PDL::Math − extended mathematical operations and special functions

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

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 .

**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.

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

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.