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.

Many of the functions are linked from the system maths library or the Cephes maths library (determined when PDL is compiled); a few are implemented entirely in PDL.

FUNCTIONS

  acos
  Signature: (a(); [o]b())

The usual trigonometric function.
 Works inplace.

acos processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  asin
  Signature: (a(); [o]b())

The usual trigonometric function.
 Works inplace.

asin processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  atan
  Signature: (a(); [o]b())

The usual trigonometric function.
 Works inplace.

atan processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  cosh
  Signature: (a(); [o]b())

The standard hyperbolic function.
 Works inplace.

cosh processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  sinh
  Signature: (a(); [o]b())

The standard hyperbolic function.
 Works inplace.

sinh processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  tan
  Signature: (a(); [o]b())

The usual trigonometric function.
 Works inplace.

tan processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  tanh
  Signature: (a(); [o]b())

The standard hyperbolic function.
 Works inplace.

tanh processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  ceil
  Signature: (a(); [o]b())

Round to integer values in floating-point format. Works inplace.

ceil processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  floor
  Signature: (a(); [o]b())

Round to integer values in floating-point format. Works inplace.

floor processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  rint
  Signature: (a(); [o]b())

Round to integer values in floating-point format.

rint uses the 'round half to even' rounding method (also known as banker's rounding). Half-integers are rounded to the nearest even number. This avoids a slight statistical bias inherent in always rounding half-integers up or away from zero.

If you are looking to round half-integers up (regardless of sign), try floor($x+0.5). If you want to round half-integers away from zero, try "ceil(abs($x)+0.5)*($x<=>0)". Works inplace.

rint processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  pow
  Signature: (a(); b(); [o]c())

Synonym for `**'. Works inplace.

pow processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  acosh
  Signature: (a(); [o]b())

The standard hyperbolic function.
 Works inplace.

acosh processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  asinh
  Signature: (a(); [o]b())

The standard hyperbolic function.
 Works inplace.

asinh processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  atanh
  Signature: (a(); [o]b())

The standard hyperbolic function.
 Works inplace.

atanh processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  erf
  Signature: (a(); [o]b())

The error function. Works inplace.

erf processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  erfc
  Signature: (a(); [o]b())

The complement of the error function. Works inplace.

erfc processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  bessj0
  Signature: (a(); [o]b())

The regular Bessel function of the first kind, J_n Works inplace.

bessj0 processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  bessj1
  Signature: (a(); [o]b())

The regular Bessel function of the first kind, J_n Works inplace.

bessj1 processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  bessy0
  Signature: (a(); [o]b())

The regular Bessel function of the second kind, Y_n. Works inplace.

bessy0 processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  bessy1
  Signature: (a(); [o]b())

The regular Bessel function of the second kind, Y_n. Works inplace.

bessy1 processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  bessjn
  Signature: (a(); int n(); [o]b())

The regular Bessel function of the first kind, J_n . This takes a second int argument which gives the order of the function required.
 Works inplace.

bessjn processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  bessyn
  Signature: (a(); int n(); [o]b())

The regular Bessel function of the first kind, Y_n . This takes a second int argument which gives the order of the function required.
 Works inplace.

bessyn processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  lgamma
  Signature: (a(); [o]b(); int[o]s())

log gamma function

This returns 2 ndarrays -- 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.

lgamma processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  isfinite
  Signature: (a(); int [o]mask())

Sets $mask true if $a is not a "NaN" or "inf" (either positive or negative). Works inplace.

Bad values are treated as "NaN" or "inf".

  erfi
  Signature: (a(); [o]b())

The inverse of the error function. Works inplace.

erfi processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  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.

ndtri processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  polyroots
  Signature: (cr(n); ci(n); [o]rr(m=CALC($SIZE(n)-1)); [o]ri(m))

Complex roots of a complex polynomial, given coefficients in order of decreasing powers. Only works for degree >= 1. Uses the Jenkins-Traub algorithm (see <https://en.wikipedia.org/wiki/Jenkins%E2%80%93Traub_algorithm>). As of 2.086, works with native-complex data.

 $roots = polyroots($coeffs); # native complex
 ($rr, $ri) = polyroots($cr, $ci);

polyroots does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  polyfromroots
  Signature: (r(m); [o]c(n=CALC($SIZE(m)+1)))

Calculates the complex coefficients of a polynomial from its complex roots, in order of decreasing powers. Added in 2.086, works with native-complex data. Currently O(n^2).

 $coeffs = polyfromroots($roots); # native complex
 ($cr, $ci) = polyfromroots($rr, $ri);

polyfromroots does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

  polyval
  Signature: (c(n); x(); [o]y())

Complex value of a complex polynomial at given point, given coefficients in order of decreasing powers. Uses Horner recurrence. Added in 2.086, works with native-complex data.

 $y = polyval($coeffs, $x); # native complex
 ($yr, $yi) = polyval($cr, $ci, $xr, $xi);

polyval does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

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). Portions (C) Craig DeForest 2002 (deforest@boulder.swri.edu).

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 PDL copyright notice should be included in the file.