CSR Format for sparse matrices having one row full of zeros

Question

Can the following 3x3 sparse matrix be stored using CSR format in the Intel MKL library?

A = [ 0 0 1
      0 0 0
      3 1 4];

valuesA   = {1, 3, 1, 4};
columnsA  = {2, 0, 1, 2};
rowIndexA = {0, 1,      3};

How this can be differentiated from the following 2x3 matrix?

B = [ 0 0 1
      3 1 4];

valuesB   = {1, 3, 1, 4};
columnsB  = {2, 0, 1, 2};
rowIndexB = {0, 1,      3};

The reason, I have a row full of zero is matrix-indexing. This all-zero-row can happen anywhere in the matrix A. The matrix A is actually a sub-matrix of a bigger sparse matrix, which will be used in a system of equations Ax = b. Could someone kindly give me some insight?

Answer 1

If the row is empty, just repeat the corresponding value in rowIndexA.

For the matrix

0 0 1
0 0 0
3 1 4

the correct representation is:

valuesA = {1, 3, 1, 4};
columnsA = {2, 0, 1, 2};
rowIndexA = {0, 1, 1, 4};
           //   ^^^^ repeat 1

The last value in rowIndexA should be equal to the number of elements, i.e. 4 in your case. Then you get the correct number of elements in each row: 1 - 0 = 1 in the first row, 1 - 1 = 0 in the second one and 4 - 1 = 3 in the last one.