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