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From: pfeifer@charly.informatik.uni-dortmund.de (Ulrich Pfeifer)
Newsgroups: comp.lang.perl.announce,comp.lang.perl.misc
Subject: Announcing Math::Matrix and Math::Approx 0.1
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Date: 31 Oct 1995 15:38:34 GMT
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Hello!

Trying to "save the world" I made two modules public available I
currently wrote.

In a little one-shot-programs I had to invert a matrix. Since I did
not want to install Math::Pari for this little program I wrote my own
matrix module. I started with a script by Dan Carson posted in
comp.lang.perl. The script could not handle zero diagonal
elements. Also matrices with interdependent rows could not be handled.

The second module uses Math::Matrix to approximate a sample of
x,y-values by a set of functions given as parameter. E.g. polynomial
approximations can be generated.

I append parts of the documentation for convenience. Any help in
completing the modules is welcome.

You can get the modules from your favorite CPAN archive:

        .../CPAN/modules/by-module/Math


Ulrich
------------------------------------------------------------------------
NAME
       Math::Matrix

METHODS
       new

       Constructor arguments are a list of references to arrays
       of the same length.  The arrays are copied. The method
       returns undef in case of error.

               $a =3D new Math::Matrix ([rand,rand,rand],
                                      [rand,rand,rand],
                                      [rand,rand,rand]);

       concat

       Concatenates two matrices of same row count. The result is
       a new matrix or undef in case of error.

               $b =3D new Math::Matrix ([rand],[rand],[rand]);
               $c =3D $a->concat($b);

       transpose

       Returns the transposed matrix. This is the matrix where
       colums and rows of the argument matrix are swaped.

       multiply

       Multiplies two matrices where the length of the rows in
       the first matrix is the same as the length of the columns
       in the second matrix. Returns the product or undef in case
       of error.

       solve

       Solves a equation system given by the matrix. The number
       of colums must be greater than the number of rows. If
       variables are dependent from each other, the second and
       all further of the dependent coefficients are 0. This
       means the method can handle such systems. The method
       returns a matrix containing the solutions in its columns
       or undef in case of error.
[...]
------------------------------------------------------------------------
NAME
       Math::Approx

METHODS
       new

           new Math::Approx (\&poly, 5, %x);

       The first argument after the class name must be a
       reference to function which takes two arguments: The
       degree and the x value.

       For interpolation with plain polynomials poly can be
       defined as:

               sub poly {
                   my($n,$x) =3D @_;

                   return $x ** $n;
               }

       The second argument is the maximum degree which should be
       used for interpolation. Degrees start with 0.

       The rest of the arguments are treated as pairs of x and y
       samples which should be approximated.

       The method returns a Math::Approx reference.

       approx

               $approximation->approx(17);

       The method returns the approximated  y value for the x
       value given as argument.

       fit

               $approximation->fit;

       Returns the medim square error for the data points.

EXAMPLE
               use Math::Approx;

               sub poly {
                   my($n,$x) =3D @_;

                   return $x ** $n;
               }

               for (1..20) {
                   $x{$_} =3D sin($_/10)*cos($_/30)+0.3*rand;
               }

               $a =3D new Math::Approx (\&poly, 5, %x);
               $a->print;
               $a->plot("mist");
               print "Fit: ", $a->fit, "\n";