Efficient computation (solve) of Ax = b when A is symmetric
Posted: Thu Oct 05, 2017 4:28 pm
Hello,
I want to solve a SPARSE linear system Ax = b and I know, A is always a symmetric matrix (structure & values). The size of the matrix is n = 40800, it's a sparse matrix of size n x n. (containing real, double values).
As the matrix is symmetric with respect to structure and values, there might be quite some efficiency gain (up to 50%) if:
I would only copy and transfer the upper or lower triangle to Magma (Note: A single simulation I do, requires 8000-10000 matrix transfers!)
AND
Apply magmablas_dsymmetrize() ... if it's applicable to sparse matrices in CSR format and fast?
OR
Set a "symmetry" marker if it's available in Magma and if Magma would solve a linear system based on that? (another library offers such an option)
How to solve a linear system with sparse symmetric matrices efficiently?
Klaus
I want to solve a SPARSE linear system Ax = b and I know, A is always a symmetric matrix (structure & values). The size of the matrix is n = 40800, it's a sparse matrix of size n x n. (containing real, double values).
As the matrix is symmetric with respect to structure and values, there might be quite some efficiency gain (up to 50%) if:
I would only copy and transfer the upper or lower triangle to Magma (Note: A single simulation I do, requires 8000-10000 matrix transfers!)
AND
Apply magmablas_dsymmetrize() ... if it's applicable to sparse matrices in CSR format and fast?
OR
Set a "symmetry" marker if it's available in Magma and if Magma would solve a linear system based on that? (another library offers such an option)
How to solve a linear system with sparse symmetric matrices efficiently?
Klaus