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Math
Section: User Contributed Perl Documentation (3)Updated: 2002-04-08
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NAME
PDL::Math - extended mathematical operations and special functionsSYNOPSIS
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@helsinki.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.
Index
- NAME
- SYNOPSIS
- DESCRIPTION
- FUNCTIONS
- acos
- asin
- atan
- cosh
- sinh
- tan
- tanh
- ceil
- floor
- rint
- pow
- acosh
- asinh
- atanh
- erf
- erfc
- bessj0
- bessj1
- bessy0
- bessy1
- bessjn
- bessyn
- lgamma
- badmask
- isfinite
- erfi
- ndtri
- svd
- polyroots
- eigens
- simq
- squaretotri
- BUGS
- AUTHOR
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