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.\" ========================================================================
.\"
.IX Title "INTERP 3pm"
.TH INTERP 3pm "2016-10-10" "perl v5.24.1" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
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.SH "NAME"
PDL::GSL::INTERP \- PDL interface to Interpolation routines in GSL
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This is an interface to the interpolation package present in the 
\&\s-1GNU\s0 Scientific Library.
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 2
\&   use PDL;
\&   use PDL::GSL::INTERP;
\&
\&   my $x = sequence(10);
\&   my $y = exp($x);
\&
\&   my $spl = PDL::GSL::INTERP\->init(\*(Aqcspline\*(Aq,$x,$y);
\&
\&   my $res = $spl\->eval(4.35);
\&   $res = $spl\->deriv(4.35);
\&   $res = $spl\->deriv2(4.35);
\&   $res = $spl\->integ(2.1,7.4);
.Ve
.SH "FUNCTIONS"
.IX Header "FUNCTIONS"
.SS "\fIinit()\fP"
.IX Subsection "init()"
The init method initializes a new instance of \s-1INTERP.\s0 It needs as 
input an interpolation type and two piddles holding the x and y 
values to be interpolated. The \s-1GSL\s0 routines require that x be
monotonically increasing and a quicksort is performed by default to 
ensure that. You can skip the quicksort by passing the option 
{Sort => 0}.
.PP
The available interpolation types are :
.IP "linear" 2
.IX Item "linear"
.PD 0
.IP "polynomial" 2
.IX Item "polynomial"
.IP "cspline (natural cubic spline)" 2
.IX Item "cspline (natural cubic spline)"
.IP "cspline_periodic  (periodic cubic spline)" 2
.IX Item "cspline_periodic (periodic cubic spline)"
.IP "akima (natural akima spline)" 2
.IX Item "akima (natural akima spline)"
.IP "akima_periodic  (periodic akima spline)" 2
.IX Item "akima_periodic (periodic akima spline)"
.PD
.PP
Please check the \s-1GSL\s0 documentation for more information.
.PP
Usage:
.PP
.Vb 1
\&    $blessed_ref = PDL::GSL::INTERP\->init($interp_method,$x,$y,$opt);
.Ve
.PP
Example:
.PP
.Vb 2
\&    $x = sequence(10);
\&    $y = exp($x);
\&
\&    $spl = PDL::GSL::INTERP\->init(\*(Aqcspline\*(Aq,$x,$y)
\&    $spl = PDL::GSL::INTERP\->init(\*(Aqcspline\*(Aq,$x,$y,{Sort => 1}) #same as above
\&
\&    # no sorting done on x, user is certain that x is monotonically increasing
\&    $spl = PDL::GSL::INTERP\->init(\*(Aqcspline\*(Aq,$x,$y,{Sort => 0});
.Ve
.SS "\fIeval()\fP"
.IX Subsection "eval()"
The function eval returns the interpolating function at a given point. By default
it will barf if you try to extrapolate, to comply silently if the point to be
evaluated is out of range pass the option {Extrapolate => 1}
.PP
Usage:
.PP
.Vb 1
\&    $result = $spl\->eval($points,$opt);
.Ve
.PP
Example:
.PP
.Vb 2
\&    my $res = $spl\->eval($x)
\&    $res = $spl\->eval($x,{Extrapolate => 0}) #same as above
\&
\&    # silently comply if $x is out of range
\&    $res = $spl\->eval($x,{Extrapolate => 1})
.Ve
.SS "\fIderiv()\fP"
.IX Subsection "deriv()"
The deriv function returns the derivative of the 
interpolating function at a given point. By default
it will barf if you try to extrapolate, to comply silently if the point to be
evaluated is out of range pass the option {Extrapolate => 1}
.PP
Usage:
.PP
.Vb 1
\&    $result = $spl\->deriv($points,$opt);
.Ve
.PP
Example:
.PP
.Vb 2
\&    my $res = $spl\->deriv($x)
\&    $res = $spl\->deriv($x,{Extrapolate => 0}) #same as above
\&
\&    # silently comply if $x is out of range
\&    $res = $spl\->deriv($x,{Extrapolate => 1})
.Ve
.SS "\fIderiv2()\fP"
.IX Subsection "deriv2()"
The deriv2 function returns the second derivative 
of the interpolating function at a given point. By default
it will barf if you try to extrapolate, to comply silently if the point to be
evaluated is out of range pass the option {Extrapolate => 1}
.PP
Usage:
.PP
.Vb 1
\&    $result = $spl\->deriv2($points,$opt);
.Ve
.PP
Example:
.PP
.Vb 2
\&    my $res = $spl\->deriv2($x)
\&    $res = $spl\->deriv2($x,{Extrapolate => 0}) #same as above
\&
\&    # silently comply if $x is out of range
\&    $res = $spl\->deriv2($x,{Extrapolate => 1})
.Ve
.SS "\fIinteg()\fP"
.IX Subsection "integ()"
The integ function returns the integral 
of the interpolating function between two points.
By default it will barf if you try to extrapolate, 
to comply silently if one of the integration limits
is out of range pass the option {Extrapolate => 1}
.PP
Usage:
.PP
.Vb 1
\&    $result = $spl\->integ($a,$b,$opt);
.Ve
.PP
Example:
.PP
.Vb 2
\&    my $res = $spl\->integ($a,$b)
\&    $res = $spl\->integ($a,$b,{Extrapolate => 0}) #same as above
\&
\&    # silently comply if $a or $b are out of range
\&    $res = $spl\->eval($a,$b,{Extrapolate => 1})
.Ve
.SH "BUGS"
.IX Header "BUGS"
Feedback is welcome.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\s-1PDL\s0
.PP
The \s-1GSL\s0 documentation is online at
.PP
.Vb 1
\&  http://www.gnu.org/software/gsl/manual/
.Ve
.SH "AUTHOR"
.IX Header "AUTHOR"
This file copyright (C) 2003 Andres Jordan <andresj@physics.rutgers.edu>
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 copyright notice should be included in the file.
.PP
The \s-1GSL\s0 interpolation module was written by Gerard Jungman.