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.

Many of the functions are linked from the system maths library or the Cephes maths library (determined when PDL is compiled); a few are implemented entirely in PDL.

FUNCTIONS

acos

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

The usual trigonometric function. Note that when input is a perl scalar and the real-value based function would return NaN, it now returns a cdouble. Works inplace.

asin

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

The usual trigonometric function. Note that when input is a perl scalar and the real-value based function would return NaN, it now returns a cdouble. Works inplace.

atan

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

The usual trigonometric function. Note that when input is a perl scalar and the real-value based function would return NaN, it now returns a cdouble. Works inplace.

cosh

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

The standard hyperbolic function. Note that when input is a perl scalar and the real-value based function would return NaN, it now returns a cdouble. Works inplace.

sinh

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

The standard hyperbolic function. Note that when input is a perl scalar and the real-value based function would return NaN, it now returns a cdouble. Works inplace.

tan

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

The usual trigonometric function. Note that when input is a perl scalar and the real-value based function would return NaN, it now returns a cdouble. Works inplace.

tanh

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

The standard hyperbolic function. Note that when input is a perl scalar and the real-value based function would return NaN, it now returns a cdouble. Works inplace.

ceil

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

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

floor

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

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

rint

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

Round to integer values in floating-point format.

rint uses the 'round half to even' rounding method (also known as banker's rounding). Half-integers are rounded to the nearest even number. This avoids a slight statistical bias inherent in always rounding half-integers up or away from zero.

If you are looking to round half-integers up (regardless of sign), try floor($x+0.5). If you want to round half-integers away from zero, try ceil(abs($x)+0.5)*($x<=>0). Works inplace.

pow

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

Synonym for `**'. Works inplace.

acosh

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

The standard hyperbolic function. Note that when input is a perl scalar and the real-value based function would return NaN, it now returns a cdouble. Works inplace.

asinh

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

The standard hyperbolic function. Note that when input is a perl scalar and the real-value based function would return NaN, it now returns a cdouble. Works inplace.

atanh

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

The standard hyperbolic function. Note that when input is a perl scalar and the real-value based function would return NaN, it now returns a cdouble. 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 regular Bessel function of the first kind, J_n Works inplace.

bessj1

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

The regular Bessel function of the first kind, J_n Works inplace.

bessy0

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

The regular Bessel function of the second kind, Y_n. Works inplace.

bessy1

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

The regular Bessel function of the second kind, Y_n. Works inplace.

bessjn

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

The regular Bessel function of the first kind, J_n . This takes a second int argument which gives the order of the function required. Works inplace.

bessyn

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

The regular Bessel function of the first kind, Y_n . This takes a second int 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 $x inplace:

  badmask($x->inplace,0);
  $x->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.

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);

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). Portions (C) Craig DeForest 2002 (deforest@boulder.swri.edu).

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 PDL copyright notice should be included in the file.

cpanm PDL

perl -MCPAN -e shell
install PDL