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PDL::Math.3pm

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. Works inplace.

acos does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

asin

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

The usual trigonometric function. Works inplace.

asin does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

atan

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

The usual trigonometric function. Works inplace.

atan does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

cosh

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

The standard hyperbolic function. Works inplace.

cosh does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

sinh

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

The standard hyperbolic function. Works inplace.

sinh does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

tan

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

The usual trigonometric function. Works inplace.

tan does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

tanh

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

The standard hyperbolic function. Works inplace.

tanh does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

ceil

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

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

ceil does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

floor

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

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

floor does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

rint

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

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

rint does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

pow

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

Synonym for `**'. Works inplace.

pow does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

acosh

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

The standard hyperbolic function. Works inplace.

acosh does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

asinh

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

The standard hyperbolic function. Works inplace.

asinh does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

atanh

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

The standard hyperbolic function. Works inplace.

atanh does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

erf

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

The error function. Works inplace.

erf does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

erfc

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

The complement of the error function. Works inplace.

erfc does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

bessj0

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

The standard Bessel function. Works inplace.

bessj0 does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

bessj1

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

The standard Bessel function. Works inplace.

bessj1 does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

bessy0

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

The standard Bessel function. Works inplace.

bessy0 does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

bessy1

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

The standard Bessel function. Works inplace.

bessy1 does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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.

bessjn does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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.

bessyn does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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.

lgamma does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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);
 
 

If bad values are present, these are also cleared.

isfinite

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

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

Bad values are treated as "NaN" or "inf".

erfi

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

The inverse of the error function. Works inplace.

erfi does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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.

ndtri does handle bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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);
 
 

polyroots does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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.