使用 cuda 7.0 RC 中的 cusolver 计算特征值和特征向量

Question

我正在尝试使用 CUDA 7.0 RC 中发布的 cuSolver 计算最大的特征值/特征向量对。问题是我收到了 CUSOLVER_INTERNAL_ERROR，我不知道该怎么办。

这是我得心应手的东西，用来调用 cuda/cusparse/cusolver 函数。

// my handy stuff
#define CUDA_CALL(value) do {                                                     \
    cudaError_t _m_cudaStat = value;                                                  \
    if (_m_cudaStat != cudaSuccess) {                                               \
        fprintf(stderr, "Error %s at line %d in file %s\N",                 \
                cudaGetErrorString(_m_cudaStat), __LINE__, __FILE__);       \
        exit(-1);                                                                             \
    } 
} while(0)

#define CUSPARSE_CALL(value) do {                                                                 \
    cusparseStatus_t _m_status = value;                                                             \
    if (_m_status != CUSPARSE_STATUS_SUCCESS){                                                      \
        fprintf(stderr, "Error %d at line %d in file %s\N", (int)_m_status, __LINE__, __FILE__);    \
    exit(-5);                                                                                     \
    }                                                                                             \
} while(0)

#define CUSOLVER_CALL(value) do {                                                                 \
    cusolverStatus_t _m_status = value;                                                             \
    if (_m_status != CUSOLVER_STATUS_SUCCESS){                                                      \
        fprintf(stderr, "Error %d at line %d in file %s\N", (int)_m_status, __LINE__, __FILE__);    \
    exit(-5);                                                                                     \
    }                                                                                             \
} while(0)

这是我的代码

#include "cusparse.h"
#include "cusolverSp.h"
#include <cuda_runtime.h>
#include <math.h>

void dpss( size_t N, double NW, double *eigenvector );

int main()
{
    // parameters for generation of dpss
    size_t N = 128;
    double NW = 1;

    double *eigenvector = NULL;
    eigenvector = new double[ N*sizeof( double ) ];
    dpss( N, NW, eigenvector );

    return 0;
}

void dpss( size_t N, double NW, double *eigenvector )
{
    // define matrix T (NxN) 
    double** T = new double*[ N ];
    for(int i = 0; i < N; ++i)
        T[ i ] = new double[ N ];

    // fill in T as function of ( N, W ) 
    // T is a tridiagonal matrix, i. e., it has diagonal, subdiagonal and superdiagonal
    // the others elements are 0
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            if( j == i - 1 ) // subdiagonal
                T[ i ][ j ] = ( (double)N - i )*i/2;
            else if( j == i ) // diagonal
                T[ i ][ j ] = pow( (double)(N-1)/2 - i, 2 )*std::cos( 2*NW/(double)N*M_PI )*( j == i );
            else if( j == i + 1 ) // superdiagonal
                T[ i ][ j ] = ( i + 1 )*( (double)N - 1 - i )/2*( j == i + 1 );
            else // others elements
                T[ i ][ j ] = 0;
        }
    }

    // declarations needed
    cusolverStatus_t statCusolver = CUSOLVER_STATUS_SUCCESS;
    cusolverSpHandle_t handleCusolver = NULL;
    cusparseHandle_t handleCusparse = NULL;
    cusparseMatDescr_t descrA = NULL;
    int *h_cooRowIndex = NULL, *h_cooColIndex = NULL;
    double *h_cooVal = NULL; 
    int *d_cooRowIndex = NULL, *d_cooColIndex = NULL, *d_csrRowPtr = NULL; 
    double *d_cooVal = NULL; 
    int nnz; 
    double *h_eigenvector0 = NULL, *d_eigenvector0 = NULL, *d_eigenvector = NULL;
    double max_lambda;

    // define interval of eigenvalues of T
    // interval is [-max_lambda,max_lambda]
    max_lambda = ( N - 1 )*( N + 2 ) + N*( N + 1 )/8 + 0.25;

    // amount of nonzero elements of T
    nnz = 3*N - 2;

    // allocate host memory
    h_cooRowIndex = new int[ nnz*sizeof( int ) ];
    h_cooColIndex = new int[ nnz*sizeof( int ) ];
    h_cooVal = new double[ nnz*sizeof( double ) ];
    h_eigenvector0 = new double[ N*sizeof( double ) ];

    // fill in vectors that describe T as a sparse matrix
    int counter = 0;
    for (int i = 0; i < N; i++ ) {
        for( int j = 0; j < N; j++ ) {
            if( T[ i ][ j ] != 0 ) {
                h_cooColIndex[counter] = j;
                h_cooRowIndex[counter] = i;
                h_cooVal[counter++] = T[ i ][ j ];
            }
        }
    }

    // fill in initial eigenvector guess  
    for( int i = 0; i < N; i++ )
        h_eigenvector0[ i ] =  (double)1/(i+1);

    // allocate device memory
    CUDA_CALL( cudaMalloc((void**)&d_cooRowIndex,nnz*sizeof( int )) ); 
    CUDA_CALL( cudaMalloc((void**)&d_cooColIndex,nnz*sizeof( int )) ); 
    CUDA_CALL( cudaMalloc((void**)&d_cooVal, nnz*sizeof( double )) );
    CUDA_CALL( cudaMalloc((void**)&d_csrRowPtr, (N+1)*sizeof( int )) );
    CUDA_CALL( cudaMalloc((void**)&d_eigenvector0, N*sizeof( double )) );
    CUDA_CALL( cudaMalloc((void**)&d_eigenvector, N*sizeof(d_eigenvector[0])) );

    // copy data to device
    CUDA_CALL( cudaMemcpy( d_cooRowIndex, h_cooRowIndex, (size_t)(nnz*sizeof( int )), cudaMemcpyHostToDevice ) );
    CUDA_CALL( cudaMemcpy( d_cooColIndex, h_cooColIndex, (size_t)(nnz*sizeof( int )), cudaMemcpyHostToDevice ) );
    CUDA_CALL( cudaMemcpy( d_cooVal, h_cooVal, (size_t)(nnz*sizeof( double )), cudaMemcpyHostToDevice ) );
    CUDA_CALL( cudaMemcpy( d_eigenvector0, h_eigenvector0, (size_t)(N*sizeof( double )), cudaMemcpyHostToDevice ) );

    // initialize cusparse and cusolver
    CUSOLVER_CALL( cusolverSpCreate( &handleCusolver ) );
    CUSPARSE_CALL( cusparseCreate( &handleCusparse ) );

    // create and define cusparse matrix descriptor
    CUSPARSE_CALL( cusparseCreateMatDescr(&descrA) );
    CUSPARSE_CALL( cusparseSetMatType(descrA, CUSPARSE_MATRIX_TYPE_GENERAL ) );
    CUSPARSE_CALL( cusparseSetMatIndexBase(descrA, CUSPARSE_INDEX_BASE_ZERO ) );

    // transform from coordinates (COO) values to compressed row pointers (CSR) values
    CUSPARSE_CALL( cusparseXcoo2csr( handleCusparse, d_cooRowIndex, nnz, N, d_csrRowPtr, CUSPARSE_INDEX_BASE_ZERO ) );

    // define some parameters and call cusolverSpScsreigvsi
    int maxite = 1e6;
    double tol = 1;
    double mu = 0;
    statCusolver = cusolverSpDcsreigvsi( handleCusolver, N ,nnz, descrA, d_cooVal, d_csrRowPtr, d_cooColIndex, max_lambda, d_eigenvector0, maxite, tol, &mu, d_eigenvector );
// here statCusolver = CUSOLVER_INTERNAL_ERROR

    cudaDeviceSynchronize();
    CUDA_CALL( cudaGetLastError() );

    // copy from device to host
    CUDA_CALL( cudaMemcpy( h_eigenvector0, d_eigenvector, (size_t)(N*sizeof( double )), cudaMemcpyDeviceToHost ) );

    // destroy and free stuff
    CUSPARSE_CALL( cusparseDestroyMatDescr( descrA ) );
    CUSPARSE_CALL( cusparseDestroy( handleCusparse ) );
    CUSOLVER_CALL( cusolverSpDestroy( handleCusolver ) );
    CUDA_CALL( cudaFree( d_cooRowIndex ) );
    CUDA_CALL( cudaFree( d_cooColIndex ) );
    CUDA_CALL( cudaFree( d_cooVal ) );
    CUDA_CALL( cudaFree( d_csrRowPtr ) );
    CUDA_CALL( cudaFree( d_eigenvector0 ) );
    CUDA_CALL( cudaFree( d_eigenvector ) );
    delete[] h_eigenvector0;
    delete[] h_cooRowIndex;
    delete[] h_cooColIndex;
    delete[] h_cooVal;
}

我已经尝试了初始特征值猜测（即 max_lambda - 或 cuSolver 库教程中的 mu0）、初始特征向量猜测（h_eigenvector0 或 d_eigenvector0）、容差 (tol)、甚至最大迭代量 (maxite) 的不同选择。

我已经检查了稀疏矩阵是否正确编写（对我来说似乎是正确的）。我还用Matlab检查了返回的特征向量，它们完全不同（我认为它们不应该如此）。

我不知道我还能做什么，但如果有人这样做，请告诉我！！

提前致谢。

Answer 1

似乎（对我而言）cuSolver 文档在 mu 参数方面可能不正确。

文档似乎表明这是在主机内存空间中，即倒数第二个参数应该是主机指针。

如果我把它改成设备指针：

double mu = 0;
double *d_mu;
CUDA_CALL(cudaMalloc(&d_mu, sizeof(double)));
CUDA_CALL(cudaMemset(d_mu, 0, sizeof(double)));
CUSOLVER_CALL(cusolverSpDcsreigvsi( handleCusolver, N ,nnz, descrA, d_cooVal, d_csrRowPtr, d_cooColIndex, max_lambda, d_eigenvector0, maxite, tol, d_mu, d_eigenvector ));

...
CUDA_CALL(cudaMemcpy(&mu, d_mu, sizeof(double), cudaMemcpyDeviceToHost));

我可以让您的代码版本在没有任何 API 错误或 cuda-memcheck 错误的情况下运行。 （我不能保证结果。）

我已经向 NVIDIA 提交了文档查询。如果您可以确认通过此更改获得了合理的结果，那也可能很有用。我查看了得到的特征值和特征向量，虽然它们看起来并不奇怪，但我无法让它们与我在 Octave 中做同样事情的尝试完全相关。