NAME

PDL::Math - extended mathematical operations and special functions

SYNOPSIS

 use PDL::Math;
 use PDL::Graphics::TriD;
 imag3d [SURF2D,bessj0(rvals(zeroes(50,50))/2)];

DESCRIPTION

This module extends PDL with more advanced mathematical functions than provided by standard Perl.

All the functions have one input pdl, and one output, unless otherwise stated.

The functions are usually available from the system maths library, however if they are not (determined when PDL is compiled) a version from the Cephes math library is used.

FUNCTIONS

acos

  Signature: (a(); [o]b())

The usual trigonometric function. Works inplace.

asin

  Signature: (a(); [o]b())

The usual trigonometric function. Works inplace.

atan

  Signature: (a(); [o]b())

The usual trigonometric function. Works inplace.

cosh

  Signature: (a(); [o]b())

The standard hyperbolic function. Works inplace.

sinh

  Signature: (a(); [o]b())

The standard hyperbolic function. Works inplace.

tan

  Signature: (a(); [o]b())

The usual trigonometric function. Works inplace.

tanh

  Signature: (a(); [o]b())

The standard hyperbolic function. Works inplace.

ceil

  Signature: (a(); [o]b())

Round to integral values in floating-point format. Works inplace.

floor

  Signature: (a(); [o]b())

Round to integral values in floating-point format. Works inplace.

rint

  Signature: (a(); [o]b())

Round to integral values in floating-point format. Works inplace.

pow

  Signature: (a(); b(); [o]c())

Synonym for `**'. Works inplace.

acosh

  Signature: (a(); [o]b())

The standard hyperbolic function. Works inplace.

asinh

  Signature: (a(); [o]b())

The standard hyperbolic function. Works inplace.

atanh

  Signature: (a(); [o]b())

The standard hyperbolic function. Works inplace.

erf

  Signature: (a(); [o]b())

The error function. Works inplace.

erfc

  Signature: (a(); [o]b())

The complement of the error function. Works inplace.

bessj0

  Signature: (a(); [o]b())

The standard Bessel function. Works inplace.

bessj1

  Signature: (a(); [o]b())

The standard Bessel function. Works inplace.

bessy0

  Signature: (a(); [o]b())

The standard Bessel function. Works inplace.

bessy1

  Signature: (a(); [o]b())

The standard Bessel function. Works inplace.

bessjn

  Signature: (a(); int n(); [o]b())

The standard Bessel function. This has a second integer argument which gives the order of the function required. Works inplace.

bessyn

  Signature: (a(); int n(); [o]b())

The standard Bessel function. This has a second integer argument which gives the order of the function required. Works inplace.

lgamma

  Signature: (a(); [o]b(); int[o]s())

log gamma function

This returns 2 piddles -- the first set gives the log(gamma) values, while the second set, of integer values, gives the sign of the gamma function. This is useful for determining factorials, amongst other things.

badmask

  Signature: (a(); b(); [o]c())

Clears all infs and nans in $a to the corresponding value in $b.

badmask can be run with $a inplace:

  badmask($a->inplace,0);
  $a->inplace->badmask(0);

isfinite

  Signature: (a(); int [o]mask())

Sets $mask true if $a is not a NaN or inf (either positive or negative). Works inplace.

erfi

  Signature: (a(); [o]b())

The inverse of the error function. Works inplace.

ndtri

  Signature: (a(); [o]b())

The value for which the area under the Gaussian probability density function (integrated from minus infinity) is equal to the argument (cf erfi). Works inplace.

svd

  Signature: (a(n,m); [o]u(n,m); [o,phys]z(n); [o]v(n,n))

Singular value decomposition of array.

 ($u, $s, $v) = svd($a);

polyroots

  Signature: (cr(n); ci(n); [o]rr(m); [o]ri(m))

Complex roots of a complex polynomial, given coefficients in order of decreasing powers.

 ($rr, $ri) = polyroots($cr, $ci);

eigens

  Signature: ([phys]a(m); [o,phys]ev(n,n); [o,phys]e(n))

Eigenvalues and -vectors of a symmetric square matrix. If passed an asymmetric matrix, the routine will warn and symmetrize it.

 ($e, $ev) = eigens($a);

simq

  Signature: ([phys]a(n,n); [phys]b(n); [o,phys]x(n); int [o,phys]ips(n); int flag)

Solution of simultaneous linear equations, a x = b.

$a is an n x n matrix (i.e., a vector of length n*n), stored row-wise: that is, a(i,j) = a[ij], where ij = i*n + j. While this is the transpose of the normal column-wise storage, this corresponds to normal PDL usage. The contents of matrix a may be altered (but may be required for subsequent calls with flag = -1).

$b, $x, $ips are vectors of length n.

Set flag=0 to solve. Set flag=-1 to do a new back substitution for different $b vector using the same a matrix previously reduced when flag=0 (the $ips vector generated in the previous solution is also required).

squaretotri

  Signature: (a(n,n); b(m))

Convert a symmetric square matrix to triangular vector storage

BUGS

Hasn't been tested on all platforms to ensure Cephes versions are picked up automatically and used correctly.

AUTHOR

Copyright (C) R.J.R. Williams 1997 (rjrw@ast.leeds.ac.uk), Karl Glazebrook (kgb@aaoepp.aao.gov.au) and Tuomas J. Lukka (Tuomas.Lukka@helsinki.fi)

All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file.