矩阵乘法通过缓存命中率提升运算效率

矩阵乘法通过缓存命中率提升运算效率 

import numpy as np
n = 512
 
 
a = np.full([n,n],1,dtype='int32')
a
 
 
b = np.full([n,n],2,dtype='int32')
b
 
 
c = np.random.randint(0,5,[n,n])
c
 
%%timeit
for i in range(0,a.shape[0]):
    for j in range(0,b.shape[1]):
        for k in range(0,a.shape[1]):
            if k == 0:
                c[i,j] = 0
            c[i,j] += a[i,k]*b[k,j]     
 
%%timeit
for i in range(0,a.shape[0]):
    for k in range(0,a.shape[1]):
        for j in range(0,b.shape[1]):
            if  k == 0:
                c[i,j] = 0
            c[i,j] += a[i,k]*b[k,j] 

测试环境为：ubuntu 18.04

CPU MHz:             800.682
CPU max MHz:         2101.0000
CPU min MHz:         800.0000
BogoMIPS:            4200.00
Virtualization:      VT-x
L1d cache:           32K
L1i cache:           32K
L2 cache:            1024K
L3 cache:            11264K

这里32KB，一个32位的int占字节数为4B，这里可以L1缓存可以存放8k个int，矩阵相乘每次需要3个矩阵空间，这里测试矩阵宽度为1024

测试结果为：

下面采用cpp做了同样的测试，在矩阵维度越大效果越明显。下面依次是矩阵维度在512,1024,2048三个维度下两种矩阵乘法的计算效率。

 代码如下：

#include 
#include 
#include 
 
using namespace std;
 
 
void vec_mul1(const vectorint>> a,const vectorint>> b,vectorint>> c){
    for(int i = 0;i < a.size();i++){
        for(int j = 0;j < b[0].size();j++){
            for(int k = 0;k < a[0].size();k++){
                if(k == 0)
                    c[i][j] = 0;
                c[i][j] += a[i][k]*b[k][j];
            }
        }
    }
}
 
void vec_mul2(const vectorint>> a,const vectorint>> b,vectorint>> c){
    for(int i = 0;i < a.size();i++){
        for(int k = 0;k < a[0].size();k++){
            for(int j = 0;j < b[0].size();j++){
                if(k == 0)
                    c[i][j] = 0;
                c[i][j] += a[i][k]*b[k][j];
            }
        }
    }
}
 
void test(){
    int n = 2048;
    vectorint>> a(n,vector<int>(n,1));
    vectorint>> b(n,vector<int>(n,2));
    vectorint>> c(n,vector<int>(n,3));
 
    int loop = 10;
 
    clock_t start,end;
    start = clock();
    for(int i = 0;i < loop;i++)
        vec_mul1(a,b,c);
    end = clock();
    cout<<"vec multi 1 time = "<<double(end-start)/CLOCKS_PER_SEC/loop<<"s"<
 
 
    start = clock();
    for(int i = 0;i < loop;i++)
        vec_mul2(a,b,c);
    end = clock();
    cout<<"vec multi 2 time = "<<double(end-start)/CLOCKS_PER_SEC/loop<<"s"<
 
 
}
 
int main() {
    std::cout << "Hello, World!" << std::endl;
    test();
    return 0;
}