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// Correlation Coefficient
//
// correlation_coefficient - corr
//
// Pearson r = (n*Σxy - Σx*Σy) / √((n*Σx²-Σx²)(n*Σy²-Σy²))
//
// Inputs: 2
// Outputs: 1 (r)
// Constants: 1 (period)
#include <math.h>
#include "ts.h"
typedef struct {
uint_t k;
} ts_correlation_coefficient_params_t;
ts_parameter_t const ts_correlation_coefficient_p = { .n_inputs = 2, .n_outputs = 1, .n_constants = 1, .params_size = sizeof(ts_correlation_coefficient_params_t) };
uint_t ts_correlation_coefficient_offset( ts_constant_t const *c )
{
( void )c;
return ( c ? ((ts_correlation_coefficient_params_t const *)c)->k - 1 : 0 );
}
int ts_correlation_coefficient(
fp_t * const *y, uint_t y_n,
fp_t const * const *x, uint_t x_n,
uint_t n, ts_constant_t const *c
)
{
TS_PROLOGUE( ts_correlation_coefficient_p );
if ( !c ) return -1;
uint_t k = ((ts_correlation_coefficient_params_t const *)c)->k;
if (k == 0 || n < k) return -1;
fp_t sum_x = 0, sum_y = 0, sum_xy = 0, sum_x2 = 0, sum_y2 = 0;
for ( uint_t i = 0; i < k; ++i )
{
fp_t xi = x[0][i];
fp_t yi = x[1][i];
sum_x += xi;
sum_y += yi;
sum_xy += xi * yi;
sum_x2 += xi * xi;
sum_y2 += yi * yi;
}
fp_t denom = ( k * sum_x2 - sum_x * sum_x ) * ( k * sum_y2 - sum_y * sum_y );
fp_t numer = k * sum_xy - sum_x * sum_y;
y[0][k - 1] = denom > 0 ? numer / sqrt( denom ) : 0;
for ( uint_t i = k; i < n; ++i )
{
fp_t xi_old = x[0][i - k];
fp_t yi_old = x[1][i - k];
fp_t xi_new = x[0][i];
fp_t yi_new = x[1][i];
sum_x = sum_x - xi_old + xi_new;
sum_y = sum_y - yi_old + yi_new;
sum_xy = sum_xy - xi_old * yi_old + xi_new * yi_new;
sum_x2 = sum_x2 - xi_old * xi_old + xi_new * xi_new;
sum_y2 = sum_y2 - yi_old * yi_old + yi_new * yi_new;
denom = ( k * sum_x2 - sum_x * sum_x ) * ( k * sum_y2 - sum_y * sum_y );
numer = k * sum_xy - sum_x * sum_y;
y[0][i] = denom > 0 ? numer / sqrt( denom ) : 0;
}
return 0;
}
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