#
# GENERATED WITH PDL::PP! Don't modify!
#
package PDL::GSL::INTEG;
@EXPORT_OK = qw( gslinteg_qng gslinteg_qag gslinteg_qags gslinteg_qagp
gslinteg_qagi gslinteg_qagiu gslinteg_qagil gslinteg_qawc
gslinteg_qaws gslinteg_qawo gslinteg_qawf PDL::PP qng_meat PDL::PP qag_meat PDL::PP qags_meat PDL::PP qagp_meat PDL::PP qagi_meat PDL::PP qagiu_meat PDL::PP qagil_meat PDL::PP qawc_meat PDL::PP qaws_meat PDL::PP qawo_meat PDL::PP qawf_meat );
%EXPORT_TAGS = (Func=>[@EXPORT_OK]);
use PDL::Core;
use PDL::Exporter;
use DynaLoader;
@ISA = ( 'PDL::Exporter','DynaLoader' );
push @PDL::Core::PP, __PACKAGE__;
bootstrap PDL::GSL::INTEG ;
=head1 NAME
PDL::GSL::INTEG - PDL interface to numerical integration routines in GSL
=head1 DESCRIPTION
This is an interface to the numerical integration package present in the
GNU Scientific Library, which is an implementation of QUADPACK.
Functions are named B<gslinteg_{algorithm}> where {algorithm}
is the QUADPACK naming convention. The available functions are:
=over 3
=item gslinteg_qng: Non-adaptive Gauss-Kronrod integration
=item gslinteg_qag: Adaptive integration
=item gslinteg_qags: Adaptive integration with singularities
=item gslinteg_qagp: Adaptive integration with known singular points
=item gslinteg_qagi: Adaptive integration on infinite interval of the form (-\infty,\infty)
=item gslinteg_qagiu: Adaptive integration on infinite interval of the form (a,\infty)
=item gslinteg_qagil: Adaptive integration on infinite interval of the form (-\infty,b)
=item gslinteg_qawc: Adaptive integration for Cauchy principal values
=item gslinteg_qaws: Adaptive integration for singular functions
=item gslinteg_qawo: Adaptive integration for oscillatory functions
=item gslinteg_qawf: Adaptive integration for Fourier integrals
=back
Each algorithm computes an approximation to the integral, I,
of the function f(x)w(x), where w(x) is a weight function
(for general integrands w(x)=1). The user provides absolute
and relative error bounds (epsabs,epsrel) which specify
the following accuracy requirement:
|RESULT - I| <= max(epsabs, epsrel |I|)
The routines will fail to converge if the
error bounds are too stringent, but always return the best
approximation obtained up to that stage
All functions return the result, and estimate of the absolute
error and an error flag (which is zero if there were no problems).
You are responsible for checking for any errors, no warnings are issued
unless the option {Warn => 'y'} is specified in which case
the reason of failure will be printed.
You can nest integrals up to 20 levels. If you find yourself in
the unlikely situation that you need more, you can change the value
of 'max_nested_integrals' in the first line of the file 'FUNC.c'
and recompile.
=for ref
Please check the GSL documentation for more information.
=head1 SYNOPSIS
use PDL;
use PDL::GSL::INTEG;
my $a = 1.2;
my $b = 3.7;
my $epsrel = 0;
my $epsabs = 1e-6;
# Non adaptive integration
my ($res,$abserr,$ierr,$neval) = gslinteg_qng(\&myf,$a,$b,$epsrel,$epsabs);
# Warnings on
my ($res,$abserr,$ierr,$neval) = gslinteg_qng(\&myf,$a,$b,$epsrel,$epsabs,{Warn=>'y'});
# Adaptive integration with warnings on
my $limit = 1000;
my $key = 5;
my ($res,$abserr,$ierr) = gslinteg_qag(\&myf,$a,$b,$epsrel,
$epsabs,$limit,$key,{Warn=>'y'});
sub myf{
my ($x) = @_;
return exp(-$x**2);
}
=head1 FUNCTIONS
=cut
sub gslinteg_qng{
my ($opt,$warn);
if (ref($_[$#_]) eq 'HASH'){ $opt = pop @_; }
else{ $opt = {Warn => 'n'}; }
if($$opt{Warn}=~/y/i) { $warn = 1;}
else {$warn = 0;}
my ($f,$a,$b,$epsabs,$epsrel) = @_;
barf 'Usage: gslinteg_qng($function_ref,$a,$b,$epsabs,$epsrel,[opt]) '
unless ($#_ == 4);
my ($res,$abserr,$neval,$ierr) = qng_meat($a,$b,$epsabs,$epsrel,$warn,$f);
return ($res,$abserr,$ierr,$neval);
}
=head2 qng_meat
=for sig
Signature: (double a(); double b(); double epsabs();
double epsrel(); double [o] result(); double [o] abserr();
int [o] neval(); int [o] ierr(); int gslwarn(); SV* function)
=for ref
info not available
=for bad
qng_meat does not process bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
=cut
*qng_meat = \&PDL::qng_meat;
sub gslinteg_qag{
my ($opt,$warn);
if (ref($_[$#_]) eq 'HASH'){ $opt = pop @_; }
else{ $opt = {Warn => 'n'}; }
if($$opt{Warn}=~/y/i) { $warn = 1;}
else {$warn = 0;}
my ($f,$a,$b,$epsabs,$epsrel,$limit,$key) = @_;
barf 'Usage: gslinteg_qag($function_ref,$a,$b,$epsabs,$epsrel,$limit,$key,[opt]) '
unless ($#_ == 6);
my ($res,$abserr,$ierr) = qag_meat($a,$b,$epsabs,$epsrel,$limit,$key,$limit,$warn,$f);
return ($res,$abserr,$ierr);
}
=head2 qag_meat
=for sig
Signature: (double a(); double b(); double epsabs();double epsrel(); int limit();
int key(); double [o] result(); double [o] abserr();int n();int [o] ierr();int gslwarn();; SV* function)
=for ref
info not available
=for bad
qag_meat 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.
=cut
*qag_meat = \&PDL::qag_meat;
sub gslinteg_qags{
my ($opt,$warn);
if (ref($_[$#_]) eq 'HASH'){ $opt = pop @_; }
else{ $opt = {Warn => 'n'}; }
if($$opt{Warn}=~/y/i) { $warn = 1;}
else {$warn = 0;}
my ($f,$a,$b,$epsabs,$epsrel,$limit) = @_;
barf 'Usage: gslinteg_qags($function_ref,$a,$b,$epsabs,$epsrel,$limit,[opt]) '
unless ($#_ == 5);
my ($res,$abserr,$ierr) = qags_meat($a,$b,$epsabs,$epsrel,$limit,$limit,$warn,$f);
return ($res,$abserr,$ierr);
}
=head2 qags_meat
=for sig
Signature: (double a(); double b(); double epsabs();double epsrel(); int limit();
double [o] result(); double [o] abserr();int n();int [o] ierr();int gslwarn();; SV* function)
=for ref
info not available
=for bad
qags_meat does not process bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
=cut
*qags_meat = \&PDL::qags_meat;
sub gslinteg_qagp{
my ($opt,$warn);
if (ref($_[$#_]) eq 'HASH'){ $opt = pop @_; }
else{ $opt = {Warn => 'n'}; }
if($$opt{Warn}=~/y/i) { $warn = 1;}
else {$warn = 0;}
my ($f,$points,$epsabs,$epsrel,$limit) = @_;
barf 'Usage: gslinteg_qagp($function_ref,$points,$epsabs,$epsrel,$limit,[opt]) '
unless ($#_ == 4);
my ($res,$abserr,$ierr) = qagp_meat($points,$epsabs,$epsrel,$limit,$limit,$warn,$f);
return ($res,$abserr,$ierr);
}
=head2 qagp_meat
=for sig
Signature: (double pts(l); double epsabs();double epsrel();int limit();
double [o] result(); double [o] abserr();int n();int [o] ierr();int gslwarn();; SV* function)
=for ref
info not available
=for bad
qagp_meat 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.
=cut
*qagp_meat = \&PDL::qagp_meat;
sub gslinteg_qagi{
my ($opt,$warn);
if (ref($_[$#_]) eq 'HASH'){ $opt = pop @_; }
else{ $opt = {Warn => 'n'}; }
if($$opt{Warn}=~/y/i) { $warn = 1;}
else {$warn = 0;}
my ($f,$epsabs,$epsrel,$limit) = @_;
barf 'Usage: gslinteg_qagi($function_ref,$epsabs,$epsrel,$limit,[opt]) '
unless ($#_ == 3);
my ($res,$abserr,$ierr) = qagi_meat($epsabs,$epsrel,$limit,$limit,$warn,$f);
return ($res,$abserr,$ierr);
}
=head2 qagi_meat
=for sig
Signature: (double epsabs();double epsrel(); int limit();
double [o] result(); double [o] abserr(); int n(); int [o] ierr();int gslwarn();; SV* function)
=for ref
info not available
=for bad
qagi_meat does not process bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
=cut
*qagi_meat = \&PDL::qagi_meat;
sub gslinteg_qagiu{
my ($opt,$warn);
if (ref($_[$#_]) eq 'HASH'){ $opt = pop @_; }
else{ $opt = {Warn => 'n'}; }
if($$opt{Warn}=~/y/i) { $warn = 1;}
else {$warn = 0;}
my ($f,$a,$epsabs,$epsrel,$limit) = @_;
barf 'Usage: gslinteg_qagiu($function_ref,$a,$epsabs,$epsrel,$limit,[opt]) '
unless ($#_ == 4);
my ($res,$abserr,$ierr) = qagiu_meat($a,$epsabs,$epsrel,$limit,$limit,$warn,$f);
return ($res,$abserr,$ierr);
}
=head2 qagiu_meat
=for sig
Signature: (double a(); double epsabs();double epsrel();int limit();
double [o] result(); double [o] abserr();int n();int [o] ierr();int gslwarn();; SV* function)
=for ref
info not available
=for bad
qagiu_meat 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.
=cut
*qagiu_meat = \&PDL::qagiu_meat;
sub gslinteg_qagil{
my ($opt,$warn);
if (ref($_[$#_]) eq 'HASH'){ $opt = pop @_; }
else{ $opt = {Warn => 'n'}; }
if($$opt{Warn}=~/y/i) { $warn = 1;}
else {$warn = 0;}
my ($f,$b,$epsabs,$epsrel,$limit) = @_;
barf 'Usage: gslinteg_qagil($function_ref,$b,$epsabs,$epsrel,$limit,[opt]) '
unless ($#_ == 4);
my ($res,$abserr,$ierr) = qagil_meat($b,$epsabs,$epsrel,$limit,$limit,$warn,$f);
return ($res,$abserr,$ierr);
}
=head2 qagil_meat
=for sig
Signature: (double b(); double epsabs();double epsrel();int limit();
double [o] result(); double [o] abserr();int n();int [o] ierr();int gslwarn();; SV* function)
=for ref
info not available
=for bad
qagil_meat does not process bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
=cut
*qagil_meat = \&PDL::qagil_meat;
sub gslinteg_qawc{
my ($opt,$warn);
if (ref($_[$#_]) eq 'HASH'){ $opt = pop @_; }
else{ $opt = {Warn => 'n'}; }
if($$opt{Warn}=~/y/i) { $warn = 1;}
else {$warn = 0;}
my ($f,$a,$b,$c,$epsabs,$epsrel,$limit) = @_;
barf 'Usage: gslinteg_qawc($function_ref,$a,$b,$c,$epsabs,$epsrel,$limit,[opt]) '
unless ($#_ == 6);
my ($res,$abserr,$ierr) = qawc_meat($a,$b,$c,$epsabs,$epsrel,$limit,$limit,$warn,$f);
return ($res,$abserr,$ierr);
}
=head2 qawc_meat
=for sig
Signature: (double a(); double b(); double c(); double epsabs();double epsrel();int limit();
double [o] result(); double [o] abserr();int n();int [o] ierr();int gslwarn();; SV* function)
=for ref
info not available
=for bad
qawc_meat 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.
=cut
*qawc_meat = \&PDL::qawc_meat;
sub gslinteg_qaws{
my ($opt,$warn);
if (ref($_[$#_]) eq 'HASH'){ $opt = pop @_; }
else{ $opt = {Warn => 'n'}; }
if($$opt{Warn}=~/y/i) { $warn = 1;}
else {$warn = 0;}
my ($f,$alpha,$beta,$mu,$nu,$a,$b,$epsabs,$epsrel,$limit) = @_;
barf 'Usage: gslinteg_qaws($function_ref,$alpha,$beta,$mu,$nu,$a,$b,$epsabs,$epsrel,$limit,[opt]) '
unless ($#_ == 9);
my ($res,$abserr,$ierr) = qaws_meat($a,$b,$epsabs,$epsrel,$limit,$limit,$alpha,$beta,$mu,$nu,$warn,$f);
return ($res,$abserr,$ierr);
}
=head2 qaws_meat
=for sig
Signature: (double a(); double b();double epsabs();double epsrel();int limit();
double [o] result(); double [o] abserr();int n();
double alpha(); double beta(); int mu(); int nu();int [o] ierr();int gslwarn();; SV* function)
=for ref
info not available
=for bad
qaws_meat does not process bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
=cut
*qaws_meat = \&PDL::qaws_meat;
sub gslinteg_qawo{
my ($opt,$warn);
if (ref($_[$#_]) eq 'HASH'){ $opt = pop @_; }
else{ $opt = {Warn => 'n'}; }
if($$opt{Warn}=~/y/i) { $warn = 1;}
else {$warn = 0;}
my ($f,$omega,$sincosopt,$a,$b,$epsabs,$epsrel,$limit) = @_;
barf 'Usage: gslinteg_qawo($function_ref,$omega,$sin_or_cos,$a,$b,$epsabs,$epsrel,$limit,[opt]) '
unless ($#_ == 7);
my $OPTION_SIN_COS;
if($sincosopt=~/cos/i){ $OPTION_SIN_COS = 0;}
elsif($sincosopt=~/sin/i){ $OPTION_SIN_COS = 1;}
else { barf("Error in argument 3 of function gslinteg_qawo: specify 'cos' or 'sin'\n");}
my $L = $b - $a;
my $nlevels = $limit;
my ($res,$abserr,$ierr) = qawo_meat($a,$b,$epsabs,$epsrel,$limit,$limit,$OPTION_SIN_COS,$omega,$L,$nlevels,$warn,$f);
return ($res,$abserr,$ierr);
}
=head2 qawo_meat
=for sig
Signature: (double a(); double b();double epsabs();double epsrel();int limit();
double [o] result(); double [o] abserr();int n();
int sincosopt(); double omega(); double L(); int nlevels();int [o] ierr();int gslwarn();; SV* function)
=for ref
info not available
=for bad
qawo_meat does not process bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
=cut
*qawo_meat = \&PDL::qawo_meat;
sub gslinteg_qawf{
my ($opt,$warn);
if (ref($_[$#_]) eq 'HASH'){ $opt = pop @_; }
else{ $opt = {Warn => 'n'}; }
if($$opt{Warn}=~/y/i) { $warn = 1;}
else {$warn = 0;}
my ($f,$omega,$sincosopt,$a,$epsabs,$limit) = @_;
barf 'Usage: gslinteg_qawf($function_ref,$omega,$sin_or_cos,$a,$epsabs,$limit,[opt]) '
unless ($#_ == 5);
my $OPTION_SIN_COS;
if($sincosopt=~/cos/i){ $OPTION_SIN_COS = 0;}
elsif($sincosopt=~/sin/i){ $OPTION_SIN_COS = 1;}
else { barf("Error in argument 3 of function gslinteg_qawf: specify 'cos' or 'sin'\n");}
my $nlevels = $limit;
my ($res,$abserr,$ierr) = qawf_meat($a,$epsabs,$limit,$limit,$OPTION_SIN_COS,$omega,$nlevels,$warn,$f);
return ($res,$abserr,$ierr);
}
=head2 qawf_meat
=for sig
Signature: (double a(); double epsabs();int limit();
double [o] result(); double [o] abserr();int n();
int sincosopt(); double omega(); int nlevels();int [o] ierr();int gslwarn();; SV* function)
=for ref
info not available
=for bad
qawf_meat 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.
=cut
*qawf_meat = \&PDL::qawf_meat;
;
=head2 gslinteg_qng
Non-adaptive Gauss-Kronrod integration
This function applies the Gauss-Kronrod 10-point, 21-point, 43-point and 87-point
integration rules in succession until an estimate of the integral of f over ($a,$b)
is achieved within the desired absolute and relative error limits, $epsabs and $epsrel.
It is meant for fast integration of smooth functions. It returns an array with the
result, an estimate of the absolute error, an error flag and the number of function
evaluations performed.
=for usage
Usage:
($res,$abserr,$ierr,$neval) = gslinteg_qng($function_ref,$a,$b,
$epsrel,$epsabs,[{Warn => $warn}]);
=for example
Example:
my ($res,$abserr,$ierr,$neval) = gslinteg_qng(\&f,0,1,0,1e-9);
# with warnings on
my ($res,$abserr,$ierr,$neval) = gslinteg_qng(\&f,0,1,0,1e-9,{Warn => 'y'});
sub f{
my ($x) = @_;
return ($x**2.6)*log(1.0/$x);
}
=head2 gslinteg_qag
Adaptive integration
This function applies an integration rule adaptively until an estimate of
the integral of f over ($a,$b) is achieved within the desired absolute and
relative error limits, $epsabs and $epsrel. On each iteration the adaptive
integration strategy bisects the interval with the largest error estimate;
the maximum number of allowed subdivisions is given by the parameter $limit.
The integration rule is determined by the
value of $key, which has to be one of (1,2,3,4,5,6) and correspond to
the 15, 21, 31, 41, 51 and 61 point Gauss-Kronrod rules respectively.
It returns an array with the result, an estimate of the absolute error
and an error flag.
=for ref
Please check the GSL documentation for more information.
=for usage
Usage:
($res,$abserr,$ierr) = gslinteg_qag($function_ref,$a,$b,$epsrel,
$epsabs,$limit,$key,[{Warn => $warn}]);
=for example
Example:
my ($res,$abserr,$ierr) = gslinteg_qag(\&f,0,1,0,1e-10,1000,1);
# with warnings on
my ($res,$abserr,$ierr) = gslinteg_qag(\&f,0,1,0,1e-10,1000,1,{Warn => 'y'});
sub f{
my ($x) = @_;
return ($x**2.6)*log(1.0/$x);
}
=head2 gslinteg_qags
Adaptive integration with singularities
This function applies the Gauss-Kronrod 21-point integration rule
adaptively until an estimate of the integral of f over ($a,$b) is
achieved within the desired absolute and relative error limits,
$epsabs and $epsrel. The algorithm is such that it
accelerates the convergence of the integral in the presence of
discontinuities and integrable singularities.
The maximum number of allowed subdivisions done by the adaptive
algorithm must be supplied in the parameter $limit.
=for ref
Please check the GSL documentation for more information.
=for usage
Usage:
($res,$abserr,$ierr) = gslinteg_qags($function_ref,$a,$b,$epsrel,
$epsabs,$limit,[{Warn => $warn}]);
=for example
Example:
my ($res,$abserr,$ierr) = gslinteg_qags(\&f,0,1,0,1e-10,1000);
# with warnings on
($res,$abserr,$ierr) = gslinteg_qags(\&f,0,1,0,1e-10,1000,{Warn => 'y'});
sub f{
my ($x) = @_;
return ($x)*log(1.0/$x);
}
=head2 gslinteg_qagp
Adaptive integration with known singular points
This function applies the adaptive integration algorithm used by
gslinteg_qags taking into account the location of singular points
until an estimate of
the integral of f over ($a,$b) is achieved within the desired absolute and
relative error limits, $epsabs and $epsrel.
Singular points are supplied in the piddle $points, whose endpoints
determine the integration range.
So, for example, if the function has singular points at x_1 and x_2 and the
integral is desired from a to b (a < x_1 < x_2 < b), $points = pdl(a,x_1,x_2,b).
The maximum number of allowed subdivisions done by the adaptive
algorithm must be supplied in the parameter $limit.
=for ref
Please check the GSL documentation for more information.
=for usage
Usage:
($res,$abserr,$ierr) = gslinteg_qagp($function_ref,$points,$epsabs,
$epsrel,$limit,[{Warn => $warn}])
=for example
Example:
my $points = pdl(0,1,sqrt(2),3);
my ($res,$abserr,$ierr) = gslinteg_qagp(\&f,$points,0,1e-3,1000);
# with warnings on
($res,$abserr,$ierr) = gslinteg_qagp(\&f,$points,0,1e-3,1000,{Warn => 'y'});
sub f{
my ($x) = @_;
my $x2 = $x**2;
my $x3 = $x**3;
return $x3 * log(abs(($x2-1.0)*($x2-2.0)));
}
=head2 gslinteg_qagi
Adaptive integration on infinite interval
This function estimates the integral of the function f over the
infinite interval (-\infty,+\infty) within the desired absolute and
relative error limits, $epsabs and $epsrel.
After a transformation, the algorithm
of gslinteg_qags with a 15-point Gauss-Kronrod rule is used.
The maximum number of allowed subdivisions done by the adaptive
algorithm must be supplied in the parameter $limit.
=for ref
Please check the GSL documentation for more information.
=for usage
Usage:
($res,$abserr,$ierr) = gslinteg_qagi($function_ref,$epsabs,
$epsrel,$limit,[{Warn => $warn}]);
=for example
Example:
my ($res,$abserr,$ierr) = gslinteg_qagi(\&myfn,1e-7,0,1000);
# with warnings on
($res,$abserr,$ierr) = gslinteg_qagi(\&myfn,1e-7,0,1000,{Warn => 'y'});
sub myfn{
my ($x) = @_;
return exp(-$x - $x*$x) ;
}
=head2 gslinteg_qagiu
Adaptive integration on infinite interval
This function estimates the integral of the function f over the
infinite interval (a,+\infty) within the desired absolute and
relative error limits, $epsabs and $epsrel.
After a transformation, the algorithm
of gslinteg_qags with a 15-point Gauss-Kronrod rule is used.
The maximum number of allowed subdivisions done by the adaptive
algorithm must be supplied in the parameter $limit.
=for ref
Please check the GSL documentation for more information.
=for usage
Usage:
($res,$abserr,$ierr) = gslinteg_qagiu($function_ref,$a,$epsabs,
$epsrel,$limit,[{Warn => $warn}]);
=for example
Example:
my $alfa = 1;
my ($res,$abserr,$ierr) = gslinteg_qagiu(\&f,99.9,1e-7,0,1000);
# with warnings on
($res,$abserr,$ierr) = gslinteg_qagiu(\&f,99.9,1e-7,0,1000,{Warn => 'y'});
sub f{
my ($x) = @_;
if (($x==0) && ($alfa == 1)) {return 1;}
if (($x==0) && ($alfa > 1)) {return 0;}
return ($x**($alfa-1))/((1+10*$x)**2);
}
=head2 gslinteg_qagil
Adaptive integration on infinite interval
This function estimates the integral of the function f over the
infinite interval (-\infty,b) within the desired absolute and
relative error limits, $epsabs and $epsrel.
After a transformation, the algorithm
of gslinteg_qags with a 15-point Gauss-Kronrod rule is used.
The maximum number of allowed subdivisions done by the adaptive
algorithm must be supplied in the parameter $limit.
=for ref
Please check the GSL documentation for more information.
=for usage
Usage:
($res,$abserr,$ierr) = gslinteg_qagl($function_ref,$b,$epsabs,
$epsrel,$limit,[{Warn => $warn}]);
=for example
Example:
my ($res,$abserr,$ierr) = gslinteg_qagil(\&myfn,1.0,1e-7,0,1000);
# with warnings on
($res,$abserr,$ierr) = gslinteg_qagil(\&myfn,1.0,1e-7,0,1000,{Warn => 'y'});
sub myfn{
my ($x) = @_;
return exp($x);
}
=head2 gslinteg_qawc
Adaptive integration for Cauchy principal values
This function computes the Cauchy principal value of the integral of f over (a,b),
with a singularity at c, I = \int_a^b dx f(x)/(x - c). The integral is
estimated within the desired absolute and relative error limits, $epsabs and $epsrel.
The maximum number of allowed subdivisions done by the adaptive
algorithm must be supplied in the parameter $limit.
=for ref
Please check the GSL documentation for more information.
=for usage
Usage:
($res,$abserr,$ierr) = gslinteg_qawc($function_ref,$a,$b,$c,$epsabs,$epsrel,$limit)
=for example
Example:
my ($res,$abserr,$ierr) = gslinteg_qawc(\&f,-1,5,0,0,1e-3,1000);
# with warnings on
($res,$abserr,$ierr) = gslinteg_qawc(\&f,-1,5,0,0,1e-3,1000,{Warn => 'y'});
sub f{
my ($x) = @_;
return 1.0 / (5.0 * $x * $x * $x + 6.0) ;
}
=head2 gslinteg_qaws
Adaptive integration for singular functions
The algorithm in gslinteg_qaws is designed for integrands with algebraic-logarithmic
singularities at the end-points of an integration region.
Specifically, this function computes the integral given by
I = \int_a^b dx f(x) (x-a)^alpha (b-x)^beta log^mu (x-a) log^nu (b-x).
The integral is
estimated within the desired absolute and relative error limits, $epsabs and $epsrel.
The maximum number of allowed subdivisions done by the adaptive
algorithm must be supplied in the parameter $limit.
=for ref
Please check the GSL documentation for more information.
=for usage
Usage:
($res,$abserr,$ierr) =
gslinteg_qawc($function_ref,$alpha,$beta,$mu,$nu,$a,$b,
$epsabs,$epsrel,$limit,[{Warn => $warn}]);
=for example
Example:
my ($res,$abserr,$ierr) = gslinteg_qaws(\&f,0,0,1,0,0,1,0,1e-7,1000);
# with warnings on
($res,$abserr,$ierr) = gslinteg_qaws(\&f,0,0,1,0,0,1,0,1e-7,1000,{Warn => 'y'});
sub f{
my ($x) = @_;
if($x==0){return 0;}
else{
my $u = log($x);
my $v = 1 + $u*$u;
return 1.0/($v*$v);
}
}
=head2 gslinteg_qawo
Adaptive integration for oscillatory functions
This function uses an adaptive algorithm to compute the integral of f over
(a,b) with the weight function sin(omega*x) or cos(omega*x) -- which of
sine or cosine is used is determined by the parameter $opt ('cos' or 'sin').
The integral is
estimated within the desired absolute and relative error limits, $epsabs and $epsrel.
The maximum number of allowed subdivisions done by the adaptive
algorithm must be supplied in the parameter $limit.
=for ref
Please check the GSL documentation for more information.
=for usage
Usage:
($res,$abserr,$ierr) = gslinteg_qawo($function_ref,$omega,$sin_or_cos,
$a,$b,$epsabs,$epsrel,$limit,[opt])
=for example
Example:
my $PI = 3.14159265358979323846264338328;
my ($res,$abserr,$ierr) = PDL::GSL::INTEG::gslinteg_qawo(\&f,10*$PI,'sin',0,1,0,1e-7,1000);
# with warnings on
($res,$abserr,$ierr) = PDL::GSL::INTEG::gslinteg_qawo(\&f,10*$PI,'sin',0,1,0,1e-7,1000,{Warn => 'y'});
sub f{
my ($x) = @_;
if($x==0){return 0;}
else{ return log($x);}
}
=head2 gslinteg_qawf
Adaptive integration for Fourier integrals
This function attempts to compute a Fourier integral of the function
f over the semi-infinite interval [a,+\infty). Specifically, it attempts
tp compute I = \int_a^{+\infty} dx f(x)w(x), where w(x) is sin(omega*x)
or cos(omega*x) -- which of sine or cosine is used is determined by
the parameter $opt ('cos' or 'sin').
The integral is
estimated within the desired absolute error limit $epsabs.
The maximum number of allowed subdivisions done by the adaptive
algorithm must be supplied in the parameter $limit.
=for ref
Please check the GSL documentation for more information.
=for usage
Usage:
gslinteg_qawf($function_ref,$omega,$sin_or_cos,$a,$epsabs,$limit,[opt])
=for example
Example:
my ($res,$abserr,$ierr) = gslinteg_qawf(\&f,$PI/2.0,'cos',0,1e-7,1000);
# with warnings on
($res,$abserr,$ierr) = gslinteg_qawf(\&f,$PI/2.0,'cos',0,1e-7,1000,{Warn => 'y'});
sub f{
my ($x) = @_;
if ($x == 0){return 0;}
return 1.0/sqrt($x)
}
=head1 BUGS
Feedback is welcome. Log bugs in the PDL bug database (the
database is always linked from L<http://pdl.perl.org>).
=head1 SEE ALSO
L<PDL>
The GSL documentation is online at
http://www.gnu.org/software/gsl/manual/
=head1 AUTHOR
This file copyright (C) 2003,2005 Andres Jordan <ajordan@eso.org>
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 copyright notice should be included in the file.
The GSL integration routines were written by Brian Gough. QUADPACK
was written by Piessens, Doncker-Kapenga, Uberhuber and Kahaner.
=cut
# Exit with OK status
1;