                            PwrStar 2.16 Help File
     Copyright (c) 1986, 1987, 1988 HyperStuffWare, 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.  PwrStar  was
written in Turbo Pascal which performs all real number operations in 11 digit
precision and therefore roundoff errors limit the maximum polynomial fit to a
10th order least squares fit.

  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.  Version 1.2 now also gives you the
    normalized values Xn and Fn(Xn) as previously described.


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).  Starting with version 1.36 you can now select an
[A]utomatic  point sequencing for entry (recommeded) or [M]anually  selecting
the sequence.

SubOption [M]anual Sequence.   After selecting this option you will be  asked
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 300
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....

SubOption [A]utomatic Sequence.  After  selecting this option you'll be asked
to enter X and  F(X) pairs very much like  the [M]anual option.  However, you
will not be prompted for the point number which is automatically provided and
you must wait until after entering  ALL the data to correct any mistakes with
the [E]dit option.  After each point is entered you will be asked  whether to
continue or stop.  Hitting Y or C/R continues the input while N or ESC stops.

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 and path names are ok.  If  your provide the
path name only, then PwrStar will  change its default  directory to  your new
name if its legal.  Please note that PwrStar must be in the same directory as
the *.BGI files when the [G]raph option is run for the first time.


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.

Note that Version 1.35 now normalizes your X, F(X) input before performing the
least squares fit by dividing the X values by their average so that  Xn=X/Xavg
and the F(X) by the corresponding average so Fn(Xn) F(X)/Favg.  This  mod  was
required to increase the numerical stability of the matrix inversion algorithm
and reduce susceptibility to crashes for ill-conditioned data.

To use the Fn(Xn) equation now calculated by  the program, first devide your X
input value by the Xavg value given by  PwrStar, then plug into given equation
and mult