CUSP CG convergence

Question

I use CUSP conjugate gradient method to solve my symmetric sparse matrix. And I have no idea why it doesn't converge. Dimensions of matrices I use are not that large (1K to 100K). The same linear systems are easily solved by MKL, so the matrix is not ill-conditioned. However I tried adding preconditioner, but it gave no results:

diagonal preconditioner and AINV (incomplete Cholesky) gave unlimited growth of residual (as long as cg and bicgstab)

Here's my code:

cusp::csr_matrix <int, float, cusp::device_memory> A (n, n, nnz);

for (i = 0; i < n + 1; i++)
    A.row_offsets[i] = csrRowPtr[i] - 1;
for (i = 0; i < nnz; i++)
    A.values[i] = csrVal[i];
for (i = 0; i < nnz; i++)
    A.column_indices[i] = csrColInd[i] - 1;

cusp::array1d <float, cusp::device_memory> x (A.num_rows, 0);
cusp::array1d <float, cusp::device_memory> b (A.num_rows, 1);

for (i = 0; i < n; i++)
    b[i] = b_host[i];

cusp::verbose_monitor<float> monitor(b, 100, 1e-3);
cusp::identity_operator<float, MemorySpace> M(A.num_rows, A.num_rows);
    /*
    cusp::precond::diagonal<float, MemorySpace> M(A);
    cusp::precond::scaled_bridson_ainv<float, MemorySpace> M(A, .1);
    */
cusp::krylov::cg(A, x, b, monitor, M);

for (i = 0; i < n; i++)
    x_host[i] = x[i];

Why isn't it working correctly?

PS As I understand CUSP supposes zero-based index, that's why I decrease csrRowPtr and csrColInd. When I used nVidia cuSparse library there was an option to set other parameters like matrix type and fill mode. How can I be sure they are set correctly in CUSP?

Answer 1

Only elements from the upper triangle are stored in MKL's CSR format, but all the elements must be stored in CUSP's CSR format even if you are solving a symmetric linear system.

Also I think

for (i = 0; i < n; i++)
    x_host[i] = x[i];

is not a good idea; first transfer it back to host_memory

cusp::array1d<float, cusp::host_memory> _x = x;

then copy it back to x_host or whatever your result array is

for (i = 0; i < n; i++)
    x_host[i] = _x[i];