Sparse matrix-vector multiplication in CUDA
I'm trying to implement a matrix-vector Multiplication on GPU (using CUDA).
In my C++ code (CPU), I load the matrix as a dense matrix, and then I perform the matrix-vector multiplication using CUDA. I'm also using shared memory to improve the performance.
- How can I load the matrix in an efficient way, knowing that my matrix is a sparse matrix?
Below is my C++ function to load the matrix:
int readMatrix( char* filename, float* &matrix, unsigned int *dim = NULL, int majority = ROW_MAJOR )
{
unsigned int w, h, x, y, num_entries;
float val;
std::ifstream file( filename );
if ( file )
{
file >> h >> w >> num_entries;
cout << w << " " << h << " " << num_entries << "\n";
assert( w == h || w == 1 || h == 1 );
if( dim != NULL ) *dim = std::max( w, h );
matrix = new float[ w * h ];
unsigned int i;
for( i = 0; i < num_entries; i++ ){
if( file.eof() ) break;
file >> y >> x >> val;
if( majority == ROW_MAJOR ){
matrix[ w * y + x ] = val;
} else if( majority == COLUMN_MAJOR ){
matrix[ h * x + y ] = val;
}
}
file.close();
if( i == num_entries )
std::cout << "\nFile read successfully\n";
else
std::cout << "\nFile read successfully but seems defective:\n num entries read = " << i << ", entries epected = " << num_entries << "\n";
// print first few elements
if( w == h ){
for( unsigned int i = 0; i < w; i++ ){
printf("\n");
for( unsigned int j = 0; j < h; j++ ){
printf("%.2f ", matrix[ j + w * i ] );
}
}
}
else{
printf("\n");
for( unsigned int j = 0; j < h; j++ ){
printf("%.2f ", matrix[ j ] );
}
}
} else {
std::cout << "Unable to open file\n";
return false;
}
return true;
}
Below is my CUDA Kernel function that handles the matrix-vector multiplication:
__global__ void
_cl_matrix_vector_( float *A, float *b, float *x, int dim )
{
extern __shared__ float vec[];
unsigned int idx = blockIdx.x * blockDim.x + threadIdx.x;
float temp = 0.0;
int vOffs = 0;
//load vector into shared memory
for (int i = 0; i < (dim/blockDim.x) + 1 ; ++i, vOffs+= blockDim.x) {
vec[vOffs + threadIdx.x] = b[vOffs + threadIdx.x];
}
//make sure all threads are synchronized
__syncthreads();
if (idx < dim) {
temp = 0.0;
//dot product (multiplication)
for (int i = 0; i < dim; i++){
temp += A[idx * dim + i] * vec[i];
}
x[idx] = temp;
}
}
- What are the necessary changes that I have to make on my CUDA code to take into account that my matrix is a sparse matrix?
- I found out from a forum that we can also use padding to be able to optimize the performance, but this requires me to change the way I read the matrix / sort the matrix. Any ideas how to implement this padding in the way I read the matrix and perform the calculation?
Answer
This is a very old post and I want to highlight that cuSPARSE (since some time now) makes routines for the multiplication between sparse matrices or between a sparse matrix and a dense vector available.
For the csr format, the relevant routine for the multiplication between a sparse matrix and a dense vector is cusparse<t>csrmv. Below, a fully worked example showing its use.
#include <stdio.h>
#include <stdlib.h>
#include <iostream>
#include <assert.h>
#include "Utilities.cuh"
#include <cuda_runtime.h>
#include <cusparse_v2.h>
/********/
/* MAIN */
/********/
int main()
{
// --- Initialize cuSPARSE
cusparseHandle_t handle; cusparseSafeCall(cusparseCreate(&handle));
/**************************/
/* SETTING UP THE PROBLEM */
/**************************/
const int N = 4; // --- Number of rows and columns
// --- Host side dense matrices
double *h_A_dense = (double*)malloc(N * N * sizeof(double));
double *h_x_dense = (double*)malloc(N * sizeof(double));
double *h_y_dense = (double*)malloc(N * sizeof(double));
// --- Column-major ordering
h_A_dense[0] = 0.4612; h_A_dense[4] = -0.0006; h_A_dense[8] = 0.3566; h_A_dense[12] = 0.0;
h_A_dense[1] = -0.0006; h_A_dense[5] = 0.4640; h_A_dense[9] = 0.0723; h_A_dense[13] = 0.0;
h_A_dense[2] = 0.3566; h_A_dense[6] = 0.0723; h_A_dense[10] = 0.7543; h_A_dense[14] = 0.0;
h_A_dense[3] = 0.; h_A_dense[7] = 0.0; h_A_dense[11] = 0.0; h_A_dense[15] = 0.1;
// --- Initializing the data and result vectors
for (int k = 0; k < N; k++) {
h_x_dense[k] = 1.;
h_y_dense[k] = 0.;
}
// --- Create device arrays and copy host arrays to them
double *d_A_dense; gpuErrchk(cudaMalloc(&d_A_dense, N * N * sizeof(double)));
double *d_x_dense; gpuErrchk(cudaMalloc(&d_x_dense, N * sizeof(double)));
double *d_y_dense; gpuErrchk(cudaMalloc(&d_y_dense, N * sizeof(double)));
gpuErrchk(cudaMemcpy(d_A_dense, h_A_dense, N * N * sizeof(double), cudaMemcpyHostToDevice));
gpuErrchk(cudaMemcpy(d_x_dense, h_x_dense, N * sizeof(double), cudaMemcpyHostToDevice));
gpuErrchk(cudaMemcpy(d_y_dense, h_y_dense, N * sizeof(double), cudaMemcpyHostToDevice));
// --- Descriptor for sparse matrix A
cusparseMatDescr_t descrA; cusparseSafeCall(cusparseCreateMatDescr(&descrA));
cusparseSafeCall(cusparseSetMatType (descrA, CUSPARSE_MATRIX_TYPE_GENERAL));
cusparseSafeCall(cusparseSetMatIndexBase(descrA, CUSPARSE_INDEX_BASE_ONE));
int nnzA = 0; // --- Number of nonzero elements in dense matrix A
const int lda = N; // --- Leading dimension of dense matrix
// --- Device side number of nonzero elements per row of matrix A
int *d_nnzPerVectorA; gpuErrchk(cudaMalloc(&d_nnzPerVectorA, N * sizeof(*d_nnzPerVectorA)));
cusparseSafeCall(cusparseDnnz(handle, CUSPARSE_DIRECTION_ROW, N, N, descrA, d_A_dense, lda, d_nnzPerVectorA, &nnzA));
// --- Host side number of nonzero elements per row of matrix A
int *h_nnzPerVectorA = (int *)malloc(N * sizeof(*h_nnzPerVectorA));
gpuErrchk(cudaMemcpy(h_nnzPerVectorA, d_nnzPerVectorA, N * sizeof(*h_nnzPerVectorA), cudaMemcpyDeviceToHost));
printf("Number of nonzero elements in dense matrix A = %i\n\n", nnzA);
for (int i = 0; i < N; ++i) printf("Number of nonzero elements in row %i for matrix = %i \n", i, h_nnzPerVectorA[i]);
printf("\n");
// --- Device side sparse matrix
double *d_A; gpuErrchk(cudaMalloc(&d_A, nnzA * sizeof(*d_A)));
int *d_A_RowIndices; gpuErrchk(cudaMalloc(&d_A_RowIndices, (N + 1) * sizeof(*d_A_RowIndices)));
int *d_A_ColIndices; gpuErrchk(cudaMalloc(&d_A_ColIndices, nnzA * sizeof(*d_A_ColIndices)));
cusparseSafeCall(cusparseDdense2csr(handle, N, N, descrA, d_A_dense, lda, d_nnzPerVectorA, d_A, d_A_RowIndices, d_A_ColIndices));
// --- Host side sparse matrices
double *h_A = (double *)malloc(nnzA * sizeof(*h_A));
int *h_A_RowIndices = (int *)malloc((N + 1) * sizeof(*h_A_RowIndices));
int *h_A_ColIndices = (int *)malloc(nnzA * sizeof(*h_A_ColIndices));
gpuErrchk(cudaMemcpy(h_A, d_A, nnzA * sizeof(*h_A), cudaMemcpyDeviceToHost));
gpuErrchk(cudaMemcpy(h_A_RowIndices, d_A_RowIndices, (N + 1) * sizeof(*h_A_RowIndices), cudaMemcpyDeviceToHost));
gpuErrchk(cudaMemcpy(h_A_ColIndices, d_A_ColIndices, nnzA * sizeof(*h_A_ColIndices), cudaMemcpyDeviceToHost));
printf("\nOriginal matrix A in CSR format\n\n");
for (int i = 0; i < nnzA; ++i) printf("A[%i] = %f ", i, h_A[i]); printf("\n");
printf("\n");
for (int i = 0; i < (N + 1); ++i) printf("h_A_RowIndices[%i] = %i \n", i, h_A_RowIndices[i]); printf("\n");
printf("\n");
for (int i = 0; i < nnzA; ++i) printf("h_A_ColIndices[%i] = %i \n", i, h_A_ColIndices[i]);
printf("\n");
for (int i = 0; i < N; ++i) printf("h_x[%i] = %f \n", i, h_x_dense[i]); printf("\n");
const double alpha = 1.;
const double beta = 0.;
cusparseSafeCall(cusparseDcsrmv(handle, CUSPARSE_OPERATION_NON_TRANSPOSE, N, N, nnzA, &alpha, descrA, d_A, d_A_RowIndices, d_A_ColIndices, d_x_dense,
&beta, d_y_dense));
gpuErrchk(cudaMemcpy(h_y_dense, d_y_dense, N * sizeof(double), cudaMemcpyDeviceToHost));
printf("\nResult vector\n\n");
for (int i = 0; i < N; ++i) printf("h_y[%i] = %f ", i, h_y_dense[i]); printf("\n");
}