Question

6.18.1

Consider the sparse matrix X below and write C code that would store this code in Yale Sparse Matrix Format.

Row 1 [1, 2, 0, 0, 0, 0]

Row 2 [0, 0, 1, 1, 0, 0]

Row 3 [0, 0, 0, 0, 9, 0]

Row 4 [2, 0, 0, 0, 0, 2]

Row 5 [0, 0, 3, 3, 0, 7]

Row 6 [1, 3, 0, 0, 0, 1]

6.18.2

In terms of storage space, assuming that each element in matrix X is single-precision floating point, compute the amount of storage used to store the matrix above in Yale Sparse Matrix Format.

Answer 1

//Include necessary header files
#include <stdio.h>

int main()
{
//Define the sparse matrix X
int X[6][6] = {1, 2, 0, 0, 0, 0,
0, 0, 1, 1, 0, 0,
0, 0, 0, 0, 9, 0,
2, 0, 0, 0, 0, 2,
0, 0, 3, 3, 0, 7,
1, 3, 0, 0, 0, 1};
int A[6*6];
int IA[6];
int JA[6*6];

//Display the matrix in sparse atrix format
printf("Sparse Matrix X");
for(int i=0; i<6; i++)
{
printf(" ");
for(int j=0; j<6; j++)
printf("%d ", X[i][j]);
}
  
//Read all non zero elements of matrix X and store in array A
int k = 0, l = 0;
for(int i=0; i<6; i++)
{
//IA array represents the matrix X into row splits
IA[l++] = k;
for(int j=0; j<6; j++)
if(X[i][j] != 0)
{
  
//Store the element in A and then increment the index k
A[k] = X[i][j];
  
//Store the column index in array JA
JA[k++] = j;
}
}
  
  
  
printf(" Yale Sparse Matrix Format A = ");
for(int i=0; i<k; i++)
printf("%d ", A[i]);

printf(" IA = ");
for(int i=0; i<l; i++)
printf("%d ", IA[i]);
  
printf(" JA = ");
for(int i=0; i<k; i++)
printf("%d ", JA[i]);
return 0;
}

Screenshot of Code Screen:

Screenshot of Output: