矩阵运算.txt

关于矩阵计算的一些代码

1,矩阵运算规则: (1)只有同型矩阵才能相加减,矩阵可与一个标量相加减; (2)只有有相邻公共阶的两矩阵才能相乘 Cm...(4)左除(\)运算两矩阵的行数相等,右除(/)运算两矩 阵的列数相等. 2,数组运算规则: 参与数组运算的数组必须...

 1/**//***
  2*
  3*   author:XieXiaokui
  5*    purpose:Defines functions for matrix
  6*
  7***/
  8#pragma once
  9
 10#include <iostream>
 11#include <fstream>
 12
 13#include <string>
 14#include <sstream>
 15#include <algorithm>
 16#include <functional>
 17#include <numeric>
 18#include <iterator>
 19#include <cassert>
 20
 21#include "MatrixException.h"
 22
 23using namespace std;
 24
 25class Matrix
 26{
 27public:
 28  
 29    // Constructors
 30    explicit Matrix();
 31    explicit Matrix(int size);
 32    Matrix(int row,int col);
 33    Matrix(const Matrix& m);
 34
 35    // Destructor
 36    ~Matrix();
 37
 38    // Assignment operators
 39    Matrix& operator= (const Matrix& m);
 40
 41    // Value extraction method
 42    int GetRow() const;
 43    int GetCol() const;
 44
 45    // Subscript operator
 46    double operator()(int i,int j)const;    //subscript operator to get individual elements
 47    double& operator()(int i,int j);    //subscript operator to set individual elements
 48
 49    // Unary operators
 50    Matrix operator+() const;    //unary negation operator
 51    Matrix operator-() const;    //unary negation operator
 52
 53    //Binary operators
 54    Matrix operator+(const Matrix& m) const;
 55    Matrix operator-(const Matrix& m) const;
 56    Matrix operator*(const Matrix& m) const;
 57//    Matrix operator*(double d)const;
 58    Matrix operator/(const Matrix& m) const;
 59    Matrix operator/(double d) const;
 60    Matrix operator^(int pow) const;
 61
 62    bool operator== (const Matrix& m) const;    //logical equal-to operator
 63    bool operator!= (const Matrix& m) const;    //logical not-equal-to operator
 64
 65    friend Matrix operator* (double d,const Matrix& m);
 66    friend Matrix operator/ (double d,const Matrix& m);
 67
 68
 69
 70    // Combined assignment - calculation operators
 71    Matrix& operator +=(const Matrix& m) const;
 72    Matrix& operator -=(const Matrix& m) const;
 73    Matrix& operator *=(const Matrix& m) const;
 74    Matrix& operator *=(double d) const;
 75    Matrix& operator /=(const Matrix& m) const;
 76    Matrix& operator /=(double d) const;
 77    Matrix& operator ^=(int pow) const;
 78
 79    // Miscellaneous -methods
 80    void SetZero() ;    //zero matrix:零阵
 81    void SetUnit() ;    //unit matrix:单位阵
 82    void SetSize(int size) ;    //rsizing matrix
 83    void SetSize(int row,int col) ;    //resizing matrix
 84
 85    // Utility methods
 86    Matrix Solve(const Matrix& m)const;    //
 87    Matrix Adjoin() const;    //adjoin matrix:伴随矩阵
 88    double Determinant() const;    //determinant:行列式
 89    double Norm() const;    //norm:模
 90    Matrix Inverse() const;    //inverse:逆阵
 91    Matrix Transpose() const;    //transpose:转置
 92    double Cofactor() const;    //confactor
 93    double Condition() const;    //the condition number of a matrix
 94    int Pivot(int row) const;    // partial pivoting
 95
 96    //primary change
 97    Matrix& Exchange(int i,int j);//　初等变换　对调两行：ri<-->rj
 98    Matrix& Multiple(int index,double k);    //初等变换　第index 行乘以k
 99    Matrix& MultipleAdd(int index,int src,double k);    //初等变换 第src行乘以k加到第index行
100   
101
102    // Type of matrices
103    bool IsSquare() const;    //determine if the matrix is square:方阵
104    bool IsSingular() const;    //determine if the matrix is singular奇异阵
105    bool IsDiagonal() const;    //determine if the matrix is diagonal对角阵
106    bool IsScalar() const;    //determine if the matrix is scalar数量阵
107    bool IsUnit() const;    //determine if the matrix is unit单位阵
108    bool IsZero() const;    //determine if the matrix is zero零矩阵
109    bool IsSymmetric() const;    //determine if the matrix is symmetric对称阵
110    bool IsSkewSymmetric() const;    //determine if the matrix is skew-symmetric斜对称阵
111    bool IsUpperTriangular() const;    //determine if the matrix is upper-triangular上三角阵
112    bool IsLowerTriangular() const;    //determine if the matrix is lower-triangular下三角阵
113
114    // output stream function
115    friend ostream& operator<<(ostream& os,const Matrix& m);
116
117    // input stream function
118    friend istream& operator>>(istream& is,Matrix& m);
119
120    //conert to string
121    string ToString() const;
122
123protected:
124
125    //delete the matrix
126    void Create(int row,int col);
127    void Clear();
128
129private:
130
131    const static double epsilon;
132
133    double** m_data;
134    size_t m_row;
135    size_t m_col;
136
137};实现文件

  1/**//***
  2*
  3*    
  4*   author:XieXiaokui
  5*    purpose:Defines functions for matrix
  6*
  7***/
  8#include "stdafx.h"
  9
 10#include <iostream>
 11#include <fstream>
 12
 13#include <string>
 14#include <sstream>
 15#include <algorithm>
 16#include <functional>
 17#include <numeric>
 18#include <iterator>
 19#include <cmath>
 20#include <cassert>
 21
 22#include "matrix.h"
 23
 24using namespace std;
 25
 26const double Matrix::epsilon = 1e-7;
 27
 28// constructor
 29
 30Matrix::Matrix():m_row(0),m_col(0),m_data(0)
 31{
 32}
 33
 34
 35// constructor
 36Matrix::Matrix(int size):m_row(size),m_col(size)
 37{
 38    if(size<=0)
 39    {
 40        m_row=0;
 41        m_col=0;
 42        m_data=0;
 43
 44        ostringstream oss;
 45        oss<<"In Matrix::Matrix(int size) size "<<size<<" <=0.Please check it.";
 46        throw oss.str();
 47        
 48    }
 49    
 50    m_data=new double*[size];
 51
 52    for(int i=0;i<size;i++)
 53    {
 54        m_data[i]=new double[size];
 55    }
 56
 57}
 58
 59// constructor
 60Matrix::Matrix(int row,int col):m_row(row),m_col(col)
 61{
 62    if(row<=0)
 63    {
 64        m_row=0;
 65        m_col=0;
 66        m_data=0;
 67
 68        ostringstream oss;
 69        oss<<"In Matrix::Matrix(int row,int col),row "<<row<<" <=0.Please check it.";
 70        throw oss.str();
 71    }
 72    if(col<=0)
 73    {
 74        m_row=0;
 75        m_col=0;
 76        m_data=0;
 77
 78        ostringstream oss;
 79        oss<<" In Matrix::Matrix(int row,int col),col "<<col<<" <=0.Pleasecheck it.";
 80        throw oss.str();
 81    }
 82
 83    m_data=new double*[row];
 84    for(int i=0;i<row;i++)
 85    {
 86        m_data[i]=new double[col];
 87    }
 88}
 89
 90//copy  constructor
 91Matrix::Matrix(const Matrix& m):m_row(m.m_row),m_col(m.m_col)
 92{
 93    m_data = new double*[m_row];
 94    for(int i=0;i<m_row;i++)
 95    {
 96        m_data[i] = new double[m_col];
 97    }
 98
 99    for(int i=0;i<m_row;i++)
100    {
101        copy(m.m_data[i],m.m_data[i]+m_col,m_data[i]);
102    }
103
104}
105
106Matrix::~Matrix()
107{
108    if(m_data != 0)
109    {
110        for(int i=0;i<m_row;i++)
111        {
112            delete[] m_data[i];
113        }
114        delete[] m_data;
115    }
116}
117
118void Matrix::SetZero()
119{
120    for(int i=0;i<m_row;i++)
121        fill(m_data[i],m_data[i]+m_col,0);
122}
123
124void Matrix::SetUnit()
125{
126    for(int i=0;i<m_row;i++)
127        for(int j=0;j<m_col;j++)
128            m_data[i][j] = (i==j)?1:0;
129}
130
131void Matrix::SetSize(int size)
132{
133    Clear();
134    Create(size,size);
135}
136
137
138void Matrix::SetSize(int row,int col)
139{
140    Clear();
141    Create(row,col);
142}
143
144
145void Matrix::Clear()
146{
147
148    if(m_data != 0)
149    {    
150        for(int i=0;i<m_row;i++)
151        {
152            delete[] m_data[i];
153        }
154        delete[] m_data;
155    }
156
157    m_row=0;
158    m_col=0;
159    m_data=0;
160}
161
162/**//*
163Matrix& Matrix::Create(int size)
164{
165    if(size<=0)
166    {
167        ostringstream oss;
168        oss<<"In Matrix::Create(int size),size "<<size<<" <=0.Please check it.";
169
170        throw oss.str();
171    }
172
173    if(m_data != 0)
174    {
175        for(int i=0;i<m_row;i++)
176        {
177            delete[] m_data[i];
178        }
179        delete[] m_data;
180    }
181
182    m_row=size;
183    m_col=size;
184
185    m_data=new double*[size];
186    for(int i=0;i<size;i++)
187    {
188        m_data[i]=new double[size];
189    }
190
191    for(int i=0;i<size;i++)
192    {
193        for(int j=0;j<size;j++)
194        {
195            m_data[i][j] = ((i==j)?1:0);
196        }
197    }
198
199    return *this;
200}
201*/
202
203void Matrix::Create(int row,int col)
204{
205    if(row<=0)
206    {
207        ostringstream oss;
208        oss<<"In Matrix::Create(int row,int col),row "<<row<<" <=0.Please check it.";
209        throw oss.str();
210    }
211    if(col<=0)
212    {
213        ostringstream oss;
214        oss<<"In Matrix::Create(int row,int col),col  "<<col<<" <=0.Please check it.";
215        throw oss.str();
216    }
217
218    if(m_data != 0)
219    {
220        for(int i=0;i<m_row;i++)
221        {
222            delete[] m_data[i];
223        }
224        delete[] m_data;
225    }
226
227    m_row=row;
228    m_col=col;
229    m_data=new double*[row];
230    for(int i=0;i<row;i++)
231    {
232        m_data[i]=new double[col];
233    }
234}
235
236
237int Matrix::GetRow() const
238{
239    return m_row;
240}
241
242int Matrix::GetCol() const
243{
244    return m_col;
245}
246
247//transpose 转置
248Matrix Matrix::Transpose() const
249{
250    Matrix ret(m_col,m_row);
251    for(int i=0;i<m_row;i++)
252    {
253        for(int j=0;j<m_col;j++)
254        {
255            ret.m_data[j][i] = m_data[i][j];
256        }
257    }
258    return ret;
259}
260
261int Matrix::Pivot(int row) const
262{
263    int index=row;
264
265    for(int i=row+1;i<m_row;i++)
266    {
267        if(m_data[i][row] > m_data[index][row])
268            index=i;
269    }
270
271    return index;
272}
273
274
275Matrix&  Matrix::Exchange(int i,int j)    //　初等变换：对调两行ri<-->rj
276{
277    if(i<0 || i>=m_row)
278    {
279        ostringstream oss;
280        oss<<"In void Matrix::Exchange(int i,int j)    ,i "<<i<<" out of bounds.Please check it.";
281        throw oss.str();
282    }
283
284    if(j<0 || j>=m_row)
285    {
286        ostringstream oss;
287        oss<<"In void Matrix::Exchange(int i,int j)    ,j "<<j<<" out of bounds.Please check it.";
288        throw oss.str();
289    }