cuda-samples/Samples/4_CUDA_Libraries/cuSolverSp_LowlevelQR/cuSolverSp_LowlevelQR.cpp

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#include <assert.h>
#include <ctype.h>
#include <cuda_runtime.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#include "cusolverSp.h"
#include "cusolverSp_LOWLEVEL_PREVIEW.h"
#include "helper_cuda.h"
#include "helper_cusolver.h"

template <typename T_ELEM>
int loadMMSparseMatrix(char    *filename,
                       char     elem_type,
                       bool     csrFormat,
                       int     *m,
                       int     *n,
                       int     *nnz,
                       T_ELEM **aVal,
                       int    **aRowInd,
                       int    **aColInd,
                       int      extendSymMatrix);

void UsageSP(void)
{
    printf("<options>\n");
    printf("-h          : display this help\n");
    printf("-file=<filename> : filename containing a matrix in MM format\n");
    printf("-device=<device_id> : <device_id> if want to run on specific GPU\n");

    exit(0);
}

void parseCommandLineArguments(int argc, char *argv[], struct testOpts &opts)
{
    memset(&opts, 0, sizeof(opts));

    if (checkCmdLineFlag(argc, (const char **)argv, "-h")) {
        UsageSP();
    }

    if (checkCmdLineFlag(argc, (const char **)argv, "file")) {
        char *fileName = 0;
        getCmdLineArgumentString(argc, (const char **)argv, "file", &fileName);

        if (fileName) {
            opts.sparse_mat_filename = fileName;
        }
        else {
            printf("\nIncorrect filename passed to -file \n ");
            UsageSP();
        }
    }
}

int main(int argc, char *argv[])
{
    struct testOpts    opts;
    cusolverSpHandle_t cusolverSpH = NULL; // reordering, permutation and 1st LU factorization
    cusparseHandle_t   cusparseH   = NULL; // residual evaluation
    cudaStream_t       stream      = NULL;
    cusparseMatDescr_t descrA      = NULL; // A is a base-0 general matrix

    csrqrInfoHost_t h_info = NULL; // opaque info structure for LU with parital pivoting
    csrqrInfo_t     d_info = NULL; // opaque info structure for LU with parital pivoting

    int rowsA = 0; // number of rows of A
    int colsA = 0; // number of columns of A
    int nnzA  = 0; // number of nonzeros of A
    int baseA = 0; // base index in CSR format

    // CSR(A) from I/O
    int    *h_csrRowPtrA = NULL; // <int> n+1
    int    *h_csrColIndA = NULL; // <int> nnzA
    double *h_csrValA    = NULL; // <double> nnzA

    double *h_x     = NULL; // <double> n,  x = A \ b
    double *h_b     = NULL; // <double> n, b = ones(m,1)
    double *h_bcopy = NULL; // <double> n, b = ones(m,1)
    double *h_r     = NULL; // <double> n, r = b - A*x

    size_t size_internal = 0;
    size_t size_chol     = 0;    // size of working space for csrlu
    void  *buffer_cpu    = NULL; // working space for Cholesky
    void  *buffer_gpu    = NULL; // working space for Cholesky

    int    *d_csrRowPtrA = NULL; // <int> n+1
    int    *d_csrColIndA = NULL; // <int> nnzA
    double *d_csrValA    = NULL; // <double> nnzA
    double *d_x          = NULL; // <double> n, x = A \ b
    double *d_b          = NULL; // <double> n, a copy of h_b
    double *d_r          = NULL; // <double> n, r = b - A*x

    // the constants used in residual evaluation, r = b - A*x
    const double minus_one = -1.0;
    const double one       = 1.0;
    const double zero      = 0.0;
    // the constant used in cusolverSp
    // singularity is -1 if A is invertible under tol
    // tol determines the condition of singularity
    int          singularity = 0;
    const double tol         = 1.e-14;

    double x_inf = 0.0; // |x|
    double r_inf = 0.0; // |r|
    double A_inf = 0.0; // |A|

    parseCommandLineArguments(argc, argv, opts);

    findCudaDevice(argc, (const char **)argv);

    if (opts.sparse_mat_filename == NULL) {
        opts.sparse_mat_filename = sdkFindFilePath("lap2D_5pt_n32.mtx", argv[0]);
        if (opts.sparse_mat_filename != NULL)
            printf("Using default input file [%s]\n", opts.sparse_mat_filename);
        else
            printf("Could not find lap2D_5pt_n32.mtx\n");
    }
    else {
        printf("Using input file [%s]\n", opts.sparse_mat_filename);
    }

    printf("step 1: read matrix market format\n");

    if (opts.sparse_mat_filename) {
        if (loadMMSparseMatrix<double>(opts.sparse_mat_filename,
                                       'd',
                                       true,
                                       &rowsA,
                                       &colsA,
                                       &nnzA,
                                       &h_csrValA,
                                       &h_csrRowPtrA,
                                       &h_csrColIndA,
                                       true)) {
            return 1;
        }
        baseA = h_csrRowPtrA[0]; // baseA = {0,1}
    }
    else {
        fprintf(stderr, "Error: input matrix is not provided\n");
        return 1;
    }

    if (rowsA != colsA) {
        fprintf(stderr, "Error: only support square matrix\n");
        return 1;
    }

    printf("sparse matrix A is %d x %d with %d nonzeros, base=%d\n", rowsA, colsA, nnzA, baseA);

    checkCudaErrors(cusolverSpCreate(&cusolverSpH));
    checkCudaErrors(cusparseCreate(&cusparseH));
    checkCudaErrors(cudaStreamCreate(&stream));
    checkCudaErrors(cusolverSpSetStream(cusolverSpH, stream));
    checkCudaErrors(cusparseSetStream(cusparseH, stream));

    checkCudaErrors(cusparseCreateMatDescr(&descrA));

    checkCudaErrors(cusparseSetMatType(descrA, CUSPARSE_MATRIX_TYPE_GENERAL));

    if (baseA) {
        checkCudaErrors(cusparseSetMatIndexBase(descrA, CUSPARSE_INDEX_BASE_ONE));
    }
    else {
        checkCudaErrors(cusparseSetMatIndexBase(descrA, CUSPARSE_INDEX_BASE_ZERO));
    }

    h_x     = (double *)malloc(sizeof(double) * colsA);
    h_b     = (double *)malloc(sizeof(double) * rowsA);
    h_bcopy = (double *)malloc(sizeof(double) * rowsA);
    h_r     = (double *)malloc(sizeof(double) * rowsA);

    assert(NULL != h_x);
    assert(NULL != h_b);
    assert(NULL != h_bcopy);
    assert(NULL != h_r);

    checkCudaErrors(cudaMalloc((void **)&d_csrRowPtrA, sizeof(int) * (rowsA + 1)));
    checkCudaErrors(cudaMalloc((void **)&d_csrColIndA, sizeof(int) * nnzA));
    checkCudaErrors(cudaMalloc((void **)&d_csrValA, sizeof(double) * nnzA));
    checkCudaErrors(cudaMalloc((void **)&d_x, sizeof(double) * colsA));
    checkCudaErrors(cudaMalloc((void **)&d_b, sizeof(double) * rowsA));
    checkCudaErrors(cudaMalloc((void **)&d_r, sizeof(double) * rowsA));

    for (int row = 0; row < rowsA; row++) {
        h_b[row] = 1.0;
    }

    memcpy(h_bcopy, h_b, sizeof(double) * rowsA);

    printf("step 2: create opaque info structure\n");
    checkCudaErrors(cusolverSpCreateCsrqrInfoHost(&h_info));

    printf("step 3: analyze qr(A) to know structure of L\n");
    checkCudaErrors(
        cusolverSpXcsrqrAnalysisHost(cusolverSpH, rowsA, colsA, nnzA, descrA, h_csrRowPtrA, h_csrColIndA, h_info));

    printf("step 4: workspace for qr(A)\n");
    checkCudaErrors(cusolverSpDcsrqrBufferInfoHost(cusolverSpH,
                                                   rowsA,
                                                   colsA,
                                                   nnzA,
                                                   descrA,
                                                   h_csrValA,
                                                   h_csrRowPtrA,
                                                   h_csrColIndA,
                                                   h_info,
                                                   &size_internal,
                                                   &size_chol));

    if (buffer_cpu) {
        free(buffer_cpu);
    }
    buffer_cpu = (void *)malloc(sizeof(char) * size_chol);
    assert(NULL != buffer_cpu);

    printf("step 5: compute A = L*L^T \n");
    checkCudaErrors(cusolverSpDcsrqrSetupHost(
        cusolverSpH, rowsA, colsA, nnzA, descrA, h_csrValA, h_csrRowPtrA, h_csrColIndA, zero, h_info));

    checkCudaErrors(cusolverSpDcsrqrFactorHost(cusolverSpH, rowsA, colsA, nnzA, NULL, NULL, h_info, buffer_cpu));

    printf("step 6: check if the matrix is singular \n");
    checkCudaErrors(cusolverSpDcsrqrZeroPivotHost(cusolverSpH, h_info, tol, &singularity));

    if (0 <= singularity) {
        fprintf(stderr, "Error: A is not invertible, singularity=%d\n", singularity);
        return 1;
    }

    printf("step 7: solve A*x = b \n");
    checkCudaErrors(cusolverSpDcsrqrSolveHost(cusolverSpH, rowsA, colsA, h_b, h_x, h_info, buffer_cpu));

    printf("step 8: evaluate residual r = b - A*x (result on CPU)\n");
    // use GPU gemv to compute r = b - A*x
    checkCudaErrors(cudaMemcpy(d_csrRowPtrA, h_csrRowPtrA, sizeof(int) * (rowsA + 1), cudaMemcpyHostToDevice));
    checkCudaErrors(cudaMemcpy(d_csrColIndA, h_csrColIndA, sizeof(int) * nnzA, cudaMemcpyHostToDevice));
    checkCudaErrors(cudaMemcpy(d_csrValA, h_csrValA, sizeof(double) * nnzA, cudaMemcpyHostToDevice));

    checkCudaErrors(cudaMemcpy(d_r, h_bcopy, sizeof(double) * rowsA, cudaMemcpyHostToDevice));
    checkCudaErrors(cudaMemcpy(d_x, h_x, sizeof(double) * colsA, cudaMemcpyHostToDevice));

    /* Wrap raw data into cuSPARSE generic API objects */
    cusparseSpMatDescr_t matA = NULL;
    if (baseA) {
        checkCudaErrors(cusparseCreateCsr(&matA,
                                          rowsA,
                                          colsA,
                                          nnzA,
                                          d_csrRowPtrA,
                                          d_csrColIndA,
                                          d_csrValA,
                                          CUSPARSE_INDEX_32I,
                                          CUSPARSE_INDEX_32I,
                                          CUSPARSE_INDEX_BASE_ONE,
                                          CUDA_R_64F));
    }
    else {
        checkCudaErrors(cusparseCreateCsr(&matA,
                                          rowsA,
                                          colsA,
                                          nnzA,
                                          d_csrRowPtrA,
                                          d_csrColIndA,
                                          d_csrValA,
                                          CUSPARSE_INDEX_32I,
                                          CUSPARSE_INDEX_32I,
                                          CUSPARSE_INDEX_BASE_ZERO,
                                          CUDA_R_64F));
    }

    cusparseDnVecDescr_t vecx = NULL;
    checkCudaErrors(cusparseCreateDnVec(&vecx, colsA, d_x, CUDA_R_64F));
    cusparseDnVecDescr_t vecAx = NULL;
    checkCudaErrors(cusparseCreateDnVec(&vecAx, rowsA, d_r, CUDA_R_64F));

    /* Allocate workspace for cuSPARSE */
    size_t bufferSize = 0;
    checkCudaErrors(cusparseSpMV_bufferSize(cusparseH,
                                            CUSPARSE_OPERATION_NON_TRANSPOSE,
                                            &minus_one,
                                            matA,
                                            vecx,
                                            &one,
                                            vecAx,
                                            CUDA_R_64F,
                                            CUSPARSE_SPMV_ALG_DEFAULT,
                                            &bufferSize));
    void *buffer = NULL;
    checkCudaErrors(cudaMalloc(&buffer, bufferSize));

    checkCudaErrors(cusparseSpMV(cusparseH,
                                 CUSPARSE_OPERATION_NON_TRANSPOSE,
                                 &minus_one,
                                 matA,
                                 vecx,
                                 &one,
                                 vecAx,
                                 CUDA_R_64F,
                                 CUSPARSE_SPMV_ALG_DEFAULT,
                                 buffer));

    checkCudaErrors(cudaMemcpy(h_r, d_r, sizeof(double) * rowsA, cudaMemcpyDeviceToHost));

    x_inf = vec_norminf(colsA, h_x);
    r_inf = vec_norminf(rowsA, h_r);
    A_inf = csr_mat_norminf(rowsA, colsA, nnzA, descrA, h_csrValA, h_csrRowPtrA, h_csrColIndA);

    printf("(CPU) |b - A*x| = %E \n", r_inf);
    printf("(CPU) |A| = %E \n", A_inf);
    printf("(CPU) |x| = %E \n", x_inf);
    printf("(CPU) |b - A*x|/(|A|*|x|) = %E \n", r_inf / (A_inf * x_inf));

    printf("step 9: create opaque info structure\n");
    checkCudaErrors(cusolverSpCreateCsrqrInfo(&d_info));

    checkCudaErrors(cudaMemcpy(d_csrRowPtrA, h_csrRowPtrA, sizeof(int) * (rowsA + 1), cudaMemcpyHostToDevice));
    checkCudaErrors(cudaMemcpy(d_csrColIndA, h_csrColIndA, sizeof(int) * nnzA, cudaMemcpyHostToDevice));
    checkCudaErrors(cudaMemcpy(d_csrValA, h_csrValA, sizeof(double) * nnzA, cudaMemcpyHostToDevice));
    checkCudaErrors(cudaMemcpy(d_b, h_bcopy, sizeof(double) * rowsA, cudaMemcpyHostToDevice));

    printf("step 10: analyze qr(A) to know structure of L\n");
    checkCudaErrors(
        cusolverSpXcsrqrAnalysis(cusolverSpH, rowsA, colsA, nnzA, descrA, d_csrRowPtrA, d_csrColIndA, d_info));

    printf("step 11: workspace for qr(A)\n");
    checkCudaErrors(cusolverSpDcsrqrBufferInfo(cusolverSpH,
                                               rowsA,
                                               colsA,
                                               nnzA,
                                               descrA,
                                               d_csrValA,
                                               d_csrRowPtrA,
                                               d_csrColIndA,
                                               d_info,
                                               &size_internal,
                                               &size_chol));

    printf("GPU buffer size = %lld bytes\n", (signed long long)size_chol);
    if (buffer_gpu) {
        checkCudaErrors(cudaFree(buffer_gpu));
    }
    checkCudaErrors(cudaMalloc(&buffer_gpu, sizeof(char) * size_chol));

    printf("step 12: compute A = L*L^T \n");
    checkCudaErrors(cusolverSpDcsrqrSetup(
        cusolverSpH, rowsA, colsA, nnzA, descrA, d_csrValA, d_csrRowPtrA, d_csrColIndA, zero, d_info));

    checkCudaErrors(cusolverSpDcsrqrFactor(cusolverSpH, rowsA, colsA, nnzA, NULL, NULL, d_info, buffer_gpu));

    printf("step 13: check if the matrix is singular \n");
    checkCudaErrors(cusolverSpDcsrqrZeroPivot(cusolverSpH, d_info, tol, &singularity));

    if (0 <= singularity) {
        fprintf(stderr, "Error: A is not invertible, singularity=%d\n", singularity);
        return 1;
    }

    printf("step 14: solve A*x = b \n");
    checkCudaErrors(cusolverSpDcsrqrSolve(cusolverSpH, rowsA, colsA, d_b, d_x, d_info, buffer_gpu));

    checkCudaErrors(cudaMemcpy(d_r, h_bcopy, sizeof(double) * rowsA, cudaMemcpyHostToDevice));

    checkCudaErrors(cusparseSpMV(cusparseH,
                                 CUSPARSE_OPERATION_NON_TRANSPOSE,
                                 &minus_one,
                                 matA,
                                 vecx,
                                 &one,
                                 vecAx,
                                 CUDA_R_64F,
                                 CUSPARSE_SPMV_ALG_DEFAULT,
                                 buffer));

    checkCudaErrors(cudaMemcpy(h_r, d_r, sizeof(double) * rowsA, cudaMemcpyDeviceToHost));

    r_inf = vec_norminf(rowsA, h_r);

    printf("(GPU) |b - A*x| = %E \n", r_inf);
    printf("(GPU) |b - A*x|/(|A|*|x|) = %E \n", r_inf / (A_inf * x_inf));

    if (cusolverSpH) {
        checkCudaErrors(cusolverSpDestroy(cusolverSpH));
    }
    if (cusparseH) {
        checkCudaErrors(cusparseDestroy(cusparseH));
    }
    if (stream) {
        checkCudaErrors(cudaStreamDestroy(stream));
    }
    if (descrA) {
        checkCudaErrors(cusparseDestroyMatDescr(descrA));
    }
    if (h_info) {
        checkCudaErrors(cusolverSpDestroyCsrqrInfoHost(h_info));
    }
    if (d_info) {
        checkCudaErrors(cusolverSpDestroyCsrqrInfo(d_info));
    }

    if (matA) {
        checkCudaErrors(cusparseDestroySpMat(matA));
    }
    if (vecx) {
        checkCudaErrors(cusparseDestroyDnVec(vecx));
    }
    if (vecAx) {
        checkCudaErrors(cusparseDestroyDnVec(vecAx));
    }

    if (h_csrValA) {
        free(h_csrValA);
    }
    if (h_csrRowPtrA) {
        free(h_csrRowPtrA);
    }
    if (h_csrColIndA) {
        free(h_csrColIndA);
    }

    if (h_x) {
        free(h_x);
    }
    if (h_b) {
        free(h_b);
    }
    if (h_bcopy) {
        free(h_bcopy);
    }
    if (h_r) {
        free(h_r);
    }

    if (buffer_cpu) {
        free(buffer_cpu);
    }
    if (buffer_gpu) {
        checkCudaErrors(cudaFree(buffer_gpu));
    }

    if (d_csrValA) {
        checkCudaErrors(cudaFree(d_csrValA));
    }
    if (d_csrRowPtrA) {
        checkCudaErrors(cudaFree(d_csrRowPtrA));
    }
    if (d_csrColIndA) {
        checkCudaErrors(cudaFree(d_csrColIndA));
    }
    if (d_x) {
        checkCudaErrors(cudaFree(d_x));
    }
    if (d_b) {
        checkCudaErrors(cudaFree(d_b));
    }
    if (d_r) {
        checkCudaErrors(cudaFree(d_r));
    }

    return 0;
}