Singular values calculation only with CUDA - cuda

Question

I'm trying to use the new cusolverDnSgesvd routine of CUDA 7.0 for the calculation of the singular values. The full code is reported below:
#include "cuda_runtime.h"
#include "device_launch_parameters.h"
#include <stdio.h>
#include<iostream>
#include<stdlib.h>
#include<stdio.h>
#include <cusolverDn.h>
#include <cuda_runtime_api.h>
/***********************/
/* CUDA ERROR CHECKING */
/***********************/
void gpuAssert(cudaError_t code, char *file, int line, bool abort=true)
{
if (code != cudaSuccess)
{
fprintf(stderr,"GPUassert: %s %s %d\n", cudaGetErrorString(code), file, line);
if (abort) { exit(code); }
}
}
void gpuErrchk(cudaError_t ans) { gpuAssert((ans), __FILE__, __LINE__); }
/********/
/* MAIN */
/********/
int main(){
int M = 10;
int N = 10;
// --- Setting the host matrix
float *h_A = (float *)malloc(M * N * sizeof(float));
for(unsigned int i = 0; i < M; i++){
for(unsigned int j = 0; j < N; j++){
h_A[j*M + i] = (i + j) * (i + j);
}
}
// --- Setting the device matrix and moving the host matrix to the device
float *d_A; gpuErrchk(cudaMalloc(&d_A, M * N * sizeof(float)));
gpuErrchk(cudaMemcpy(d_A, h_A, M * N * sizeof(float), cudaMemcpyHostToDevice));
// --- host side SVD results space
float *h_U = (float *)malloc(M * M * sizeof(float));
float *h_V = (float *)malloc(N * N * sizeof(float));
float *h_S = (float *)malloc(N * sizeof(float));
// --- device side SVD workspace and matrices
int work_size = 0;
int *devInfo; gpuErrchk(cudaMalloc(&devInfo, sizeof(int)));
float *d_U; gpuErrchk(cudaMalloc(&d_U, M * M * sizeof(float)));
float *d_V; gpuErrchk(cudaMalloc(&d_V, N * N * sizeof(float)));
float *d_S; gpuErrchk(cudaMalloc(&d_S, N * sizeof(float)));
cusolverStatus_t stat;
// --- CUDA solver initialization
cusolverDnHandle_t solver_handle;
cusolverDnCreate(&solver_handle);
stat = cusolverDnSgesvd_bufferSize(solver_handle, M, N, &work_size);
if(stat != CUSOLVER_STATUS_SUCCESS ) std::cout << "Initialization of cuSolver failed. \N";
float *work; gpuErrchk(cudaMalloc(&work, work_size * sizeof(float)));
//float *rwork; gpuErrchk(cudaMalloc(&rwork, work_size * sizeof(float)));
// --- CUDA SVD execution
//stat = cusolverDnSgesvd(solver_handle, 'A', 'A', M, N, d_A, M, d_S, d_U, M, d_V, N, work, work_size, NULL, devInfo);
stat = cusolverDnSgesvd(solver_handle, 'N', 'N', M, N, d_A, M, d_S, d_U, M, d_V, N, work, work_size, NULL, devInfo);
cudaDeviceSynchronize();
int devInfo_h = 0;
gpuErrchk(cudaMemcpy(&devInfo_h, devInfo, sizeof(int), cudaMemcpyDeviceToHost));
std::cout << "devInfo = " << devInfo_h << "\n";
switch(stat){
case CUSOLVER_STATUS_SUCCESS: std::cout << "SVD computation success\n"; break;
case CUSOLVER_STATUS_NOT_INITIALIZED: std::cout << "Library cuSolver not initialized correctly\n"; break;
case CUSOLVER_STATUS_INVALID_VALUE: std::cout << "Invalid parameters passed\n"; break;
case CUSOLVER_STATUS_INTERNAL_ERROR: std::cout << "Internal operation failed\n"; break;
}
if (devInfo_h == 0 && stat == CUSOLVER_STATUS_SUCCESS) std::cout << "SVD successful\n\n";
// --- Moving the results from device to host
gpuErrchk(cudaMemcpy(h_S, d_S, N * sizeof(float), cudaMemcpyDeviceToHost));
for(int i = 0; i < N; i++) std::cout << "d_S["<<i<<"] = " << h_S[i] << std::endl;
cusolverDnDestroy(solver_handle);
return 0;
}
If I ask for the computation of the full SVD (commented line with jobu = 'A' and jobvt = 'A') everything works fine. If I ask for the computation of the singular values only (line with jobu = 'N' and jobvt = 'N'), cusolverDnSgesvd returns
CUSOLVER_STATUS_INVALID_VALUE
Please note that, in this case devInfo = 0, so I cannot spot the invalid parameter.
Please also note that the documentation PDF lacks information about the rwork parameter so that I have dealt with it as a dummy parameter.

Answer 1

At this time the cuSolver gesvd function only supports jobu = 'A' and jobvt = 'A'
So the error when you specify other combinations is expected. From the documentation:
Remark 2: gesvd only supports jobu='A' and jobvt='A' and returns matrix U and VH

Answer 2

USE OF cusolver<T>nSgesvd
As remarked by lebedov, as of CUDA 8.0, it is now possible to calculate the singular values only by cusolverDnSgesvd. I report below a slightly modified version of your code with two calls to cusolverDnSgesvd, one performing the singular values calculation only
cusolverDnSgesvd(solver_handle, 'N', 'N', M, N, d_A, M, d_S, NULL, M, NULL, N, work, work_size, NULL, devInfo)
and one performing the full SVD calculation
cusolverDnSgesvd(solver_handle, 'A', 'A', M, N, d_A, M, d_S, d_U, M, d_V, N, work, work_size, NULL, devInfo)
As you already remarked, the two 'A' fields for the full SVD case are changed to 'N' in the singular values only case. Please, note that, in the singular values only case, there is no need to store space for the singular vector matrices U and V. Indeed, a NULL pointer is passed.
The singular values calculation only is faster than the full SVD calculation. On a GTX 960, for a 1000x1000 matrix, the timing has been the following:
Singular values only: 559 ms
Full SVD: 2239 ms
Here is the full code:
#include "cuda_runtime.h"
#include "device_launch_parameters.h"
#include <stdio.h>
#include<iostream>
#include<stdlib.h>
#include<stdio.h>
#include <cusolverDn.h>
#include <cuda_runtime_api.h>
#include "Utilities.cuh"
#include "TimingGPU.cuh"
/********/
/* MAIN */
/********/
int main(){
int M = 1000;
int N = 1000;
TimingGPU timerGPU;
float elapsedTime;
// --- Setting the host matrix
float *h_A = (float *)malloc(M * N * sizeof(float));
for (unsigned int i = 0; i < M; i++){
for (unsigned int j = 0; j < N; j++){
h_A[j*M + i] = (i + j) * (i + j);
}
}
// --- Setting the device matrix and moving the host matrix to the device
float *d_A; gpuErrchk(cudaMalloc(&d_A, M * N * sizeof(float)));
gpuErrchk(cudaMemcpy(d_A, h_A, M * N * sizeof(float), cudaMemcpyHostToDevice));
// --- host side SVD results space
float *h_U = (float *)malloc(M * M * sizeof(float));
float *h_V = (float *)malloc(N * N * sizeof(float));
float *h_S = (float *)malloc(N * sizeof(float));
// --- device side SVD workspace and matrices
int work_size = 0;
int *devInfo; gpuErrchk(cudaMalloc(&devInfo, sizeof(int)));
float *d_U; gpuErrchk(cudaMalloc(&d_U, M * M * sizeof(float)));
float *d_V; gpuErrchk(cudaMalloc(&d_V, N * N * sizeof(float)));
float *d_S; gpuErrchk(cudaMalloc(&d_S, N * sizeof(float)));
cusolverStatus_t stat;
// --- CUDA solver initialization
cusolverDnHandle_t solver_handle;
cusolveSafeCall(cusolverDnCreate(&solver_handle));
cusolveSafeCall(cusolverDnSgesvd_bufferSize(solver_handle, M, N, &work_size));
float *work; gpuErrchk(cudaMalloc(&work, work_size * sizeof(float)));
// --- CUDA SVD execution - Singular values only
timerGPU.StartCounter();
cusolveSafeCall(cusolverDnSgesvd(solver_handle, 'N', 'N', M, N, d_A, M, d_S, NULL, M, NULL, N, work, work_size, NULL, devInfo));
elapsedTime = timerGPU.GetCounter();
int devInfo_h = 0;
gpuErrchk(cudaMemcpy(&devInfo_h, devInfo, sizeof(int), cudaMemcpyDeviceToHost));
if (devInfo_h == 0)
printf("SVD successfull for the singular values calculation only\n\n");
else if (devInfo_h < 0)
printf("SVD unsuccessfull for the singular values calculation only. Parameter %i is wrong\n", -devInfo_h);
else
printf("SVD unsuccessfull for the singular values calculation only. A number of %i superdiagonals of an intermediate bidiagonal form did not converge to zero\n", devInfo_h);
printf("Calculation of the singular values only: %f ms\n\n", elapsedTime);
// --- Moving the results from device to host
//gpuErrchk(cudaMemcpy(h_S, d_S, N * sizeof(float), cudaMemcpyDeviceToHost));
//for (int i = 0; i < N; i++) std::cout << "d_S[" << i << "] = " << h_S[i] << std::endl;
// --- CUDA SVD execution - Full SVD
timerGPU.StartCounter();
cusolveSafeCall(cusolverDnSgesvd(solver_handle, 'A', 'A', M, N, d_A, M, d_S, d_U, M, d_V, N, work, work_size, NULL, devInfo));
elapsedTime = timerGPU.GetCounter();
devInfo_h = 0;
gpuErrchk(cudaMemcpy(&devInfo_h, devInfo, sizeof(int), cudaMemcpyDeviceToHost));
if (devInfo_h == 0)
printf("SVD successfull for the full SVD calculation\n\n");
else if (devInfo_h < 0)
printf("SVD unsuccessfull for the full SVD calculation. Parameter %i is wrong\n", -devInfo_h);
else
printf("SVD unsuccessfull for the full SVD calculation. A number of %i superdiagonals of an intermediate bidiagonal form did not converge to zero\n", devInfo_h);
printf("Calculation of the full SVD calculation: %f ms\n\n", elapsedTime);
cusolveSafeCall(cusolverDnDestroy(solver_handle));
return 0;
}
EDIT - PERFORMANCE ACROSS DIFFERENT VERSIONS OF CUDA
I have compared the performance of the singular values only calculation and the the Full SVD computations for CUDA 8.0, CUDA 9.1 and CUDA 10.0, for a 5000x5000 matrix. Here are the results on a GTX 960.
Computation type CUDA 8.0 CUDA 9.1 CUDA 10.0
__________________________________________________________________
Singular values only 17s 15s 15s
Full SVD 161s 159s 457s
__________________________________________________________________