矩陣的乘法

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;// 矩陣乘法 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; }//矩陣轉置 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; }//讀入矩陣 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];}} }//矩陣打印 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;} }//計算偏差 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);//轉置處理a = mat_transpose(a);cin>>x>>y;read_mat(b,x,y);//轉置處理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:最佳勾兌后的結果Matrix ans = new Matrix();Matrix Y = new Matrix();static double INF = 1e19;static double EPS = 1e-6;double diff = INF;// 矩陣乘法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;}//矩陣轉置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;}//矩陣打印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();}}//計算偏差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;}//勾兌算法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，這里要用重載的構造函數！！！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);}}//打印最終X結果矩陣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);}//測試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);//轉置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);//轉置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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