Function Plotter version 4.00 documentation. THIS PROGRAM IS SHAREWARE.
Please support our efforts, registration is only $15.

To start function plotter for the first time type "fcnplt x", where x is:
h -for hercules
c -for cga
e -for ega (with color monitor)

If after running the program, you create a configuration file, type
"fcnplt" (no parameters). Function plotter will then use the
configuration file with your custom configuration. If you want the
configuration file in the root directory simply put it there and type
"fcnplt r" . Function plotter will then look in the root directory for
the configuration file.

files: fcnplt.exe......The main program.
hercules.exe ...Hercules driver. This file is needed to print from
a hercules compatible display.
ega.exe ........EGA driver. This file is needed to print from an EGA
compatible display.
func.fcn........Sample function file for demonstration.
data.dat........Sample data file for demonstration.
readme.doc......This documentation.

SHAREWARE

If you find this program useful, please register. Your support is vital
and has a number of benefits. You will be put on the mailing list for
future upgrades, in fact the upgrades will only be offered to registered
users. Your questions, submitted in writing will be answered. A printed
manual will be available in the future and will only be offered to
registered users. All this for only $15! Please send your registration
fee to: (also questions, comments)

Robert G. Kaires
609 Glover Dr.
Runnemede, NJ 08078


USES

1) Quickly reviewing data in a linear or log format. Data is in column
format and can have up to 9 columns. You can plot any column vs. any
other column.
2) Entering function strings and converting to data. This data can then be
plotted or read out to a data file.
3) Use it as an educational tool. Examine Taylor series, Fourier series
and Chebyshev series approximations. Look for roots of polynomials.
Look at functional behavior as you vary parameters.
4) Reading very dense data files and then examining detail using "exploded"
views.
5) Use the calc mode as an intelligent formula calculator.


OVERVIEW

This program plots functions entered from the keyboard. The functions
can also be read in from an external file and placed on the line being
edited. This program can convert the function to data and then write the
data to an external file. Data from an external file, which can have
many columns, can be read in and plotted in the format of any column
verses any other column. Multiple sets of data can exit simultaneously
in memory in a data "stack". This allows one to quickly overlay data, to
experiment with different formats, without having to constantly read in
or generate new data. Data can be plotted in a linear or logarithmic
fashion. The actual data values can be examined point by point (alt v)
using the cursor keys. When using this alt v feature on a log-log plot,
slopes can be quickly determined since the log of the value is displayed.
Other features include, windowing of data with cursor or mouse, control
of tic marks, grid control, autoscaling of data, custom configuration
file, and more. The configuration file can be edited (very carefully) to
allow any number of data points (default is 500) and any number of stack
positions (default is 5). Of course there are memory limitations. More
on this later.

SUPPPORT

This program supports Hercules, CGA and EGA. Hercules and CGA have been
tested. EGA has been tested on an EGA color monitor. I HAVE NOT TESTED
EGA ON A MONOCHROME MONITOR. I suspect there might be some problems with
this setup. Printer drivers are supplied for Hercules and EGA, for use
with DOT MATRIX printers (sorry laser printer owners). Of course, those
using CGA should load the memory resident program, graphics.com, first,
and then use PrtSc to get a printout. Hercules and EGA users, make sure
the file hercules.exe or ega.exe is on your disk. When using these
drivers, use a margin of "0" if your printer doesn't support "esc l" (see
your printer manual).


QUICK INTRODUCTION

When function plotter starts, the cursor is located in the "window"
reserved for function "strings". Simply type in a valid function. If
you type "Enter" or press the tab key, the cursor will advance to the
next editing position, which is the number of points (the back tab key
will move the cursor to the previous editing position). If your function
is not valid the cursor won't advance and an error message will be
issued. If you need to see the valid functions press the F1 key.
Functions can have "x","y" and "z" as variables (or no variables). "X"
is the horizontal plotting variable. "Y" and "z" are really constants
that you are solicited for when you "update" the function (generate
data). Unfortunately I've also labeled the vertical axis as "y" (I hope
to correct this in the next version). The "ymin" and "ymax" on the
second line refer to the minimum and maximum vertical (data) values and
have nothing to do with "y" in functions.

Now assuming you have a function, move the cursor to the "points"
position. This will be the number of data points generated for the
function you entered. Enter a number from 2 to 500. The next four
editing positions are the minimums and maximums for the x (horizontal)
and y (vertical) axis. Pay particular attention to the x axis limits,
the data will be generated between these limits. The y axis limits are
less important, the data is not truncated at these limits, the plot
simply is. You can always use the F8 key to bring the full y values on
scale, after the data has been generated. Now press the F2 key. This
generates N data points from the function between the x limits you set.
N is the number of "points" you entered. Now you have data. You should
understand, however, that typing in a new function at this point could be
confusing. The data doesn't "update" to represent the new function UNTIL
you press the F2 key again! Now, just for practice, position the cursor
in the function position again. Now press the down arrow key (make sure
num lock is off). You are now at stack position 2. Enter a function,
set limits, and press F2. Now you have new data. The old data is not
lost! Just position the cursor on the function again and press the up
arrow key, the old function and data are still there. Now you can
overlay the plots if you like (are the scales are the same). Be careful
if you change the number of points. If the data is actually 100 points
for instance and you change "points" to 50, only the first 50 points will
plot. On the other hand, if you change "points" to 200, the last 100
points (which don't exits) will be plotted at 0,0. No real harm done.
Confusion can also result if you changed x or y limits for the two

functions (or they were changed "for you" with the autoscale feature).
You data may be off screen or not scales correctly. Listen closely, if
you press F8 the y axis will scale TO WITHIN THE X AXIS LIMITS (not
necessarily the full x range). If you press F9, the x AND y axis will
autoscale and all you data will be visible.

CONTROL KEYS

Certain control key are "active". These control the third line options.
For a list of active control keys in function plotter press Alt h (help).
Note that on the third line, certain letters are capitalized, these
correspond to the Alt or Ctrl keys which activate those items.

The following lists and describes the control keys. The first 4 control
keys can be used only in the function editing position.

Alt f : Gets a function from an external file.
Ctrl f : Puts the function (string) into an external file. The file is
created if it doesn't exist or appended to if it does.
Alt d : Gets data from an external file. If "auto" is on (use Alt a to
turn it on), the x and y axis is autoscaled as the data is read
in. "Points" are set to however many data points are read in.
X axis data is assumed to be in "xcol" (change with Alt x, see
below). Y axis data is assumed to be in "ycol" (change with
Alt y, see below).
Ctrl d : Puts the data, that was generated from your function, into an
external file.

Alt e : Toggles the "erase" flag. When on, the plotting area is erased
before plotting.
Alt a : Toggles the "Autoscale" flag. When on, the y axis is autoscaled
before plotting. Autoscale cannot scale a constant function
(eg. 1.5); ymin will equal ymax. If you try to plot this you
will get an error messages.
Alt t : Toggles "extended functions". These are additional functions
which I have defined using the "intrinsic" (more elementary)
functions. They can be turned off for faster "compilation".
Alt g : Toggles the grid.
Alt l : Toggles linear/log scaling. This toggles in a binary fashion.
Try it to see what I mean!
Alt x : Changes "xcol", which is the column for x axis data that is
used when you read in data from an external file.
Ctrl x : Changes the number of divisions of the x axis.
Alt y : Changes "ycol", the column for the y axis data, used for reading
Ctrl y : Changes the number of divisions of the y axis.
Alt c : Gets a screen value with cursor or mouse.
Alt m : Get a screen value with mouse. This is a little easier to use
for those of you with mice.
Alt v : Gets values on the function using the cursor keypad. Using the
left/right arrow keys moves you along the function or data. The
x and y values are displayed as you move along. CAUTION: a
cursor will be displayed on the plotted points starting in the
middle of the data set. If points are plotted off scale you may
not see this cursor! You can use the up/down cursor to change
the size of the cursor. Also use the tab, home, and end keys.
Alt S : Changes the plotting symbol and toggles a connecting line.
Alt h : Prints the control key menu.
Alt w : Windows the data using the cursor keypad or a mouse if one is
installed. Use F3 to plot the data after using alt w. Use F9
to effectively "un-window" the data.
Alt z : Saves the setup in a configuration file called fcnplt.cfg.

The configuration file is a normal text file and can be edited, but very
carefully. No error checking is done as the file is read in on startup.
Since alt z is the usual way to write to the file, this is not normally a
problem. There are two parameters that can be changed ONLY by editing
the configuration file however. These are 1) the maximun number of data
points and 2) the number of stack positions. The defaults are 500 and 5
respectively. Subject to memory limitations, you can set these numbers
to anything you desire. Once again, be careful editing this file. If
the program crashes unexplainably, and you have edited the configuration
file, delete the file fcnplt.cfg, and start over. Just use Ctrl z from
inside the program to create a new fcnplt.cfg. The following is an
example configuration file:

hercules,data.dat,func.fcn,circle
1234,100,7,-6.28319,6.28319,-1.1,1.1
on,off,on,off,off,off,on,on
1,2,10,10,.5

line 1: display card, default data file, default function file, default
symbol (valid symbols are: none, circle, square, dot)
line 2: MAXIMUM NUMBER OF DATA POINTS, default number of data points,
NUMBER OF STACK LOCATIONS, xmin, xmax, ymin, ymax
line 3: automatic erase before plot, autoscale, extended functions, xlog,
ylog, grid, connecting line (for plotted points), symbol fill
line 4: x column, y column (to use when reading in external data), number
of divisions of x axis, number of divisions of y axis, symbol size

The capitalization in line 2 indicates the items you can't change in the
program (using alt z). In the example configuration file, the maximum
number of data points is 1234, and the number of stack locations is 7.

MISCELLANEOUS

While editing you are always in insert mode. Pressing the control PgDn
key deletes the entire entry. The following keys are useful: del,
backspace/del, home, end. When editing the function the "up arrow" and
"down arrow" keys chance stack position. These keys do nothing in you are
in any other editing position (ex. you are editing xmin).

While reading functions from an external file, up arrow, down arrow, home
and end keys are active. These keys change the line you are viewing.
Simply press return to read in the function on the line you are viewing.
In the sample file "func.fcn", I have included comments on some lines.
The comment precedes the function. Don't read in the comment. If you do
no harm is really done, you just can't process it. Use Ctrl PgDn to
delete the line and use alt f again, to read the function file again.

When in the cursor mode (alt c), window mode (alt w) or mouse mode (alt
m, with no mouse) the following keys are active: tabs, PgUp, PgDn, home,
end. Also right, left, up, and down arrows.

While editing xmin,xmax,ymin,ymax you can enter numeric expressions such
as pi + cos(.5) + (.5)^3 , just like you would in the calculator mode.
Sorry, you cannot use the "extended" functions here. For instance you
cannot use cosh(3) for xmin even if extended functions are active. You
can however, use cosh(3) in the calculator if extended functions are
active.

Extended functions, of course, can be plotted and their values "picked
off" with the cursor (alt v). They are called extended because I process
them so that they are transformed to the "intrinsic" functions. eg.
cosh(x) is transformed to .5(exp(x)+exp(-x)) . They can be used
recursively. eg. cosh(cosh(x)) or cosh(exp(sinh(x))) etc. They can be
turned off. Why? Because eventually they may consume an inordinate
amount of time (when I add more functions). Currently, when you type a
functional expression, if it does not compute (so to speak), additional
processing is done to see if it contains my so called external functions.
This happens even when you type a mistake, such as "cos(x))". Currently
the delay is very slight.

Floating point exceptions (overflow and underflow) are handled by setting
the value there equal to zero (plot tan(x) to see how this affects your
plots). If anyone has a better idea, let me know.

Data data files (for reading) must be in column format with at least one
space separating data items. Any column can be plotted verses any other
column (by changing xcol and ycol with alt x and alt y). When you change
a function to data and write it out to a file there only two columns.
You can, however, read in data which was generated with another program
containing more than two columns.

When using the "d" option to get a directory listing, the program
"shells" out to DOS and does a "dir/p". After the directory is listed
you must hit ENTER, even though you are not specifically asked to do so,
in order to return to the program.

The program is not case sensitive (as far as I know), except in one small
area. When you are in the calculator mode and you are entering x,y or z
values for a function, you must use lower case q to quit.

EXAMPLES

WRITING FUNCTIONAL DATA TO DISK:
Enter a function, set all limits and use F2 to generate data. Then type
Ctrl d and enter a file name.

READING EXTERNAL DATA FROM DISK:
Hit up arrow or down arrow if you want to get to an unused stack
position. Press Alt d and enter a file name. When the data is read in,
the program will automatically scale x and y limits if "Auto" is on. If
you had it off, simply hit F9 to autoscale x and y. The number of points
will automatically be updated to reflect your data. Be careful when
changing stack positions after reading data because now you may have the
wrong number of points for THAT stack position. (I'll correct this in a
future version by having a unique number of points for each stack
position). If you try to read in more than 500 points, the data will be
truncated. You can overcome this however by creating a configuration
file and then editing it. See the section following the "alt z"
description above.

WRITING A FUNCTION (STRING) TO DISK:
Enter a function, press Ctrl f, then enter a file name. Your function
(string) will be appended to that file. A file will be created if none
exits.

READING A FUNCTION FROM DISK:
Go to an unused stack position if desired. Press Alt f, enter a file
name. You are now "viewing" that file, line by line. Simply press ENTER
and that line will be read in. Note that in the sample file "func.fcn",
I include "comment" lines. These are treated just like function strings,
eg. you can (accidentally) read them in. No harm, just delete it and
start over. You can, by the way, write your own comment lines, by
typing in a "function" which is really a comment (don't try to use F2!!).
Then use Ctrl f and write this comment to a file. Of course you can also
use an editor outside the program to create/edit a function file. I had
some trouble doing this because some editors embed different control
characters in files. (end of file character, end of line character, etc.)
What function plotter "needs" is one CR and one LF character after EACH
line. (CR = carriage return, LF = line feed). Here is an example of how
you can get into trouble. You create a new function file using (say)
Sidekick Plus (TM). It puts an end of file character at the end of your
file. In function plotter you append a few lines of functions. You exit
function plotter and bring up Sikekick to look at your file and you don't
see your new lines. What happened? Well, Sidekick will ignore anything
after the EOF mark, and that's exactly where you appended your lines.

SHAREWARE


If you find this program useful, please register. Your support is vital
and has a number of benefits. You will be put on the mailing list for
future upgrades, in fact the upgrades will only be offered to register
users. Your questions, submitted in writing will be answered. A printed
manual will be available in the future and will only be offered to
registered users. All this for only $15! Please send your registration
fee to: (also questions, comments)

Robert G. Kaires
609 Glover Dr.
Runnemede, NJ 08078