/* Homework 3 problem 1
 * Given 3 2D vectors 
 * Covariance matrix and its eigenvalues are calculated
*/
#include <stdio.h>
#include <math.h>

int main( int argc, char** argv )
{
  
  // a, b, c are the user input vectors
  float a[2];
  float b[2];
  float c[2];

  // Covariance Matrix
  float cov[2][2]={0,0,0,0};
  float avg[2];
  float eigen[2];
  


  // Prompt user to enter vectors
  printf("Please enter a[0]\n");
  scanf("%f",&a[0]);
  printf("Please enter a[1]\n");
  scanf("%f",&a[1]);


  printf("Please enter b[0]\n");
  scanf("%f",&b[0]);
  printf("Please enter b[1]\n");
  scanf("%f",&b[1]);

  printf("Please enter c[0]\n");
  scanf("%f",&c[0]);
  printf("Please enter c[1]\n");
  scanf("%f",&c[1]);
 

  // Show user what was entered
  printf("a[0]=%f a[1]=%f\n",a[0],a[1]);
  printf("b[0]=%f b[1]=%f\n",b[0],b[1]);
  printf("c[0]=%f c[1]=%f\n",c[0],c[1]);
 
  int i,j; // holly counter duo

  for(i=0; i<2; i++){
    avg[i] = (a[i] + b[i] + c[i])/3;
  }

  for(i=0; i<2; i++){
    a[i] = (a[i] - avg[i]);
  }
  for(i=0; i<2; i++){
    b[i] = (b[i] - avg[i]);
  }
  for(i=0; i<2; i++){
    c[i] = (c[i] - avg[i]);
  } 
  

  for(i=0; i<2; i++){
     for(j=0; j<2; j++){
       cov[i][j] += a[i]*a[j];
     }
  }
  
  for(i=0; i<2; i++){
     for(j=0; j<2; j++){
       cov[i][j] += b[i]*b[j];
     }
  }

  for(i=0; i<2; i++){
     for(j=0; j<2; j++){
       cov[i][j] += c[i]*c[j];
     }
  }
  
  for(i=0; i<2; i++){
     for(j=0; j<2; j++){
       cov[i][j] = (cov[i][j]/2);
     }
  }

  printf("Covariance matrix is:\n");
  for(i=0; i<2; i++){
     for(j=0; j<2; j++){
       printf("%f\t",cov[i][j]);
     }
     printf("\n");
  }


  // visit  http://en.wikipedia.org/wiki/Eigenvalue_algorithm to see how eigenvalues for 2x2 matrices are found

  eigen[0] = (cov[0][0]+cov[1][1])/2 - sqrt(4*cov[0][1]*cov[1][0]+((cov[0][0]-cov[1][1])*(cov[0][0]-cov[1][1]))) /2;
  eigen[1] = (cov[0][0]+cov[1][1])/2 + sqrt(4*cov[0][1]*cov[1][0]+((cov[0][0]-cov[1][1])*(cov[0][0]-cov[1][1]))) /2;

  for(i=0; i<2; i++){
    printf("eigenvalue %d is %f\n",i,eigen[i]);
  }
      
 
  exit( 0 );
}