矩阵的乘法

0x00 C++版本

#include <bits/stdc++.h>using namespace std;
const int N = 25;
const double INF = 1e19;
const double EPS = 1e-6;struct Matrix
{int rowCount,colCount;double mat[N][N];
} e;
Matrix a,b;// 矩阵乘法
Matrix mat_mult(Matrix a,Matrix b)
{Matrix ans;for(int i = 0; i < a.rowCount; i++){for(int j = 0; j < b.colCount; j++){double tmp = 0;for(int k = 0; k < a.colCount; k++){tmp += a.mat[i][k] * b.mat[k][j];}ans.mat[i][j] = tmp;}}ans.rowCount = a.rowCount;ans.colCount = b.colCount;return ans;
}//矩阵转置
Matrix mat_transpose(Matrix a)
{Matrix res;for(int i = 0; i < a.rowCount; i++){for(int j = 0; j < a.colCount; j++){res.mat[j][i] = a.mat[i][j];}}res.rowCount = a.colCount;res.colCount = a.rowCount;return res;
}//读入矩阵
void read_mat(Matrix &a,int m,int n)
{a.rowCount = m;a.colCount = n;for(int i = 0; i < a.rowCount; i++){for(int j = 0; j < a.colCount; j++){cin>>a.mat[i][j];}}
}//矩阵打印
void print_mat(Matrix res)
{cout<<"-------------------"<<endl;for(int i = 0; i < res.rowCount; i++){for(int j = 0; j < res.colCount; j++){cout<<res.mat[i][j]<<" ";}cout<<endl;}
}//计算偏差
double calc_diff(Matrix Y)
{double diff = 0;for(int i = 0 ; i < Y.rowCount; i++){for(int j = 0; j < Y.colCount; j++){diff += fabs(Y.mat[i][j] - b.mat[i][j])/b.mat[i][j];}}return diff/Y.rowCount;
}
double diff = INF;
Matrix X,ans;void dfs(Matrix X,int n,int cnt,double sum)
{//可行性剪枝if(sum > 1.0 || (cnt == n&&sum != 1))return;if(cnt == n){Matrix res = mat_mult(a,X);double now_diff = calc_diff(res);if(diff - now_diff > EPS){diff = now_diff;ans = X;}return;}for (int j = 0; j <= 100; ++j){X.mat[cnt][0] = j / 100.0;dfs(X,n,cnt+1,sum+j/100.0);}
}int main()
{int m,n,x,y;cin>>m>>n;read_mat(a,m,n);//转置处理a = mat_transpose(a);cin>>x>>y;read_mat(b,x,y);//转置处理b = mat_transpose(b);X.rowCount = a.colCount;X.colCount = 1;dfs(X,a.colCount,0,0);cout<<"TargetX:"<<endl;print_mat(ans);cout<<"diff:"<<diff<<endl;cout<<"Y:"<<endl;print_mat(mat_transpose(mat_mult(a,ans)));return 0;
}
/*
3 3 21 2 -1
-1 3 4
1 1 15 6
-5 -6
6 0
*/
/*
res:
-11 -6
4 -24
6 0
*//*
4 2
2.89 0.376
3.18 0.272
2.49 0.393
3.28 0.3081 2
3.06 0.322
*/

0x01 java版本

package Demo;class Matrix{static int N = 25;int rowCount;int colCount;double [][] mat = new double[N][N];Matrix() {}Matrix(int rows,int cols,double[][] m) {rowCount = rows;colCount = cols;for(int i = 0; i < rowCount; i++) {for(int j = 0; j < colCount; j++){mat[i][j] = m[i][j];}}}Matrix(Matrix X) {rowCount = X.rowCount;colCount = X.colCount;for(int i = 0; i < rowCount; i++) {for(int j = 0; j < colCount; j++){mat[i][j] = X.mat[i][j];}}}
} public class BlendAlgorithm {Matrix a = new Matrix();Matrix b = new Matrix();Matrix X = new Matrix();//ans:各批的比例，Y:最佳勾兑后的结果Matrix ans = new Matrix();Matrix Y = new Matrix();static double INF = 1e19;static double EPS = 1e-6;double diff = INF;// 矩阵乘法Matrix matrixMultiply(Matrix a,Matrix b){Matrix ans = new Matrix();for(int i = 0; i < a.rowCount; i++){for(int j = 0; j < b.colCount; j++){double tmp = 0;for(int k = 0; k < a.colCount; k++){tmp += a.mat[i][k] * b.mat[k][j];}ans.mat[i][j] = tmp;}}ans.rowCount = a.rowCount;ans.colCount = b.colCount;return ans;}//矩阵转置Matrix matrixTranspose(Matrix a){Matrix res = new Matrix();for(int i = 0; i < a.rowCount; i++){for(int j = 0; j < a.colCount; j++){res.mat[j][i] = a.mat[i][j];}}res.rowCount = a.colCount;res.colCount = a.rowCount;return res;}//矩阵打印void printMatrix(Matrix res){System.out.println("------------------------");System.out.printf("rowCont=%d colCount=%d\n",res.rowCount,res.colCount);for(int i = 0; i < res.rowCount; i++){for(int j = 0; j < res.colCount; j++){System.out.printf("%f ",res.mat[i][j]);}System.out.println();}}//计算偏差double calcDiff(Matrix Y){//printMatrix(Y);double diff = 0;for(int i = 0 ; i < Y.rowCount; i++){for(int j = 0; j < Y.colCount; j++){diff += Math.abs(Y.mat[i][j] - b.mat[i][j])/b.mat[i][j];}}return diff/Y.rowCount;}//勾兑算法public void blend(Matrix X,int n,int cnt,double sum) {//可行性剪枝if(sum > 1.0 || (cnt == n && sum != 1.0)) {return;}if(cnt == n){Matrix res = matrixMultiply(a,X);double now_diff = calcDiff(res);if(diff - now_diff > EPS) {diff = now_diff;//ans = X是引用，这里要用重载的构造函数！！！ans = new Matrix(X);}return;}for (int j = 0; j <= 100; ++j){X.mat[cnt][0] = j / 100.0;blend(X,n,cnt+1,sum+j/100.0);}}//打印最终X结果矩阵void printAnswer() {System.out.println("*******************");System.out.println("TargetX:");printMatrix(ans);   System.out.println("*******************");System.out.println("diff:\n------------------------");System.out.println(diff);System.out.println("*******************");System.out.println("Y:");Y = matrixTranspose(matrixMultiply(a,ans));printMatrix(Y);}//测试public static void main(String[] args) {BlendAlgorithm f = new BlendAlgorithm();//4，2double[][] a = new double[][]{{2.89,0.376},{3.18,0.272},{2.49,0.393},{3.28,0.308}};f.a = new Matrix(4,2,a);//转置f.a = f.matrixTranspose(f.a);//f.printMatrix(f.a);//1，2double [][] b = new double[][] {{3.06,0.322}};f.b = new Matrix(1,2,b);//转置f.b = f.matrixTranspose(f.b);//f.printMatrix(f.b);f.X.rowCount = f.a.colCount;f.X.colCount = 1;f.blend(f.X,f.a.colCount,0,0);f.printAnswer();}
}

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矩阵的乘法通用模板（C++/Java）

矩阵的乘法

0x00 C++版本

0x01 java版本

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