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// Simple Least Squares Moving Linear Regression
//
// regression_linear_simple_least_squares - slrls
//
// ((k * sum_{i=0}^{n}[x_i * y_i]) - (sum_{i=0}^{n}[x_i] * sum_{i=0}^{n}[y_i]))
// β = ────────────────────────────────────────────────────────────────────────
// ((k * sum_{i=0}^{n}[x_i^2]) - (sum_{i=0}^{n}[x_i^2])^2)
//
// α = E(y) - β * E(x)
// = μ_y - β * μ_x
//
// ( E( xy ) - E( μ_x ) * E( μ_y ) )
// r_xy = ────────────────────────────────────────────────────────────────────────
// ((E(x^2) - E(x)^2) - (E(y^2) - E(y)^2))^(1 / 2)
//
// y = α + βx
//
// Inputs: 2
// Outputs: 3
// Constants: 0
#include <math.h>
#include "ts.h"
typedef struct {
uint_t k;
} ts_regression_linear_least_squares_params_t;
ts_parameter_t const ts_regression_linear_least_squares_p = { .n_inputs = 2, .n_outputs = 3, .n_constants = 1, .params_size = sizeof(ts_regression_linear_least_squares_params_t) };
uint_t ts_regression_linear_least_squares_offset( ts_constant_t const *c )
{
( void )c;
return ( c ? ((ts_regression_linear_least_squares_params_t *)c)->k : 0 );
}
int ts_regression_linear_least_squares(
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_regression_linear_least_squares_p );
if ( !c ) return -1;
uint_t k = ((ts_regression_linear_least_squares_params_t *)c)->k;
if (k == 0 || n < k) return -1;
uint_t xi = k;
uint_t yi = k;
fp_t var_x, var_y, cov_xy;
for( ; xi < n; ++xi, ++yi )
{
// Two-pass variance/covariance for numerical stability
fp_t mean_x = 0, mean_y = 0;
for (uint_t j = xi - k + 1; j <= xi; j++) {
mean_x += x[0][j];
mean_y += x[1][j];
}
mean_x /= (fp_t)k;
mean_y /= (fp_t)k;
var_x = 0; var_y = 0; cov_xy = 0;
for (uint_t j = xi - k + 1; j <= xi; j++) {
fp_t dx = x[0][j] - mean_x;
fp_t dy = x[1][j] - mean_y;
var_x += dx * dx;
var_y += dy * dy;
cov_xy += dx * dy;
}
var_x /= (fp_t)k;
var_y /= (fp_t)k;
cov_xy /= (fp_t)k;
if ( var_x != 0 )
{
y[0][yi] = cov_xy / var_x;
y[1][yi] = mean_y - y[0][yi] * mean_x;
}
else
{
y[0][yi] = 0;
y[1][yi] = mean_y;
}
fp_t prod = var_x * var_y;
y[2][yi] = prod > 0 ? cov_xy / sqrt( prod ) : 0;
}
return 0;
}
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