NAME

Math::MatrixReal::Aug - Additional methods for Math::MatrixReal.

SYNOPSIS

  use Math::MatrixReal;
  use Math::MatrixReal::Aug;

DESCRIPTION

These are certain extra methods for Math::MatrixReal, in the tradition of Math::MatrixReal::Ext1;

• $matrix1->augmentright($matrix2);

  Creates a new matrix of the form [$matrix1 $matrix2]. $matrix1 and $matrix2 must have the same number of rows.

  Example:

   $A = Math::MatrixReal->new_from_cols([[1,0]]);
   $B = Math::MatrixReal->new_from_cols([[1,2],[2,1]]);
  
   $C = $A / $B
   print $C;
   [  1.000000000000E+00  1.000000000000E+00  2.000000000000E+00 ]
   [  0.000000000000E+00  2.000000000000E+00  1.000000000000E+00 ]

• $matrix1->augmentbelow($matrix2);

  Creates a new matrix of the form [ $matrix1 ] [ $matrix2 ]. $matrix1 and $matrix2 must have the same number of columns.

  Example:

   $A = Math::MatrixReal->new_from_cols([[1,0],[0,1]]);
   $B = Math::MatrixReal->new_from_cols([[1,2],[2,1]]);
  
   $C = $A / $B
   print $C;
   [  1.000000000000E+00  0.000000000000E+00 ]
   [  0.000000000000E+00  1.000000000000E+00 ]
   [  1.000000000000E+00  2.000000000000E+00 ]
   [  2.000000000000E+00  1.000000000000E+00 ]

• $matrix->applyfunction($coderef)

  Applies &$coderef to each element of $matrix, and returns the result. $coderef should be a reference to a subroutine that takes four parameters: ($matrix, $matrix->element($i,$j), $i, $j) where $i and $j are the row and column indices of the current element.

  Example:

   sub increment {
       my ($matrix,$element, $i,$j)=@_;
       return $element+1;
   }
  
   $A = Math::MatrixReal->new_from_cols([[1,0],[0,1]]);
  
   $E=$A->applyfunction(\&increment);
   print $E;
   [  2.000000000000E+00  1.000000000000E+00 ]
   [  1.000000000000E+00  2.000000000000E+00 ]

• $matrix->largeexponential($exponent)

  Finds $matrix^$exponent using the square-and-multiply method. $matrix must be square and $exponent must be a positive integer. Much more efficient for large $exponent than $matrix->$exponential($exponent) in that approximately log2($exponent) multiplications are required instead of approximately $exponent.

• $matrix->fill($const);

  Sets all elements of $matrix equal to $const.

  Example:

   $A = new Math::MatrixReal(3,3);
   $A->fill(4);
   print $A;
   [  4.000000000000E+00  4.000000000000E+00  4.000000000000E+00 ]
   [  4.000000000000E+00  4.000000000000E+00  4.000000000000E+00 ]
   [  4.000000000000E+00  4.000000000000E+00  4.000000000000E+00 ]

• $new_matrix = $some_matrix->newfill($rows,$columns,$const); $new_matrix = Math::MatrixReal->newfill($rows,$columns,$const);

  Creates a new matrix of the specified size, all the elements of which are $const.

  Example:

   $A = Math::MatrixReal->newfill(3,3,4);
   print $A;
   [  4.000000000000E+00  4.000000000000E+00  4.000000000000E+00 ]
   [  4.000000000000E+00  4.000000000000E+00  4.000000000000E+00 ]
   [  4.000000000000E+00  4.000000000000E+00  4.000000000000E+00 ]

OVERLOADED OPERATORS

New Binary operators:

x, .

x

Right augmenting binary operator.

 $A x $B 
is the same as 
 $A->augmentright($B)

.

Bottom augmenting binary operator.

 $A . $B  
is the same as 
 $A->augmentbelow($B)

NOTES

The augmentright operator has a higher precence than the augmentbelow operator, so $A x $B . $B x $A is [ $A $B ] [ $B $A ]

BUGS

Provably countably infinite.

This document can be improved.

No testing routines are provided.

AUTHOR

Jacob C. Kesinger, <kesinger@math.ttu.edu>

SEE ALSO

Math::MatrixReal.