1 files changed, 92 insertions, 0 deletions
diff --git a/lib/regression_linear_least_squares.c b/lib/regression_linear_least_squares.c
new file mode 100755
index 0000000..49123bb
--- /dev/null
+++ b/lib/regression_linear_least_squares.c
@@ -0,0 +1,92 @@
+// 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;
+}
+