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

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/* Copyright (c) 2022, NVIDIA CORPORATION. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of NVIDIA CORPORATION nor the names of its
* contributors may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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*/
/*
* This example demonstrates how to use the cuBLAS library API
* for lower-upper (LU) decomposition of a matrix. LU decomposition
* factors a matrix as the product of upper triangular matrix and
* lower trianglular matrix.
*
* https://en.wikipedia.org/wiki/LU_decomposition
*
* This sample uses 10000 matrices of size 4x4 and performs
* LU decomposition of them using batched decomposition API
* of cuBLAS library. To test the correctness of upper and lower
* matrices generated, they are multiplied and compared with the
* original input matrix.
*
*/
#include <stdio.h>
#include <stdlib.h>
// cuda libraries and helpers
#include <cublas_v2.h>
#include <cuda_runtime.h>
#include <helper_cuda.h>
// configurable parameters
// dimension of matrix
#define N 4
#define BATCH_SIZE 10000
// use double precision data type
#define DOUBLE_PRECISION /* comment this to use single precision */
#ifdef DOUBLE_PRECISION
#define DATA_TYPE double
#define MAX_ERROR 1e-15
#else
#define DATA_TYPE float
#define MAX_ERROR 1e-6
#endif /* DOUBLE_PRCISION */
// use pivot vector while decomposing
#define PIVOT /* comment this to disable pivot use */
// helper functions
// wrapper around cublas<t>getrfBatched()
cublasStatus_t cublasXgetrfBatched(cublasHandle_t handle, int n,
DATA_TYPE* const A[], int lda, int* P,
int* info, int batchSize) {
#ifdef DOUBLE_PRECISION
return cublasDgetrfBatched(handle, n, A, lda, P, info, batchSize);
#else
return cublasSgetrfBatched(handle, n, A, lda, P, info, batchSize);
#endif
}
// wrapper around malloc
// clears the allocated memory to 0
// terminates the program if malloc fails
void* xmalloc(size_t size) {
void* ptr = malloc(size);
if (ptr == NULL) {
printf("> ERROR: malloc for size %zu failed..\n", size);
exit(EXIT_FAILURE);
}
memset(ptr, 0, size);
return ptr;
}
// initalize identity matrix
void initIdentityMatrix(DATA_TYPE* mat) {
// clear the matrix
memset(mat, 0, N * N * sizeof(DATA_TYPE));
// set all diagonals to 1
for (int i = 0; i < N; i++) {
mat[(i * N) + i] = 1.0;
}
}
// initialize matrix with all elements as 0
void initZeroMatrix(DATA_TYPE* mat) {
memset(mat, 0, N * N * sizeof(DATA_TYPE));
}
// fill random value in column-major matrix
void initRandomMatrix(DATA_TYPE* mat) {
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
mat[(j * N) + i] =
(DATA_TYPE)1.0 + ((DATA_TYPE)rand() / (DATA_TYPE)RAND_MAX);
}
}
// diagonal dominant matrix to insure it is invertible matrix
for (int i = 0; i < N; i++) {
mat[(i * N) + i] += (DATA_TYPE)N;
}
}
// print column-major matrix
void printMatrix(DATA_TYPE* mat) {
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
printf("%20.16f ", mat[(j * N) + i]);
}
printf("\n");
}
printf("\n");
}
// matrix mulitplication
void matrixMultiply(DATA_TYPE* res, DATA_TYPE* mat1, DATA_TYPE* mat2) {
initZeroMatrix(res);
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
for (int k = 0; k < N; k++) {
res[(j * N) + i] += mat1[(k * N) + i] * mat2[(j * N) + k];
}
}
}
}
// check matrix equality
bool checkRelativeError(DATA_TYPE* mat1, DATA_TYPE* mat2, DATA_TYPE maxError) {
DATA_TYPE err = (DATA_TYPE)0.0;
DATA_TYPE refNorm = (DATA_TYPE)0.0;
DATA_TYPE relError = (DATA_TYPE)0.0;
DATA_TYPE relMaxError = (DATA_TYPE)0.0;
for (int i = 0; i < N * N; i++) {
refNorm = abs(mat1[i]);
err = abs(mat1[i] - mat2[i]);
if (refNorm != 0.0 && err > 0.0) {
relError = err / refNorm;
relMaxError = MAX(relMaxError, relError);
}
if (relMaxError > maxError) return false;
}
return true;
}
// decode lower and upper matrix from single matrix
// returned by getrfBatched()
void getLUdecoded(DATA_TYPE* mat, DATA_TYPE* L, DATA_TYPE* U) {
// init L as identity matrix
initIdentityMatrix(L);
// copy lower triangular values from mat to L (skip diagonal)
for (int i = 0; i < N; i++) {
for (int j = 0; j < i; j++) {
L[(j * N) + i] = mat[(j * N) + i];
}
}
// init U as all zero
initZeroMatrix(U);
// copy upper triangular values from mat to U
for (int i = 0; i < N; i++) {
for (int j = i; j < N; j++) {
U[(j * N) + i] = mat[(j * N) + i];
}
}
}
// generate permutation matrix from pivot vector
void getPmatFromPivot(DATA_TYPE* Pmat, int* P) {
int pivot[N];
// pivot vector in base-1
// convert it to base-0
for (int i = 0; i < N; i++) {
P[i]--;
}
// generate permutation vector from pivot
// initialize pivot with identity sequence
for (int k = 0; k < N; k++) {
pivot[k] = k;
}
// swap the indices according to pivot vector
for (int k = 0; k < N; k++) {
int q = P[k];
// swap pivot(k) and pivot(q)
int s = pivot[k];
int t = pivot[q];
pivot[k] = t;
pivot[q] = s;
}
// generate permutation matrix from pivot vector
initZeroMatrix(Pmat);
for (int i = 0; i < N; i++) {
int j = pivot[i];
Pmat[(j * N) + i] = (DATA_TYPE)1.0;
}
}
int main(int argc, char** argv) {
// cuBLAS variables
cublasStatus_t status;
cublasHandle_t handle;
// host variables
size_t matSize = N * N * sizeof(DATA_TYPE);
DATA_TYPE* h_AarrayInput;
DATA_TYPE* h_AarrayOutput;
DATA_TYPE* h_ptr_array[BATCH_SIZE];
int* h_pivotArray;
int* h_infoArray;
// device variables
DATA_TYPE* d_Aarray;
DATA_TYPE** d_ptr_array;
int* d_pivotArray;
int* d_infoArray;
int err_count = 0;
// seed the rand() function with time
srand(12345);
// find cuda device
printf("> initializing..\n");
int dev = findCudaDevice(argc, (const char**)argv);
if (dev == -1) {
return (EXIT_FAILURE);
}
// initialize cuBLAS
status = cublasCreate(&handle);
if (status != CUBLAS_STATUS_SUCCESS) {
printf("> ERROR: cuBLAS initialization failed..\n");
return (EXIT_FAILURE);
}
#ifdef DOUBLE_PRECISION
printf("> using DOUBLE precision..\n");
#else
printf("> using SINGLE precision..\n");
#endif
#ifdef PIVOT
printf("> pivot ENABLED..\n");
#else
printf("> pivot DISABLED..\n");
#endif
// allocate memory for host variables
h_AarrayInput = (DATA_TYPE*)xmalloc(BATCH_SIZE * matSize);
h_AarrayOutput = (DATA_TYPE*)xmalloc(BATCH_SIZE * matSize);
h_pivotArray = (int*)xmalloc(N * BATCH_SIZE * sizeof(int));
h_infoArray = (int*)xmalloc(BATCH_SIZE * sizeof(int));
// allocate memory for device variables
checkCudaErrors(cudaMalloc((void**)&d_Aarray, BATCH_SIZE * matSize));
checkCudaErrors(
cudaMalloc((void**)&d_pivotArray, N * BATCH_SIZE * sizeof(int)));
checkCudaErrors(cudaMalloc((void**)&d_infoArray, BATCH_SIZE * sizeof(int)));
checkCudaErrors(
cudaMalloc((void**)&d_ptr_array, BATCH_SIZE * sizeof(DATA_TYPE*)));
// fill matrix with random data
printf("> generating random matrices..\n");
for (int i = 0; i < BATCH_SIZE; i++) {
initRandomMatrix(h_AarrayInput + (i * N * N));
}
// copy data to device from host
printf("> copying data from host memory to GPU memory..\n");
checkCudaErrors(cudaMemcpy(d_Aarray, h_AarrayInput, BATCH_SIZE * matSize,
cudaMemcpyHostToDevice));
// create pointer array for matrices
for (int i = 0; i < BATCH_SIZE; i++) h_ptr_array[i] = d_Aarray + (i * N * N);
// copy pointer array to device memory
checkCudaErrors(cudaMemcpy(d_ptr_array, h_ptr_array,
BATCH_SIZE * sizeof(DATA_TYPE*),
cudaMemcpyHostToDevice));
// perform LU decomposition
printf("> performing LU decomposition..\n");
#ifdef PIVOT
status = cublasXgetrfBatched(handle, N, d_ptr_array, N, d_pivotArray,
d_infoArray, BATCH_SIZE);
#else
status = cublasXgetrfBatched(handle, N, d_ptr_array, N, NULL, d_infoArray,
BATCH_SIZE);
#endif /* PIVOT */
if (status != CUBLAS_STATUS_SUCCESS) {
printf("> ERROR: cublasDgetrfBatched() failed with error %s..\n",
_cudaGetErrorEnum(status));
return (EXIT_FAILURE);
}
// copy data to host from device
printf("> copying data from GPU memory to host memory..\n");
checkCudaErrors(cudaMemcpy(h_AarrayOutput, d_Aarray, BATCH_SIZE * matSize,
cudaMemcpyDeviceToHost));
checkCudaErrors(cudaMemcpy(h_infoArray, d_infoArray, BATCH_SIZE * sizeof(int),
cudaMemcpyDeviceToHost));
#ifdef PIVOT
checkCudaErrors(cudaMemcpy(h_pivotArray, d_pivotArray,
N * BATCH_SIZE * sizeof(int),
cudaMemcpyDeviceToHost));
#endif /* PIVOT */
// verify the result
printf("> verifying the result..\n");
for (int i = 0; i < BATCH_SIZE; i++) {
if (h_infoArray[i] == 0) {
DATA_TYPE* A = h_AarrayInput + (i * N * N);
DATA_TYPE* LU = h_AarrayOutput + (i * N * N);
DATA_TYPE L[N * N];
DATA_TYPE U[N * N];
getLUdecoded(LU, L, U);
// test P * A = L * U
int* P = h_pivotArray + (i * N);
DATA_TYPE Pmat[N * N];
#ifdef PIVOT
getPmatFromPivot(Pmat, P);
#else
initIdentityMatrix(Pmat);
#endif /* PIVOT */
// perform matrix multiplication
DATA_TYPE PxA[N * N];
DATA_TYPE LxU[N * N];
matrixMultiply(PxA, Pmat, A);
matrixMultiply(LxU, L, U);
// check for equality of matrices
if (!checkRelativeError(PxA, LxU, (DATA_TYPE)MAX_ERROR)) {
printf("> ERROR: accuracy check failed for matrix number %05d..\n",
i + 1);
err_count++;
}
} else if (h_infoArray[i] > 0) {
printf(
"> execution for matrix %05d is successful, but U is singular and "
"U(%d,%d) = 0..\n",
i + 1, h_infoArray[i] - 1, h_infoArray[i] - 1);
} else // (h_infoArray[i] < 0)
{
printf("> ERROR: matrix %05d have an illegal value at index %d = %lf..\n",
i + 1, -h_infoArray[i],
*(h_AarrayInput + (i * N * N) + (-h_infoArray[i])));
}
}
// free device variables
checkCudaErrors(cudaFree(d_ptr_array));
checkCudaErrors(cudaFree(d_infoArray));
checkCudaErrors(cudaFree(d_pivotArray));
checkCudaErrors(cudaFree(d_Aarray));
// free host variables
if (h_infoArray) free(h_infoArray);
if (h_pivotArray) free(h_pivotArray);
if (h_AarrayOutput) free(h_AarrayOutput);
if (h_AarrayInput) free(h_AarrayInput);
// destroy cuBLAS handle
status = cublasDestroy(handle);
if (status != CUBLAS_STATUS_SUCCESS) {
printf("> ERROR: cuBLAS uninitialization failed..\n");
return (EXIT_FAILURE);
}
if (err_count > 0) {
printf("> TEST FAILED for %d matrices, with precision: %g\n", err_count,
MAX_ERROR);
return (EXIT_FAILURE);
}
printf("> TEST SUCCESSFUL, with precision: %g\n", MAX_ERROR);
return (EXIT_SUCCESS);
}