/* Solve Ax=b using the conjugate gradient method a) without any preconditioning, b) using an Incomplete Cholesky preconditioner and c) using an ILU0 preconditioner. */
int main(int argc, char **argv)
{
const int max_iter = 1000;
int k, M = 0, N = 0, nz = 0, *I = NULL, *J = NULL;
int *d_col, *d_row;
int qatest = 0;
const float tol = 1e-12f;
float *x, *rhs;
float r0, r1, alpha, beta;
float *d_val, *d_x;
float *d_zm1, *d_zm2, *d_rm2;
float *d_r, *d_p, *d_omega, *d_y;
float *val = NULL;
float *d_valsILU0;
float *valsILU0;
float rsum, diff, err = 0.0;
float qaerr1, qaerr2 = 0.0;
float dot, numerator, denominator, nalpha;
const float floatone = 1.0;
const float floatzero = 0.0;
int nErrors = 0;
printf("conjugateGradientPrecond starting...\n");
/* QA testing mode */
if (checkCmdLineFlag(argc, (const char **)argv, "qatest"))
{
qatest = 1;
}
/* This will pick the best possible CUDA capable device */
cudaDeviceProp deviceProp;
int devID = findCudaDevice(argc, (const char **)argv);
printf("GPU selected Device ID = %d \n", devID);
if (devID < 0)
{
printf("Invalid GPU device %d selected, exiting...\n", devID);
exit(EXIT_SUCCESS);
}
checkCudaErrors(cudaGetDeviceProperties(&deviceProp, devID));
/* Statistics about the GPU device */
printf("> GPU device has %d Multi-Processors, SM %d.%d compute capabilities\n\n",
deviceProp.multiProcessorCount, deviceProp.major, deviceProp.minor);
int version = (deviceProp.major * 0x10 + deviceProp.minor);
if (version < 0x11)
{
printf("%s: requires a minimum CUDA compute 1.1 capability\n", sSDKname);
// cudaDeviceReset causes the driver to clean up all state. While
// not mandatory in normal operation, it is good practice. It is also
// needed to ensure correct operation when the application is being
// profiled. Calling cudaDeviceReset causes all profile data to be
// flushed before the application exits
cudaDeviceReset();
exit(EXIT_SUCCESS);
}
/* Generate a random tridiagonal symmetric matrix in CSR (Compressed Sparse Row) format */
M = N = 16384;
nz = 5*N-4*(int)sqrt((double)N);
I = (int *)malloc(sizeof(int)*(N+1)); // csr row pointers for matrix A
J = (int *)malloc(sizeof(int)*nz); // csr column indices for matrix A
val = (float *)malloc(sizeof(float)*nz); // csr values for matrix A
x = (float *)malloc(sizeof(float)*N);
rhs = (float *)malloc(sizeof(float)*N);
for (int i = 0; i < N; i++)
{
rhs[i] = 0.0; // Initialize RHS
x[i] = 0.0; // Initial approximation of solution
}
genLaplace(I, J, val, M, N, nz, rhs);
/* Create CUBLAS context */
cublasHandle_t cublasHandle = 0;
cublasStatus_t cublasStatus;
cublasStatus = cublasCreate(&cublasHandle);
checkCudaErrors(cublasStatus);
/* Create CUSPARSE context */
cusparseHandle_t cusparseHandle = 0;
cusparseStatus_t cusparseStatus;
cusparseStatus = cusparseCreate(&cusparseHandle);
checkCudaErrors(cusparseStatus);
/* Description of the A matrix*/
cusparseMatDescr_t descr = 0;
cusparseStatus = cusparseCreateMatDescr(&descr);
checkCudaErrors(cusparseStatus);
/* Define the properties of the matrix */
cusparseSetMatType(descr,CUSPARSE_MATRIX_TYPE_GENERAL);
cusparseSetMatIndexBase(descr,CUSPARSE_INDEX_BASE_ZERO);
/* Allocate required memory */
checkCudaErrors(cudaMalloc((void **)&d_col, nz*sizeof(int)));
checkCudaErrors(cudaMalloc((void **)&d_row, (N+1)*sizeof(int)));
checkCudaErrors(cudaMalloc((void **)&d_val, nz*sizeof(float)));
checkCudaErrors(cudaMalloc((void **)&d_x, N*sizeof(float)));
checkCudaErrors(cudaMalloc((void **)&d_y, N*sizeof(float)));
checkCudaErrors(cudaMalloc((void **)&d_r, N*sizeof(float)));
checkCudaErrors(cudaMalloc((void **)&d_p, N*sizeof(float)));
checkCudaErrors(cudaMalloc((void **)&d_omega, N*sizeof(float)));
cudaMemcpy(d_col, J, nz*sizeof(int), cudaMemcpyHostToDevice);
cudaMemcpy(d_row, I, (N+1)*sizeof(int), cudaMemcpyHostToDevice);
cudaMemcpy(d_val, val, nz*sizeof(float), cudaMemcpyHostToDevice);
cudaMemcpy(d_x, x, N*sizeof(float), cudaMemcpyHostToDevice);
cudaMemcpy(d_r, rhs, N*sizeof(float), cudaMemcpyHostToDevice);
/* Conjugate gradient without preconditioning.
------------------------------------------
Follows the description by Golub & Van Loan, "Matrix Computations 3rd ed.", Section 10.2.6 */
printf("Convergence of conjugate gradient without preconditioning: \n");
k = 0;
r0 = 0;
cublasSdot(cublasHandle, N, d_r, 1, d_r, 1, &r1);
while (r1 > tol*tol && k <= max_iter)
{
k++;
if (k == 1)
{
cublasScopy(cublasHandle, N, d_r, 1, d_p, 1);
}
else
{
beta = r1/r0;
cublasSscal(cublasHandle, N, &beta, d_p, 1);
cublasSaxpy(cublasHandle, N, &floatone, d_r, 1, d_p, 1) ;
}
cusparseScsrmv(cusparseHandle,CUSPARSE_OPERATION_NON_TRANSPOSE, N, N, nz, &floatone, descr, d_val, d_row, d_col, d_p, &floatzero, d_omega);
cublasSdot(cublasHandle, N, d_p, 1, d_omega, 1, &dot);
alpha = r1/dot;
cublasSaxpy(cublasHandle, N, &alpha, d_p, 1, d_x, 1);
nalpha = -alpha;
cublasSaxpy(cublasHandle, N, &nalpha, d_omega, 1, d_r, 1);
r0 = r1;
cublasSdot(cublasHandle, N, d_r, 1, d_r, 1, &r1);
}
printf(" iteration = %3d, residual = %e \n", k, sqrt(r1));
cudaMemcpy(x, d_x, N*sizeof(float), cudaMemcpyDeviceToHost);
/* check result */
err = 0.0;
for (int i = 0; i < N; i++)
{
rsum = 0.0;
for (int j = I[i]; j < I[i+1]; j++)
{
rsum += val[j]*x[J[j]];
}
diff = fabs(rsum - rhs[i]);
if (diff > err)
{
err = diff;
}
}
printf(" Convergence Test: %s \n", (k <= max_iter) ? "OK" : "FAIL");
nErrors += (k > max_iter) ? 1 : 0;
qaerr1 = err;
if (0)
{
// output result in matlab-style array
int n=(int)sqrt((double)N);
printf("a = [ ");
for (int iy=0; iy<n; iy++)
{
for (int ix=0; ix<n; ix++)
{
printf(" %f ", x[iy*n+ix]);
}
if (iy == n-1)
{
printf(" ]");
}
printf("\n");
}
}
/* Preconditioned Conjugate Gradient using ILU.
--------------------------------------------
Follows the description by Golub & Van Loan, "Matrix Computations 3rd ed.", Algorithm 10.3.1 */
printf("\nConvergence of conjugate gradient using incomplete LU preconditioning: \n");
int nzILU0 = 2*N-1;
valsILU0 = (float *) malloc(nz*sizeof(float));
checkCudaErrors(cudaMalloc((void **)&d_valsILU0, nz*sizeof(float)));
checkCudaErrors(cudaMalloc((void **)&d_zm1, (N)*sizeof(float)));
checkCudaErrors(cudaMalloc((void **)&d_zm2, (N)*sizeof(float)));
checkCudaErrors(cudaMalloc((void **)&d_rm2, (N)*sizeof(float)));
/* create the analysis info object for the A matrix */
cusparseSolveAnalysisInfo_t infoA = 0;
cusparseStatus = cusparseCreateSolveAnalysisInfo(&infoA);
checkCudaErrors(cusparseStatus);
/* Perform the analysis for the Non-Transpose case */
cusparseStatus = cusparseScsrsv_analysis(cusparseHandle, CUSPARSE_OPERATION_NON_TRANSPOSE,
N, nz, descr, d_val, d_row, d_col, infoA);
checkCudaErrors(cusparseStatus);
/* Copy A data to ILU0 vals as input*/
cudaMemcpy(d_valsILU0, d_val, nz*sizeof(float), cudaMemcpyDeviceToDevice);
/* generate the Incomplete LU factor H for the matrix A using cudsparseScsrilu0 */
cusparseStatus = cusparseScsrilu0(cusparseHandle, CUSPARSE_OPERATION_NON_TRANSPOSE, N, descr, d_valsILU0, d_row, d_col, infoA);
checkCudaErrors(cusparseStatus);
/* Create info objects for the ILU0 preconditioner */
cusparseSolveAnalysisInfo_t info_u;
cusparseCreateSolveAnalysisInfo(&info_u);
cusparseMatDescr_t descrL = 0;
cusparseStatus = cusparseCreateMatDescr(&descrL);
cusparseSetMatType(descrL,CUSPARSE_MATRIX_TYPE_GENERAL);
cusparseSetMatIndexBase(descrL,CUSPARSE_INDEX_BASE_ZERO);
cusparseSetMatFillMode(descrL, CUSPARSE_FILL_MODE_LOWER);
cusparseSetMatDiagType(descrL, CUSPARSE_DIAG_TYPE_UNIT);
cusparseMatDescr_t descrU = 0;
cusparseStatus = cusparseCreateMatDescr(&descrU);
cusparseSetMatType(descrU,CUSPARSE_MATRIX_TYPE_GENERAL);
cusparseSetMatIndexBase(descrU,CUSPARSE_INDEX_BASE_ZERO);
cusparseSetMatFillMode(descrU, CUSPARSE_FILL_MODE_UPPER);
cusparseSetMatDiagType(descrU, CUSPARSE_DIAG_TYPE_NON_UNIT);
cusparseStatus = cusparseScsrsv_analysis(cusparseHandle, CUSPARSE_OPERATION_NON_TRANSPOSE, N, nz, descrU, d_val, d_row, d_col, info_u);
/* reset the initial guess of the solution to zero */
for (int i = 0; i < N; i++)
{
x[i] = 0.0;
}
checkCudaErrors(cudaMemcpy(d_r, rhs, N*sizeof(float), cudaMemcpyHostToDevice));
checkCudaErrors(cudaMemcpy(d_x, x, N*sizeof(float), cudaMemcpyHostToDevice));
k = 0;
cublasSdot(cublasHandle, N, d_r, 1, d_r, 1, &r1);
while (r1 > tol*tol && k <= max_iter)
{
// Forward Solve, we can re-use infoA since the sparsity pattern of A matches that of L
cusparseStatus = cusparseScsrsv_solve(cusparseHandle, CUSPARSE_OPERATION_NON_TRANSPOSE, N, &floatone, descrL,
d_valsILU0, d_row, d_col, infoA, d_r, d_y);
checkCudaErrors(cusparseStatus);
// Back Substitution
cusparseStatus = cusparseScsrsv_solve(cusparseHandle, CUSPARSE_OPERATION_NON_TRANSPOSE, N, &floatone, descrU,
d_valsILU0, d_row, d_col, info_u, d_y, d_zm1);
checkCudaErrors(cusparseStatus);
k++;
if (k == 1)
{
cublasScopy(cublasHandle, N, d_zm1, 1, d_p, 1);
}
else
{
cublasSdot(cublasHandle, N, d_r, 1, d_zm1, 1, &numerator);
cublasSdot(cublasHandle, N, d_rm2, 1, d_zm2, 1, &denominator);
beta = numerator/denominator;
cublasSscal(cublasHandle, N, &beta, d_p, 1);
cublasSaxpy(cublasHandle, N, &floatone, d_zm1, 1, d_p, 1) ;
}
cusparseScsrmv(cusparseHandle,CUSPARSE_OPERATION_NON_TRANSPOSE, N, N, nzILU0, &floatone, descrU, d_val, d_row, d_col, d_p, &floatzero, d_omega);
cublasSdot(cublasHandle, N, d_r, 1, d_zm1, 1, &numerator);
cublasSdot(cublasHandle, N, d_p, 1, d_omega, 1, &denominator);
alpha = numerator / denominator;
cublasSaxpy(cublasHandle, N, &alpha, d_p, 1, d_x, 1);
cublasScopy(cublasHandle, N, d_r, 1, d_rm2, 1);
cublasScopy(cublasHandle, N, d_zm1, 1, d_zm2, 1);
nalpha = -alpha;
cublasSaxpy(cublasHandle, N, &nalpha, d_omega, 1, d_r, 1);
cublasSdot(cublasHandle, N, d_r, 1, d_r, 1, &r1);
}
printf(" iteration = %3d, residual = %e \n", k, sqrt(r1));
cudaMemcpy(x, d_x, N*sizeof(float), cudaMemcpyDeviceToHost);
/* check result */
err = 0.0;
for (int i = 0; i < N; i++)
{
rsum = 0.0;
for (int j = I[i]; j < I[i+1]; j++)
{
rsum += val[j]*x[J[j]];
}
diff = fabs(rsum - rhs[i]);
if (diff > err)
{
err = diff;
}
}
printf(" Convergence Test: %s \n", (k <= max_iter) ? "OK" : "FAIL");
nErrors += (k > max_iter) ? 1 : 0;
qaerr2 = err;
/* Destroy parameters */
cusparseDestroySolveAnalysisInfo(infoA);
cusparseDestroySolveAnalysisInfo(info_u);
/* Destroy contexts */
cusparseDestroy(cusparseHandle);
cublasDestroy(cublasHandle);
/* Free device memory */
free(I);
free(J);
free(val);
free(x);
free(rhs);
free(valsILU0);
cudaFree(d_col);
cudaFree(d_row);
cudaFree(d_val);
cudaFree(d_x);
cudaFree(d_y);
cudaFree(d_r);
cudaFree(d_p);
cudaFree(d_omega);
cudaFree(d_valsILU0);
cudaFree(d_zm1);
cudaFree(d_zm2);
cudaFree(d_rm2);
// cudaDeviceReset causes the driver to clean up all state. While
// not mandatory in normal operation, it is good practice. It is also
// needed to ensure correct operation when the application is being
// profiled. Calling cudaDeviceReset causes all profile data to be
// flushed before the application exits
cudaDeviceReset();
printf(" Test Summary:\n");
printf(" Counted total of %d errors\n", nErrors);
printf(" qaerr1 = %f qaerr2 = %f\n\n", fabs(qaerr1), fabs(qaerr2));
exit((nErrors == 0 &&fabs(qaerr1)<1e-5 && fabs(qaerr2) < 1e-5 ? EXIT_SUCCESS : EXIT_FAILURE));
}
magma_int_t
magma_scustomicsetup(
magma_s_matrix A,
magma_s_matrix b,
magma_s_preconditioner *precond,
magma_queue_t queue )
{
magma_int_t info = 0;
cusparseHandle_t cusparseHandle=NULL;
cusparseMatDescr_t descrL=NULL;
cusparseMatDescr_t descrU=NULL;
magma_s_matrix hA={Magma_CSR};
char preconditionermatrix[255];
snprintf( preconditionermatrix, sizeof(preconditionermatrix),
"precondL.mtx" );
CHECK( magma_s_csr_mtx( &hA, preconditionermatrix , queue) );
// for CUSPARSE
CHECK( magma_smtransfer( hA, &precond->M, Magma_CPU, Magma_DEV , queue ));
// copy the matrix to precond->L and (transposed) to precond->U
CHECK( magma_smtransfer(precond->M, &(precond->L), Magma_DEV, Magma_DEV, queue ));
CHECK( magma_smtranspose( precond->L, &(precond->U), queue ));
// extract the diagonal of L into precond->d
CHECK( magma_sjacobisetup_diagscal( precond->L, &precond->d, queue ));
CHECK( magma_svinit( &precond->work1, Magma_DEV, hA.num_rows, 1, MAGMA_S_ZERO, queue ));
// extract the diagonal of U into precond->d2
CHECK( magma_sjacobisetup_diagscal( precond->U, &precond->d2, queue ));
CHECK( magma_svinit( &precond->work2, Magma_DEV, hA.num_rows, 1, MAGMA_S_ZERO, queue ));
// CUSPARSE context //
CHECK_CUSPARSE( cusparseCreate( &cusparseHandle ));
CHECK_CUSPARSE( cusparseCreateMatDescr( &descrL ));
CHECK_CUSPARSE( cusparseSetMatType( descrL, CUSPARSE_MATRIX_TYPE_TRIANGULAR ));
CHECK_CUSPARSE( cusparseSetMatDiagType( descrL, CUSPARSE_DIAG_TYPE_NON_UNIT ));
CHECK_CUSPARSE( cusparseSetMatIndexBase( descrL, CUSPARSE_INDEX_BASE_ZERO ));
CHECK_CUSPARSE( cusparseSetMatFillMode( descrL, CUSPARSE_FILL_MODE_LOWER ));
CHECK_CUSPARSE( cusparseCreateSolveAnalysisInfo( &precond->cuinfoL ));
CHECK_CUSPARSE( cusparseScsrsv_analysis( cusparseHandle,
CUSPARSE_OPERATION_NON_TRANSPOSE, precond->M.num_rows,
precond->M.nnz, descrL,
precond->M.val, precond->M.row, precond->M.col, precond->cuinfoL ));
CHECK_CUSPARSE( cusparseCreateMatDescr( &descrU ));
CHECK_CUSPARSE( cusparseSetMatType( descrU, CUSPARSE_MATRIX_TYPE_TRIANGULAR ));
CHECK_CUSPARSE( cusparseSetMatDiagType( descrU, CUSPARSE_DIAG_TYPE_NON_UNIT ));
CHECK_CUSPARSE( cusparseSetMatIndexBase( descrU, CUSPARSE_INDEX_BASE_ZERO ));
CHECK_CUSPARSE( cusparseSetMatFillMode( descrU, CUSPARSE_FILL_MODE_LOWER ));
CHECK_CUSPARSE( cusparseCreateSolveAnalysisInfo( &precond->cuinfoU ));
CHECK_CUSPARSE( cusparseScsrsv_analysis( cusparseHandle,
CUSPARSE_OPERATION_TRANSPOSE, precond->M.num_rows,
precond->M.nnz, descrU,
precond->M.val, precond->M.row, precond->M.col, precond->cuinfoU ));
cleanup:
cusparseDestroy( cusparseHandle );
cusparseDestroyMatDescr( descrL );
cusparseDestroyMatDescr( descrU );
cusparseHandle=NULL;
descrL=NULL;
descrU=NULL;
magma_smfree( &hA, queue );
return info;
}
