Question

consider the following sparse matrix, [[1, 0, 3], [4, 0, 0 ], [6, 2, 5]], which sparse matrix formats can store [1, 2, 3, 4, 5, 6] for the array of non-zero matrix values in memory? consider the following sparse matrix, [[1, 0, 3], [4, 0, 0 ], [6, 2, 5]], which sparse matrix formats can store [1, 2, 3, 4, 5, 6] for the array of non-zero matrix values in memory? coo csr jds ell none of the above

Answer 1

None of the provided sparse matrix formats (COO, CSR, JDS, ELL) will store the non-zero values [1, 2, 3, 4, 5, 6] in the specified order, as they organize non-zero values based on their position in the matrix rather than sorting them numerically.

Step-by-step explanation:

The sparse matrix in question is [[1, 0, 3], [4, 0, 0], [6, 2, 5]]. To store this matrix in a format that contains the array of non-zero values as [1, 2, 3, 4, 5, 6], none of the provided formats (COO, CSR, JDS, ELL) would store them in this exact sequence. The reason is that sparse matrix formats typically store non-zero values based on their occurrence in the matrix, not in sorted order. Each provided format has its own unique structure:

• COO (Coordinate Format) stores a list of (row, column, value) tuples.
• CSR (Compressed Sparse Row) stores three one-dimensional arrays for row pointers, column indices, and non-zero values, with values sorted by row-major order.
• JDS (Jagged Diagonal Storage) sorts columns by the number of non-zero entries and aligns by padding with zeros.
• ELL (ELLpack Format) stores non-zero values and column indices in fixed size arrays, optimized for matrices with a regular number of non-zeroes per row.

Since the desired ordering [1, 2, 3, 4, 5, 6] does not correspond to the way these formats store non-zero elements, 'none of the above' is the correct answer to the question posed by the student.