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[Math-GSL.git] / Multifit.i
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1 %module "Math::GSL::Multifit"
3 %include "typemaps.i"
4 %apply double *OUTPUT { double * y, double * y_err, double * chisq, size_t * rank};
6 %{
7 #include "gsl/gsl_types.h"
8 #include "gsl/gsl_multifit.h"
9 #include "gsl/gsl_multifit_nlin.h"
12 %include "gsl/gsl_types.h"
13 %include "gsl/gsl_multifit.h"
14 %include "gsl/gsl_multifit_nlin.h"
16 %perlcode %{
17 @EXPORT_OK = qw/
18 gsl_multifit_linear_alloc
19 gsl_multifit_linear_free
20 gsl_multifit_linear
21 gsl_multifit_linear_svd
22 gsl_multifit_wlinear
23 gsl_multifit_wlinear_svd
24 gsl_multifit_linear_est
25 gsl_multifit_linear_residuals
26 gsl_multifit_gradient
27 gsl_multifit_covar
28 gsl_multifit_fsolver_alloc
29 gsl_multifit_fsolver_free
30 gsl_multifit_fsolver_set
31 gsl_multifit_fsolver_iterate
32 gsl_multifit_fsolver_name
33 gsl_multifit_fsolver_position
34 gsl_multifit_fdfsolver_alloc
35 gsl_multifit_fdfsolver_set
36 gsl_multifit_fdfsolver_iterate
37 gsl_multifit_fdfsolver_free
38 gsl_multifit_fdfsolver_name
39 gsl_multifit_fdfsolver_position
40 gsl_multifit_test_delta
41 gsl_multifit_test_gradient
42 $gsl_multifit_fdfsolver_lmder
43 $gsl_multifit_fdfsolver_lmsder;
45 %EXPORT_TAGS = ( all => [ @EXPORT_OK ] );
47 __END__
49 =head1 NAME
51 Math::GSL::Multifit - Least-squares functions for a general linear model with multiple parameters
53 =head1 SYNOPSIS
55 use Math::GSL::Multifit qw /:all/;
57 =head1 DESCRIPTION
59 The functions in this module perform least-squares fits to a general linear model, y = X c where y is a vector of n observations, X is an n by p matrix of predictor variables, and the elements of the vector c are the p unknown best-fit parameters which are to be estimated.
61 Here is a list of all the functions in this module :
63 =over
65 =item C<gsl_multifit_linear_alloc($n, $p)> - This function allocates a workspace for fitting a model to $n observations using $p parameters.
67 =item C<gsl_multifit_linear_free($work)> - This function frees the memory associated with the workspace w.
69 =item C<gsl_multifit_linear($X, $y, $c, $cov, $work)> - This function computes the best-fit parameters vector $c of the model y = X c for the observations vector $y and the matrix of predictor variables $X. The variance-covariance matrix of the model parameters vector $cov is estimated from the scatter of the observations about the best-fit. The sum of squares of the residuals from the best-fit, \chi^2, is returned after 0 if the operation succeeded, 1 otherwise. If the coefficient of determination is desired, it can be computed from the expression R^2 = 1 - \chi^2 / TSS, where the total sum of squares (TSS) of the observations y may be computed from gsl_stats_tss. The best-fit is found by singular value decomposition of the matrix $X using the preallocated workspace provided in $work. The modified Golub-Reinsch SVD algorithm is used, with column scaling to improve the accuracy of the singular values. Any components which have zero singular value (to machine precision) are discarded from the fit.
71 =item C<gsl_multifit_linear_svd($X, $y, $tol, $c, $cov, $work)> - This function computes the best-fit parameters c of the model y = X c for the observations vector $y and the matrix of predictor variables $X. The variance-covariance matrix of the model parameters vector $cov is estimated from the scatter of the observations about the best-fit. The sum of squares of the residuals from the best-fit, \chi^2, is returned after 0 if the operation succeeded, 1 otherwise. If the coefficient of determination is desired, it can be computed from the expression R^2 = 1 - \chi^2 / TSS, where the total sum of squares (TSS) of the observations y may be computed from gsl_stats_tss. In this second form of the function the components are discarded if the ratio of singular values s_i/s_0 falls below the user-specified tolerance $tol, and the effective rank is returned after the sum of squares of the residuals from the best-fit.
73 =item C<gsl_multifit_wlinear($X, $w, $y, $c, $cov, $work> - This function computes the best-fit parameters vector $c of the weighted model y = X c for the observations y with weights $w and the matrix of predictor variables $X. The covariance matrix of the model parameters $cov is computed with the given weights. The weighted sum of squares of the residuals from the best-fit, \chi^2, is returned after 0 if the operation succeeded, 1 otherwise. If the coefficient of determination is desired, it can be computed from the expression R^2 = 1 - \chi^2 / WTSS, where the weighted total sum of squares (WTSS) of the observations y may be computed from gsl_stats_wtss. The best-fit is found by singular value decomposition of the matrix $X using the preallocated workspace provided in $work. Any components which have zero singular value (to machine precision) are discarded from the fit.
75 =item C<gsl_multifit_wlinear_svd($X, $w, $y, $tol, $rank, $c, $cov, $work) > This function computes the best-fit parameters vector $c of the weighted model y = X c for the observations y with weights $w and the matrix of predictor variables $X. The covariance matrix of the model parameters $cov is computed with the given weights. The weighted sum of squares of the residuals from the best-fit, \chi^2, is returned after 0 if the operation succeeded, 1 otherwise. If the coefficient of determination is desired, it can be computed from the expression R^2 = 1 - \chi^2 / WTSS, where the weighted total sum of squares (WTSS) of the observations y may be computed from gsl_stats_wtss. The best-fit is found by singular value decomposition of the matrix $X using the preallocated workspace provided in $work. In this second form of the function the components are discarded if the ratio of singular values s_i/s_0 falls below the user-specified tolerance $tol, and the effective rank is returned after the sum of squares of the residuals from the best-fit..
77 =item C<gsl_multifit_linear_est($x, $c, $cov)> - This function uses the best-fit multilinear regression coefficients vector $c and their covariance matrix $cov to compute the fitted function value $y and its standard deviation $y_err for the model y = x.c at the point $x, in the form of a vector. The functions returns 3 values in this order : 0 if the operation succeeded, 1 otherwise, the fittes function value and its standard deviation.
79 =item C<gsl_multifit_linear_residuals($X, $y, $c, $r)> - This function computes the vector of residuals r = y - X c for the observations vector $y, coefficients vector $c and matrix of predictor variables $X. $r is also a vector.
81 =item C<gsl_multifit_gradient($J, $f, $g)> - This function computes the gradient $g of \Phi(x) = (1/2) ||F(x)||^2 from the Jacobian matrix $J and the function values $f, using the formula $g = $J^T $f. $g and $f are vectors.
83 =item C<gsl_multifit_test_gradient($g, $epsabas)> - This function tests the residual gradient vector $g against the absolute error bound $epsabs. Mathematically, the gradient should be exactly zero at the minimum. The test returns $GSL_SUCCESS if the following condition is achieved, \sum_i |g_i| < $epsabs and returns $GSL_CONTINUE otherwise. This criterion is suitable for situations where the precise location of the minimum, x, is unimportant provided a value can be found where the gradient is small enough.
85 =item C<gsl_multifit_test_delta($dx, $x, $epsabs, $epsrel)> - This function tests for the convergence of the sequence by comparing the last step vector $dx with the absolute error $epsabs and relative error $epsrel to the current position x. The test returns $GSL_SUCCESS if the following condition is achieved, |dx_i| < epsabs + epsrel |x_i| for each component of x and returns $GSL_CONTINUE otherwise.
87 =back
89 The following functions are not yet implemented. Patches Welcome!
91 =over
93 =item C<gsl_multifit_covar >
95 =item C<gsl_multifit_fsolver_alloc($T, $n, $p)>
97 =item C<gsl_multifit_fsolver_free >
99 =item C<gsl_multifit_fsolver_set >
101 =item C<gsl_multifit_fsolver_iterate >
103 =item C<gsl_multifit_fsolver_name >
105 =item C<gsl_multifit_fsolver_position >
107 =item C<gsl_multifit_fdfsolver_alloc >
109 =item C<gsl_multifit_fdfsolver_set >
111 =item C<gsl_multifit_fdfsolver_iterate >
113 =item C<gsl_multifit_fdfsolver_free >
115 =item C<gsl_multifit_fdfsolver_name >
117 =item C<gsl_multifit_fdfsolver_position >
120 =back
122 For more informations on the functions, we refer you to the GSL offcial
123 documentation: L<http://www.gnu.org/software/gsl/manual/html_node/>
125 Tip : search on google: site:http://www.gnu.org/software/gsl/manual/html_node/ name_of_the_function_you_want
127 =head1 EXAMPLES
131 =head1 AUTHORS
133 Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
135 =head1 COPYRIGHT AND LICENSE
137 Copyright (C) 2008 Jonathan Leto and Thierry Moisan
139 This program is free software; you can redistribute it and/or modify it
140 under the same terms as Perl itself.
142 =cut