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 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.