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.\" ========================================================================
.\"
.IX Title "INTERP 3pm"
.TH INTERP 3pm "2023-06-17" "perl v5.36.0" "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::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 = $spl\->integ(2.1,7.4);
.Ve
.SH "NOMENCLATURE"
.IX Header "NOMENCLATURE"
Throughout this documentation we strive to use the same variables that
are present in the original \s-1GSL\s0 documentation (see See
Also). Oftentimes those variables are called \f(CW\*(C`a\*(C'\fR and
\&\f(CW\*(C`b\*(C'\fR. Since good Perl coding practices discourage the use of Perl
variables \f(CW$a\fR and \f(CW$b\fR, here we refer to Parameters \f(CW\*(C`a\*(C'\fR and \f(CW\*(C`b\*(C'\fR
as \f(CW$pa\fR and \f(CW$pb\fR, respectively, and Limits (of domain or
integration) as \f(CW$la\fR and \f(CW$lb\fR.
#line 64 \*(L"\s-1INTERP\s0.pm\*(R"
.SH "FUNCTIONS"
.IX Header "FUNCTIONS"
.SS "init"
.IX Subsection "init"
.Vb 1
\&  Signature: (double x(n); double y(n); gsl_spline *spl)
.Ve
.PP
The init method initializes a new instance of \s-1INTERP.\s0 It needs as
input an interpolation type and two ndarrays 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
.PP
init 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.
.SS "eval"
.IX Subsection "eval"
.Vb 1
\&  Signature: (double x(); double [o] out(); gsl_spline *spl;gsl_interp_accel *acc)
.Ve
.PP
The function eval returns the interpolating function at a given point.
It will barf with an \*(L"input domain error\*(R" if you try to extrapolate.
.PP
Usage:
.PP
.Vb 1
\&    $result = $spl\->eval($points);
.Ve
.PP
Example:
.PP
.Vb 1
\&    my $res = $spl\->eval($x)
.Ve
.PP
eval 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.
.SS "deriv"
.IX Subsection "deriv"
.Vb 1
\&  Signature: (double x(); double [o] out(); gsl_spline *spl;gsl_interp_accel *acc)
.Ve
.PP
The deriv function returns the derivative of the
interpolating function at a given point.
It will barf with an \*(L"input domain error\*(R" if you try to extrapolate.
.PP
Usage:
.PP
.Vb 1
\&    $result = $spl\->deriv($points);
.Ve
.PP
Example:
.PP
.Vb 1
\&    my $res = $spl\->deriv($x)
.Ve
.PP
deriv 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.
.SS "deriv2"
.IX Subsection "deriv2"
.Vb 1
\&  Signature: (double x(); double [o] out(); gsl_spline *spl;gsl_interp_accel *acc)
.Ve
.PP
The deriv2 function returns the second derivative
of the interpolating function at a given point.
It will barf with an \*(L"input domain error\*(R" if you try to extrapolate.
.PP
Usage:
.PP
.Vb 1
\&    $result = $spl\->deriv2($points);
.Ve
.PP
Example:
.PP
.Vb 1
\&    my $res = $spl\->deriv2($x)
.Ve
.PP
deriv2 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.
.SS "integ"
.IX Subsection "integ"
.Vb 1
\&  Signature: (double a(); double b(); double [o] out(); gsl_spline *spl;gsl_interp_accel *acc)
.Ve
.PP
The integ function returns the integral
of the interpolating function between two points.
It will barf with an \*(L"input domain error\*(R" if you try to extrapolate.
.PP
Usage:
.PP
.Vb 1
\&    $result = $spl\->integ($la,$lb);
.Ve
.PP
Example:
.PP
.Vb 1
\&    my $res = $spl\->integ($la,$lb)
.Ve
.PP
integ 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.
.SH "BUGS"
.IX Header "BUGS"
Feedback is welcome.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\s-1PDL\s0
.PP
The \s-1GSL\s0 documentation for interpolation is online at
<https://www.gnu.org/software/gsl/doc/html/interp.html>
.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.