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.\" ========================================================================
.\"
.IX Title "Math 3pm"
.TH Math 3pm "2012-05-30" "perl v5.14.2" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
PDL::Math \- extended mathematical operations and special functions
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\& use PDL::Math;
\&
\& use PDL::Graphics::TriD;
\& imag3d [SURF2D,bessj0(rvals(zeroes(50,50))/2)];
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This module extends \s-1PDL\s0 with more advanced mathematical functions than
provided by standard Perl.
.PP
All the functions have one input pdl, and one output, unless otherwise
stated.
.PP
Many of the functions are linked from the system maths library or the 
Cephes maths library (determined when \s-1PDL\s0 is compiled); a few are implemented
entirely in \s-1PDL\s0.
.SH "FUNCTIONS"
.IX Header "FUNCTIONS"
.SS "acos"
.IX Subsection "acos"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The usual trigonometric function. Works inplace.
.PP
acos does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "asin"
.IX Subsection "asin"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The usual trigonometric function. Works inplace.
.PP
asin does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "atan"
.IX Subsection "atan"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The usual trigonometric function. Works inplace.
.PP
atan does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "cosh"
.IX Subsection "cosh"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The standard hyperbolic function. Works inplace.
.PP
cosh does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "sinh"
.IX Subsection "sinh"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The standard hyperbolic function. Works inplace.
.PP
sinh does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "tan"
.IX Subsection "tan"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The usual trigonometric function. Works inplace.
.PP
tan does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "tanh"
.IX Subsection "tanh"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The standard hyperbolic function. Works inplace.
.PP
tanh does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "ceil"
.IX Subsection "ceil"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
Round to integer values in floating-point format. Works inplace.
.PP
ceil does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "floor"
.IX Subsection "floor"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
Round to integer values in floating-point format. Works inplace.
.PP
floor does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "rint"
.IX Subsection "rint"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
Round to integer values in floating-point format.
.PP
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.
.PP
If you are looking to round half-integers up (regardless of sign), try
\&\f(CW\*(C`floor($x+0.5)\*(C'\fR.  If you want to round half-integers away from zero,
try \f(CW\*(C`floor(abs($x)+0.5)*($x<=>0)\*(C'\fR. Works inplace.
.PP
rint does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "pow"
.IX Subsection "pow"
.Vb 1
\&  Signature: (a(); b(); [o]c())
.Ve
.PP
Synonym for `**'. Works inplace.
.PP
pow does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "acosh"
.IX Subsection "acosh"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The standard hyperbolic function. Works inplace.
.PP
acosh does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "asinh"
.IX Subsection "asinh"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The standard hyperbolic function. Works inplace.
.PP
asinh does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "atanh"
.IX Subsection "atanh"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The standard hyperbolic function. Works inplace.
.PP
atanh does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "erf"
.IX Subsection "erf"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The error function. Works inplace.
.PP
erf does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "erfc"
.IX Subsection "erfc"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The complement of the error function. Works inplace.
.PP
erfc does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "bessj0"
.IX Subsection "bessj0"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The regular Bessel function of the first kind, J_n Works inplace.
.PP
bessj0 does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "bessj1"
.IX Subsection "bessj1"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The regular Bessel function of the first kind, J_n Works inplace.
.PP
bessj1 does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "bessy0"
.IX Subsection "bessy0"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The regular Bessel function of the second kind, Y_n. Works inplace.
.PP
bessy0 does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "bessy1"
.IX Subsection "bessy1"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The regular Bessel function of the second kind, Y_n. Works inplace.
.PP
bessy1 does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "bessjn"
.IX Subsection "bessjn"
.Vb 1
\&  Signature: (a(); int n(); [o]b())
.Ve
.PP
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.
.PP
bessjn does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "bessyn"
.IX Subsection "bessyn"
.Vb 1
\&  Signature: (a(); int n(); [o]b())
.Ve
.PP
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.
.PP
bessyn does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "lgamma"
.IX Subsection "lgamma"
.Vb 1
\&  Signature: (a(); [o]b(); int[o]s())
.Ve
.PP
log gamma function
.PP
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.
.PP
lgamma does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "badmask"
.IX Subsection "badmask"
.Vb 1
\&  Signature: (a(); b(); [o]c())
.Ve
.PP
Clears all \f(CW\*(C`infs\*(C'\fR and \f(CW\*(C`nans\*(C'\fR in \f(CW$a\fR to the corresponding value in \f(CW$b\fR.
.PP
badmask can be run with \f(CW$a\fR inplace:
.PP
.Vb 2
\&  badmask($a\->inplace,0);
\&  $a\->inplace\->badmask(0);
.Ve
.PP
If bad values are present, these are also cleared.
.SS "isfinite"
.IX Subsection "isfinite"
.Vb 1
\&  Signature: (a(); int [o]mask())
.Ve
.PP
Sets \f(CW$mask\fR true if \f(CW$a\fR is not a \f(CW\*(C`NaN\*(C'\fR or \f(CW\*(C`inf\*(C'\fR (either positive or negative). Works inplace.
.PP
Bad values are treated as \f(CW\*(C`NaN\*(C'\fR or \f(CW\*(C`inf\*(C'\fR.
.SS "erfi"
.IX Subsection "erfi"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The inverse of the error function. Works inplace.
.PP
erfi does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "ndtri"
.IX Subsection "ndtri"
.Vb 1
\&  Signature: (a(); [o]b())
.Ve
.PP
The value for which the area under the
Gaussian probability density function (integrated from
minus infinity) is equal to the argument (cf erfi). Works inplace.
.PP
ndtri does handle bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "polyroots"
.IX Subsection "polyroots"
.Vb 1
\&  Signature: (cr(n); ci(n); [o]rr(m); [o]ri(m))
.Ve
.PP
Complex roots of a complex polynomial, given coefficients in order
of decreasing powers.
.PP
.Vb 1
\& ($rr, $ri) = polyroots($cr, $ci);
.Ve
.PP
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.
.SH "BUGS"
.IX Header "BUGS"
Hasn't been tested on all platforms to ensure Cephes
versions are picked up automatically and used correctly.
.SH "AUTHOR"
.IX Header "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).
.PP
All rights reserved. There is no warranty. You are allowed
to redistribute this software / documentation under certain
conditions. For details, see the file \s-1COPYING\s0 in the \s-1PDL\s0
distribution. If this file is separated from the \s-1PDL\s0 distribution,
the \s-1PDL\s0 copyright notice should be included in the file.