# FreeBSD Manual Pages

Math::GSL::Fit(3)     User Contributed Perl Documentation    Math::GSL::Fit(3)

NAME
Math::GSL::Fit -	Least-squares functions	for a general linear model
with one- or two-parameter regression

SYNOPSIS
use Math::GSL::Fit qw/:all/;

DESCRIPTION
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.

Here is a list of all the functions in this module :

gsl_fit_linear($x,$xstride, $y,$ystride, $n) This function computes the best-fit linear regression coefficients (c0,c1) of the model Y = c_0 + c_1 X for the dataset ($x, $y), two vectors (in form of arrays) of length$n with strides $xstride and$ystride. The errors	on y are assumed unknown so the	variance-
covariance matrix for the parameters	(c0, c1) is estimated from the
scatter of the points around	the best-fit line and returned via the
parameters (cov00, cov01, cov11). The sum of	squares	of the
residuals from the best-fit line is returned	in sumsq. Note:	the
correlation coefficient of the data can be computed using
gsl_stats_correlation (see Correlation), it does not	depend on the
fit.	The function returns the following values in this order	: 0 if
the operation succeeded, 1 otherwise, c0, c1, cov00,	cov01, cov11
and sumsq.

gsl_fit_wlinear($x,$xstride, $w,$wstride, $y,$ystride, $n) This function computes the best-fit linear regression coefficients (c0,c1) of the model Y = c_0 + c_1 X for the weighted dataset ($x,
$y), two vectors (in form of arrays) of length$n with strides
$xstride and$ystride. The vector (also in the form of an array)
$w, of length$n and	stride $wstride, specifies the weight of each datapoint. The weight is the reciprocal of the variance for each datapoint in y. The covariance matrix for the parameters (c0, c1) is computed using the weights and returned via the parameters (cov00, cov01, cov11). The weighted sum of squares of the residuals from the best-fit line, \chi^2, is returned in chisq. The function returns the following values in this order : 0 if the operation succeeded, 1 otherwise, c0, c1, cov00, cov01, cov11 and sumsq. gsl_fit_linear_est($x, $c0,$c1,	$cov00,$cov01,	$cov11) This function uses the best-fit linear regression coefficients$c0,
$c1 and their covariance$cov00, $cov01,$cov11 to compute the
fitted function y and its standard deviation	y_err for the model Y
= c_0 + c_1 X at the	point $x. The function returns the following values in this order : 0 if the operation succeeded, 1 otherwise, y and y_err. gsl_fit_mul($x, $xstride,$y, $ystride,$n)
This	function computes the best-fit linear regression coefficient
c1 of the model Y = c_1 X for the datasets ($x,$y),	two vectors
(in form of arrays) of length $n with strides$xstride and
$ystride. The errors on y are assumed unknown so the variance of the parameter c1 is estimated from the scatter of the points around the best-fit line and returned via the parameter cov11. The sum of squares of the residuals from the best-fit line is returned in sumsq. The function returns the following values in this order : 0 if the operation succeeded, 1 otherwise, c1, cov11 and sumsq. gsl_fit_wmul($x,	$xstride,$w, $wstride,$y, $ystride,$n)
This	function computes the best-fit linear regression coefficient
c1 of the model Y = c_1 X for the weighted datasets ($x,$y), two
vectors (in form of arrays) of length $n with strides$xstride and
$ystride. The vector (also in the form of an array)$w, of length
$n and stride$wstride, specifies the weight	of each	datapoint. The
weight is the reciprocal of the variance for	each datapoint in y.
The variance	of the parameter c1 is computed	using the weights and
returned via	the parameter cov11. The weighted sum of squares of
the residuals from the best-fit line, \chi^2, is returned in	chisq.
The function	returns	the following values in	this order : 0 if the
operation succeeded,	1 otherwise, c1, cov11 and sumsq.

gsl_fit_mul_est($x,$c1,	$cov11) This function uses the best-fit linear regression coefficient$c1
and its covariance $cov11 to compute the fitted function y and its standard deviation y_err for the model Y = c_1 X at the point$x.
The function	returns	the following values in	this order : 0 if the
operation succeeded,	1 otherwise, y and y_err.

For more	informations on	the functions, we refer	you to the GSL offcial
documentation: <http://www.gnu.org/software/gsl/manual/html_node/>

EXAMPLES
This example shows how to use the function gsl_fit_linear. It's
important to see	that the array passed to to function must be an	array
reference, not a	simple array. Also when	you use	strides, you need to
initialize all the value	in the range used, otherwise you will get
warnings.

my @norris_x	= (0.2,	337.4, 118.2, 884.6, 10.1, 226.5, 666.3, 996.3,
448.6, 777.0, 558.2, 0.4, 0.6, 775.5, 666.9, 338.0,
447.5, 11.6, 556.0, 228.1, 995.8, 887.6,	120.2, 0.3,
0.3, 556.8, 339.1, 887.2, 999.0,	779.0, 11.1, 118.3,
229.2, 669.1, 448.9, 0.5	) ;
my @norris_y	= ( 0.1, 338.8,	118.1, 888.0, 9.2, 228.1, 668.5, 998.5,
449.1, 778.9, 559.2, 0.3, 0.1, 778.1, 668.8, 339.3,
448.9, 10.8, 557.7, 228.3, 998.0, 888.8,	119.6, 0.3,
0.6, 557.6, 339.3, 888.0, 998.5,	778.9, 10.2, 117.6,
228.9, 668.4, 449.2, 0.2);
my $xstride = 2; my$wstride = 3;
my $ystride = 5; my ($x, $w,$y);
for my $i (0 .. 175) {$x->[$i] = 0;$w->[$i] = 0;$y->[$i] = 0; } for my$i (0	.. 35)
{
$x->[$i*$xstride] =$norris_x[$i];$w->[$i*$wstride] = 1.0;
$y->[$i*$ystride] =$norris_y[$i]; } my ($status,	@results) = gsl_fit_linear($x,$xstride, $y,$ystride, 36);

AUTHORS
Jonathan	"Duke" Leto <jonathan@leto.net>	and Thierry Moisan
<thierry.moisan@gmail.com>