矩阵乘法优化

step1:更改循环顺序

//--------------- c = a * b -------------------------//
	
	for(int i=1;i<N;i++)
		for(int k=1;k<N;k++)
			for(int j=1;j<N;j++)
				c[i][j] += a[i][k]*b[k][j];
	
//--------------------------------------------------//

step2:矩阵分块

//--------------- c = a * b -------------------------//
	int blocksize=10;
	double sum=0;
	for (int kk = 0; kk < N; kk += blocksize) { 
          for (int jj = 0; jj < N; jj += blocksize) {
            for (int i = 0; i < N; i++) {
		for (int j = jj; j < jj + blocksize; j++) {
		    sum = c[i][j];
                    for (int k = kk; k < kk + blocksize; k++) {
                         sum += a[i][k]*b[k][j];
                    }
                    c[i][j] = sum;
                }
            }
        }
	}

//--------------------------------------------------//

（blocksize取值经反复试验后取值为10 速度达到最快（仅适用于本机及当前500*500矩阵，各有差异））

step3:分块后效果太不明显
上并行）

#include<stdio.h>
#include<omp.h>
#include<stdlib.h>
#include<math.h>

const int N = 500;

double a[500][500];
double b[500][500];
double c_0[500][500];
double c[500][500];

int main(){

//------------------------------------------// 
	FILE* f1;
	FILE* f2;
	FILE* out;
		
	f1 = fopen("data_a.txt", "r");
	f2 = fopen("data_b.txt", "r");
	out = fopen("data_c.txt", "w");
	
	for(int i=1;i<N;i++){
	
		for(int j=1;j<N;j++){
			fscanf(f1,"%lf",&a[i][j]);
			fscanf(f2,"%lf",&b[i][j]);
		}}
//--------------------------------------------------//	

	double t0,t1;
	double T0,T1;
	
	
//----------------------------------// 
	t0 = omp_get_wtime();
	//mul
	for(int i=1;i<N;i++)
		for(int j=1;j<N;j++)
			for(int k=1;k<N;k++)
				c_0[i][j] += a[i][k]*b[k][j];
	
	t1 = omp_get_wtime();
	
	T0 = (t1-t0)*1000;
	printf("优化前矩阵乘法耗时: %f ms\n", T0);
//---------------------------------------------------//	

	t0 = omp_get_wtime();
	
//---------------------// 
//--------------- c = a * b -------------------------//
	#pragma omp parallel for schedule(dynamic)
	for(int i=1;i<N;i++)
		for(int k=1;k<N;k++)
			for(int j=1;j<N;j++)
				c[i][j] += a[i][k]*b[k][j];
	
//--------------------------------------------------//	

	t1 = omp_get_wtime();
	
	T1 = (t1-t0)*1000;
	printf("优化后矩阵乘法运行耗时: %f ms\n", T1);	

	printf("加速比为%f\n",T0/T1);

//-------------------------------------------// 
	for(int i=1;i<N;i++)
		for(int j=1;j<N;j++)
			fprintf(out,"%lf\n",c[i][j]);
//---------------------------------------------------//			
			
	fclose(f1);
	fclose(f2);
	fclose(out);			
}