/* Copyright (c) 2021, 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 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /* Computation of eigenvalues of a large symmetric, tridiagonal matrix */ // includes, system #include #include #include #include #include // includes, project #include "helper_functions.h" #include "helper_cuda.h" #include "config.h" #include "structs.h" #include "util.h" #include "matlab.h" #include "bisect_large.cuh" // includes, kernels #include "bisect_kernel_large.cuh" #include "bisect_kernel_large_onei.cuh" #include "bisect_kernel_large_multi.cuh" //////////////////////////////////////////////////////////////////////////////// //! Initialize variables and memory for result //! @param result handles to memory //! @param matrix_size size of the matrix //////////////////////////////////////////////////////////////////////////////// void initResultDataLargeMatrix(ResultDataLarge &result, const unsigned int mat_size) { // helper variables to initialize memory unsigned int zero = 0; unsigned int mat_size_f = sizeof(float) * mat_size; unsigned int mat_size_ui = sizeof(unsigned int) * mat_size; float *tempf = (float *)malloc(mat_size_f); unsigned int *tempui = (unsigned int *)malloc(mat_size_ui); for (unsigned int i = 0; i < mat_size; ++i) { tempf[i] = 0.0f; tempui[i] = 0; } // number of intervals containing only one eigenvalue after the first step checkCudaErrors(cudaMalloc((void **)&result.g_num_one, sizeof(unsigned int))); checkCudaErrors(cudaMemcpy(result.g_num_one, &zero, sizeof(unsigned int), cudaMemcpyHostToDevice)); // number of (thread) blocks of intervals with multiple eigenvalues after // the first iteration checkCudaErrors( cudaMalloc((void **)&result.g_num_blocks_mult, sizeof(unsigned int))); checkCudaErrors(cudaMemcpy(result.g_num_blocks_mult, &zero, sizeof(unsigned int), cudaMemcpyHostToDevice)); checkCudaErrors(cudaMalloc((void **)&result.g_left_one, mat_size_f)); checkCudaErrors(cudaMalloc((void **)&result.g_right_one, mat_size_f)); checkCudaErrors(cudaMalloc((void **)&result.g_pos_one, mat_size_ui)); checkCudaErrors(cudaMalloc((void **)&result.g_left_mult, mat_size_f)); checkCudaErrors(cudaMalloc((void **)&result.g_right_mult, mat_size_f)); checkCudaErrors(cudaMalloc((void **)&result.g_left_count_mult, mat_size_ui)); checkCudaErrors(cudaMalloc((void **)&result.g_right_count_mult, mat_size_ui)); checkCudaErrors( cudaMemcpy(result.g_left_one, tempf, mat_size_f, cudaMemcpyHostToDevice)); checkCudaErrors(cudaMemcpy(result.g_right_one, tempf, mat_size_f, cudaMemcpyHostToDevice)); checkCudaErrors(cudaMemcpy(result.g_pos_one, tempui, mat_size_ui, cudaMemcpyHostToDevice)); checkCudaErrors(cudaMemcpy(result.g_left_mult, tempf, mat_size_f, cudaMemcpyHostToDevice)); checkCudaErrors(cudaMemcpy(result.g_right_mult, tempf, mat_size_f, cudaMemcpyHostToDevice)); checkCudaErrors(cudaMemcpy(result.g_left_count_mult, tempui, mat_size_ui, cudaMemcpyHostToDevice)); checkCudaErrors(cudaMemcpy(result.g_right_count_mult, tempui, mat_size_ui, cudaMemcpyHostToDevice)); checkCudaErrors(cudaMalloc((void **)&result.g_blocks_mult, mat_size_ui)); checkCudaErrors(cudaMemcpy(result.g_blocks_mult, tempui, mat_size_ui, cudaMemcpyHostToDevice)); checkCudaErrors(cudaMalloc((void **)&result.g_blocks_mult_sum, mat_size_ui)); checkCudaErrors(cudaMemcpy(result.g_blocks_mult_sum, tempui, mat_size_ui, cudaMemcpyHostToDevice)); checkCudaErrors(cudaMalloc((void **)&result.g_lambda_mult, mat_size_f)); checkCudaErrors(cudaMemcpy(result.g_lambda_mult, tempf, mat_size_f, cudaMemcpyHostToDevice)); checkCudaErrors(cudaMalloc((void **)&result.g_pos_mult, mat_size_ui)); checkCudaErrors(cudaMemcpy(result.g_pos_mult, tempf, mat_size_ui, cudaMemcpyHostToDevice)); } //////////////////////////////////////////////////////////////////////////////// //! Cleanup result memory //! @param result handles to memory //////////////////////////////////////////////////////////////////////////////// void cleanupResultDataLargeMatrix(ResultDataLarge &result) { checkCudaErrors(cudaFree(result.g_num_one)); checkCudaErrors(cudaFree(result.g_num_blocks_mult)); checkCudaErrors(cudaFree(result.g_left_one)); checkCudaErrors(cudaFree(result.g_right_one)); checkCudaErrors(cudaFree(result.g_pos_one)); checkCudaErrors(cudaFree(result.g_left_mult)); checkCudaErrors(cudaFree(result.g_right_mult)); checkCudaErrors(cudaFree(result.g_left_count_mult)); checkCudaErrors(cudaFree(result.g_right_count_mult)); checkCudaErrors(cudaFree(result.g_blocks_mult)); checkCudaErrors(cudaFree(result.g_blocks_mult_sum)); checkCudaErrors(cudaFree(result.g_lambda_mult)); checkCudaErrors(cudaFree(result.g_pos_mult)); } //////////////////////////////////////////////////////////////////////////////// //! Run the kernels to compute the eigenvalues for large matrices //! @param input handles to input data //! @param result handles to result data //! @param mat_size matrix size //! @param precision desired precision of eigenvalues //! @param lg lower limit of Gerschgorin interval //! @param ug upper limit of Gerschgorin interval //! @param iterations number of iterations (for timing) //////////////////////////////////////////////////////////////////////////////// void computeEigenvaluesLargeMatrix(const InputData &input, const ResultDataLarge &result, const unsigned int mat_size, const float precision, const float lg, const float ug, const unsigned int iterations) { dim3 blocks(1, 1, 1); dim3 threads(MAX_THREADS_BLOCK, 1, 1); StopWatchInterface *timer_step1 = NULL; StopWatchInterface *timer_step2_one = NULL; StopWatchInterface *timer_step2_mult = NULL; StopWatchInterface *timer_total = NULL; sdkCreateTimer(&timer_step1); sdkCreateTimer(&timer_step2_one); sdkCreateTimer(&timer_step2_mult); sdkCreateTimer(&timer_total); sdkStartTimer(&timer_total); // do for multiple iterations to improve timing accuracy for (unsigned int iter = 0; iter < iterations; ++iter) { sdkStartTimer(&timer_step1); bisectKernelLarge<<>>( input.g_a, input.g_b, mat_size, lg, ug, 0, mat_size, precision, result.g_num_one, result.g_num_blocks_mult, result.g_left_one, result.g_right_one, result.g_pos_one, result.g_left_mult, result.g_right_mult, result.g_left_count_mult, result.g_right_count_mult, result.g_blocks_mult, result.g_blocks_mult_sum); getLastCudaError("Kernel launch failed."); checkCudaErrors(cudaDeviceSynchronize()); sdkStopTimer(&timer_step1); // get the number of intervals containing one eigenvalue after the first // processing step unsigned int num_one_intervals; checkCudaErrors(cudaMemcpy(&num_one_intervals, result.g_num_one, sizeof(unsigned int), cudaMemcpyDeviceToHost)); dim3 grid_onei; grid_onei.x = getNumBlocksLinear(num_one_intervals, MAX_THREADS_BLOCK); dim3 threads_onei; // use always max number of available threads to better balance load times // for matrix data threads_onei.x = MAX_THREADS_BLOCK; // compute eigenvalues for intervals that contained only one eigenvalue // after the first processing step sdkStartTimer(&timer_step2_one); bisectKernelLarge_OneIntervals<<>>( input.g_a, input.g_b, mat_size, num_one_intervals, result.g_left_one, result.g_right_one, result.g_pos_one, precision); getLastCudaError("bisectKernelLarge_OneIntervals() FAILED."); checkCudaErrors(cudaDeviceSynchronize()); sdkStopTimer(&timer_step2_one); // process intervals that contained more than one eigenvalue after // the first processing step // get the number of blocks of intervals that contain, in total when // each interval contains only one eigenvalue, not more than // MAX_THREADS_BLOCK threads unsigned int num_blocks_mult = 0; checkCudaErrors(cudaMemcpy(&num_blocks_mult, result.g_num_blocks_mult, sizeof(unsigned int), cudaMemcpyDeviceToHost)); // setup the execution environment dim3 grid_mult(num_blocks_mult, 1, 1); dim3 threads_mult(MAX_THREADS_BLOCK, 1, 1); sdkStartTimer(&timer_step2_mult); bisectKernelLarge_MultIntervals<<>>( input.g_a, input.g_b, mat_size, result.g_blocks_mult, result.g_blocks_mult_sum, result.g_left_mult, result.g_right_mult, result.g_left_count_mult, result.g_right_count_mult, result.g_lambda_mult, result.g_pos_mult, precision); getLastCudaError("bisectKernelLarge_MultIntervals() FAILED."); checkCudaErrors(cudaDeviceSynchronize()); sdkStopTimer(&timer_step2_mult); } sdkStopTimer(&timer_total); printf("Average time step 1: %f ms\n", sdkGetTimerValue(&timer_step1) / (float)iterations); printf("Average time step 2, one intervals: %f ms\n", sdkGetTimerValue(&timer_step2_one) / (float)iterations); printf("Average time step 2, mult intervals: %f ms\n", sdkGetTimerValue(&timer_step2_mult) / (float)iterations); printf("Average time TOTAL: %f ms\n", sdkGetTimerValue(&timer_total) / (float)iterations); sdkDeleteTimer(&timer_step1); sdkDeleteTimer(&timer_step2_one); sdkDeleteTimer(&timer_step2_mult); sdkDeleteTimer(&timer_total); } //////////////////////////////////////////////////////////////////////////////// //! Process the result, that is obtain result from device and do simple sanity //! checking //! @param input handles to input data //! @param result handles to result data //! @param mat_size matrix size //! @param filename output filename //////////////////////////////////////////////////////////////////////////////// bool processResultDataLargeMatrix(const InputData &input, const ResultDataLarge &result, const unsigned int mat_size, const char *filename, const unsigned int user_defined, char *exec_path) { bool bCompareResult = false; const unsigned int mat_size_ui = sizeof(unsigned int) * mat_size; const unsigned int mat_size_f = sizeof(float) * mat_size; // copy data from intervals that contained more than one eigenvalue after // the first processing step float *lambda_mult = (float *)malloc(sizeof(float) * mat_size); checkCudaErrors(cudaMemcpy(lambda_mult, result.g_lambda_mult, sizeof(float) * mat_size, cudaMemcpyDeviceToHost)); unsigned int *pos_mult = (unsigned int *)malloc(sizeof(unsigned int) * mat_size); checkCudaErrors(cudaMemcpy(pos_mult, result.g_pos_mult, sizeof(unsigned int) * mat_size, cudaMemcpyDeviceToHost)); unsigned int *blocks_mult_sum = (unsigned int *)malloc(sizeof(unsigned int) * mat_size); checkCudaErrors(cudaMemcpy(blocks_mult_sum, result.g_blocks_mult_sum, sizeof(unsigned int) * mat_size, cudaMemcpyDeviceToHost)); unsigned int num_one_intervals; checkCudaErrors(cudaMemcpy(&num_one_intervals, result.g_num_one, sizeof(unsigned int), cudaMemcpyDeviceToHost)); unsigned int sum_blocks_mult = mat_size - num_one_intervals; // copy data for intervals that contained one eigenvalue after the first // processing step float *left_one = (float *)malloc(mat_size_f); float *right_one = (float *)malloc(mat_size_f); unsigned int *pos_one = (unsigned int *)malloc(mat_size_ui); checkCudaErrors(cudaMemcpy(left_one, result.g_left_one, mat_size_f, cudaMemcpyDeviceToHost)); checkCudaErrors(cudaMemcpy(right_one, result.g_right_one, mat_size_f, cudaMemcpyDeviceToHost)); checkCudaErrors(cudaMemcpy(pos_one, result.g_pos_one, mat_size_ui, cudaMemcpyDeviceToHost)); // extract eigenvalues float *eigenvals = (float *)malloc(mat_size_f); // singleton intervals generated in the second step for (unsigned int i = 0; i < sum_blocks_mult; ++i) { eigenvals[pos_mult[i] - 1] = lambda_mult[i]; } // singleton intervals generated in the first step unsigned int index = 0; for (unsigned int i = 0; i < num_one_intervals; ++i, ++index) { eigenvals[pos_one[i] - 1] = left_one[i]; } if (1 == user_defined) { // store result writeTridiagSymMatlab(filename, input.a, input.b + 1, eigenvals, mat_size); // getLastCudaError( sdkWriteFilef( filename, eigenvals, mat_size, 0.0f)); printf("User requests non-default argument(s), skipping self-check!\n"); bCompareResult = true; } else { // compare with reference solution float *reference = NULL; unsigned int input_data_size = 0; char *ref_path = sdkFindFilePath("reference.dat", exec_path); assert(NULL != ref_path); sdkReadFile(ref_path, &reference, &input_data_size, false); assert(input_data_size == mat_size); // there's an imprecision of Sturm count computation which makes an // additional offset necessary float tolerance = 1.0e-5f + 5.0e-6f; if (sdkCompareL2fe(reference, eigenvals, mat_size, tolerance) == true) { bCompareResult = true; } else { bCompareResult = false; } free(ref_path); free(reference); } freePtr(eigenvals); freePtr(lambda_mult); freePtr(pos_mult); freePtr(blocks_mult_sum); freePtr(left_one); freePtr(right_one); freePtr(pos_one); return bCompareResult; }