PDL::Math - extended mathematical operations and special functions

- 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

# 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@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.