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PDL-LinearAlgebra-0.433
River stage one • 2 direct dependents • 3 total dependents
/ PDL::LinearAlgebra::Special

NAME

PDL::LinearAlgebra::Special - Special matrices for PDL

SYNOPSIS


            

              
              
use PDL::LinearAlgebra::Special;
$a = mhilb(5,5);

DESCRIPTION

This module provides some constructors of well known matrices.

FUNCTIONS

mhilb

Construct Hilbert matrix from specifications list or template ndarray


            

              
              
PDL(Hilbert)  = mpart(PDL(template) | ARRAY(specification))

            

          

            

              
              
my $hilb   = mhilb(float,5,5);

mtri

Return zeroed matrix with upper or lower triangular part from another matrix. Return trapezoid matrix if entry matrix is not square. Supports threading. Uses tricpy or tricpy.


            

              
              
PDL = mtri(PDL, SCALAR)
SCALAR : UPPER = 0 | LOWER = 1, default = 0

            

          

            

              
              
my $a = random(10,10);
my $b = mtri($a, 0);

mvander

Return (primal) Vandermonde matrix from vector.

mvander(M,P) is a rectangular version of mvander(P) with M Columns.

mpart

Return antisymmetric and symmetric part of a real or complex square matrix.


            

              
              
( PDL(antisymmetric), PDL(symmetric) )  = mpart(PDL, SCALAR(conj))
conj : if true Return AntiHermitian, Hermitian part.

            

          

            

              
              
my $a = random(10,10);
my ( $antisymmetric, $symmetric )  = mpart($a);

mhankel

Return Hankel matrix also known as persymmetric matrix. Handles complex data.


            

              
              
mhankel(c,r), where c and r are vectors, returns matrix whose first column
is c and whose last row is r. The last element of c prevails.
mhankel(c) returns matrix with element below skew diagonal (anti-diagonal) equals
to zero. If c is a scalar number, make it from sequence beginning at one.

The elements are:


            

              
              
H (i,j) = c (i+j),  i+j+1 <= m;
H (i,j) = r (i+j-m+1),  otherwise
where m is the size of the vector.

If c is a scalar number, its determinant can be computed by:


            

              
              
                floor(n/2)    n
Det(H(n)) = (-1)      *      n

mtoeplitz

Return toeplitz matrix. Handles complex data.


            

              
              
mtoeplitz(c,r), where c and r are vectors, returns matrix whose first column
is c and whose last row is r. The last element of c prevails.
mtoeplitz(c) returns symmetric matrix.

mpascal

Return Pascal matrix (from Pascal's triangle) of order N.


            

              
              
mpascal(N,uplo).
uplo:
        0 => upper triangular (Cholesky factor),
        1 => lower triangular (Cholesky factor),
        2 => symmetric.

This matrix is obtained by writing Pascal's triangle (whose elements are binomial coefficients from index and/or index sum) as a matrix and truncating appropriately. The symmetric Pascal is positive definite, its inverse has integer entries.

Their determinants are all equal to one and:


            

              
              
S = L * U
where S, L, U are symmetric, lower and upper pascal matrix respectively.

mcompanion

Return a matrix with characteristic polynomial equal to p if p is monic. If p is not monic the characteristic polynomial of A is equal to p/c where c is the coefficient of largest degree in p (here p is in descending order).


            

              
              
mcompanion(PDL(p),SCALAR(charpol)).
charpol:
        0 => first row is -P(1:n-1)/P(0),
        1 => last column is -P(1:n-1)/P(0),

AUTHOR

Copyright (C) Grégory Vanuxem 2005-2007.

This library is free software; you can redistribute it and/or modify it under the terms of the artistic license as specified in the Artistic file.