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// Linear Regression
//
// linear_regression
//
// Linear regression line
//
// y = a + b*x via least squares
//
// Inputs: 1
// Outputs: 1
// Constants: 0
#include <math.h>
#include "ts.h"
typedef struct {
uint_t k;
} ts_linear_regression_params_t;
ts_parameter_t const ts_linear_regression_p = { .n_inputs = 1, .n_outputs = 1, .n_constants = 1, .params_size = sizeof(ts_linear_regression_params_t) };
uint_t ts_linear_regression_offset( ts_constant_t const *c )
{
( void )c;
return ( c ? ((ts_linear_regression_params_t const *)c)->k - 1 : 0 );
}
int ts_linear_regression(
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_linear_regression_p );
if ( !c ) return -1;
TS_CHECK_INPUT(x, x_n, n);
uint_t k = ((ts_linear_regression_params_t const *)c)->k;
if (k == 0 || n < k) return -1;
// Precompute constant x sums (x values are always 0..k-1)
fp_t sum_x = 0, sum_x2 = 0;
for ( uint_t j = 0; j < k; ++j )
{
fp_t xv = (fp_t)j;
sum_x += xv;
sum_x2 += xv * xv;
}
fp_t denom = (fp_t)k * sum_x2 - sum_x * sum_x;
fp_t fk = (fp_t)k;
// Initial window
fp_t sum_y = 0, sum_xy = 0;
for ( uint_t j = 0; j < k; ++j )
{
fp_t yv = x[0][j];
sum_y += yv;
sum_xy += (fp_t)j * yv;
}
if (denom == 0) {
y[0][k - 1] = sum_y / fk;
} else {
fp_t slope = (fk * sum_xy - sum_x * sum_y) / denom;
fp_t intercept = (sum_y - slope * sum_x) / fk;
y[0][k - 1] = intercept + slope * (fp_t)(k - 1);
}
// Sliding window: sum_xy_new = sum_xy_old - sum_y_new + k * y_new
for ( uint_t i = k; i < n; ++i )
{
fp_t y_new = x[0][i];
fp_t y_old = x[0][i - k];
fp_t sum_y_old = sum_y;
sum_y = sum_y - y_old + y_new;
sum_xy = sum_xy - sum_y_old + y_old + (fk - 1) * y_new;
if (denom == 0) {
y[0][i] = sum_y / fk;
} else {
fp_t slope = (fk * sum_xy - sum_x * sum_y) / denom;
fp_t intercept = (sum_y - slope * sum_x) / fk;
y[0][i] = intercept + slope * (fp_t)(k - 1);
}
}
return 0;
}
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