// 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;
}