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Math

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 integer 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 integer 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 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($x+0.5)". If you want to round half-integers away from zero, try "floor(abs($x)+0.5)*($x<=>0)". 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 regular Bessel function of the first kind, J_n 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 regular Bessel function of the first kind, J_n 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 regular Bessel function of the second kind, Y_n. 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 regular Bessel function of the second kind, Y_n. 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 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.

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 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.

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 AT ast DOT leeds DOT ac DOT uk), Karl Glazebrook (kgb AT aaoepp DOT aao DOT gov DOT au) and Tuomas J. Lukka (Tuomas DOT Lukka AT helsinki DOT fi). Portions (C) Craig DeForest 2002 (deforest AT boulder DOT swri DOT 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.

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