#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;}