重構-C++實現矩陣的簡單實例
#include <iostream>#include <cmath> using namespace std;double cofactor(double* detPtr,int rank,int t); //代數余子式 double valDet( double *detPtr, int rank); //行列式 template <class T>void exchange(T& t1,T& t2){T temp;temp=t1;t1=t2;t2=temp;} //交換 class SquareMatrix;class Matrix{ public: friend class SquareMatrix; //配合轉換函數食用 Matrix(){m=n=mn=0;} //默認構造函數 Matrix(int mt,int nt); //構造矩陣 Matrix(const Matrix& mtrx); //復制構造函數 Matrix(int mt,int nt,double* a); //數組初始化矩陣 Matrix transposeMtrx(); //轉置矩陣 //初等變換 void exchangeRow(int r1,int r2,int c=0); //交換行 void multiRow(int r,int k,int c=0); //數乘行 void addMultiRow(int r1,int r2,int k=1,int c=0); //r1+=k*r2 void exchangeColumn(int c1,int c2,int r=0); //交換列 void multiColumn(int c,int k,int r=0); //數乘列 void addMultiColumn(int c1,int c2,int k=1,int r=0); //c1+=k*c2 Matrix& operator =(const Matrix& mtrx); //賦值構造函數 friend istream& operator>>(istream& input,Matrix& mtrx); friend ostream& operator<<(ostream& output,Matrix& mtrx); //輸出矩陣 friend Matrix operator*(Matrix& m1,Matrix& m2); //矩陣乘法 protected: int m; int n; int mn; double* matrixPtr;};class SquareMatrix:public Matrix{ public: SquareMatrix():Matrix(){} //默認構造函數 SquareMatrix(int mt):Matrix(mt,mt){}; //構造函數 SquareMatrix(int mt,double* a):Matrix(mt,mt,a){}; //數組初始化方陣 SquareMatrix(const Matrix& mtrx); //矩陣到方陣轉換 SquareMatrix transposeSqrMtrx(); //轉置方陣 SquareMatrix adjugateSqrMatrix(); //伴隨矩陣 SquareMatrix inverseSqrMatrix(); //逆矩陣 friend istream& operator>>(istream& input,SquareMatrix& mtrx); //輸入方陣 friend SquareMatrix operator *(SquareMatrix& sm1,SquareMatrix& sm2); //方陣乘法 double getDet(); //行列式的值 private:};Matrix::Matrix(int mt,int nt){ //初始化m*n矩陣 m=mt;n=nt;mn=m*n; matrixPtr=new double[mn];}Matrix::Matrix(const Matrix& mtrx){ //復制構造函數 m=mtrx.m;n=mtrx.n;mn=mtrx.mn; matrixPtr=new double[mn]; for(int i=0;i<mn;i++) matrixPtr[i]=mtrx.matrixPtr[i];}Matrix::Matrix(int mt,int nt,double* a){ //數組初始化m*n矩陣 m=mt;n=nt;mn=m*n; matrixPtr=new double[mn]; for(int i=0;i<mn;i++) matrixPtr[i]=a[i];}istream& operator>>(istream& input,Matrix& mtrx){ //重載>> if(!mtrx.m){ cout<<"enter the m,n of matrix:"; input>>mtrx.m>>mtrx.n; mtrx.mn=mtrx.m*mtrx.n; mtrx.matrixPtr=new double[mtrx.mn]; cout<<"enter the matrix:"<<endl; } else cout<<"enter a "<<mtrx.m<<'*'<<mtrx.n<<" matrix:"<<endl; for(int i=0;i<mtrx.mn;i++) input>>mtrx.matrixPtr[i]; return input;}Matrix Matrix::transposeMtrx(){ //轉置矩陣 Matrix mtrx(n,m); for(int i=0;i<n;i++) for(int j=0;j<m;j++) mtrx.matrixPtr[m*i+j]=matrixPtr[n*j+i]; return mtrx;}void Matrix::exchangeRow(int r1,int r2,int c){ //交換行,默認c=0 for(int i=c;i<n;i++) exchange(matrixPtr[n*r1+i],matrixPtr[n*r2+i]);}void Matrix::multiRow(int r,int k,int c){ //數乘行,默認c=0 for(int i=c;i<n;i++) matrixPtr[n*r+i]*=k;}void Matrix::addMultiRow(int r1,int r2,int k,int c){ //r1+=k*r2,默認k=1,c=0 for(int i=c;i<n;i++) matrixPtr[n*r1+i]+=matrixPtr[n*r2+i]*k;}void Matrix::exchangeColumn(int c1,int c2,int r){ //交換列,默認r=0 for(int i=r;i<m;i++) exchange(matrixPtr[n*i+c1],matrixPtr[n*i+c2]);}void Matrix::multiColumn(int c,int k,int r){ //數乘列,默認k=1,r=0 for(int i=r;i<m;i++) matrixPtr[n*i+c]*=k;}void Matrix::addMultiColumn(int c1,int c2,int k,int r){ //c1+=k*c2,默認r=0 for(int i=r;i<m;i++) matrixPtr[n*i+c1]+=matrixPtr[n*i+c2]*k;}Matrix& Matrix::operator=(const Matrix& mtrx){ //重載= m=mtrx.m;n=mtrx.n;mn=m*n; matrixPtr=new double[mn]; for(int i=0;i<mn;i++) matrixPtr[i]=mtrx.matrixPtr[i]; return *this;}ostream& operator<<(ostream& output,Matrix& mtrx){ //重載<< output<<endl; for(int i=0;i<mtrx.m;i++){ for(int j=0;j<mtrx.n;j++) output<<mtrx.matrixPtr[mtrx.n*i+j]<<' '; output<<endl; } output<<endl; return output;}Matrix operator *(Matrix& m1,Matrix& m2){ //重載* Matrix m3(m1.m,m2.n); for(int i=0;i<m3.m;i++) for(int j=0;j<m3.n;j++){ double val=0; for(int k=0;k<m2.m;k++) val+=m1.matrixPtr[m1.n*i+k]*m2.matrixPtr[m2.n*k+j]; m3.matrixPtr[m3.n*i+j]=val; } return m3;}//我是萌萌噠分割線-------------------------------------------------------SquareMatrix::SquareMatrix(const Matrix& mtrx){ //構造函數 m=n=mtrx.m;mn=m*n;matrixPtr=new double[mn]; for(int i=0;i<mn;i++) matrixPtr[i]=mtrx.matrixPtr[i];} istream& operator>>(istream& input,SquareMatrix& mtrx){ //重載>> if(!mtrx.m){ cout<<"enter the m of squareMatrix:"; input>>mtrx.m; mtrx.n=mtrx.m;mtrx.mn=mtrx.m*mtrx.n; mtrx.matrixPtr=new double[mtrx.mn]; cout<<"enter the squareMatrix:"<<endl; } else cout<<"enter a "<<mtrx.m<<" order squareMatrix:"<<endl; for(int i=0;i<mtrx.mn;i++) input>>mtrx.matrixPtr[i]; return input;}SquareMatrix SquareMatrix::transposeSqrMtrx(){ //轉置方陣 return SquareMatrix((*this).transposeMtrx());} SquareMatrix SquareMatrix::adjugateSqrMatrix(){ //伴隨矩陣 SquareMatrix aSM(m); for(int i=0;i<mn;i++) aSM.matrixPtr[i]=cofactor(matrixPtr,m,i); aSM=aSM.transposeSqrMtrx(); return aSM;}SquareMatrix SquareMatrix::inverseSqrMatrix(){ //逆矩陣 double det=getDet(); if(det==0){ cerr<<"this is a singular matrix!"<<endl; //判斷奇異矩陣 return 0; } SquareMatrix aSM(m),iSM(m); aSM=adjugateSqrMatrix(); for(int i=0;i<mn;i++) iSM.matrixPtr[i]=aSM.matrixPtr[i]/det; return iSM;}SquareMatrix operator *(SquareMatrix& sm1,SquareMatrix& sm2){ //重載* SquareMatrix sm3(sm1.m); for(int i=0;i<sm3.m;i++) for(int j=0;j<sm3.n;j++){ double val=0; for(int k=0;k<sm2.m;k++) val+=sm1.matrixPtr[sm1.n*i+k]*sm2.matrixPtr[sm2.n*k+j]; sm3.matrixPtr[sm3.n*i+j]=val; } return sm3;}double SquareMatrix::getDet(){ //行列式 return valDet(matrixPtr,m);}//又是一條萌萌噠分割線------------------------------------------double valDet( double *detPtr, int rank){ double val=0; if(rank==1) return detPtr[0]; for(int i=0;i<rank;i++) //計算余子式保存在nextDetPtr[]中 { double *nextDetPtr=new double[(rank-1)*(rank-1)]; for(int j=0;j<rank-1;j++) for(int k=0;k<i;k++) nextDetPtr[j*(rank-1)+k]=detPtr[(j+1)*rank+k]; for(int j=0;j<rank-1;j++) for(int k=i;k<rank-1;k++) nextDetPtr[j*(rank-1)+k]=detPtr[(j+1)*rank+k+1]; val+=detPtr[i]*valDet(nextDetPtr,rank-1)*pow(-1.0,i); } return val;}double cofactor(double* detPtr,int rank,int t){ //計算代數余子式 double *nextDetPtr=new double[(rank-1)*(rank-1)]; for(int i=0,j=0;i<rank*rank;i++) if(i>=(t/rank)*rank&&i<(t/rank)*rank+rank||!((t-i)%rank)); //如果i和t同行或同列 else{ nextDetPtr[j]=detPtr[i]; j++; } return valDet(nextDetPtr,rank-1)*pow(-1.0,t/rank+t%rank);} int main(){ cout<<endl<<"測試驅動程序-------------------"<<endl; /* cout<<endl<<"輸入任意矩陣-------------------"<<endl; Matrix m1;cin>>m1;cout<<m1; cout<<endl<<"輸入任意方陣-------------------"<<endl; SquareMatrix sm1;cin>>sm1;cout<<sm1; cout<<endl<<"輸入3*2矩陣--------------------"<<endl; Matrix m2(3,2);cin>>m2;cout<<m2; cout<<endl<<"輸入2階方陣--------------------"<<endl; SquareMatrix sm2(2);cin>>sm2;cout<<sm2; */ cout<<endl<<"數組初始化矩陣-----------------"<<endl; double a1[6]={1,2,3,7,8,9}; Matrix m3(2,3,a1);cout<<m3; cout<<endl<<"數組初始化方陣-----------------"<<endl; double a2[4]={3,4,5,6}; SquareMatrix sm3(2,a2);cout<<sm3; cout<<endl<<"復制構造方陣/矩陣--------------"<<endl; Matrix m4;m4=m3;Matrix m5(m3); cout<<m4<<m5; SquareMatrix sm4;sm4=sm3;SquareMatrix sm5(sm3); cout<<sm4<<sm5; cout<<endl<<"矩陣/方陣乘法------------------"<<endl; double a3[6]={1,0,3,2,1,0},a4[9]={4,1,0,-1,1,3,2,0,1}; Matrix m6(2,3,a3),m7(3,3,a4); Matrix m8=m6*m7;cout<<m8; double a5[4]={1,2,2,3},a6[4]={2,3,4,1}; SquareMatrix sm6(2,a5),sm7(2,a6); SquareMatrix sm8(sm6*sm7);cout<<sm8; cout<<endl<<"矩陣轉換為方陣-----------------"<<endl; SquareMatrix sm9(m7);cout<<m7<<sm9; cout<<endl<<"轉置矩陣/方陣------------------"<<endl; Matrix m9(m6.transposeMtrx()); cout<<m6<<m9; SquareMatrix sm10=sm9.transposeSqrMtrx(); cout<<sm9<<sm10; cout<<endl<<"初等變換-----------------------"<<endl; cout<<m3<<m4; m4.exchangeRow(0,1,2);cout<<m3<<m4; m4.exchangeRow(0,1);cout<<m4; m4.exchangeColumn(0,2);cout<<m4; m4.multiRow(1,2);cout<<m4; m4.multiColumn(1,2,1);cout<<m4; m4.addMultiRow(0,1);cout<<m4; m4.addMultiColumn(0,2,2,1);cout<<m4; cout<<sm3<<sm4; sm4.exchangeRow(0,1);cout<<sm3<<sm4; cout<<endl<<"方陣的行列式值-----------------"<<endl; cout<<sm3<<sm3.getDet()<<endl; cout<<endl<<"逆矩陣-------------------------"<<endl; SquareMatrix sm11=sm3.inverseSqrMatrix();cout<<sm11; SquareMatrix sm12=sm3*sm11;cout<<sm12; return 0;} 以上這篇重構-C++實現矩陣的簡單實例就是小編分享給大家的全部內容了，希望能給大家一個參考，也希望大家多多支持VEVB武林網。
