add lsqe (13-2)

source/lsqe.c

@@ -0,0 +1,44 @@
+//
+//  lsqe.c
+//  Algorithms
+//
+//  Created by YourtionGuo on 16/05/2017.
+//  Copyright © 2017 Yourtion. All rights reserved.
+//
+
+
+#include <math.h>
+
+#include "nummeths.h"
+
+#pragma mark - Public
+
+
+void lsqe(const double *x, const double *y, int n, double *b1, double *b0)
+{
+  double    sumx, sumy, sumx2, sumxy;
+  int       i;
+
+  /// 计算合计结果
+
+  sumx = 0.0;
+  sumy = 0.0;
+  sumx2 = 0.0;
+  sumxy = 0.0;
+
+  for (i = 0; i < n; i++) {
+
+    sumx = sumx + x[i];
+    sumy = sumy + y[i];
+    sumx2 = sumx2 + pow(x[i], 2.0);
+    sumxy = sumxy + (x[i] * y[i]);
+
+  }
+
+  /// 计算最小二乘估计
+
+  *b1 = (sumxy - ((sumx * sumy)/(double)n)) / (sumx2-(pow(sumx,2.0)/(double)n));
+  *b0 = (sumy - ((*b1) * sumx)) / (double)n;
+
+  return;
+}