重构-C++实现矩阵的简单实例

重构–C++实现矩阵的简单实例

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#include <iostream>

#include <cmath>

using namespace std;

double cofactor(double* detPtr,int rank,int t); //代数余子式

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;} //交换

class SquareMatrix;

class Matrix{

public:

friend class SquareMatrix; //配合转换函数食用

Matrix(){m=n=mn=0;} //默认构造函数

Matrix(int mt,int nt); //构造矩阵

Matrix(const Matrix& mtrx); //复制构造函数

Matrix(int mt,int nt,double* a); //数组初始化矩阵

Matrix transposeMtrx(); //转置矩阵

//初等变换

void exchangeRow(int r1,int r2,int c=0); //交换行

void multiRow(int r,int k,int c=0); //数乘行

void addMultiRow(int r1,int r2,int k=1,int c=0); //r1+=k*r2

void exchangeColumn(int c1,int c2,int r=0); //交换列

void multiColumn(int c,int k,int r=0); //数乘列

void addMultiColumn(int c1,int c2,int k=1,int r=0); //c1+=k*c2

Matrix& operator =(const Matrix& mtrx); //赋值构造函数

friend istream& operator>>(istream& input,Matrix& mtrx);

friend ostream& operator<<(ostream& output,Matrix& mtrx); //输出矩阵

friend Matrix operator*(Matrix& m1,Matrix& m2); //矩阵乘法

protected:

int m;

int n;

int mn;

double* matrixPtr;

};

class SquareMatrix:public Matrix{

public:

SquareMatrix():Matrix(){} //默认构造函数

SquareMatrix(int mt):Matrix(mt,mt){}; //构造函数

SquareMatrix(int mt,double* a):Matrix(mt,mt,a){}; //数组初始化方阵

SquareMatrix(const Matrix& mtrx); //矩阵到方阵转换

SquareMatrix transposeSqrMtrx(); //转置方阵

SquareMatrix adjugateSqrMatrix(); //伴随矩阵

SquareMatrix inverseSqrMatrix(); //逆矩阵

friend istream& operator>>(istream& input,SquareMatrix& mtrx);

//输入方阵

friend SquareMatrix operator *(SquareMatrix& sm1,SquareMatrix& sm2);

//方阵乘法

double getDet(); //行列式的值

private:

};

Matrix::Matrix(int mt,int nt){ //初始化m*n矩阵

m=mt;n=nt;mn=m*n;

matrixPtr=new double[mn];

}

Matrix::Matrix(const Matrix& mtrx){ //复制构造函数

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){ //数组初始化m*n矩阵

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){ //重载>>

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(){ //转置矩阵

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){ //交换行,默认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){ //数乘行,默认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,默认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){ //交换列,默认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){ //数乘列,默认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,默认r=0

for(int i=r;i<m;i++)

matrixPtr[n*i+c1]+=matrixPtr[n*i+c2]*k;

}

Matrix& Matrix::operator=(const Matrix& mtrx){ //重载=

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){ //重载<<

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){ //重载*

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;

}

//我是萌萌哒分割线-------------------------------------------------------

SquareMatrix::SquareMatrix(const Matrix& mtrx){ //构造函数

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){ //重载>>

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(){ //转置方阵

return SquareMatrix((*this).transposeMtrx());

}

SquareMatrix SquareMatrix::adjugateSqrMatrix(){ //伴随矩阵

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(){ //逆矩阵

double det=getDet();

if(det==0){

cerr<<"this is a singular matrix!"<<endl; //判断奇异矩阵

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){ //重载*

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);

}

//又是一条萌萌哒分割线------------------------------------------

double valDet( double *detPtr, int rank)

{

double val=0;

if(rank==1) return detPtr[0];

for(int i=0;i<rank;i++) //计算余子式保存在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){ //计算代数余子式

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<<"测试驱动程序-------------------"<<endl;

/*

cout<<endl<<"输入任意矩阵-------------------"<<endl;

Matrix m1;cin>>m1;cout<<m1;

cout<<endl<<"输入任意方阵-------------------"<<endl;

SquareMatrix sm1;cin>>sm1;cout<<sm1;

cout<<endl<<"输入3*2矩阵--------------------"<<endl;

Matrix m2(3,2);cin>>m2;cout<<m2;

cout<<endl<<"输入2阶方阵--------------------"<<endl;

SquareMatrix sm2(2);cin>>sm2;cout<<sm2;

*/

cout<<endl<<"数组初始化矩阵-----------------"<<endl;

double a1[6]={1,2,3,7,8,9};

Matrix m3(2,3,a1);cout<<m3;

cout<<endl<<"数组初始化方阵-----------------"<<endl;

double a2[4]={3,4,5,6};

SquareMatrix sm3(2,a2);cout<<sm3;

cout<<endl<<"复制构造方阵/矩阵--------------"<<endl;

Matrix m4;m4=m3;Matrix m5(m3);

cout<<m4<<m5;

SquareMatrix sm4;sm4=sm3;SquareMatrix sm5(sm3);

cout<<sm4<<sm5;

cout<<endl<<"矩阵/方阵乘法------------------"<<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<<"矩阵转换为方阵-----------------"<<endl;

SquareMatrix sm9(m7);cout<<m7<<sm9;

cout<<endl<<"转置矩阵/方阵------------------"<<endl;

Matrix m9(m6.transposeMtrx());

cout<<m6<<m9;

SquareMatrix sm10=sm9.transposeSqrMtrx();

cout<<sm9<<sm10;

cout<<endl<<"初等变换-----------------------"<<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<<"方阵的行列式值-----------------"<<endl;

cout<<sm3<<sm3.getDet()<<endl;

cout<<endl<<"逆矩阵-------------------------"<<endl;

SquareMatrix sm11=sm3.inverseSqrMatrix();cout<<sm11;

SquareMatrix sm12=sm3*sm11;cout<<sm12;

return 0;

}

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