                             PwrStar 1.02 Help File
          Copyright 1986, The Right StuffWare, All Rights Reserved

  PwrStar is a user friendly  program dedicated to numerical analysis of user
provided data.  Each option is selected by merely touching the first key of a
function name  such as [K]bdInput.  The  purpose of the current version is to
provide a polynomial best  fit to a given set of data by the method  of least
squares.  The user may interactively choose up to a 10th order polynomial fit
and get an automatic display of the input and the fitted curve.

  There is a definite  sequence of events that should be  followed to get the
most out of the program, but you are  encouraged to improvise.   For example:

1.  Use [K]bdInput to enter the data from the keyboard or [F]ileInput to read
    a previously  generated ASCII  file with the input.  When using files not
    generated by PwrStar, the format must be the same as provided in the file
    SAMPLE.DAT

2.  Use [S]ave to save the results on disk before starting any modifications.

3.  Use [E]dit to verify that the input was correct and modify, delete or add
    additional points.

4.  Use [S]ave again to save the results.

5.  Use [L]sqFit  to calculate  a polynomial fit of up to 10th order.  A good
    rule of thumb is to use the lowest order  polynomial that provides a good
    fit.   The correlation  coefficient calculated  by [L]sqFit indicates how
    good the fit really is with 1.0 being an exact fit.

6.  Use [G]raph to display the input data and goodness of the polynomial fit.

7.  Repeat steps 5 and 6 until satisfied with the results.

8.  Use [P]rint  to get a  hardcopy of the input data, the calculated results,
    the coefficient of the polynomial, and the correlation coefficient.

9.  Once the  polynomial fit is defined, [I]nterpolate can be used to find new
    values for F(x) at a given value of x.


OPTION [K]bdInput: This is  the most basic  option of PwrStar used to enter a
list of points from the keyboard for display  & analysis.  The first input is
the independent variable x and the second is the independent F(x) variable as
a function of x; thus F(x).  After selecting [K]bdInput, you will be asked to
first enter a point number, then x and F(x).  The process continues until you
enter C/R  at the point number prompt.  When  you are prompted for x and F(x),
hitting a C/R  enters a value of  0.0 for each  one.  You can enter up to 100
points in any order and to correct a mistake simply reenter the same point. By
allowing points to be entered in any  order, you  have greater flexibility to
fix mistakes as you enter the data.  However, it is imperative that no points
be left undefined or you  will get unpredictable results.  For example if you
enter 8 points in the following order:  1,2,3,3,10,7,5,6,6,9  points number 4
and 8 will be undefined or have some strange values  in them.  PwrStar should
catch the error and  tell you to fix  the problem with  [E]dit PRIOR to doing
anything else....WITH GREAT POWER COMES GREAT RESPONSIBILITY....


OPTION [F]ileInput:  This option allows you to enter data from a previously
defined ASCII file.  The file may be generated with the [S]ave option after
first entering from the keyboard or with your favorite wordprocessor/editor.
If the file is not generated by PwrStar then it must have the same format as
shown below and in SAMPLE.DAT

3 = Total Number of Points
I    x       F(x)
1  0.05    1.2545
2  0.10    2.3810
3  0.2     4.5678

When [F]ileInput is selected, the program checks to see if it exists and beeps
if it does not.  If no extension is given then '.DAT' is assumed.


OPTION [D]ir:  Is  used to provide a  directory listing of files that match a
given template.  Wild characters are ok but trying to use path names will not
work.


OPTION [E]dit:  Used to interactively delete, insert, or delete points from a
set of data that have been entered.  You have four options with [E]dit

[V]iew    Displays the set of data currently in memory.
[I]nsert  Allows you to insert a new point AFTER the one you will specify.
[D]elete  Allows you to delete any point.
[M]odify  Allows you to enter new values of x & F(x) for a specified point. If
you choose the wrong number just hit  C/R at the x and F(x) prompt to keep the
old values.

To end [E]dit just hit C/R or ESC at the options prompt.


OPTION [L]sqFit:  Calculates the best fitting polynomial up to order 10 by the
method of least squares.  The only  input that is required is the order of the
polynomial the program  takes care of the  rest.  At the present time, to find
the best fit requires inversion of  up to a  10x10 matrix with  a Gauss-Jordan
scheme that uses full pivoting.  However, the  matrix that must be inverted is
usually highly illconditioned or near singular and can cause a fatal execution
error.  A numeric overflow error #01 is the only one that will currently cause
PwrStar to terminate  without warning so  make sure  your input data are saved
before running this option and start with the lowest order polynomial then you
may increase the order  one step at a time.  The overflow error is inherent to
the Gauss-Jordan algorithm  and is compounded by having only 11 digits of real
number accuracy in Turbo Pascal.  Future versions of PwrStar will use the 8087
coprocessor and the Gauss-Sidel iteration scheme to resolve the problem. Until
then, take the  [L]sqFit option in  increments of one, save your  input before
running the option, and remember the most useful polynomial fits are less than
5th order.

The program prints out: Pt, x, F(x), F(x) Calc, RESID where:
Pt       : point number
x        : input value of independent variable
F(x)     : input value of dependent variable
F(x) CALC: Value of dependent variable calculate at x from the polynomial fit
RESID    : Residual error = F(x) CALC - F(x)

You also get the values A1...A11 for the polynomial coefficients and estimates
of how much error there may be in each one where: F(x) = A1 + A2*x +A3*x*x . .

Finally, the correlation coefficient gives you a direct indication of how well
the polynomial fits the data with 1.0 being an exact fit.

NOTE:  The maximum order of the polynomial will one less than the total number
of data points available.  Therefore for 8 points a  maximum 7th order fit can
be used.


OPTION [G]raph:  The purpose of this option is to provide  a QUICK look at how
well the curve fits the data and spot any  problems with  input.  PwrStar will
calculate the proper minimum and maximum for  each axis to maximize use of the
screen.  To use the default values hit  C/R after the defaults are printed for
each axis.  You may also  enter your own axis scale by typing [Y]es when asked
to change?  For each axis  minimum and maximum, hitting  C/R uses the  default
values.  The following values are printed at the bottom of the screen:

Horizontal Axis
Hmin = Minimum value of x axis     Htick = Value of each x axis tick mark

Vertical  Axis
Vmin = Minimum value of F(x) axis  Vtick = Value of each F(x) axis tick mark

To get  a graphics dump  of the screen, you  must first  run GRAPHICS.COM from
your DOS diskette or GRAFTRAX.COM  prior  to running PwrStar.  To get a screen
dump run  [G]raph and  hit the  Shift-PrtScr combination when the  bell sounds
indicating  that PwrStar  is waiting  for you to  make your copy.  Hitting C/R
instead will get you back to the Command Menu.


OPTION [I]nterpolate:   Is used after data have been  entered and a polynomial
fit defined.  Hitting [I]nterpolate  will have PwrStar prompt  you for the new
independent variable x and it will calculate  a new value  of F(x) and ask for
more (Y/N)?  Hitting C/R  or Y makes PwrStar ask for another value and hitting
ESC or N sends it back to the Command Menu.


Option [S]ave:   Takes whatever  data are  currently in memory and  saves to a
user specified disk file.  This  option should  be run immediately  after data
are input from the keyboard to guard against GREMLINS.   When selecting [S]ave
you will be asked for the name of the disk file.  If it already exists you may
then [O]verwrite, [A]ppend to it, or hit C/R or ESC to return  to the Command
Menu.  If you use the [A]ppend  option, you  must then modify the file with an
editor because only the first input set will be used by PwrStar.


OPTION [P]rint:  Takes whatever data are currently in memory and sends to the
printer.


OPTION [H]elp:  Displays this file interactively.

OPTION [Q]uit:  Ends execution.

We are anxious to hear from you how to make PwrStar more usefull to you.
Please mail all comments/suggestions to:

                          HyperStuffWare
                       E.G. [Hank] Hernandez
                       5019 Silver Arrorw Dr
                       Dayton, oh 45424-4813
COMPUTERS

So far, PwrStar will run on: IBM-PC/XT/Jr, Zenith 148/150, Sanyo MBC-555

KNOW PROBLEMS

Hitting the NumLock key on the Sanyo MBC-555 when PwrStar expects an input
will crash the program - so make sure NumLock is set before running PwrStar.