利用C++實(shí)現(xiàn)矩陣的構(gòu)造，通過運(yùn)算符的重載實(shí)現(xiàn)矩陣的乘法、加法等。并且實(shí)現(xiàn)矩陣形狀的打印，矩陣的打印。
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#include<iostream>#include<memory>#include<assert.h>#include<stdlib.h>using namespace std;class Matrix{ public: Matrix(int row, int col); //構(gòu)造函數(shù) Matrix(int row, int col, int num);//構(gòu)造函數(shù)重載 ~Matrix(); //析構(gòu)函數(shù) Matrix(const Matrix & other); //賦值函數(shù) Matrix operator*(const Matrix& other); //矩陣相乘 Matrix operator+(const Matrix& other); //矩陣相加 Matrix operator-(const Matrix& other); //矩陣相減 int **a = nullptr; //初始化一共空指針 int row, col; void shape(); //打印矩陣形狀 void Ma_pri(); //打印矩陣};int main(){ Matrix a(2,1); //構(gòu)造一個(gè)（2,1）矩陣 Matrix b(1,2); //構(gòu)造一個(gè)（1，2）矩陣 a.a[0][0] = 4; //初始化矩陣 a.a[1][0] = 2; b.a[0][0] = 3; b.a[0][1] = 5; a.shape(); //矩陣形狀打印 b.shape(); Matrix c = a*b; //矩陣相乘 c.shape(); c.Ma_pri(); //矩陣打印 Matrix d(3,3,1); d.Ma_pri(); system("pause"); return 0;}Matrix::Matrix(int row, int col){ this->row = row; this->col = col; this->a = new int*[row]; for(int i=0;i<this->row;i++){ a[i] = new int[this->col]; }}Matrix::Matrix(int row, int col, int num){ this->row = row; this->col = col; this->a = new int*[row]; for(int i=0;i<this->row;i++){ a[i] = new int[this->col]; } for(int i = 0; i < this->row; i++){ for(int j =0; j <this->row; j++){ this->a[i][j] = num; } }}Matrix::~Matrix(){ for(int i=0;i<this->row;i++){ if(a[i] != nullptr){ delete[] a[i]; a[i] = nullptr; } } if(a != nullptr){ delete[] a; a = nullptr; }}Matrix::Matrix(const Matrix& other){ row = other.row; col = other.col; a = new int*[row]; for(int i=0;i<row;i++){ a[i] = new int[col]; memcpy(a[i], other.a[i],sizeof(int)*col); }}Matrix Matrix::operator*(const Matrix& other){ if(this->col != other.row){ cout<<"shape error"<<endl; exit(0); } Matrix m(this->row,other.col); for(int i=0; i<this->row; i++){ for(int j=0;j<other.col;j++){ int sum = 0; for(int k=0;k<this->col;k++){ sum += this->a[i][k] * other.a[k][j]; } m.a[i][j] = sum; } } return m;}Matrix Matrix::operator+(const Matrix& other){ if(this->col != other.col or this->row != other.row){ cout<<"shape error"<<endl; exit(0); } Matrix m(this->row,this->col); for(int i = 0;i < this->row; i++){ for(int j = 0; j < this-> col; j++){ m.a[i][j] = this->a[i][j] + other.a[i][j]; } } return m;}Matrix Matrix::operator-(const Matrix& other){ if(this->col != other.col or this->row != other.row){ cout<<"shape error"<<endl; exit(0); } Matrix m(this->row,this->col); for(int i = 0;i < this->row; i++){ for(int j = 0; j < this-> col; j++){ m.a[i][j] = this->a[i][j] - other.a[i][j]; } } return m;}void Matrix::shape(){ cout<<"("<<this->row<<","<<this->col<<")"<<endl;}void Matrix::Ma_pri(){ for(int i = 0; i < this->row; i++){ for(int j =0; j <this->row; j++){ cout<<this->a[i][j]<<" "; } cout<<endl; }} |
矩陣求逆算法及程序?qū)崿F(xiàn)
在做課題時(shí)，遇到了求多項(xiàng)式問題，利用了求逆方法。矩陣求逆一般使用簡(jiǎn)單的算法，還有快速算法 如全選主元高斯-約旦消元法，但本文程序主要寫了簡(jiǎn)單的矩陣求逆算法定義法之伴隨矩陣求逆公式如下，其中A可逆：A^{-1}=\frac{A^*}{|A|}，其中A^*是A的伴隨矩陣。。
1.給定一個(gè)方陣，非奇異（不是也可，程序有考慮）；
2.由矩陣得到其行列式，求其值如|A|；
3.求其伴隨矩陣A^*；
4.得到其逆矩陣。
主要函數(shù)如下：
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//得到給定矩陣src的逆矩陣保存到des中。bool GetMatrixInverse(double src[N][N],int n,double des[N][N]){ double flag=getA(src,n); double t[N][N]; if(flag==0) { return false; } else { getAStart(src,n,t); for(int i=0;i<n;i++) { for(int j=0;j<n;j++) { des[i][j]=t[i][j]/flag; } } } return true;} |
計(jì)算|A|:
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//按第一行展開計(jì)算|A|double getA(double arcs[N][N],int n){ if(n==1) { return arcs[0][0]; } double ans = 0; double temp[N][N]={0.0}; int i,j,k; for(i=0;i<n;i++) { for(j=0;j<n-1;j++) { for(k=0;k<n-1;k++) { temp[j][k] = arcs[j+1][(k>=i)?k+1:k]; } } double t = getA(temp,n-1); if(i%2==0) { ans += arcs[0][i]*t; } else { ans -= arcs[0][i]*t; } } return ans;} |
計(jì)算伴隨矩陣：
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//計(jì)算每一行每一列的每個(gè)元素所對(duì)應(yīng)的余子式，組成A*void getAStart(double arcs[N][N],int n,double ans[N][N]){ if(n==1) { ans[0][0] = 1; return; } int i,j,k,t; double temp[N][N]; for(i=0;i<n;i++) { for(j=0;j<n;j++) { for(k=0;k<n-1;k++) { for(t=0;t<n-1;t++) { temp[k][t] = arcs[k>=i?k+1:k][t>=j?t+1:t]; } } ans[j][i] = getA(temp,n-1); if((i+j)%2 == 1) { ans[j][i] = - ans[j][i]; } } }} |
到此這篇關(guān)于C++矩陣運(yùn)算的實(shí)現(xiàn)簡(jiǎn)單的文章就介紹到這了,更多相關(guān)C++ 矩陣運(yùn)算內(nèi)容請(qǐng)搜索服務(wù)器之家以前的文章或繼續(xù)瀏覽下面的相關(guān)文章希望大家以后多多支持服務(wù)器之家！
原文鏈接：https://blog.csdn.net/victor_JZ/article/details/120069521
