Lab 3

1. Lab 3

2. Why Compressed Row Storage • A sparse matrix has a lot of elements of value zero. • Using a two dimensional array to store a sparse matrix wastes a lot of memory. • Compressed Row Storage (CRS) format only stores the nonzero elements. • Using CRS format to store a sparse matrix will save a lot of memory.

3. Compressed Row Storage • val array stores the values of the nonzero elements in a row-wise fashion. • col_ind array stores the corresponding column indices of the elements in the val array. • E.g. col_ind[5] stores the column index of val[5]. • row_ptr array stores the locations in the val array and col_ind array that start a row.

4. 0 1 2 3 4 5 0 1 2 3 4 5 0 2 5 16 10 -2 3 9 3 7 8 7 … 4 2 -1 val 1 5 1 2 6 2 3 4 … 2 5 6 col_ind the number of nonzero elements in a matrix 0 2 5 8 12 16 19 row_ptr the number of rows +1 • The number of nonzero elements of row i = row_ptr[i+1] - row_ptr[ i ] • The value of nonzero elements of row i: val[ row_ptr[ i ] ], ... , val[ row_ptr[ i+1 ] -1 ]

5. //Compressed Row Storage format //for a sparse square (mSize X mSize) matrix public class CRS{ //the values of the nonzero elements of the matrix float[] val; //the column indices of the elements in val array int[] col_idx; //locations in the val and col_idx array that start a row int[] row_ptr; //the size of the matrix: the number of rows int mSize=0; //constructor that takes a sparse matrix and convert it to a CRS object CRS( float[][] matrix){... } //print the matrix in CRS format. public void printCRS(){... } //test the program public static void main(String[] args){... } }

6. CRS( float[][] matrix){ int i, j, index; //the total number of nonzero in the matrix int totalNonZeros; //get the number of rows and columns mSize = matrix.length; //get the total number of nonzero entries in the matrix totalNonZeros = 0; for( i=0; i<mSize; i++){ for( j=0; j<mSize; j++){ if(matrix[i][j] != 0) totalNonZeros++; } } //allocate memory for val and col_idx array val = new float[ totalNonZeros ]; col_idx = new int[ totalNonZeros ]; //allocate memory for row_ptr row_ptr = new int[ mSize+1]; row_ptr[ 0 ] = 0;

7. val x x ... index //store the matrix in CRS format index = 0;// point to the next position to store the value for( i=0; i<mSize; i++ ){//each row for( j=0; j<mSize; j++ ){//each column if( matrix[i][j] != 0 ){ //add the value to val val[ index ] = matrix[ i ][ j ]; //record the column index in col_idx col_idx[ index ] = j; index++; } } //update row_ptr row_ptr[ i+1 ] = index; } }//end of CRS( float[][] matrix)

8. //test the program public static void main(String[] args){ float[][] matrix = {{10, 0, 0, 0, -2, 0}, {3, 9, 0, 0, 0, 3}, {0, 7, 8, 7, 0, 0}, {3, 0, 8, 7, 5, 0}, {0, 8, 0, 9, 9, 13}, {0, 4, 0, 0, 2, -1}}; System.out.println("the original sparse matrix"); for(int i=0; i<6; i++){ for(int j=0; j<6; j++){ System.out.print(matrix[i][j]+", "); } System.out.println(); } System.out.println(); CRS crs = new CRS(matrix); crs.printMatrix(); crs.printCRS(); }