/* diagonal.c  find equation a k^2 + b j^2 + c k j + d k +  e j + f = i */
/*                                                                      */
/*       j=0  j=1  j=2  j=3  j=4  j=5  j=6                              */
/*  k=0   0    2    5    9   14   20   27                               */
/*  k=1   1    4    8   13   19   26                                    */
/*  k=2   3    7   12   18   25                                         */
/*  k=3   6   11   17   24                                              */
/*  k=4  10   16   23                                                   */
/*  k=5  15   22                                                        */
/*  k=6  21                                                             */


#include <stdio.h>
#include "simeq.h"
int main(int argc, char *srgv[])
{
  double A[36] = {1.0, 0.0, 0.0, 1.0, 0.0, 1.0,
                  0.0, 1.0, 0.0, 0.0, 1.0, 1.0,
                  4.0, 0.0, 0.0, 2.0, 0.0, 1.0,
                  1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
                  0.0, 4.0, 0.0, 0.0, 2.0, 1.0,
                  9.0, 0.0, 0.0, 3.0, 0.0, 1.0};
  double Y[6] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0};  
  double X[6];
  double AA[36] = {0.0, 1.0, 0.0, 0.0, 1.0, 1.0,
                   4.0, 0.0, 0.0, 2.0, 0.0, 1.0,
                   1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
                   0.0, 4.0, 0.0, 0.0, 2.0, 1.0,
                   9.0, 0.0, 0.0, 3.0, 0.0, 1.0,
                   4.0, 1.0, 2.0, 2.0, 1.0, 1.0};
  double YY[6] = { 2.0, 3.0, 4.0, 5.0, 6.0, 7.0};  
  double XX[6];
  int i, j, k, n;

  printf("diagonal.c running \n");
  n = 6;
  printf("1..6 \n");
  simeq(n, A, Y, X);
  for(i=0; i<n; i++)
    printf("%d = %g \n", i, X[i]);
  printf("2..7 \n");
  simeq(n, AA, YY, XX);
  for(i=0; i<n; i++)
    printf("%c = %g \n", 'a'+i, XX[i]);

  printf("multiplying by 2, collecting terms, yeilds \n");
  printf(" ((k+j)^2 + k + 3 j)/2 = value \n");
  for(j=0; j<n; j++)
    for(k=0; k<n; k++)
      printf("j=%d, k=%d, val=%d \n", j, k, ((k+j)*(k+j)+k+3*j)/2); 

  return 0;
}