Math(3) 						User Contributed Perl Documentation						   Math(3)

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@hel-
       sinki.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.

perl v5.8.0							    2003-01-29								   Math(3)