// lsfit_lect.c  from lecture notes
//               compile   gcc -o lsfit_lect lsfit_lect.c simeq.c -lm
//               run       lsfit_lect > lsfit_lect_c.out

#include "simeq.h" // needed to solve simultaneous equations
#include <stdio.h>
#include <stdlib.h>

int main(int argc, char* argv[])
{
  double xd[6][3] = {{1.0, 2.5, 3.7},  // 1
                     {2.0, 2.5, 3.6},  // 2
                     {3.0, 2.7, 3.5},  // 3
	 	     {2.2, 2.1, 3.1},  // 4
		     {1.5, 2.0, 2.6},  // 5
		     {1.6, 2.0, 3.1}}; // 6
  double yd[6] = {32.5, 7.2, 6.9, 22.4, 10.4, 11.3}; // Y actual
  double A[3][3];
  double X[3];
  double Y[3];     // |A| * |X| = |Y|  |X| will be  a, b, c
  int i, j, k;

  printf("lsfit_lect.c run to make lsfit_lect_c.out \n");
  for(i=0; i<3; i++)
  {
    Y[i] = 0.0; // must start sum with zero
    for(k=0; k<6; k++) Y[i] += xd[k][i]*yd[k]; // Xi * Yk

    for(j=0; j<3; j++)
    {
      A[i][j] = 0.0;  // must start sum with zero
      for(k=0; k<6; k++) // run through observations
      {
        A[i][j] += xd[k][j]*xd[k][i];  // Xj * Xi
      }
    }
  }  // end i
  simeq2(3, A, Y, X); // pick correct argument list
  printf("a=%f, b=%f, c=%f \n", X[0], X[1], X[2]);
  // check
  printf("really bad fit \n");
  for(k=0; k<6; k++)  // k is observation
       printf("Y_actual=%f, Y_approximate=%f \n",
               yd[k], X[0]*xd[k][0]+X[1]*xd[k][1]+X[2]*xd[k][2]);
  return 0;
} // end lsfit_lect.c