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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;
- }
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