=COSH(0), Y=1 L 1390 DE DECM(X) The signed decimal fraction of the number X with no rounding. op: -123.456DE 456.789DE 789.123DE func: Y=DECM(-123.456), Y=-.456 Y=DECM(456.789), Y=.789 Can be used to calculate the MOD(X) to base Z which may be decimal. Use Y=Z*DECM(X/Z). Y=16*DECM(19/16), Y=3 Y=.5*DECM(1.3/.5), Y=.3 EX EXP(X) The natural or Naperian antilog, base "e". L 1400 op: 1EX 0EX .51534EX func: Y=EXP(1), Y=2.71828. Y=EXP(0), Y=1. FA FACT(X) Factorial of X. X may be a signed integer or decimal. FACT(6) = 6 * 5 * 4 * 3 * 2 *1 X=0, FACT(0)=1 X>0, FACT(X)= X*(X-1)*(X-2)....*1 X<0, FACT(X)= X*(X+1)*(X+2)....*-1 op: 4FA=24, -4FA=24, 3FA=6, -3FA=-6, 0FA=1, 1FA=1 -3.3FA=-9.867, -4.3FA=+42.4281 L 1410 func: Y=FACT(4), Y=24. Y=FACT(-3), Y=-6. FI FIX(X) Truncate X to an integer. No rounding. The value of X must always be less than 1E16 for this to be a meaningful calculation. op: -5.75FI 12.65FI 4.567FI func: Y=FIX(2.3), Y=2. Y=FIX(-56.70), Y=-56. LN LOG(X) The natural or Naperian log of X. X must be greater than 0.0 L 1420 op: 2.71828LN 1LN 6.784LN func: Y=LOG(2.71828), Y=1. Y=LOG(1), Y=0. LG LOG10(X) The log, base 10, of X. X must be > 0.0. op: 10LG 1LG 1002LG func: Y=LOG10(10), Y=1. Y=LOG10(1), Y=0. ---------- 2.30 -- Glossary of Intrinsic MATH FUNCTIONS and Function --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 32 -- NZ NZE(X) The "not zero" function. If X=0 then X=10^-30, a very small number. Useful in division to prevent divide by zero errors. L 1430 op: 0NZ 1NZ .000001NZ func: Y=NZE(0), Y=1D-30 Y=NZE(1D-15), Y=1D-15 RA RAND(X) Generates a random number from 0 to 1. The argument X controls the seeding: X<0 reseeds the random number generator. X=0 repeats the last number generate. X>0 generates the next number in the sequence. op: -1RA, new sequence. 1RA, generates the next random number. L 1440 func: Y=RAND(-1), new sequence. Y=RAND(1), generates the next random number. RN RND(X) Round the number X to two decimal places. Useful in financial calculations in order to round decimal fractions to cents. op: 123.456RN -123.543RN 735.196RN func: Y=RND(123.456), Y=123.46 Y=RND(-123.543), Y=-123.54 To round to other numbers of decimal digits, use the L 1450 function CINT. For example, to round X to 3 decimal places use CINT(1000*X)/1000. SF SFACT(X) "Skip" factorial of X. X may be a signed integer or decimal. Similar to FACT(X) except decrement is by 2.0. If X is an even integer than SFACT(X) is the product of the even integers and if X is an odd integer than SFACT(X) is the product of the odd integers. SFACT(6) = 6 * 4 * 2, SFACT(7) = 7 * 5 * 3 * 1 L 1460 X=0, SFACT(0)=1 X>0, SFACT(X)= X*(X-2)*(X-4)....*(1 or 2) X<0, FACT(X)= X*(X+2)*(X+4)....*(-1 or -2) op: 6SF=48, -5SF=-15, 3SF=3, -3SF=3, 0SF=1, 1SF=1 -3.3SF=+4.29, -5.3SF=-22.737 func: Y=SFACT(8), Y=384. Y=SFACT(-7), Y=105. SG SIGN(X) Returns the sign of the argument X. op: -123SG 0SG 256SG func: Y=SIGN(-123), Y=-1. Y=SIGN(0), Y=0. L 1470 Y=SIGN(256), Y=1. ---------- 2.30 -- Glossary of Intrinsic MATH FUNCTIONS and Function --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 33 -- SI SIN(X) The sine of X. X is in radians. op: 0SI 1.085SI .657SI func: Y=SIN(0), Y=0. Y=SIN(1.570796), Y=1. SC SINC(X) The sinc function ( SIN(X)/X ) of X. op: 0SI 3.0SC -9.9SC func: Y=SINC(0), Y=1. Y=SINC(4.9), Y=-0.200501 L 1480 SD SIND(X) The sine of X. X is in degrees. op: 0SD 90SD 45SD func: Y=SIND(0), Y=0. Y=SIND(90), Y=1 SH SINH(X) The hyperbolic sine of X. op: 1SH 0SH .56123SH func: Y=SINH(1), Y=1.17520. Y=SINH(0), Y=0 SQ SQR(X) The square root of the argument X. X must be > or = to 0.0 L 1490 op: 144SQ 100SQ 256SQ func: Y=SQR(144), Y=12. Y=SQR(100), Y=10. TA TAN(X) The tangent of X. X is in radians. op: .815TA 0TA .312TA func: Y=TAN(3.15193/4), Y=1. Y=TAN(0), Y=0. TD TAND(X) The tangent of X. X is in degrees. op: 45TD 0TD 60TD func: Y=TAND(45), Y=1. Y=TAND(0), Y=0 L 1500 TH TANH(X) The hyperbolic tangent of X. op: 1TH 0TH .3765TH func: Y=TANH(1), Y=0.76159. Y=TANH(0), Y=0 UI UIF(X) The unit impulse (delta) function of X. If X = 0 then UIF(X)=1 or if X < 0 or X > 0 then UIF(X)=0. op: 0UI 6UI -56UI func: Y=UIF(3), Y=0. Y=USF(X-6), X=6, Y=1, X=5, Y=0. L 1510 UR URF(X) The unit ramp function of X. If X > 0 then URF(X)=X or if X < 0 or X = 0 then URF(X)=0. op: 0UR 6UR -56UR func: Y=URF(3), Y=3. Y=URF(X-6), X=6, Y=0, X=5, Y=0. US USF(X) The unit step function of X. If X > 0 or X = 0 then USF(X)=1 or if X < 0 then USF(X)=0. op: 3US -6US -56US ---------- 2.30 -- Glossary of Intrinsic MATH FUNCTIONS and Function --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 34 -- func: Y=USF(3), Y=1. Y=USF(X-6), X=7, Y=1, X=5, Y=0. L 1520 ╒════════════════╕ │ NUMBER FORMATS └────────────────────────────────────────────────────── 2.40 Numbers: Format-free, Examples of Formats ──────────────────────────────────────────────────────────────────────── Numbers can be entered in many convenient forms which usually depend on their magnitudes. ■ DECIMALS: 0.567, -.903 L 1530 ■ FRACTIONS: 1/4, -45/64, 16/4 ■ INTEGERS: -1, 2, -123 ■ FLOATING POINT: 1.2E3, 1.2e3, -123e-2, 1.2D4, 34d1 (Note: E means 10^ thus 1E2 equal 1*10^2 or 100 and usage of "E" and "D" are equivalent. Thus 1E2 and 1D2 are identical. Maximum FP value of 1E+25. FP numbers with exponents greater L 1540 than +25 will be ignored.) Numbers can also be entered as the result of a mathematical expression: (34+45)/2, (10+34+56+78)*45, 2*COSD(30)-.467 and so. Commas and spaces within numbers are ignored. Thus 1,002 and 1 002 and 1002 are all equivalent. Also 18.89 and 1,8.8,9 and 1 8 . 8 9 and 1,,,8 .,,,,8 9 and so on are also equivalent. L 1550 Numbers can also include references to previously defined variables. For example: PAYMT$-100, PRINCPL$+100. Numbers can also have function operators attached: 45SD, 3*60CD-1/3 and so on. ╒════════════════╕ │ DECIMAL DIGITS └────────────────────────────────────────────────────── 2.42 Controlling the Number of Decimal Digits L 1560 ──────────────────────────────────────────────────────────────────────── The number of significant decimal digits shown in the main equation display can be controlled in two ways: globally with ------------------- 2.42 -- Controlling the Number of Decimal Digits --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 35 -- the 'DEC apostrophe command and locally for any variable by appending the decimal operator to dependent and independent variable name. The 'DEC apostrophe command sets the default number of decimal digits. For example, 'DEC 2 (enter) would specify 2 decimal digits. Global defaults also apply to the displayed values of the storage variables and numbers displayed L 1570 on the plot. A variable such as "A" will display up to 7 decimal digits in single precision and up to 16 in double precision. Appending a period followed by an integer from 0 to 16 to the end of the variable name will result in from 0 to 16 decimal digits being displayed. However, the internal representation of the number always has full 16 digit resolution. for example, if A =7.123456789012345 then a variable A.1 would display 7.1, A.2, 7.12, ...., A.14, 7.1234567890123 (if double precision display) L 1580 and so on. A.0 or A. would round out the decimal and display 7. The decimal operator overrides the global default. The variable names are now A.1, A.2, .... and they must be referenced that way. For example, a.3=2*x-67. The decimal operator is most useful for dependent variables since it can be used to display more digits when a lower value has been globally set with the 'DEC apostrophe command. L 1590 As with the foreground and background colors, the global value of the decimal digits is saved with the equations and remains in effect when new equations are read into the program. ╒════════════════╕ │ PROGRAM LIMITS └────────────────────────────────────────────────────── 2.45 Maximum Number of Equations, Variables and Constants ──────────────────────────────────────────────────────────────────────── L 1600 ■ The maximum number of equations that may be entered is 63. For 61 to 63 equations, there is a maximum of 3 independent vars and the comment is not displayed. For 58 to 60 equations, 6 ind vars. For 1 to 3 equations, 63 independent vars, etc. The equations and ind vars must add up to 64 to 66 or less. The equation(s) can contain a maximum of 1840 characters (23 lines). The maximum number of operations such as additions, multiplications, etc. is approximately 1000. "% USE" is the percentage of codespace in use and is displayed after the program name/version. About 12 operations equal 1 %. If % USE L 1610 ------- 2.45 -- Maximum Number of Equations, Variables and Constants --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 36 -- exceeds 99% then immediate calculations may not have sufficient codespace. ■ The maximum number of dependent and independent variables is 66. The maximum number of storage variables is 256. Note: With storage variables, 63 equations with 259 independent variables can be entered if the storage variables are first defined. Only 3 independent variables can be displayed. Three or less equations can contain up to 319 variables: 63 independent variables and 256 storage vars. L 1620 ■ The minimum number of constants is 256 and the maximum number is (322-[total number of variables]). For example, if there are 2 dependent and 2 independent variables, then there can be a maximum of (322-[2+2])=318 constants. ╒═════════════════════╕ │ AFIT3 PROGRAM LIMITS└─═─────────────────────────────────────────────── 2.46 Maximum Number of Data Points and Data Coordinates L 1630 ──────────────────────────────────────────────────────────────────────── ■ The maximum number of data points is 224/(# coordinates + 1). If a data point has one coordinate (X,Y) then max points is 112. If a data point has two coordinates (X:Z,Y) then max points is 74. ■ The maximum number of coordinate variables for a data point is 14. The minimum number of optimized variables ("active") is 1 and the maximum number is 30 - # coordinate variables. Thus, L 1640 with (X,Y) data points, (1 coordinate variable X), up to 30-1 or 29 variables can be optimized ("active"). As the number of optimized variables increases, the accuracy of initial guesses must also increase! ╒═══════════════════╕ │ ERROR EXPLANATION └─────────────────────────────────────────────────── 2.50 Errors During Equation Evaluation and Elsewhere ──────────────────────────────────────────────────────────────────────── L 1650 The program will evaluate the equations by the rules and regulations discussed above. If an error is detected, then the program will display the location of the error in the equation and a brief error comment describing its nature. Type any key to continue the program. The user should correct these errors ------------ 2.50 -- Errors During Equation Evaluation and Elsewhere --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 37 -- and evaluate the equations again. An equation-error summary can be found within this help file. Other errors, particularly overflows, may cause the program to L 1660 display the EXEC ERROR message and return to the "? Equation(s)" prompt. Type (enter) to return to the main equation display. Record the error # and line number and report it! See below. ╒══════════════════╕ │ DIRECTORY SCREEN └─────────────────────────────────────────────────── 3.01 Directory Screen: Commands During Display ──────────────────────────────────────────────────────────────────────── L 1670 The asterisk commands: * or (F7), !* and @* are used to generate a directory of 1) equation files with the default extension of .EQU, 2) storage files with the default extension of .STO or 3) application help files with the default extension of .HLP, respectively. A path for the location of the directory can be specified. If the desired directory is the current one, simply type (enter) at the prompt or (end esc) "" (enter) to clear any existing path. The extensions of the files need not be the default ones (.equ, .sto or .hlp). L 1680 However, the selected file will always be loaded as EQU, STO or HLP depending on what asterisk command was used. The directory does not use the DOS SHELL and COMMAND.COM is not required in any directory. PATH descriptions can be the same as for the DOS DIR command. Note: If a filename is used then it must end in a period or the default extension is used and and if there is no extension then the default extension will always be used. Wildcards "*" and "?" can be used. Some paths might be: \CALC \CALC\ANALYSIS \CALC\data??? FORMULA??. *.DAT and so on. To search for all files beginning with the letter "a", only, enter L 1690 a path like \CALC\A* and so on. A summary of the commands used to locate and select a file follow: Note: If less than 8 filenames, some commands have no function. If more than 192 files, then only the last 192 are listed. -> move to first file name of current row (home) - Move highlighted cursor to column 1, the first file of a row L 1700 -> move to first file of first row ------------------ 3.01 -- Directory Screen: Commands During Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 38 -- (ctrl) (home) - Move cursor to column 1, row 1, the first file. -> move to last file of current row (end) - Move cursor to column 8 of the current row, if possible. -> move to last file of last row L 1710 (ctrl) (end) - Move cursor to column 8, last row, if possible. -> move to top file of current column (PgUp) - Move cursor to top row of current column. -> move to bottom file of current column (PgDn) - Move cursor to bottom row of current column. L 1720 -> move cursor to next file (cursor) (right) or (tab) - Move cursor to next file. -> move cursor to previous file (cursor) (left) or (backspace) - move cursor backwards. -> move up by one row L 1730 (cursor) (up) - move cursor up one file in a column. -> move down by one row (cursor) (Dn) - move down one file in a column. -> return info on highlighted file (space) - returns date and other file info for .EQU files only. L 1740 Displays date (saved with equations) and approx. 68 characters of comment and equations (if comment is less than 68 characters). -> new path prompt \ - Prompt for new path description. Use (end esc) "" (enter) to clear the old name. ------------------ 3.01 -- Directory Screen: Commands During Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 39 -- -> exit directory screen to main equation screen L 1750 (esc) or (ctrl Q) - exit from directory to main equation display -> choose a file (enter) - Select file and load as EQU, STO or HLP. -> search names by first letter L 1760 letters and other characters - jump to next filename starting with that character, if possible. ╒═══════════════╕ │ PLOT COMMANDS └─────────────────────────────────────────────────────── 3.05 Commands Used While Plot Screen is Displayed ──────────────────────────────────────────────────────────────────────── Only "active equations" are plotted versus an x-axis which is L 1770 one of the independent variables which is designated as a coordinate variable. Active equations have dependent vars followed by a visible "=". If more than one equation, one must activate/inactivate equations, as desired, with commands "A" and "I". If more than one independent var, one must designate x-axis coordinate with command "O" or place the cursor on the desired independent var before typing "P". A coordinate var has a ":" following its name. To plot, in the equations display type "P". Enter coordinate range (like from 10 to 20) for x-axis in form: 10 to 20 (enter) or 10;20 (enter). L 1780 While in the plot screen, the following letter commands are active. -> display cursor: C C - Use cursor. X and Y values of cursor are displayed. While ">" is displayed, the following keys are used to move it around: L 1790 (Home) - Move cursor to top left corner (Up Arrow) - Move cursor one small division up --------------- 3.05 -- Commands Used While Plot Screen is Displayed --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 40 -- (PgUp) - Move cursor to top right corner (Left Arrow) - Move cursor one small division to left (Right Arrow) - Move cursor one small division to right L 1800 (End) - Move cursor to lower left corner (origin) (Down arrow) - Move cursor one small division down (PgDn) - Move cursor to lower right corner. 1 to 9 - Change the increment of cursor movement when the arrows are used and move the cursor to the right by that amount. At entry, default is 1. L 1810 ; - designate first and last values for range to be plotted. After ; is typed the second time, the program will prompt with the chosen range. Modify if needed and type (enter) to plot. (ctrl Q) or most other keys - Exit back to plot. -> dump plot screen as text file: V V - Dumps the plot to a text file. Used to save calculations or plots for inclusion in reports, etc. Includes program name, L 1820 date/time, equations, comment. Enter filename in response to prompt. Note: Filenames ending in numeric extensions from "000" to "999" are automatically incremented each time the command is used. Thus, PLOT.001 --> PLOT.002 --> PLOT.003 and so on. If file exists, program will ask to "APPEND" or to "REPLACE". -> exit back to equations display: E (esc) Use "E" or "(esc) to exit back to equations display. L 1830 -> plot range for x-axis: Use semicolon. ; - Set new range for X-axis. Enter a new range in the form num1 to num2 or num1;num2. For example -45 to 123 or -45;123. If a single number is entered then only the first or last limit is replaced. For example, -30 (enter) or -30 to (enter) or -30; (enter) will only cause -45 to be replaced in -45;123 and to 106 (enter) or ;106 (enter) will cause only 123 to be L 1840 --------------- 3.05 -- Commands Used While Plot Screen is Displayed --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 41 -- replaced. -> shift plot left L - Shift plot to left along X-axis by 1 major scale division -> shift plot right R - Shift plot to right along X-axis by 1 major scale division L 1850 -> zoom in N - Move nearer to plot. Show less of X-axis. -> zoom out F - Move far away from plot. Show more of the X-axis. ╒════════════════════╕ │ ASTROFIT COMMANDS └────────────────────────────────────────────────── L 1860 4.01 Commands Unique to this Program AFIT3.EXE. ──────────────────────────────────────────────────────────────────────── -> Enter data points into the program prior to fit: D D - Use command D to enter new data or modify data. See below for subcommands while in the data entry mode. Data are entered as data points such as (X,Y) with the data coordinates being (X) and the data values being (Y). There may be more than one L 1870 data coordinate. During the "fit", the values of each data point are substituted into the active equation's coordinate variable(s) and the calculated equation value is subtracted from the corresponding data value to generate the least squares error. Polynomial regression is performed in the data-entry screen with subcommand P. -> Load a data point into active equation and calculate error: !D Command !D substitutes a specified data point (including L 1880 coordinate(s) and data value) into coordinate variable(s) of displayed equations and calculates equation(s) and error. Enter data point #. -> Load all data points into active equation and calculate error: @D ----------------- 4.01 -- Commands Unique to this Program AFIT3.EXE. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 42 -- Command @D substitute all data points into corresponding coordinate variable(s) of displayed equations and calculates equation(s) and total error. Total error is square root of sum of individual errors squared. L 1890 -> List the results of the fit including actual and calc values: R Command R is used to list the results which include: Data #, Data Coordinate, Calculated Value, Error and Symbolic Error. Calculations are always based on the current values of the independent variables and the data. Enter the range of the data points to be listed in the form number1 to number2 or number1;number2. For example, 1 to 6 or 1;6. When more than one coordinate, the Program will list that coordinate on which L 1900 cursor resides when "R" is typed. If more than one coordinate per data point, use "cursor right" or "cursor left" keys to toggle coordinate(s) while tabulated results are displayed on screen. -> List the results of the fit to system printer LPT1: !R Command !R lists the results to the printer (LPT1:). While printing, type any key to terminate. Use "!P" to set the printer to nlq mode, if necessary. L 1910 -> List the results of the fit to a file: @R Command @R lists the results to a file for subsequent use such as inclusion in a report and so on. Enter filename in response to prompt and then enter range (first to last points). For example: FIT1.TXT (enter) and 1 to 10 (enter). Program will automatically increment number extensions. RESULTS.001 ==> RESULTS.002 ==> RESULTS.003 and so on. L 1920 -> Fit equation to Data points by optimizing active independent variables: S Command S starts the nonlinear least-squares regression by solving for the "best" values of the active independent variables which minimized the total squared error between the equation calculated with the data coordinates substituted into the coordinate variables and the data value of each data point. The accelerated-interpolation method of Cote and Herbold is used. Before typing "S", designate active equation, active ind L 1930 vars which are to be optimized, data coordinate(s). Enter data points as (data coordinate(s), data values) and then initial ----------------- 4.01 -- Commands Unique to this Program AFIT3.EXE. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 43 -- guesses for active variables. Choose a tolerance based on the assumed relative accuracies of the initial guesses. Typically, from .001 to 1 (default=.1). -> Generate correlation and fit coefficients: T Command T "tests" the fit and allows some estimate of the "goodness" of the optimized variables. A correlation L 1940 coefficient and a fit coefficient are calculated. For a perfect fit both coefficients equal 1. -> Generate residual variance and coefficient of determination: !T Command !T calculates additional statistical data to verify the "goodness" of the fit. The residual variance and coefficient of determination are calculated. For a perfect fit RESID VAR=0 and C of D=1. L 1950 ╒═════════════════════╕ │ DATA ENTRY COMMANDS └───────────────────────────────────────────────── 4.02 Commands Used to Manipulated Data Points and Their Values. ──────────────────────────────────────────────────────────────────────── Single key subcommands which can be executed while the data-entry screen is displayed (command "D") are: L 1960 B - Move backwards to the previous data point Use (backspace) for the same purpose. C - Calculate equation at coord(s) of data point. List calculated result and error separately. Use !C to calculate and replace data value. Use @C to calculate and replace data values at all points. Use $C to apply immediate calc to data coord/value of all data points. For all calculations, the active dependent variable and coordinate variable(s) refer to values of each L 1970 data point. Order of calculation: Substitute data point #1 into displayed equations, calculate displayed equation(s), set active dependent variable to data value and perform immediate calculation. Repeat with next point and so on. Note: !C, @C and $C replace data values! Be careful! E - Exit to the display of the equations -- 4.02 -- Commands Used to Manipulated Data Points and Their Val... --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 44 -- F - Move to the first data point (#1) L 1980 I - Insert a zero data point before the current data value. The total data points are increased by 1. J - Jump to a specific data point. Program prompts for the data #. L - Move to the last data point M - Move to the middle of the data points L 1990 N - Move to the next data point P - Automatic least-squares polynomial fit. Must be 2 or more data points. Enter order (maximum magnitude (N) of 15 or (# points-1)). Pos order, poly A0+A1*X^1+...AN*X^N and neg order, poly A0+A1*X^-1+...AN*X^-N. Replace equations with polynomial by answering Y to prompt. Immediate calc always replaced by poly with number coefficients. R - Remove the current data point. L 2000 The total data points are decreased by 1. # - Enter total number of data points. Max points is 1024/(# coord+1). Jump to last point. Use @# to set number of points to zero and exit. ? - Set data point (coord and value) to zero. Use !? to set data values of all data points to zero. Use @? to set all data coordinates and values to 0.0. Note: !? and @? set data values to 0.0! Be careful! L 2010 \ - Display the full 16 digit precision and position the cursor for editing the number. See below. | - Display the last immediate calculation and position the cursor after an imbedded apostrophe ('). See below. The active dependent variable and coordinate variable(s) refer to values of the current data point. Calculation order: Load data point into displayed equations, calculate displayed equation(s), set active dependent variable to data L 2020 value and perform immediate calculation. (backspace) - Move backwards to preceding data point. -- 4.02 -- Commands Used to Manipulated Data Points and Their Val... --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 45 -- (enter) - Move to the next coordinate, data value or data point (esc) - Redraw the display and/or exit if on the first data point when typed. (ctrl) Q - Exit to the display of equations. Same as "E". L 2030 (tab right) (tab left) - Move to next or previous data point. Current value - Use ":" to designate the current value of the coor or data value in calculations. For example: 4*:+:^2 or sqr(abs(:)) (enter) Edit keys - Use keys: (Home) (up arrow) (PgUp) (left arrow) (right arrow) (End) (down arrow) (PgDn) to change cursor and/or point. Note: Keys (up arrow) L 2040 (down arrow) (PgUp) and (PgDn) move cursor in the same data point only. Keys: (left arrow) (right arrow) (Home) and (End) move cursor from data point to data point. ╒════════════════════════════╕ │ INTRODUCTION: FIT EQUATIONS└────────────────────────────────────────── 4.04 Introduction to Fitting Equations to Data by Nonlinear Least-Squares Regression. L 2050 ──────────────────────────────────────────────────────────────────────── The nonlinear fit (regression) is command "S". Data must be entered into the program first. The following example is intended to illustrate the general procedures only. A second-order polynomial equation will be fitted to four data points. In order to use the subcommand "S", one must first enter an equation into the Program with at least 2 independent variables. Any equation will do. Note: the polynomial regression subcommand P can be used to solve this problem L 2060 quickly, but for now, the more general nonlinear regression (or fit) will be used. Note: You will frequently start to see apostrophe commands like 'EQU, 'VAR and 'COM appearing in the helpfile. The 'EQU field provides info for the equations display which is loaded when the highlight bar lights up on the 'EQU line and the "Type Q...." message appears at the bottom of the screen. To learn more about these commands, read the discussion of apostrophe commands in this helpfile. L 2070 ----- 4.04 -- Introduction to Fitting Equations to Data by Nonlinear --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 46 -- ║ To automatically load these equations, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU Y=A*(X-B)^2+C 'COO X 'COM "Type (F1) to return to the helpfile" L 2080 If the equation is loaded, then skip to step (5). 1) When the Program is displaying the equations screen, type (F6) or "!/" in order to get the "Equations" prompt. In response to the prompt "? Equation(s)", type: (end esc) Y=A*(X-B)^2+C) (enter) 2) In response to the prompt for a comment Type (end esc) "" (enter). Remember to type (F1) to return to this file. L 2090 3) If more than one equation were to be entered, inactivate all other equations except the the single equation whose active variables are to be optimized. To inactivate an equation and/or variable move the cursor to that variable and type I. The equal sign will disappear. The fit does not use inactive equations but these equations can still be used as intermediate equations in the calculation of the active equations. 4) Next move the blinking cursor to variable X by typing "L". Designate X as a coordinate by typing "O". A colon ":" will L 2100 appear after its name. 5) Enter the 4 (X,Y) data points. ║To load the comment and jump to the equations display, type Q ║ ║when the highlight bar is lighted on the next line. ║ 'EQU 'PT0 'DATA (0,40) (3,310) (6,400) (9,310) 'COM L 2110 Enter the four data points as (X,Y) pairs: (0,40), (3,310), (6,400) and (9,310). To verify the points or enter them one by one , Type D. For X(1), type 0 (enter). For Y(1), type 40 (enter). Now enter X(2) then Y(2) and so on. After entering Y(4) as 310, the program will advance to point #5. Type R to remove this unwanted point. Type E to exit data command and return to the equation display. Type (F1) to ----- 4.04 -- Introduction to Fitting Equations to Data by Nonlinear --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 47 -- return to the helpfile. ║To load the comment and jump to the equations display, type Q ║ ║when the highlight bar is lighted on the next line. ║ L 2120 'EQU 'VAR A=-5 B=10 C=200 'COM Set up some reasonable initial guesses. If necessary, move the cursor to A and set its value to -5. Move the cursor to B and set its value to 10 and move the cursor to C and set its value to 200. To perform a nonlinear fit, type S. In response to the prompt for a tolerance, type .1 (enter). After about 100 iterations, the program will calculate A as 10 and B as 6 and C as 400. Type any key to stop iterations after # 100 or so. Note the magnitudes of the ERROR and SIG L 2130 FIGS. As the 'fit' or regression improves, the ERROR will tend toward a minimum and SIG FIGS will grow toward 16. Type (F1) to return to the helpfile. Some additional information on the fit. A math error during the calculation will not terminate the fit but the results may be misleading because the program skips over operations that are improper, undefined or not allowed. Care should be taken to verify that errors do not occur as L 2140 convergence is approached. Data points can be defined with more than one coordinate. For example (X:W,Y) where X and W are data coordinates and Y is the data value. Use commands "T" and "!T" to calculate coefficients and variances. The point-by-point results of the fit can be tabulated on the screen by use of the command "R" or listed on the printer (LPT1:) by use of "!R". The tabulated results can L 2150 be saved in a file by use of the command "@R". The equations and data can be plotted with the command "P" and the entire calculation and data are saved with the command (F9) or "]". Summary of steps to fit equation to data: 1) Enter the equation(s) and message. If more than one equation, use "I" to inactivate all but the primary equation. There can be more than one equation on the screen, but only one equation can be fitted. L 2160 2) Designate one or more independent variables as data ----- 4.04 -- Introduction to Fitting Equations to Data by Nonlinear --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 48 -- coordinates by using "O". 3) Enter data values. Type "D". To exit, first type "R" to remove the last point if necessary and then type "E". 4) Select independent variables to be optimized by "A" and inactivate all others which are to be considered as parameters by "I". Not all independent variables have to be optimized. L 2170 5) Set active independent variable to reasonable initial guesses. 6) Type "S" to start the fit. Enter tolerance. The larger the tolerance, the wider the initial search. Typically, the tolerance should be between 0.1 and 1. 7) After ERROR or SIG FIGS is reached, type any key to stop fit. L 2180 8) To plot the fit, type "P" and answer "Y" to the "include data on plot prompt" 9) Type "T" or "!T" to check correlation coefficients. 10) Type "R" or "!R" or "@R" to tabulate results. ╒═══════════════════════════════╕ │ EXAMPLE: FIT EQUATION TO DATA └─────────────────────────────────────── L 2190 4.06 Finding Best Values of Transistor Parameters from Experimental Data by Nonlinear Least Squares. ──────────────────────────────────────────────────────────────────────── A very common problem in Engineering and Science is to estimate the best values of the coefficients of a mathematical model given a set of experimental data. In the example discussed here, the area of application is Electrical Engineering and the current problem is to extract the best values of parameters L 2200 which characterize the behavior of a transistor. By fitting the theoretical equation, discussed below, to the experimental data, one attempts to determine the DC current gain, BETA0, the critical frequency, FC, and the transition frequency, FT. In this example, the values of the DC current gain, BETA0, and the critical frequency, FC, for a transistor will be estimated by fitting the theoretical equation of BETA as a function of --------------- 4.06 -- Finding Best Values of Transistor Parameters --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 49 -- frequency F to an experimental data set in which the current gain BETA is measured at 5 different frequencies. The L 2210 transition frequency, FT, is derived from the DC current gain BETA0 and FC and is not directly extracted. The current gain, BETA, and transition frequency, FT, of a small signal rf transistor can be approximated as a function of the measurement frequency, F, by the equations: BETA=BETA0/SQR(1+F^2/FC^2) FT=BETA0*FC L 2220 where: BETA = current gain at frequency F BETA0 = low frequency current gain, CE mode, zero AC potential between collector and emitter FC = transistor cut-off frequency. Current gain drops to 0.707 (-3dB) times the low frequency value L 2230 FT = transistor unity-gain frequency The equipment used in these measurements operates to 10 MHz; therefore, it is usually not possible to measure the unity-gain frequency, FT, directly. The data set has been generated by measuring the current gain, BETA, vs. frequency, F, from 1 to 10 MHz. The experimentally measured data points are: F (MHz) BETA L 2240 1 105 2.5 90 5 80 7.5 60 10 50 First enter the equations into the program. Move the text down until the highlight bar appears on the EQU line below. L 2250 ║ To automatically load these equations, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU --------------- 4.06 -- Finding Best Values of Transistor Parameters --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 50 -- BETA=BETA0/SQR(1+F^2/FC^2) FT=BETA0*FC 'INA FT 'COO F 'COM Calculate BETA0 (DC current gain) and FC (critical frequency) for a L 2260 transistor by fitting BETA vs. F (MHz) to theoretical equation. Type (F1) to return to the helpfile. After the equations, a comment and data are entered into AFIT3, the equation display should appear similar to what is shown below: ...................................................................... --- Comment --> Calculate BETA0 (DC current gain) and FC (critical frequency) for a transistor by fitting BETA vs. F (MHz) to theoretical L 2270 equation. Type (F1) to return to the helpfile. BETA=BETA0/SQR(1+F^2/FC^2) BETA = 0 FT=BETA0*FC FT 0 11:14:05 *** Accuracy ? Warning # 8 *** 10-20-1980 L 2280 BETA0 => 0 F : 0 FC = 0 ...................................................................... The "Comment", if any, is displayed at the top. The equations BETA and FT, in the order in which they are entered, are displayed from top down. The time and date are displayed in the middle along with the "Accuracy ? Warning #8" Comment. This frequently-seen warning Comment is used to inform the user that the displayed values of the dependent variables BETA and FT may not be related to the values based on the equations and L 2290 the independent variables. To actually calculate the dependent variables, one would enter a value for an independent variable or type C. Finally the 3 independent variables BETA0, F an FC are listed at the bottom in alphabetical order. The blinking cursor ">" is positioned on BETA0. Data points consist of two numbers: a data coordinate and a data value. In the present problem, data are to be entered in (F,BETA) pairs. If necessary, to designate F as the variable associated with the data coordinate, move the cursor to F and L 2300 --------------- 4.06 -- Finding Best Values of Transistor Parameters --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 51 -- type O. The equal sign "=" will be replaced by a colon ":". A colon is used to signify that variable F is now a data coordinate. Only one of the two equations, BETA, is to be associated with the data value. The other equation must be made "invisible" or inactive. If necessary, move the cursor to FT and type I. The equal sign after FT will disappear. At this time, data points are defined as (F,BETA) pairs. Next data are entered in (F,BETA) pairs, type D. The screen will appear as shown below and enter the data. L 2310 ║ To automatically load these equations, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU 'PT0 'DATA 1 105 2.5 90 5 80 L 2320 7.5 60 10 50 'COM If desired, enter the five data points as (F,BETA) pairs: (1,105), (2.5,90), (0.5,80), (7.5,60) and (10,50). To verify the points or enter them one by one , Type D. For F(1), type 1 (enter). For BETA(1), type 105 (enter). Now enter F(2) then BETA(2) and so on. After entering BETA(5) or 50, the Program will advance to point #6. Type R to remove this unwanted point. Type E to exit data command and return to the equation display. Type (F1) to return to the helpfile. L 2330 Finally initial "guesses" for the two active independent variables BETA0 and FC are set and the problem is solved. The Program will optimize the values of the active independent variables BETA0 and FC, whose names are followed by the "=", in order to attempt to minimize the sum of squared errors between the calculated value of the single active dependent variable (with the data coordinates of each data point substituted into the coordinate variable) and the data value of each data point. In this example, each of the five data coordinates will be L 2340 substituted into F, BETA will be calculated and then the squared differences between BETA and the data value of each of the five points will be summed and minimized. ║ To automatically load these equations, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ --------------- 4.06 -- Finding Best Values of Transistor Parameters --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 52 -- 'EQU 'VAR BETA0=1 FC=1 'COM L 2350 If necessary, set the initial values of BETA0=1 and FC=1. Type S to start the fit. Use the default tolerance of 0.1. Just type (enter). The program will optimized BETA0 and FC to minimize the ERROR and the iteration counter will 'roll off' as the fit proceeds. Note that the value of the coordinate variable F stays constant. After about 64 iterations, the fit will converge as the estimated significant figures approaches 16. In this case SIG FIGS reaches 14. Type any key to stop the fit. Type (F1) to return to the helpfile. As the fit advances and the number of iterations increases, L 2360 the ERROR will tend to minimize but it will not approach 0.0 unless the fit is "perfect". The screen should appear similar to what is shown below, although the comment will be different. ...................................................................... --- Comment --> Calculate BETA0 (DC current gain) and FC (critical frequency) for a transistor by fitting BETA vs. F (MHz) to theoretical equation. BETA=BETA0/SQR(1+F^2/FC^2) BETA = 104.1315 L 2370 FT=BETA0*FC FT 568.0856 11:24:15 Iteration # 64 ERROR = 6.3589147 SIG FIGS = 14 10-20-1980 BETA0 = 104.1315 F : 0 FC = 5.455464 ...................................................................... L 2380 Obtaining a summary of results. Following optimization, one may want to list a summary of the results. Type command R from the equation display. The screen should appear as below. .................................................................. # F BETA Calculated % Error Relative % Error 1 1 105 102.425 -2.452405 ----- L 2390 2 2.5 90 94.66504 5.183378 +++++++++ --------------- 4.06 -- Finding Best Values of Transistor Parameters --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 53 -- 3 5 80 76.76686 -4.041424 ------- 4 7.5 60 61.25394 2.089902 ++++ 5 10 50 49.87006 -.2598841 0 # F BETA Calculated % Error Relative % Error L 2400 ................................................................... The "results" screen list the data point number (#), the value of the data coordinate (F), the value of the data value (BETA), the calculated value of BETA based on the equation and the optimized values of BETA0 and FC, the % ERROR which is the actual value of BETA less its calculated value expressed as a percent of the actual value. Finally the SYMBOLIC ERROR is tabulated. It is a visual representation of the uncertainty in the fit. For each point, the actual value of BETA can be L 2410 thought of as being in the middle under the C of SYMBOLIC and would correspond to a 0 if the fit were more-or-less perfect. "+" mean the fitted curve exceeds the data value at this point and the number of "+" is a relative measure of how much. "-" means the fitted curve underestimates the data value at this point and the number of "-" is a relative measure of how much. Note, the number of decimal places for the table entries is determined by the current setting as determined by the 'DEC apostrophe command. L 2420 Plotting the fitted equation and experimental data. The equation and data can be plotted to verify the "fit" visually. Type command P from the equation display.. Type (enter) in response to the prompt not to include data on plot. The screen should appear similar to below: ....................................................................... 105.-█ |a a L 2430 | a | a | a 91.- █ a | a | a | a | a █ 77.- a | a L 2440 | a | a | a 63.- a | █a | a | a a | a 49.- ||--------------|--------------|--------------|--------------|----- L 2450 1 2.96 4.91 6.87 8.83 BETA[a] vs. F --------------- 4.06 -- Finding Best Values of Transistor Parameters --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 54 -- ....................................................................... The first equation BETA is represented by "a". The 5 data points as (F,BETA) points are plotted as "█". ╒═══════════════════════════════╕ │ EXAMPLE: FIT EQUATION TO DATA └─────────────────────────────────────── L 2460 4.08 Automatic Least-squares Polynomial Regression (Linear Least Squares) ──────────────────────────────────────────────────────────────────────── The polynomial fit is subcommand "P" of the data entry subcommand "D". Data must be entered into the Program first. The use of the polynomial fit (regression) will be illustrated with an example. Polynomials of orders 1 and 3 will be fitted to four data points. In order to use the subcommand "P", one must first enter an equation into the Program with at least 2 L 2470 independent variables. Any equation will do. ║ To automatically load these equations, type Q when the ║ ║ highlight bar appears on the screen. Scroll down, if ║ ║ necessary, to light it. ║ 'EQU Y=A*X 'COO X 'COM "Type (F1) to return to the helpfile" L 2480 If the equation is loaded, then skip to step (4). 1) When the Program is displaying the equations screen, type (F6) or "!/" in order to get the "Equations" prompt. In -------------- 4.08 -- Automatic Least-squares Polynomial Regression --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 55 -- response to the prompt "? Equation(s)", type: (end esc) Y=A*X (enter) 2) In response to the prompt for a comment Type (end esc) "" (enter). Remember to type (F1) to return to this file. L 2490 3) Next move the blinking cursor to variable X by typing "L". Designate X as a coordinate by typing "O". A colon ":" will appear after its name. 4) Enter the 4 (X,Y) data points. ║To load the comment and jump to the equations display, type Q ║ ║when the highlight bar is lighted on the next line. ║ 'EQU 'PT0 L 2500 'DATA (1,-3) (2,-57) (3,-219) (4,-549) 'COM If necessary, enter the four data points as (X,Y) pairs: (1,-3), (2,-57), (3,-219) and (4,-549). Type D. For X(1), type 1 (enter). For Y(1), type -3 (enter). Now enter X(2) then Y(2) and so on. After entering Y(4) as -549, the program will advance to point #5. Type R to remove this unwanted point. Type E to exit data command and return to the equation display. Type (F1) to return to the helpfile. L 2510 ║To load the comment and jump to the equations display, type Q ║ ║when the highlight bar is lighted on the next line. ║ 'EQU 'COM The polynomial regression is part of the data entry command. Type command D first. To perform a first order fit, type P. In response to the prompt for an order, type (end esc) 1 (enter). A positive order selects a polynomial of the general form Y=A0+A1*X^1+...AN*X^N and a negative order, a polynomial of the general form Y=A0+A1*X^-1+...AN*X^-N. Type N (enter) in response to the prompt to L 2520 'REPLACE EQUATIONS'. Type E to exit data command and return to the equation display. Type (F1) to return to the helpfile. The Program will calculate A0 as 243 and A1 as -180. The Program will display the polynomial equation and a message which summarizes the first-order fit. Note the magnitudes of the residual variance and the coefficient of determination. As the order increases, the fit will improve and the residual variance will decrease toward 0.0 and the coefficient of determination will increase to 1.0. L 2530 -------------- 4.08 -- Automatic Least-squares Polynomial Regression --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 56 -- ║To load the comment and jump to the equations display, type Q ║ ║when the highlight bar is lighted on the next line. ║ 'EQU 'COM The polynomial regression is part of the data entry command. Type command D first. To perform a third order fit, type P. In response to the prompt for an order, type (end esc) 3 (enter). The Program will now calculate A0 as 3, A1 as -2, A2 as 6 and A3 as -10. Notice that the fit is 'perfect'. The residual variance is 0.0 and the coefficient L 2540 of determination is 1.0. Type Y (enter) in response to the prompt to 'REPLACE EQUATIONS'. Type E to exit data command and return to the equation display. Type (F1) to return to the helpfile. The Program will replace the main equation(s) with the polynomial Y=A0+A1*X^1+A2*X^2. If the comment is empty, it will replace it with fit information. The coefficients A0 to A2 are set equal to their least-squares values and variable X is designated as the coordinate. The immediate calc is replaced by the polynomial with explicit number coefficients. L 2550 Should this form of the equation be needed it can be viewed with the immediate calc command "|". An error during the calculation will terminate the fit and return the Program to the equations display. Warning # 451 will be generated. The most likely cause of errors are overflows from either coordinate values with large magnitudes or higher order terms. Some important points are: L 2560 1) There must be 2 or more data points. If only two points, then the order is 1 by default and need not be specified. 2) The maximum order is one less than the number of points or 15, whichever is smaller. Thus if there are 10 data points, then a polynomial of order from 1 to 9 can be chosen. 3) Polynomial coefficients are completely determined if the order of the polynomial is one less than the number of points. L 2570 Thus if there are 4 points, then a third order fit will be "perfect". As the number of points becomes much large than the order, the polynomial represents a "smoothed" approximation. 4) The Program calculates the residual variance RESID VAR and the coefficient of determination COEFF OF DETERM for each fit. -------------- 4.08 -- Automatic Least-squares Polynomial Regression --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 57 -- 5) The polynomial equation can be used to replace the current equation(s). This is useful for further analysis including the tabulation of results (command "R" in equation display), the L 2580 plotting of the equation and data (command "P" in equation display) and the saving of the equation and data (subcommand "]" in equation display). 6) The immediate calculation (command "|") is always replaced by the polynomial with number coefficients and without a dependent variable. The polynomial can be added to the main equations by exiting to the equation display, typing "/", moving the cursor to the end of the equations and typing "(alt) 1" . Remember to insert a dependent variable with a unique L 2590 name, the equal sign and at least one space! 7) An interesting relationship exists between poly A0+A1*X^1+...AN*X^N and poly A0+A1*X^-1+...AN*X-N. These two polynomials when generated from the same data set will always intersect at (N+1) points. 8) Data points can be defined with more than one coordinate. For example (X:W,Y) where X and W are data coordinates and Y is the data value. Polynomial fits of Y vs. X and Y vs. W are L 2600 possible. Position the cursor on the desired coordinate before typing "P". Note: Zero-valued terms like "+W-W" will be added to the equations to represent extra coordinates and variables such as "W" will be designated as coordinates if the polynomial equation replaces the current equation(s). ╒══════════════════════════════╕ │ ADVANCED FUNCTIONS WITH DATA └─────────────────────────────────────── 4.10 Advanced Functions using Data and Active Equation L 2610 ──────────────────────────────────────────────────────────────────────── DATA ENTRY. Data points are ordered numbers which are composed of elements called coordinate values and a single data value. Data points are always handled as a group. For example, (X,Y) signifies a simple, and perhaps the most common form of, a data point. Element X is the coordinate of the data point and element Y is the value of the data point. (X:W,Y) signifies a data point with two coordinates, sometimes referred to as 2 dimensional, and (X:W:Z,Y) signifies a data point with three L 2620 coordinates which is sometimes referred to as 3 dimensional, and so on. Data are entered into the program by first entering ---------- 4.10 -- Advanced Functions using Data and Active Equation --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 58 -- an equation with at least 2 independent variables. Before using the subcommand "D", one must designate only one of the equations as active, if there are more than one, The dependent variable of the active equation will be associated with the data or Y value of the data point. One or more of the independent variables are designate as coordinates of the data point. The name(s) of the coordinate independent variables are associated with the coordinate values of the data point. There L 2630 must always be one active independent variable which is not designated as a coordinate! Use subcommands "A" and "I" to activate/inactivate variables and subcommand "O" to designate coordinates while the main equations are displayed. Type "D" to enter data. Use the appropriate letter subcommands and arrows to enter/manipulate data. Warning! The Program automatically advanced from the last point to the next point by adding a zero data point. Type "R" to remove this unwanted data point, if necessary, before exiting back to the main equation screen. Also, while in the data entry mode, the names L 2640 of the coordinates and data value always refer to the numbers of the current data point. For example, a calculation of (space) Y=2*X (enter) will always set the the current data value to 2 times the current coordinate value. Data points can also be read in from a DATAONLY file. See Section 1.14 below. DATA TRANFORMATIONS. Mathematical operations/transformations can be applied to each individual element of a data point by using a simple equation which references the desired elements. Thus, to set the data value of the current point to the square L 2650 root of the coordinate simply type (space) Y=SQR(X) (enter). Note, start calculations with a space to avoid confusion with the letter subcommands! Furthermore, an immediate calculation can be applied to all members of a particular coordinate or all of the data, or Y, values by use of the subcommand "$C". This subcommand applies an entered immediate calculation to all of the specified members. For example, data points may be in the form (X,Y) but one desires a linear fit to data of the form (1/X, LOG(Y)). The current data can be transformed to this form by two uses of the subcommand "$C". First transform the Y L 2660 values. The general way is to type "$C" and enter (esc) Y=LOG(ABS(Y)) (enter) or, alternatively, move the cursor to a Y value, type "$C" and then type (esc) LOG(ABS(:)) (enter). Note, the ":" can be used to represent the current variable name and the result of the calculation will be assigned to the current data element because an explicit dependent variable has not been specified. Similarly, one can take the reciprocal of the X values by first typing "$C" and then either entering an ---------- 4.10 -- Advanced Functions using Data and Active Equation --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 59 -- explicit immediate calc like (esc) X=1/X (enter) or, if the cursor is on an X value when "$C" is typed, by typing (esc) 1/: L 2670 (enter). Use subcommand "P", polyfit, to calculate the desired polynomial. After this operation, data can be "untransformed" by applying reciprocal operations (Y=EXP(Y) to y values and X=1/X to X values) to the appropriate elements with subcommand "$C". SUBSTITUTING DATA INTO DISPLAYED EQUATIONS. While in the main equation screen, previously entered data points can be substituted into the displayed equations with subcommands "!D" and "@D". Use "!D" to substitute a single data point into the L 2680 main equations and "@D", to substitute all data points into the main equations. A root-mean-squared error is also calculated. This error is identical to what is calculated during the fit subcommand "S". By changing values of independent variables and typing "@D", one can actually minimize the error and optimize the values of the variable manually, if so desired! PRIORITY OF CALCULATION WITH DATA POINTS. When in the data entry mode or when using subcommands "!D" or "@D", the following priorities apply to all calculations: 1) Data L 2690 coordinate values are first substituted into the corresponding coordinate variables of the main displayed equation(s), 2) All main displayed equations are calculated and 3) The data value is substituted into the corresponding dependent variable. For example, if one has (X,Y) data points and wishes to calculate the mean of the X and Y values, Enter a set of equations such as: Y=Y+A YTOTAL=YTOTAL+Y L 2700 XTOTAL=XTOTAL+X COUNTER=COUNTER+1 YAVE=YTOTAL/COUNTER XAVE=XTOTAL/COUNTER Designate Y as the active equation. Designate X as the coordinate. Variable A is a dummy. Type "@?" to zero all. Type "@D" to calculate mean value with data points. Note, these equations can be used with other similar data sets by overlaying the equations with the "@[" subcommand which does L 2710 not change current data coordinates or values. ---------- 4.10 -- Advanced Functions using Data and Active Equation --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 60 -- ╒═════════════════════════╕ │ DATA ONLY FILES OF DATA └───────────────────────────────────────────── 4.12 Reading External Files of Data Only ──────────────────────────────────────────────────────────────────────── The Program can read a user-generated file of data points if it is written with the simple format described below. Once an L 2720 analysis has been developed, one may want to apply it repeatedly to different files of data by using an external file of data points which consists of: 1) a header record, 2) a title record and 3) 2 or more numbers with one number per record. An example of an external file of data points follows: "ASTRO3 DATAONLY","04-01-81","17:02:56" "Data only consisting of 6 numbers: 3 (x,y) or 2 (x:w,y) data points" 1.11 -1.11 L 2730 100.11 2.22 -2.22 200.22 This ascii file can be generated with a text editor like PE2, B,or a word processor like WP (save as DOS text) or even by another Program. The first record is the header record and it consists of 3 fields: "astro3 DATAONLY" must always be first, then the date and then the time. All fields are enclosed in L 2740 double quotes and separated by commas. The second record is the title record. The information in this record must be enclosed in double quotes. It will be added on to the Program message which is displayed at the top of the screen in the main equation display. The Program message can be edited with the "!/" subcommand. Null or empty fields are specified by the empty string "". Finally, the data numbers are entered one per record. In general, one should set up an equation, define coordinate(s) L 2750 and type "D" to verify the structure of the data point before reading DATAONLY files into the Program. Data points are entered coordinate(s) first in alphabetical order and then data value. Usually there is one coordinate per data point; however, there may be more than one. In the above example if points are defined as (X,Y) then there are 3 data points: (1.11,-1.11), (100.11,2.22) and (-2.22,200.22). However if points are defined with two coordinates (X:W,Y) then there are only 2 data points: (1.11:-1.11,100.11) and (2.22:-2.22,200.22). L 2760 ------------------------ 4.12 -- Reading External Files of Data Only --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 61 -- DATAONLY files are read in from the main equation display with the subcommand "[" which is also used to read in equation files. The default extension is also ".EQU". However, one can do a directory with another extension such as ".DAT" and read in the data with the directory subcommand "*" by ending the path description with *.DAT. Warning #403 indicates that the structure of the data point may not have been properly defined or setup before a data-point operation. L 2770 ╒══════════╕ │ WARNINGS └──────────────────────────────────────────────────────────── 5.01 Summary of Common WARNINGS During Calculations. ──────────────────────────────────────────────────────────────────────── The warning numbers followed by an explanation follow: 1 - Attempt to raise negative number to non-integer power. Operation was ignored. Y=X^W is ok if X=-1.3 and W=2 but is L 2780 not allowed if W=2.1. - Also, attempt to raise number to power such that the result is greater than 1E30 (overflow) or less than 1E-30 (underflow). The number was set to 1E30 for overflow and 1E-30 for underflow. 2 - Overflow from multiplication. The result of the multiplication of two numbers exceeded 1E30 in magnitude. The result of the multiplication was set to a magnitude of 1E30. 3 - Overflow from division. The result of the division of two L 2790 numbers exceeded 1E30 in magnitude. The result of the division was set to a magnitude of 1E30. 8 - The displayed values of the equation(s) may not be accurate. In other words, the values of the dependent variables may not be related to the values of the independent variables by the recipes of the equations. The most common warning message. Will be produce if a dependent variable is set to any number. Always produced after "?" command and at the entry into a calculation. Type "C" to recalculate if L 2800 uncertain about the values of the dependent variables. 15 - Attempt to take the arccosine, ACOS(...) or ACOSD(...), of a number whose absolute value is greater than 1.0. Operation was ignored. ------------ 5.01 -- Summary of Common WARNINGS During Calculations. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 62 -- 16 - Attempt to take the arcsine, ASIN(...) or ASIND(...), of a number whose absolute value is greater than 1.0. Operation was ignored. L 2810 18-19 - Same as for 15 and 16 but for ACOSD(...) and ASIND(...). 24 - Attempt to take the arccosine hyperbolic, ACOSH(...), of a number whose value is less than 1.0. Operation was ignored. 26 - Attempt to take the arctangent hyperbolic, ATANH(...), of a number whose absolute value is greater than 1.0. Operation was ignored. L 2820 28 - Attempt to take a natural antilog of a number such that the result exceeded 1E30 (overflow) or was less than 1E-30 (underflow). The program set the magnitude of the result to 1E30 for overflow and 1E-30 for underflow. 31 - Attempt to take the square root, SQR(...), of a negative number. Operation was ignored. 32 - Attempt to take natural log, LOG(...), of zero or a negative number. Operation was ignored. L 2830 33 - Attempt to take log base 10, LOG10(...), of zero or a negative number. Operation was ignored. 43 - Overflow from factorial. The result exceeded FP magnitude limit. The result of the operation was set to the sign of the number at overflow times 1D+30. Currently, X must be 33 or less in FACT(X) for no overflow. ╒═══════════════╕ L 2840 │ AFIT3 WARNINGS└─────────────────────────────────────────────────────── :WKP.5.03 Summary of WARNINGS From AstroDataFitter 3 ──────────────────────────────────────────────────────────────────────── 403 - Error in defining the active equation (There must be only 1.) and/or the number of coordinate variables (There must be at least 1 and no more than 14.) and/or the number of active independent variables (There must be at least one and no more than 15 - # of coordinates.). The Program will use default L 2850 settings in order to correct the setup. ------------ 5.01 -- Summary of Common WARNINGS During Calculations. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 63 -- 404 - The correspondence between the data coordinates and values and the intended variables may be inaccurate. This warning message is used to inform the user that the Program may have detected a situation that will result in some sort of confusion. In particular, the status of variables may have been changed and the subcommand "D" was not used before other subcommands such as "S", "R", "T" or "X". L 2860 405 - Less than 2 independent variables in the equation(s). There must be at least two independent variables in order to have one coordinate and one variable to be optimized. 406 - No data in program. Occurs for subcommands which require data such as "S", "R", "T", "X" and so on 451 - Error during least-squares polynomial calculation. Calculation terminated before completion. L 2870 ╒════════╕ │ ERRORS └────────────────────────────────────────────────────────────── 5.05 Summary of ERRORS during evaluation of equations ──────────────────────────────────────────────────────────────────────── The equation evaluation error numbers with an explanation follow. 1 - ILLEGAL OPERATION. L 2880 All mathematical operations such as ^, *, /, + and - must have two operands. Y=A*+C is not allowed. Only leading negation is allowed: Y=-A. Y=+A is not proper. 2 - OPERATION ON WRONG SIDE OF EQUATION. Only the dependent variable can appear to the left of the equal sign. Y+3=X+4 is not allowed. 3 - VARIABLE MUST BEGIN WITH A LETTER. 123ABC, %DEF, etc. are not allowed as variable names. L 2890 4 - UNMATCHED PARENTHESIS. All parentheses must be used in pairs. Total must be even. 5 - EMPTY OR ILLEGAL PARENTHESES. All parentheses must enclose something. No SIN(), Y=(), etc. 6 - MISSING ARGUMENT, ALGEBRA OPERATION. ----------- 5.05 -- Summary of ERRORS during evaluation of equations --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 64 -- All mathematical operations such as ^, *, /, + and - must have two operands. Y=A*+C is not allowed. Only leading L 2900 negation is allowed: Y=-A. Y=+A is not proper. 7 - ILLEGAL USE OF FUNCTION. A function name cannot be used as a variable name. Y=A+SIN*X is not allowed. Y=A+SIN(X) is proper. The name of something that is not an intrinsic function cannot be used as a function. Y=COTH(X) is not allowed. Y=1/TANH(X) is proper. 8 - TOO MANY EQUAL SIGNS. Only one equal sign per equation is allowed. L 2910 9 - EQUATION INCOMPLETE. An equation must contain a dependent variable, equal sign and something after the equal sign. Y= is not valid. 10 - ILLEGAL CHARACTER. Only ASCII characters, decimal 33 (!) and higher can be used as characters in equations. This range includes the numbers, upper and lower case letters, and other symbols such as the Greek letters. Remember, lower case letters are L 2920 always converted to upper case. Variable names such as ABC, 123, are not allowed. 11 - DUPLICATE NAME FOR DEPENDENT VARIABLE. Each equation of a group must have a different, and unique to 8 characters, name for the dependent variable. 12 - OUT OF ROOM! DECREASE CONSTANTS. Too many constants and variables, decrease one or the other. L 2930 13 - OUT OF ROOM! DECREASE VARIABLES. Too many variables and constants, decrease one or the other. 14 - OUT OF ROOM! WORKSPACE. Too many operations such as nested parentheses "((()))". Try to rewrite the equation(s) in a more compact way. 15 - OUT OF ROOM! CODESPACE. Too many operations. Try to rewrite equation(s) in a more compact way. Make common expressions separate equations. L 2940 16 - UNDEFINED VARIABLE. An attempt has been made to reference a variable which has not been defined. Will only occur when immediate ----------- 5.05 -- Summary of ERRORS during evaluation of equations --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 65 -- calculations are made. 17 - OUT OF ROOM! STORAGE VARIABLES. Attempt to define more than 256 storage variables. Save storage variables with "!]". Use "Z", "!Z" and "@Z" to locate and remove unwanted variables. L 2950 18 - ILLEGAL USE OF STORAGE VARIABLE! Attempt to define a storage variable as a dependent variable of one of the equations entered in response to the prompt "? Equation(s)". Not allowed! ╒════════════════╕ │ DISPLAY COLORS └────────────────────────────────────────────────────── 6.01 Setting Foreground/background Colors of Main L 2960 Equations Screen and Program ──────────────────────────────────────────────────────────────────────── For a monochrome monitor, only the default colors white on black (command "!(esc)") or the opposite colors black on white (command "@(esc)") should be used. For color monitors, there are 16 shades of foreground colors and 8 shades of background colors. The text of the comment, equations and variables are in the foreground color. The clock display and bottom-screen menu are in reverse video of these colors. Colors by number L 2970 are: 0=black, 1=blue, 2=green, 3=cyan, 4=red, 5=magenta, 6=brown, 7=white and 8 to 15 are corresponding high-intensity shades. Use command !N to toggle the next foreground color and use command @N to toggle the next background color. If the foreground and background colors are equal, then the displayed information becomes invisible. Colors wrap around from #15 to #0. Use commands "!(esc)" to set fore=#7 (white or green) and back=#0 (black) or command "@(esc)" to set fore=#0 and back=#7. Colors (except white on black, the default) are saved with the L 2980 equations and are reset when equations are read by the commands "(F8)" or "[" and "@[". Start the program with a set of equations previously saved with the desired startup colors. For example: AFIT3 CONFIG.EQU (enter). Note: Type "!(esc)" to reset the monochrome colors before exiting or the DOS colors may remain those at the program exit. ╒═══════════════╕ │ CLOCK DISPLAY └─────────────────────────────────────────────────────── L 2990 --------------- 6.01 -- Setting Foreground/background Colors of Main --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 66 -- 6.05 Clock Screen: Commands During Display ──────────────────────────────────────────────────────────────────────── To start the clock, type !C from the equations display. -> restart/redraw clock screen ! - Restart the clock and redraw the display. Use if the display is overwritten. L 3000 -> check/enter alarm time @ - Check the current alarm time, just type (enter) to exit, or set a new one, type y (enter). -> changing 12/24 hour format # - Toggle between 12 and 24 hour time format (12 hr. default). L 3010 -> exit back to equations display $ - Exit back to the equation display. (ctrl Q) - Exit back to the equation display. -> Dos shell % - Shell (exit) to DOS. Type EXIT (enter) to return to clock. L 3020 -> lock-up keyboard in security mode ^ - Security mode. Enter a password up to 8 characters. To unlock, type exact password. Alarm will stay active. If program does not respond, type (enter) first and then the exact password. While in the security mode, the (alt) and (ctrl) keys are forced off. Most "TSR" programs and emulators which are activated by hot keys should be locked out! During security mode, program will remember date/time's of L 3030 unauthorized use. If password contains "@", then typing incorrect password will immediately activate alarm-- displaying comment, sounding music and flashing screen! Type any key to return to clock. Password still must be entered correctly (with "@") to exit. ---------------------- 6.05 -- Clock Screen: Commands During Display --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 67 -- The apostrophe command 'clo can be used to display the clock, to display the clock and lock with a password and to set the alarm time and comment. Apostrophe commands can be entered almost anywhere in the program. Some examples: L 3040 'clo (enter) Display the clock, exit to equations. 'clo =big (enter) display the clock and lock-up with a security password "big". The "=" is used to indicate a password but is not part of the password. 'clo 13:23 meeting in cr 864 (enter). Set the alarm at 1:30 pm and set the comment to "meeting in cr 864". Clock is not displayed. L 3050 ╒═════════════════════╕ │ APOSTROPHE COMMANDS └───────────────────────────────────────────────── 6.10 Apostrophe Commands: What They Do and How to Use Them ──────────────────────────────────────────────────────────────────────── The apostrophe commands can be entered at most locations in the program as well as in the 'EQU fields of application help files. L 3060 The apostrophe commands begin with an apostrophe and the first three letters of the key words described below. Only the first three letters are significant. Thus 'variable, 'var, 'variety, etc. all imply the same apostrophe command: 'var. apostrophe command are case insensitive except for the 'EQU field designator in an application help file. Apostrophe commands perform many of the functions that are also performed by the single-letter commands discussed above. Some L 3070 examples: Enter an equation: 'equ y=a+b*x+c*x^2 (enter) Enter a comment: 'com This is a second-order polynomial. (enter) Assign values to many variables at one time: 'var x=1 a=2 b=3 c=4 (ent) or 'x=1 a=2 b=3 c=4 (enter). Note, if a variable name is the name of an apostrophe command, use the 'var first; L 3080 otherwise, the program will interpret the variable name as an apostrophe command. For example if a variable were named COL ------ 6.10 -- Apostrophe Commands: What They Do and How to Use Them --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 68 -- then 'col=1 (enter) would be interpreted as an improper use of the apostrophe command 'col; but, 'var col=1 (enter) is OK. Assign all variables the value of sqr(2): 'var #all=sqr(2) (enter). Make X a coordinate variable: 'coo x (enter) Change the colors to high-intensity white on red: 'col hwhite L 3090 red (ent) Move the cursor to variable X: 'cur x (enter) or '' x (enter) A summary of the apostrophe commands follows: PURPOSE COMMAND SIGNIF. SYNTAX ABBREV. Activate variables 'activate 'act 'act varname1,varname2... L 3100 'act #all Calc dependent vars 'calculate 'cal 'cal display clock 'clock 'clo 'clo clock with password 'clo =password set alarm time and 'clo hr:mn:se comment comment Chain to other ASTRO3 'chain 'cha 'cha calc L 3110 programs with current 'cha solve variables + equations. 'cha fit Make coordinates 'coordinate 'coo 'coo varname1,varname2... 'coo #ind Set display colors, 'color 'col 'col forecolor,backcolor Color names below Set Comment 'comment 'com 'com text...... L 3120 Set decimal digits 'decimal 'dec 'dec 2 Move cursor to 'cursor 'cur 'cur varname1 variable varname1 or '' ''varname1 Get an equation file 'eget 'ege 'ege mycalc named "mycalc.equ" ------ 6.10 -- Apostrophe Commands: What They Do and How to Use Them --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 69 -- Save equation file 'esave 'esa 'esa mycalc L 3130 Enter equations 'equation 'equ 'equ equation1.... Erase storage vars 'erase 'era 'era #all Exit from program 'exit 'exi 'exi Read application help 'help 'hel 'hel \calc\science file "\calc\science" Only 'help will access last opened help file. L 3140 Immediate calculation 'immediate 'imm 'imm y=25-sqr(144) 'imm y=2*4 z=sqr(144) Inactivate variables 'inactivate 'ina 'ina varname1,varname2... 'ina #dep Lite mode. 'lite 'lit 'lit Removes (F5), (F6), (F9), Y, Z functions L 3150 Set precision 'precision 'pre 'pre single or double Turn off sound 'quiet 'qui Assign values to 'variable 'var 'var varname1=value1... variables. Create 'var #all=value2 storage variables. or '' ''varname1=value1... ''#all=value2 L 3160 Get a storage file 'sget 'sge 'sge mystor named "mystor.sto" Jump to spreadsheet 'spread 'spr 'spr (equations display) Save a storage file 'ssave 'ssa 'ssa mystor The options #ALL, #DEP and #IND specify ALL variables, only the DEPENDENT variables or only the INDEPENDENT variables and can L 3170 be used with 'act, 'ina, 'coo and 'var. Foreground (forecolor) and background (backcolor) colors are: ------ 6.10 -- Apostrophe Commands: What They Do and How to Use Them --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 70 -- 0. BLACK 5. MAGENTA 10. LGREEN 1. BLUE 6. BROWN 11. LCYAN 2. GREEN 7. WHITE 12. LRED 3. CYAN 8. GRAY 13. LMAGENTA 4. RED 9. LBLUE 14. YELLOW 15. HWHITE L 3180 Note: Enter the colors not numbers in 'COLOR command. L means light and H means high-intensity. Also, Only colors from 0 to 7 should be used as backgrounds. The screen dump command "V" appends the complete equations, comment, and variable values and status to the screen display in the 'EQU field format. These files can be used to build user-generated application help files from which equations etc. can be directly loaded into this program as the help file is read. See the ASTRO3 Utility program, A3UTIL.EXE and L 3190 documentation for more details. ╒══════════════════════════╕ │ AFIT3 APOSTROPHE COMMANDS└──────────────────────────────────────────── 6.12 Apostrophe Commands Unique to AstroDataFitter. ──────────────────────────────────────────────────────────────────────── PURPOSE COMMAND SIGNIF. SYNTAX ABBREV. L 3200 Enter data 'data 'dat 'data 1 -2.1 3 3.4 4 5.7 Set data points to 0 'pt0 'pt0 'pt0 Note: Repeated use of the 'data command causes data to be merged onto the end of the existing data. To start with 0 data points use the 'PT0 command first. All data must be numbers. Data may be entered in the data point format (data coordinate, data value) or (data coord1: data coord2, data value) and so L 3210 on. For example: (1, -2.1) (3, 3.4) (4, 5.7). Variable names and other representations will be interpreted as 0's. ╒══════════════════╕ │ DOS COMMAND LINE └──────────────────────────────────────────────────── 7.01 Information After Program Name on DOS Command Line. How the Program Uses It and What It Does. ──────────────────────────────────────────────────────────────────────── L 3220 -------- 7.01 -- Information After Program Name on DOS Command Line. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 71 -- Perform certain functions from information entered after program name in DOS command line. ■ Start with a previously stored file of equations like MYCALC.EQU: AFIT3 MYCALC.EQU (enter) or AFIT3 "MYCAL.EQU" (enter) Note: Use quotes if file name contains symbols = + - * / ( or ^. Foreground/background colors are those saved with equations. Start with both storage variable file and equation file: AFIT3 MYVAR.STO MYCAL.EQU (enter) Note: Storage file must come before equation file. Default L 3230 extensions are ".STO" for storage and ".EQU" for equations. If math symbols are in filename(s), enclose both filenames in single set of quotes: AFIT3 "STO++ EQU--" (enter). ■ Start with equation(s) like Y=A*X+B: AFIT3 Y=A*X+B (enter) Note: Equation(s) must contain at least one independent variable. Foreground/background colors are the defaults. ■ Start with a directory listing of a directory such as \calc or a: L 3240 AFIT3 \calc\ (enter) or AFIT3 a:\ (enter) Note: Directory must be enclosed in "\". "\\" signifies the root directory and "\" signifies the current directory. The directory of a drive must end in "\". ■ Perform a single-shot calculations like: AFIT3 23+36+67 (enter) or AFIT3 60,123,456,789.02-40,123,456,789.01 (enter) Note: Single-shot calculations calculate one or more results and prompt "Type any key to continue...". Type (esc) to L 3250 continue the program or any other key to terminate program and return to DOS. Information must not be enclosed in quotes, must not contain independent variables, and must have at least one operation such as = + - * / ( or ^. ■ Enclose each separate calculation in parentheses: AFIT3 (23+78-90) (32-SQR(56)) (2*SIND(87)) (enter) ■ Example of a single-shot calc with 4 dependent variables: AFIT3 A=1 B=2 X=3 Y=A*X+B (enter) L 3260 ■ To start a program by reading an application help file such as A3UTIL.HLP, simply include the filename with the .HLP extension anywhere on the command line. Note, must maintain order of .STO and .EQU files as discussed above! For example: AFIT3 MYVAR.STO MYCAL.EQU A3UTIL.HLP (enter) or -------- 7.01 -- Information After Program Name on DOS Command Line. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 72 -- AFIT3 A21UTIL.HLP MYVAR MYCAL (enter) or AFIT3 MYVAR A21UTIL.HLP MYCAL (enter) or AFIT3 A21UTIL.HLP MYCAL (enter) AFIT3 ? (enter) and AFIT3 AFIT3HLP.HLP (enter) are equivalent. L 3270 ■ Do not mix equations or calculations and filenames! For example: Y=A*X+B MYCAL.EQU should not be entered! ╒═════════╕ │ LICENSE └───────────────────────────────────────────────────────────── 8.01 Product License and Warranty. ──────────────────────────────────────────────────────────────────────── L 3280 Software License Agreement (Registered Users) If you are a registered user, PCSCC grants you the right to use this Software for a single-user computer or a workstation not attached to a network. You may not rent or lease this Software without the expressed written permission of PCSCC. You may not decompile, disassemble, reverse engineer, copy, create a derivative work, or otherwise use this Software except as stated in this agreement. The license authorizes you to create and use an extra copy of the Software on a home or laptop L 3290 computer, as long as the extra copy is never loaded at the same time this Software is loaded on the primary computer on which you use this Software. If any provision of this agreement is found to be unlawful, void, or unenforceable, then that provision shall be severed from this Agreement and will not affect the validity and enforceability of any of the remaining provisions. This agreement shall be governed by the laws of the State of Delaware. L 3300 The Software and accompanying materials are provided with Restricted Rights. Use, duplication, or disclosure by the Government is subject to restrictions as set forth in subparagraph (c) (1) (ii) of The Rights in Technical Data and Computer Software clause at DFARS 252.227-7013, or subparagraphs (c) (1) and (2) of the Commercial Computer Software--Restricted Rights at 48 CFR 52.227-19, as applicable. Contractor/manufacturer is PC SuperComputer Capital, Incorporated, at the address listed below. L 3310 Non registered users must comply with the Shareware policy ------------------------------ 8.01 -- Product License and Warranty. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 73 -- described elsewhere in this software Pacakage. Type T to return to the Table of Contents. Warranty Information PC SuperComputer Capital, Inc. (PCSCC) hereby disclaims all warranties relating to this Software, whether express or L 3320 implied, including without limitation any implied warranties of merchantability or fitness for a particular purpose. PCSCC will not be liable for any special, incidental, consequential, indirect or similar damages due to loss of data, loss of profits, lost savings or any other reason, even if PCSCC or an agent of PCSCC has been advised of the possibility of such damages. In no event shall PCSCC's liability for any damages ever exceed the price paid for the license to use Software, regardless of the form of the claim. The person using the Software bears all risk as to the quality and performance of L 3330 the Software. This Software is licensed AS IS. Any action or proceeding brought by either party against the other arising out of or related to this agreement shall be brought in a STATE or FEDERAL COURT of competent jurisdiction located in Fairfield County, Connecticut. The parties hereby consent to in personam jurisdiction of said courts. Type T to return to the Table of Contents. L 3340 ╒══════════════╕ │ USER SUPPORT └──────────────────────────────────────────────────────── 8.03 User Support. ──────────────────────────────────────────────────────────────────────── This program has undergone over 5 years of "beta testing" around the world. The algorithms have been in use since 1976, are user-firendly and believed highly reliable. However, comprehensive programs of this nature may require clarification L 3350 or may develop what are called "bugs". User support is provided to all registered users for a minimum of 3 months without charge. Registered users can receive such help via phone, regular mail and E-mail. Registration also enrolls the user for notification of "bug" fixes, upgrades, new versions, new products and many more benefits. For the phone number/mail addresses see below or position the jump line here and type J. ∙Registration∙. Support will be provided to non-registered ---------------------------------------------- 8.03 -- User Support. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 74 -- users and users beyond the free support period on a time and materials basis. L 3360 ╒═════════════╕ │ ARBITRATION └───────────────────────────────────────────────────────── 8.04 Ombudsman/Arbitration Policy. ──────────────────────────────────────────────────────────────────────── PCSCC, Inc. will follow arbitration guidelines as set forth and published by the Association of Shareware Professionals (ASP). The current ASP policy is stated here: L 3370 "This program is produced by a member of the Association of Shareware Professionals (ASP). ASP wants to make sure that the shareware principle works for you. If you are unable to resolve a shareware-related problem with an ASP member by contacting the member directly, ASP may be able to help. The ASP Ombudsman can help you resolve a dispute or problem with an ASP member, but does not provide technical support for members' products. Please write to the ASP Ombudsman at 545 Grover Road, Muskegon, MI 49442-9427 USA, FAX 616-788-2765 or send a L 3380 CompuServe message via CompuServe Mail to ASP Ombudsman 70007,3536" ╒═══════════════╕ │ PRODUCT INFO └─────────────────────────────────────────────────────── 8.05 Product Information and How to Order Complete Package. ──────────────────────────────────────────────────────────────────────── AstroDataFitter 3 Product Description 8-1-1993 L 3390 AstroDataFitter 3 is a unique and innovative mathematics tool which offers productivity enhancements not found in any other software package either retail or shareware. This hands-on program combines the functions of both a spreadsheet and calculator; but it is better. Why? Because it is right between the two: Easier than a spreadsheet and more powerful than a calculator. With its special format-free interface, formula or equation-based iterations are much easier to set up than in a spreadsheet. It is designed to be "smarter" which L 3400 makes it very user-friendly for Professionals of all levels, especially for the infrequent or "computer-shy" user. Broad applications exist in many disciplines where calculations with formulas, equations or other math recipes are required such as ----- 8.05 -- Product Information and How to Order Complete Package. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 75 -- in Economics, Genetics, Chemistry, Electrical Engineering, Engineering Mechanics, Fluid Mechanics & Hydraulics, Finance, Physics, Statistics and even Nursing. Features include: ■ DOS or Windows as non-Windows application. Runs on all PC compatibles. DOS 2.1+, Monochrome display, 200K RAM, floppy or L 3410 disk. ■ DOS command line support for any direct calculation such as addition, multiplication, subtraction and division. ■ Format-free entry of up to 63 equations with at least 256 independent variables and 256 constants. Smart and "hassle-free" interpreter. ■ Equations and formulas are written according to the BASIC L 3420 conventions. Versatile library of built-in functions. ■ Advanced calculator functions including many automated numerical methods such as: ∙ Newton-Raphson for solving x in y=f(x) ∙ Advanced simplex for solving x at W=Y=Z in W=f(x), Y=g(x), Z=h(x) ∙ Numerical integration (two methods) ∙ Numerical differentiation L 3430 ∙ Summation ∙ Finding maxima and minima ∙ Plotting equations ∙ Saving/retrieving data files with full file management support ∙ Screen dumps as DOS text files for inclusion in documents ■ Highly-structured documentation, on-line with Table of Contents, Glossary and search function. Interactive with program. L 3440 ∙ On-line helpfile. Comprehensive summary of commands/functions with step-by-step examples on uses of all advanced functions. ∙ On-line user manual. A "learn by example" document which illustrates the universal nature of problem-solving with many step-by-step examples from Science, Engineering and Finance. ■ Full support for ACTION21 and ACTION11 data sets. L 3450 ----- 8.05 -- Product Information and How to Order Complete Package. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 76 -- ■ Comments from users: ∙ "... calculate circuit board drilling and routing speeds...easy to use, versatile and powerful with good documentation." J. L. New York ∙ "...used the integration capability to determine defect density...do not have any tool (either PC or host based) that does for me what ...(AstroFormCalc 3)...does." J. R. Virginia ∙ "...for Electrical Engineering practice it is better than a L 3460 spreadsheet and a calculator..." C. B. Florida ∙ "...used to do frequency spectrum work and calculations on circuits, ...of real value and a productivity tool." E. S. California ∙ "...one of a handful of scarcely available packages...in the types of numeric problems they solve." W. C. Chile This productivity-enhancing tool has been developed by the team L 3470 at PC SuperComputer Capital, Inc. Order the complete Astro 3 Package today! ╒════════════════╕ │ OTHER PRODUCTS └────────────────────────────────────────────────────── 8.06 Software Included in Astro 3 Registration ──────────────────────────────────────────────────────────────────────── Register for AstroFormulaCalculator 3 and receive, in addition L 3480 to the most recent version of ACAL3.EXE and ACAL3HLP.HLP, these 3 powerful math analysis programs: AstroEquationSolver 3, AstroDataFitter 3 and AstroShadowBox 3. Each has its own extensive and interactive on-line helpfile written just like the one your reading now. A print program is included which prints theses helpfiles to the standard printer or to a DOS text file. All Astro 3 programs are written with the same high-level user-friendly front-end requiring minimal effort to setup and execute relatively elaborate calculations. All data sets and helpfiles are compatible among members of the family. L 3490 A brief summary of the other members of the Astro 3 shareware family included with the registration package follows: ■ AstroEquationSolver 3 - Solves both linear and nonlinear simultaneous equations with up to 30 unknowns. Characterized by extremely easy setup. Uses active/inactive method of ------------------ 8.06 -- Software Included in Astro 3 Registration --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 77 -- AstroDataFitter 3 to select variables. Strictly high level. No reference to matrices at all!. Includes program ASOL3.EXE and extensive on-line help file ASOL3HLP.HLP that includes many learn-and-use examples. L 3500 ■ AstroDataFitter 3 - Fit data to any algebraic expression. Nonlinear optimization. Fully-automated polynomial regression with automatic "equation generator". Easy to use, even by a novice. Will generate interpolated tables from fitted equations. Up to 30 "active" variables. Up to 500 data points. "Smart" algorithm requires minimal user input to solve problems. DOS text plots of "fit". Point-by-point listing of fitted data. Residual variance, correlation coefficient, coefficient of determination and much more! Includes program L 3510 AFIT3.EXE and extensive on-line help file AFIT3HLP.HLP that includes many illustrated examples. ■ AstroShadowBox 3 - The pop-up resident member (TSR) of the Astro 3 team. Provides math support for other DOS programs. Pop-up via hot key, surround calculation in "shadow box", and type "(enter)" to pass result down through keyboard buffer or pop up, enter calculation and pass result down. Great for adding powerful and interactive math capabilities to DOS text editors such as Brief (tm, Borland), PE2 (tm, IBM) or L 3520 WordPerfect (tm, WordPerfect). Extensive features also include screen dumps with appends as DOS text files or as parsed columns in 123 (tm, Lotus) .WK1 files. Requires as little as 15K of main memory. Includes program ABOX3.EXE and on-line help file ABOX3HLP.HLP If you like Engineering, Science or Finance and you have ideas that you could transform into an interactive helpfile like SCIFIN.HLP (The Astro 3 Science Manual) or PHYCAL.HLP ( The Astro 3 Physics Manual) or FINCAL.HLP (The Astro 3 Finance L 3530 Manual), then you should write one and market it! If you write it in a commercial spreadsheet format, you will not likely be able to distribute a fully functional package which is the mark of a true Shareware program and the policy of the Association of Shareware Professionals! However, the AstroUtility 3 program provides the tools needed to generate an Astro 3 interactive application file with a minimum of effort AND REGISTERED USERS OF THE AstroUtility 3 PROGRAM RECEIVE A LIMITED DISTRIBUTION LICENSE WHICH ALLOWS INCLUSION OF ANY OR ALL OF THE ASTRO 3 PROGRAMS IN YOUR PACKAGE! L 3540 ■ AstroUtility 3 - Support for authors to construct their own ------------------ 8.06 -- Software Included in Astro 3 Registration --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 78 -- on-line application help files. Develop equation files in your favorite editor and translate them into .EQU format for final "test and touch-up". Likewise, develop an application file in your favorite editor, automatically include information from previously developed .EQU files, and then compile a full-feature .HLP with automatic Table of Contents, line numbers and so on. .HLP files support all apostrophe commands and many other useful features such as CalcMerge with lets you L 3550 dynamically stuff values calculated in the main equation display into the application file. As with the other Astro 3 programs, AstroUtility 3 comes with its own interactive and extensive on-line help file which can be printed, if needed. Application files can contain up to 32,000 lines! See below for instructions on ∙Registration∙. ╒══════════════╕ │ REGISTRATION └─────────────────────────────────────────────────────── L 3560 8.07 Order/Registration Form ──────────────────────────────────────────────────────────────────────── If a printer is available, position the order form (part 1) on the screen and type the "(print screen)" key to make a copy. Then, advance the text and position the order form (part 2) on the screen and type "(print screen)" again to finish. ASTRO 3 Products Order/Registration Form L 3570 Name:________________________________ Title:________________ Company:_____________________________________________________ Address:____________________________ City:___________________ State:___________ Zip:_____________ Country:______________ Date:_____/_____/_____ (Fill out form completely) L 3580 --------------------------------------------------------------- Product # Price/ea S&H Total --------------------------------------------------------------- AstroDataFitter 3 ___ _$29.95_ _$5.00_ _______ Complete Package includes ACAL3, ASOL3, AFIT3 + ABOX3 AstroUtility 3 + ASTRO3 ___ _$99.95_ _$5.00_ _______ distribution license L 3590 * Canadian Orders, Add $2.00 per copy _______ * International Orders, Add $6.00 per copy _______ * CT Residents add appropriate sales tax _______ L 3600 TOTAL ENCLOSED __________ Disk Size: [ ] 5-1/4" [ ] 3-1/2" [ ] Check [ ] Visa [ ] MC Card# __________________________________ Exp. Date ________ Signature ______________________________ How did you hear about our Products? [ ] BBS [ ] Friend [ ] Other _____________________________________________________ L 3610 Mail Completed form with Payment to: PCSCC, Inc. Dept. AF3H P. O. Box 173 Botsford, CT 06404 USA Support ONLY, 1-203-270-9079 E-mail to CIS, 72263,1657 [Mar 1994] Prices subject to change without notice. L 3620 Type T to return to the Table of Contents. ------------------------------------ 8.07 -- Order/Registration Form --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 79 -- ╒═════════════════════╕ │ MANUAL INSTALLATION └───────────────────────────────────────────────── 8.08 Instructions for Manually Installing Package. ──────────────────────────────────────────────────────────────────────── The following are minimal instructions for manually installing L 3630 AstroDataFitter 3. ■ Minimum distribution files: README.1ST, AFIT3.ICO, AFIT3.EXE, and AFIT3HLP.HLP -------------- 8.08 -- Instructions for Manually Installing Package. --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 80 -- ■ These files will probably be bundled in a compressed file such as SCIFIN.ZIP, SCIFIN.LHZ, or something similar. Please unload. ■ Create a DOS directory named ASTRO3 and change to it: cd\ (enter) md\astro3 (enter) cd \astro3 (enter) L 3640 ■ Copy AFIT3.EXE, AFIT3HLP.HLP and AFIT3.ICO into the directory ASTRO3 ■ Add these statements to AUTOEXEC.BAT in the base directory: SET ASTRO3=C:\ASTRO3 append to existing PATH statement ;C:\ASTRO3; ■ Running Under Windows as a Non-Windows Application Follow the installation instructions and install on the hard drive C. L 3650 Start WINDOWS (tm, MicroSoft). Click on FILE then click on PROPERTIES. Enter the following information for each of the fields. Description: AstroFormCalc 3, Command: AFIT3.EXE, Working Directory: \ASTRO3. Click on CHANGE ICON. Enter Filename: C:\astro3\AFIT3.ico. Click on OK to exit and click on OK to exit FILE. The AstroFormCalc 3 icon should appear in the accessory window. Click on it to run AFIT3. ■ To start with user manual: cd\astro3 (enter) AFIT3 ? (enter) To start with equation like y=a*x+b: AFIT3 y=a*x+b (enter) To start with calculation like 45.67+56.23: AFIT3 45.67+56.23 (ent) L 3660 Type (esc) to enter another calculation or any other key to exit. Access on-line help (file: AFIT3HLP.HLP) from equations display with (F1) key. ╒═════════════╕ │ AUTHOR ???? └───────────────────────────────────────────────────────── 8.09 Interested in Becoming the Author of Your Own Interactive Application File? L 3670 ──────────────────────────────────────────────────────────────────────── Many technologies are based on math/algebra. AstroDataFitter 3 and its interactive, problem-solving application files offer distinct advantages to the Author. The *.EQU templates are easy to develop and PCSCC offers complete support for compiling these into the interactive application files such as the help file AFIT3HLP.HLP which you are currently reading or SCIFIN.HLP (The Astro 3 Science Manual) or PHYCAL.HLP (The Astro 3 Physics Manual) or FINCAL.HLP (The L 3680 -------------- 8.09 -- Interested in Becoming the Author of Your Own --- -------- AFIT3HLP.HLP ----------- AFIT3 Help File -------------- 81 -- Astro 3 Finance Manual). Application files can be written for any level of user from the very beginner to the Ph.D. and distributed with any or all of the ASTRO 3 family of programs. See the OTHER PRODUCTS section above for more details. To automatically jump type "J" if the jump bar is highlighted on those words. ╒═══════════╕ │ HELP FILE └─────────────────────────────────────────────────────────── L 3690 9.01 Help File: Summary of File Viewing Commands ──────────────────────────────────────────────────────────────────────── A - Auto-search of entire text for user-supplied string. Search is in uppercase and is case insensitive. If string found, type A to continue or to enter new string, type (space) A. B,N - Move back or ahead 18 lines. Also use (backspace) for "B". E, (esc) - Exit from help file to equations display. F,T,K - Jump to the first (beginning), T.O.C or last (end) line. G - Skip to Glossary of terms or summary of functions, if present. L 3700 J,(ent) - Search line on │JUMP│, Reference is after . Jump to line number or perform autosearch ahead if text reference. L,P - Jump to line/page. Type Lxxx(ent) or Pyy(ent) to jump to line #xxx or page #yy. With + or -, ahead or back 56 lines. S,R - Skip ahead (S) or back (R) in help file to major headings W - Skip to Summary of useful calculations or warnings, if present 1 to 9 - Typing 1 to 9 advances the text by 1 to 9 lines. (ctrl Q) - Exit from help file. Same as command "E". Edit keys - Use edit keys: (Home) (up arrow) (PgUp) (left arrow) (right arrow) (End) (down arrow) (PgDn). L 3710 Entry into the application file is at/near the last position. Type: T to return to Table of Contents or E to exit the file. ---------------- 9.01 -- Help File: Summary of File Viewing Commands ---