我正在尝试使用 CUDA 10.1 解决大约 1200000 个线性系统（3x3，Ax=B），特别是使用 CUBLAS 库。我从这篇（有用的！）帖子中得到了启发，并在统一内存版本中重新编写了建议的代码。该算法首先使用 cublasgetrfBatched() 执行 LU 分解，然后连续两次调用 cublastrsm() 求解上三角线性系统或下三角线性系统。代码附在下面。它最多可以正确处理大约 10000 个矩阵，在这种情况下，执行 LU 分解需要约 570 毫秒（在 NVIDIA GeForce 930MX 上），求解系统需要约 311 毫秒。
我的问题/问题是：
过载问题：为超过 10k 的矩阵分配内存时会崩溃。为什么？如何改进我的代码以解决整批 120 万个矩阵？
时间问题：我的目标是在不到 1 秒的时间内解决所有这些系统。我目前是否遵循正确的方法？否则有什么建议吗？
是否有可能和/或有用，如果是的话，如何使用 10k 矩阵批次的“流”？
代码：
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <algorithm>
#include <cmath>
#include <iostream>
#include <vector>
#include <ctime>
#include <ratio>
#include <chrono>
#include <random>
#include <time.h>
#include <math.h>
// CUDA
#include <cuda.h>
#include <cuda_runtime.h>
#include "device_launch_parameters.h"
#include <cusolverDn.h>
//#include "Utilities.cuh"
using namespace std;
using namespace std::chrono;
/************************************/
/* COEFFICIENT REARRANGING FUNCTION */
/************************************/
void rearrange(double** vec, int* pivotArray, int N, int numMatrices) {
for (int nm = 0; nm < numMatrices; nm++) {
for (int i = 0; i < N; i++) {
double temp = vec[nm][i];
vec[nm][i] = vec[nm][pivotArray[N*i + nm] - 1];
vec[nm][pivotArray[N * i + nm] - 1] = temp;
}
}
}
/************************************/
/* MAIN */
/************************************/
int main() {
const int N = 3;
const int numMatrices = 10000; // I want 1200000
// random generator to fill matrices and coefficients
random_device device;
mt19937 generator(device());
uniform_real_distribution<double> distribution(1., 5.);
//ALLOCATE MEMORY - using unified memory
double** h_A;
cudaMallocManaged(&h_A, sizeof(double*) * numMatrices);
for (int nm = 0; nm < numMatrices; nm++) {
cudaMallocManaged(&(h_A[nm]), sizeof(double) * N * N);
}
double** h_b;
cudaMallocManaged(&h_b, sizeof(double*) * numMatrices);
for (int nm = 0; nm < numMatrices; nm++) {
cudaMallocManaged(&(h_b[nm]), sizeof(double) * N );
}
cout << " memory allocated" << endl;
// FILL MATRICES
for (int nm = 0; nm < numMatrices; nm++) {
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
h_A[nm][j * N + i] = distribution(generator);
}
}
}
cout << " Matrix filled " << endl;
// FILL COEFFICIENTS
for (int nm = 0; nm < numMatrices; nm++) {
for (int i = 0; i < N; i++) {
h_b[nm][i] = distribution(generator);
}
}
cout << " Coeff. vector filled " << endl;
cout << endl;
// --- CUDA solver initialization
cublasHandle_t cublas_handle;
cublasCreate_v2(&cublas_handle);
int* PivotArray;
cudaMallocManaged(&PivotArray, N * numMatrices * sizeof(int));
int* infoArray;
cudaMallocManaged(&infoArray, numMatrices * sizeof(int));
//CUBLAS LU SOLVER
high_resolution_clock::time_point t1 = high_resolution_clock::now();
cublasDgetrfBatched(cublas_handle, N, h_A, N, PivotArray, infoArray, numMatrices);
cudaDeviceSynchronize();
high_resolution_clock::time_point t2 = high_resolution_clock::now();
duration<double> time_span = duration_cast<duration<double>>(t2 - t1);
cout << "It took " << time_span.count() * 1000. << " milliseconds." << endl;
for (int i = 0; i < numMatrices; i++)
if (infoArray[i] != 0) {
fprintf(stderr, "Factorization of matrix %d Failed: Matrix may be singular\n", i);
}
// rearrange coefficient
// (temporarily on CPU, this step will be on a GPU Kernel as well)
high_resolution_clock::time_point tA = high_resolution_clock::now();
rearrange(h_b, PivotArray, N, numMatrices);
high_resolution_clock::time_point tB = high_resolution_clock::now();
duration<double> time_spanA = duration_cast<duration<double>>(tB - tA);
cout << "rearrangement took " << time_spanA.count() * 1000. << " milliseconds." << endl;
//INVERT UPPER AND LOWER TRIANGULAR MATRICES
// --- Function solves the triangular linear system with multiple right-hand sides
// --- Function overrides b as a result
const double alpha = 1.f;
high_resolution_clock::time_point t3 = high_resolution_clock::now();
cublasDtrsmBatched(cublas_handle, CUBLAS_SIDE_LEFT, CUBLAS_FILL_MODE_LOWER, CUBLAS_OP_N, CUBLAS_DIAG_UNIT, N, 1, &alpha, h_A, N, h_b, N, numMatrices);
cublasDtrsmBatched(cublas_handle, CUBLAS_SIDE_LEFT, CUBLAS_FILL_MODE_UPPER, CUBLAS_OP_N, CUBLAS_DIAG_NON_UNIT, N, 1, &alpha, h_A, N, h_b, N, numMatrices);
cudaDeviceSynchronize();
high_resolution_clock::time_point t4 = high_resolution_clock::now();
duration<double> time_span2 = duration_cast<duration<double>>(t4 - t3);
cout << "second step took " << time_span2.count() * 1000. << " milliseconds." << endl;
// --- Free resources
if (h_A) cudaFree(h_A);
if (h_b) cudaFree(h_b);
cudaDeviceReset();
return 0;
}