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Man Pages


Manual Reference Pages  -  PDL::MATH (3)

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NAME

PDL::Math - extended mathematical operations and special functions

CONTENTS

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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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($x+0.5). If you want to round half-integers away from zero, try floor(abs($x)+0.5)*($x<=>0). Works inplace.

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

    pow



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



Synonym for ‘**’. Works inplace.

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

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    erf



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



The error function. Works inplace.

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

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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.

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

    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);



If bad values are present, these are also cleared.

    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 piddles if the flag is set for any of the input piddles.

    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 piddles if the flag is set for any of the input piddles.

    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);



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

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.

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