重構-C++完成矩陣的簡略實例。本站提示廣大學習愛好者：（重構-C++完成矩陣的簡略實例）文章只能為提供參考，不一定能成為您想要的結果。以下是重構-C++完成矩陣的簡略實例正文
重構-C++完成矩陣的簡略實例
#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;} //交流
class SquareMatrix;
class Matrix{
public:
friend class SquareMatrix; //合營轉換函數食用
Matrix(){m=n=mn=0;} //默許結構函數
Matrix(int mt,int nt); //結構矩陣
Matrix(const Matrix& mtrx); //復制結構函數
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); //交流行
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); //交流列
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); //賦值結構函數
friend istream& operator>>(istream& input,Matrix& mtrx);
friend ostream& operator<<(ostream& output,Matrix& mtrx); //輸入矩陣
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(){} //默許結構函數
SquareMatrix(int mt):Matrix(mt,mt){}; //結構函數
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(); //隨同矩陣
SquareMatrix inverseSqrMatrix(); //逆矩陣
friend istream& operator>>(istream& input,SquareMatrix& mtrx);
//輸出方陣
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){ //復制結構函數
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){ //交流行,默許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,默許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,默許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){ //交流列,默許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,默許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,默許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;
}
//我是萌萌哒朋分線-------------------------------------------------------
SquareMatrix::SquareMatrix(const Matrix& mtrx){ //結構函數
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(){ //隨同矩陣
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; //斷定奇怪矩陣
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);
}
//又是一條萌萌哒朋分線------------------------------------------
double valDet( double *detPtr, int rank)
{
double val=0;
if(rank==1) return detPtr[0];
for(int i=0;i<rank;i++) //盤算余子式保留在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){ //盤算代數余子式
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)); //假如i和t同業或同列
else{
nextDetPtr[j]=detPtr[i];
j++;
}
return valDet(nextDetPtr,rank-1)*pow(-1.0,t/rank+t%rank);
}
int main(){
cout<<endl<<"測試驅動法式-------------------"<<endl;
/*
cout<<endl<<"輸出隨意率性矩陣-------------------"<<endl;
Matrix m1;cin>>m1;cout<<m1;
cout<<endl<<"輸出隨意率性方陣-------------------"<<endl;
SquareMatrix sm1;cin>>sm1;cout<<sm1;
cout<<endl<<"輸出3*2矩陣--------------------"<<endl;
Matrix m2(3,2);cin>>m2;cout<<m2;
cout<<endl<<"輸出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<<"復制結構方陣/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++完成矩陣的簡略實例就是小編分享給年夜家的全體內容了，願望能給年夜家一個參考，也願望年夜家多多支撐。
