Math(h) User Contributed Perl Documentation Math(h) 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(g) values, while the second set, of integer val- ues, 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(k); isfinite Signature: (a(); int [o]mask()) Sets $mask true if $a is not a "NaN" or "inf" (either pos- itive or negative). Works inplace. erfi Signature: (a(); [o]b()) The inverse of the error function. Works inplace. ndtri Signature: (a(); [o]b()) The value for which the area under the Gaussian probabil- ity density function (integrated from minus infinity) is equal to the argument (cf erfi). Works inplace. svd Signature: (a(n,m); [o]u(n,m); [o,phys]z(z); [o]v(n,n)) Singular value decomposition of array. ($u, $s, $v) = svd($a); polyroots Signature: (cr(r); ci(i); [o]rr(r); [o]ri(i)) Complex roots of a complex polynomial, given coefficients in order of decreasing powers. ($rr, $ri) = polyroots($cr, $ci); eigens Signature: ([phys]a(a); [o,phys]ev(n,n); [o,phys]e(e)) Eigenvalues and -vectors of a symmetric square matrix. If passed an asymmetric matrix, the routine will warn and symmetrize it. ($e, $ev) = eigens($a); simq Signature: ([phys]a(n,n); [phys]b(b); [o,phys]x(x); int [o,phys]ips(s); 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 col- umn-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(b)) Convert a symmetric square matrix to triangular vector storage BUGS Hasn't been tested on all platforms to ensure Cephes ver- sions 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). All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under cer- tain 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 v5.6.1 2002-04-08 Math(h)