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/* statistics/covar_source.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Jim Davies, Brian Gough
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
static double
FUNCTION(compute,covariance) (const BASE data1[], const size_t stride1,
const BASE data2[], const size_t stride2,
const size_t n,
const double mean1, const double mean2);
static double
FUNCTION(compute,covariance) (const BASE data1[], const size_t stride1,
const BASE data2[], const size_t stride2,
const size_t n,
const double mean1, const double mean2)
{
/* takes a dataset and finds the covariance */
long double covariance = 0 ;
size_t i;
/* find the sum of the squares */
for (i = 0; i < n; i++)
{
const long double delta1 = (data1[i * stride1] - mean1);
const long double delta2 = (data2[i * stride2] - mean2);
covariance += (delta1 * delta2 - covariance) / (i + 1);
}
return covariance ;
}
double
FUNCTION(gsl_stats,covariance_m) (const BASE data1[], const size_t stride1,
const BASE data2[], const size_t stride2,
const size_t n,
const double mean1, const double mean2)
{
const double covariance = FUNCTION(compute,covariance) (data1, stride1,
data2, stride2,
n,
mean1, mean2);
return covariance * ((double)n / (double)(n - 1));
}
double
FUNCTION(gsl_stats,covariance) (const BASE data1[], const size_t stride1,
const BASE data2[], const size_t stride2,
const size_t n)
{
const double mean1 = FUNCTION(gsl_stats,mean) (data1, stride1, n);
const double mean2 = FUNCTION(gsl_stats,mean) (data2, stride2, n);
return FUNCTION(gsl_stats,covariance_m)(data1, stride1,
data2, stride2,
n,
mean1, mean2);
}
/*
gsl_stats_correlation()
Calculate Pearson correlation = cov(X, Y) / (sigma_X * sigma_Y)
This routine efficiently computes the correlation in one pass of the
data and makes use of the algorithm described in:
B. P. Welford, "Note on a Method for Calculating Corrected Sums of
Squares and Products", Technometrics, Vol 4, No 3, 1962.
This paper derives a numerically stable recurrence to compute a sum
of products
S = sum_{i=1..N} [ (x_i - mu_x) * (y_i - mu_y) ]
with the relation
S_n = S_{n-1} + ((n-1)/n) * (x_n - mu_x_{n-1}) * (y_n - mu_y_{n-1})
*/
double
FUNCTION(gsl_stats,correlation) (const BASE data1[], const size_t stride1,
const BASE data2[], const size_t stride2,
const size_t n)
{
size_t i;
long double sum_xsq = 0.0;
long double sum_ysq = 0.0;
long double sum_cross = 0.0;
long double ratio;
long double delta_x, delta_y;
long double mean_x, mean_y;
long double r;
/*
* Compute:
* sum_xsq = Sum [ (x_i - mu_x)^2 ],
* sum_ysq = Sum [ (y_i - mu_y)^2 ] and
* sum_cross = Sum [ (x_i - mu_x) * (y_i - mu_y) ]
* using the above relation from Welford's paper
*/
mean_x = data1[0 * stride1];
mean_y = data2[0 * stride2];
for (i = 1; i < n; ++i)
{
ratio = i / (i + 1.0);
delta_x = data1[i * stride1] - mean_x;
delta_y = data2[i * stride2] - mean_y;
sum_xsq += delta_x * delta_x * ratio;
sum_ysq += delta_y * delta_y * ratio;
sum_cross += delta_x * delta_y * ratio;
mean_x += delta_x / (i + 1.0);
mean_y += delta_y / (i + 1.0);
}
r = sum_cross / (sqrt(sum_xsq) * sqrt(sum_ysq));
return r;
}
/*
gsl_stats_spearman()
Compute Spearman rank correlation coefficient
Inputs: data1 - data1 vector
stride1 - stride of data1
data2 - data2 vector
stride2 - stride of data2
n - number of elements in data1 and data2
work - additional workspace of size 2*n
Return: Spearman rank correlation coefficient
*/
double
FUNCTION(gsl_stats,spearman) (const BASE data1[], const size_t stride1,
const BASE data2[], const size_t stride2,
const size_t n, double work[])
{
size_t i;
gsl_vector_view ranks1 = gsl_vector_view_array(&work[0], n);
gsl_vector_view ranks2 = gsl_vector_view_array(&work[n], n);
double r;
for (i = 0; i < n; ++i)
{
gsl_vector_set(&ranks1.vector, i, data1[i * stride1]);
gsl_vector_set(&ranks2.vector, i, data2[i * stride2]);
}
/* sort data1 and update data2 at same time; compute rank of data1 */
gsl_sort_vector2(&ranks1.vector, &ranks2.vector);
compute_rank(&ranks1.vector);
/* now sort data2, updating ranks1 appropriately; compute rank of data2 */
gsl_sort_vector2(&ranks2.vector, &ranks1.vector);
compute_rank(&ranks2.vector);
/* compute correlation of rank vectors in double precision */
r = gsl_stats_correlation(ranks1.vector.data, ranks1.vector.stride,
ranks2.vector.data, ranks2.vector.stride,
n);
return r;
}
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