// 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 *)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 *)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;
}