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.
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.
Signature: (a(); [o]b())
The usual trigonometric function.
Signature: (a(); [o]b())
The usual trigonometric function.
Signature: (a(); [o]b())
The usual trigonometric function.
Signature: (a(); [o]b())
The standard hyperbolic function.
Signature: (a(); [o]b())
The standard hyperbolic function.
Signature: (a(); [o]b())
The usual trigonometric function.
Signature: (a(); [o]b())
The standard hyperbolic function.
Signature: (a(); [o]b())
Round to integral values in floating-point format
Signature: (a(); [o]b())
Round to integral values in floating-point format
Signature: (a(); [o]b())
Round to integral values in floating-point format
Signature: (a(); b(); [o]c())
Synonym for `**'
Signature: (a(); [o]b())
The standard hyperbolic function.
Signature: (a(); [o]b())
The standard hyperbolic function.
Signature: (a(); [o]b())
The standard hyperbolic function.
Signature: (a(); [o]b())
The error function
Signature: (a(); [o]b())
The complement of the error function
Signature: (a(); [o]b())
The standard Bessel Functions
Signature: (a(); [o]b())
The standard Bessel Functions
Signature: (a(); [o]b())
The standard Bessel Functions
Signature: (a(); [o]b())
The standard Bessel Functions
Signature: (a(); int n(); [o]b())
The standard Bessel Functions
Signature: (a(); int n(); [o]b())
The standard Bessel Functions
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.
Signature: (a(); b(); [o]c())
Clears all infs
and nans
in $a to the corresponding value in $b
Signature: (a(); [o]b())
The inverse of the error function
Signature: (a(); [o]b())
The value for which the area under the Gaussian probability density function (integrated from minus infinity) is equal to the argument (cf erfi)
Signature: (a(n,m); [o]u(n,m); [o,phys]z(n); [o]v(n,n))
Singular value decomposition of array.
($u, $s, $v) = svd($a);
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);
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).
Signature: (a(n,n); b(m))
Convert a symmetric square matrix to triangular vector storage
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@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.