矩阵基本运算的实现(standard C++Version)
一年前 自己动手编写的代码,尽量使用了标准C++,其中用到了一些标准模板库STL,但没有用到很高级的部分,不懂STL的朋友也应该可以看懂,建议看一下《Generic Programming and STL》,有候捷译本《泛型编程与STL》。
头文件
实现文件
实现了很多基本的操作,需要的话还可以自己扩充。如果实现那些注释掉的代码,功能就比较强了。
另有标准C语言版本。
头文件
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/***
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*
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* author:XieXiaokui
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* purpose:Defines functions for matrix
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*
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***/
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#pragma once
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#include <iostream>
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#include <fstream>
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#include <string>
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#include <sstream>
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#include <algorithm>
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#include <functional>
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#include <numeric>
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#include <iterator>
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#include <cassert>
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#include "MatrixException.h"
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using namespace std;
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class Matrix
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{
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public:
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// Constructors
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explicit Matrix();
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explicit Matrix(int size);
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Matrix(int row,int col);
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Matrix(const Matrix& m);
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// Destructor
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~Matrix();
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// Assignment operators
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Matrix& operator= (const Matrix& m);
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// Value extraction method
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int GetRow() const;
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int GetCol() const;
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// Subscript operator
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double operator()(int i,int j)const; //subscript operator to get individual elements
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double& operator()(int i,int j); //subscript operator to set individual elements
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// Unary operators
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Matrix operator+() const; //unary negation operator
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Matrix operator-() const; //unary negation operator
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//Binary operators
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Matrix operator+(const Matrix& m) const;
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Matrix operator-(const Matrix& m) const;
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Matrix operator*(const Matrix& m) const;
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// Matrix operator*(double d)const;
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Matrix operator/(const Matrix& m) const;
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Matrix operator/(double d) const;
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Matrix operator^(int pow) const;
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bool operator== (const Matrix& m) const; //logical equal-to operator
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bool operator!= (const Matrix& m) const; //logical not-equal-to operator
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friend Matrix operator* (double d,const Matrix& m);
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friend Matrix operator/ (double d,const Matrix& m);
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// Combined assignment - calculation operators
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Matrix& operator +=(const Matrix& m) const;
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Matrix& operator -=(const Matrix& m) const;
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Matrix& operator *=(const Matrix& m) const;
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Matrix& operator *=(double d) const;
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Matrix& operator /=(const Matrix& m) const;
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Matrix& operator /=(double d) const;
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Matrix& operator ^=(int pow) const;
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// Miscellaneous -methods
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void SetZero() ; //zero matrix:零阵
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void SetUnit() ; //unit matrix:单位阵
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void SetSize(int size) ; //rsizing matrix
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void SetSize(int row,int col) ; //resizing matrix
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// Utility methods
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Matrix Solve(const Matrix& m)const; //
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Matrix Adjoin() const; //adjoin matrix:伴随矩阵
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double Determinant() const; //determinant:行列式
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double Norm() const; //norm:模
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Matrix Inverse() const; //inverse:逆阵
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Matrix Transpose() const; //transpose:转置
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double Cofactor() const; //confactor
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double Condition() const; //the condition number of a matrix
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int Pivot(int row) const; // partial pivoting
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//primary change
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Matrix& Exchange(int i,int j);// 初等变换 对调两行:ri<-->rj
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Matrix& Multiple(int index,double k); //初等变换 第index 行乘以k
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Matrix& MultipleAdd(int index,int src,double k); //初等变换 第src行乘以k加到第index行
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// Type of matrices
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bool IsSquare() const; //determine if the matrix is square:方阵
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bool IsSingular() const; //determine if the matrix is singular奇异阵
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bool IsDiagonal() const; //determine if the matrix is diagonal对角阵
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bool IsScalar() const; //determine if the matrix is scalar数量阵
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bool IsUnit() const; //determine if the matrix is unit单位阵
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bool IsZero() const; //determine if the matrix is zero零矩阵
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bool IsSymmetric() const; //determine if the matrix is symmetric对称阵
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bool IsSkewSymmetric() const; //determine if the matrix is skew-symmetric斜对称阵
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bool IsUpperTriangular() const; //determine if the matrix is upper-triangular上三角阵
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bool IsLowerTriangular() const; //determine if the matrix is lower-triangular下三角阵
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// output stream function
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friend ostream& operator<<(ostream& os,const Matrix& m);
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// input stream function
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friend istream& operator>>(istream& is,Matrix& m);
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//conert to string
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string ToString() const;
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protected:
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//delete the matrix
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void Create(int row,int col);
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void Clear();
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private:
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const static double epsilon;
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double** m_data;
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size_t m_row;
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size_t m_col;
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};
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1
/***
2
*
3
*
4
* author:XieXiaokui
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* purpose:Defines functions for matrix
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*
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***/
8
#include "stdafx.h"
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#include <iostream>
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#include <fstream>
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#include <string>
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#include <sstream>
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#include <algorithm>
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#include <functional>
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#include <numeric>
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#include <iterator>
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#include <cmath>
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#include <cassert>
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#include "matrix.h"
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using namespace std;
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const double Matrix::epsilon = 1e-7;
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// constructor
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Matrix::Matrix():m_row(0),m_col(0),m_data(0)
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{
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}
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// constructor
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Matrix::Matrix(int size):m_row(size),m_col(size)
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{
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if(size<=0)
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{
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m_row=0;
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m_col=0;
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m_data=0;
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ostringstream oss;
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oss<<"In Matrix::Matrix(int size) size "<<size<<" <=0.Please check it.";
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throw oss.str();
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48
}
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50
m_data=new double*[size];
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52
for(int i=0;i<size;i++)
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{
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m_data[i]=new double[size];
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}
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}
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59
// constructor
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Matrix::Matrix(int row,int col):m_row(row),m_col(col)
61
{
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if(row<=0)
63
{
64
m_row=0;
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m_col=0;
66
m_data=0;
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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;
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m_col=0;
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m_data=0;
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ostringstream oss;
79
oss<<" In Matrix::Matrix(int row,int col),col "<<col<<" <=0.Pleasecheck it.";
80
throw oss.str();
81
}
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m_data=new double*[row];
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for(int i=0;i<row;i++)
85
{
86
m_data[i]=new double[col];
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}
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}
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//copy constructor
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Matrix::Matrix(const Matrix& m):m_row(m.m_row),m_col(m.m_col)
92
{
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m_data = new double*[m_row];
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for(int i=0;i<m_row;i++)
95
{
96
m_data[i] = new double[m_col];
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}
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for(int i=0;i<m_row;i++)
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{
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copy(m.m_data[i],m.m_data[i]+m_col,m_data[i]);
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}
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}
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Matrix::~Matrix()
107
{
108
if(m_data != 0)
109
{
110
for(int i=0;i<m_row;i++)
111
{
112
delete[] m_data[i];
113
}
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delete[] m_data;
115
}
116
}
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void Matrix::SetZero()
119
{
120
for(int i=0;i<m_row;i++)
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fill(m_data[i],m_data[i]+m_col,0);
122
}
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void Matrix::SetUnit()
125
{
126
for(int i=0;i<m_row;i++)
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for(int j=0;j<m_col;j++)
128
m_data[i][j] = (i==j)?1:0;
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}
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131
void Matrix::SetSize(int size)
132
{
133
Clear();
134
Create(size,size);
135
}
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void Matrix::SetSize(int row,int col)
139
{
140
Clear();
141
Create(row,col);
142
}
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void Matrix::Clear()
146
{
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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
}
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m_row=0;
158
m_col=0;
159
m_data=0;
160
}
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162
/*
163
Matrix& 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.";
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170
throw oss.str();
171
}
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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
}
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m_row=size;
183
m_col=size;
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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
203
void 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
237
int Matrix::GetRow() const
238
{
239
return m_row;
240
}
241
242
int Matrix::GetCol() const
243
{
244
return m_col;
245
}
246
247
//transpose 转置
248
Matrix 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
261
int 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
275
Matrix& 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
}
290
291
for(int k=0;k<m_col;k++)
292
{
293
swap(m_data[i][k],m_data[j][k]);
294
}
295
296
return *this;
297
}
298
299
300
Matrix& Matrix::Multiple(int index,double mul) //初等变换 第index 行乘以mul
301
{
302
if(index <0 || index >= m_row)
303
{
304
ostringstream oss;
305
oss<<"In void Matrix::Multiple(int index,double k) index "<<index<<" out of bounds.Please check it.";
306
throw oss.str();
307
}
308
309
transform(m_data[index],m_data[index]+m_col,m_data[index],bind2nd(multiplies<double>(),mul));
310
return *this;
311
}
312
313
314
Matrix& Matrix::MultipleAdd(int index,int src,double mul) //初等变换 第src行乘以mul加到第index行
315
{
316
if(index <0 || index >= m_row)
317
{
318
ostringstream oss;
319
oss<<"In void MultipleAdd(int index,int src,double k) index "<<index<<" out of bounds.Please check it.";
320
throw oss.str();
321
}
322
323
if(src < 0 || src >= m_row)
324
{
325
ostringstream oss;
326
oss<<"In void MultipleAdd(int index,int src,double k) src "<<src<<" out of bounds.Please check it.";
327
throw oss.str();
328
}
329
330
for(int j=0;j<m_col;j++)
331
{
332
m_data[index][j] += m_data[src][j] * mul;
333
}
334
335
return *this;
336
337
}
338
339
340
//inverse 逆阵:使用矩阵的初等变换,列主元素消去法
341
Matrix Matrix::Inverse() const
342
{
343
if(m_row != m_col) //非方阵
344
{
345
ostringstream oss;
346
oss<<"In Matrix Matrix::Invert() const. m_row "<<m_row<<" != m_col "<<m_col<<" Please check it";
347
throw oss.str();
348
}
349
350
Matrix tmp(*this);
351
Matrix ret(m_row); //单位阵
352
ret.SetUnit();
353
354
int maxIndex;
355
double dMul;
356
357
for(int i=0;i<m_row;i++)
358
{
359
360
maxIndex = tmp.Pivot(i);
361
362
if(tmp.m_data[maxIndex][i]==0)
363
{
364
ostringstream oss;
365
oss<<"In Matrix Matrix::Invert() const 行列式的值等于0.Please check it";
366
throw oss.str();
367
}
368
369
if(maxIndex != i) //下三角阵中此列的最大值不在当前行,交换
370
{
371
tmp.Exchange(i,maxIndex);
372
ret.Exchange(i,maxIndex);
373
374
}
375
376
ret.Multiple(i,1/tmp.m_data[i][i]);
377
tmp.Multiple(i,1/tmp.m_data[i][i]);
378
379
380
for(int j=i+1;j<m_row;j++)
381
{
382
dMul = -tmp.m_data[j][i];
383
tmp.MultipleAdd(j,i,dMul);
384
ret.MultipleAdd(j,i,dMul);
385
386
}
387
388
}//end for
389
390
for(int i=m_row-1;i>0;i--)
391
{
392
for(int j=i-1;j>=0;j--)
393
{
394
dMul = -tmp.m_data[j][i];
395
tmp.MultipleAdd(j,i,dMul);
396
ret.MultipleAdd(j,i,dMul);
397
}
398
}//end for
399
400
return ret;
401
}
402
403
404
405
// assignment operator 賦值运算符
406
Matrix& Matrix::operator= (const Matrix& m)
407
{
408
if(m_data != 0)
409
{
410
for(int i=0;i<m_row;i++)
411
{
412
delete[] m_data[i];
413
}
414
delete[] m_data;
415
}
416
417
m_row = m.m_row;
418
m_col = m.m_col;
419
420
m_data = new double*[m_row];
421
for(int i=0;i< m_row;i++)
422
{
423
m_data[i] = new double[m_col];
424
}
425
426
for(int i=0;i<m_row;i++)
427
{
428
copy(m.m_data[i],m.m_data[i]+m_col,m_data[i]);
429
}
430
return *this;
431
}
432
433
434
//binary addition 矩阵加
435
Matrix Matrix::operator+ (const Matrix& m) const
436
{
437
if(m_row != m.m_row)
438
{
439
ostringstream oss;
440
oss<<"In Matrix::operator+(const Matrix& m) this->m_row "<<m_row<<" != m.m_row "<<m.m_row<<" Please check it.";
441
throw oss.str();
442
}
443
if(m_col != m.m_col)
444
{
445
ostringstream oss;
446
oss<<" Matrix::operator+ (const Matrix& m) this->m_col "<<m_col<<" != m.m_col "<<m.m_col<<" Please check it.";
447
throw oss.str();
448
}
449
450
Matrix ret(m_row,m_col);
451
for(int i=0;i<m_row;i++)
452
{
453
transform(m_data[i],m_data[i]+m_col,m.m_data[i],ret.m_data[i],plus<double>());
454
}
455
return ret;
456
}
457
458
//unary addition 求正
459
Matrix Matrix::operator+() const
460
{
461
return *this;
462
}
463
464
//binary subtraction 矩阵减
465
Matrix Matrix::operator- (const Matrix& m) const
466
{
467
if(m_row != m.m_row)
468
{
469
ostringstream oss;
470
oss<<"In Matrix::operator-(const Matrix& m) this->m_row "<<m_row<<" != m.m_row "<<m.m_row<<" Please check it.";
471
throw oss.str();
472
}
473
if(m_col != m.m_col)
474
{
475
ostringstream oss;
476
oss<<"In Matrix::operator- (const Matrix& m) this->m_col "<<m_col<<" != m.m_col "<<m.m_col<<" Please check it.";
477
throw oss.str();
478
}
479
480
Matrix ret(m_row,m_col);
481
for(int i=0;i<m_row;i++)
482
{
483
transform(m_data[i],m_data[i]+m_col,m.m_data[i],ret.m_data[i],minus<double>());
484
}
485
return ret;
486
}
487
488
//unary substraction 求负
489
Matrix Matrix::operator-() const
490
{
491
Matrix ret(*this);
492
493
for(int i=0;i<m_row;i++)
494
for(int j=0;j<m_col;j++)
495
ret.m_data[i][j] *= -1;
496
497
return ret;
498
499
}
500
501
502
//binary multiple 矩阵乘
503
Matrix Matrix::operator*(const Matrix& m) const
504
{
505
if(m_col != m.m_row)
506
{
507
ostringstream oss;
508
oss<<"In Matrix::operator*(const Matrix& m) this->m_col "<<m_col<<" != m.m_row "<<m.m_row<<" Please check it.";
509
throw oss.str();
510
}
511
512
Matrix ret(m_row,m.m_col);
513
Matrix tmp=m.Transpose();
514
515
for(int i=0;i<m_row;i++)
516
{
517
for(int j=0;j<m.m_col;j++)
518
{
519
ret.m_data[i][j]=inner_product(m_data[i],m_data[i]+m_col,tmp.m_data[j],0.0);
520
}
521
}
522
523
return ret;;
524
}
525
526
//friend scalar multiple 数乘
527
Matrix operator* (double d,const Matrix& m)
528
{
529
Matrix ret(m);
530
531
for(int i=0;i<ret.m_row;i++)
532
for(int j=0;j<ret.m_col;j++)
533
ret.m_data[i][j] *= d;
534
535
return ret;
536
537
}
538
539
//binary matrix division equivalent to multiple inverse矩阵除,等价于乘以逆阵
540
Matrix Matrix::operator/(const Matrix& m) const
541
{
542
return *this * m.Inverse();
543
}
544
545
//binary scalar division equivalent to multiple reciprocal数除,等价于乘以此数的倒数
546
Matrix Matrix::operator/(double d) const
547
{
548
return 1/d * (*this);
549
}
550
551
//friend division
552
Matrix operator/(double d,const Matrix& m)
553
{
554
return d * m.Inverse();
555
}
556
557
558
// subscript operator to get individual elements 下标运算符
559
double Matrix::operator()(int i,int j) const
560
{
561
if(i<0 || i>= m_row)
562
{
563
ostringstream oss;
564
oss<<"In double Matrix::operator()(int i,int j) const.i "<<i<<" out of bounds.Please check it";
565
throw oss.str();
566
}
567
if(j<0 || j>= m_col)
568
{
569
ostringstream oss;
570
oss<<"In double Matrix::operator()(int i,int j) const.j "<<j<<" out of bounds.Please check it";
571
throw oss.str();
572
}
573
574
return m_data[i][j];
575
}
576
577
// subscript operator to set individual elements 下标运算符
578
double& Matrix::operator ()(int i,int j)
579
{
580
if(i<0 || i>= m_row)
581
{
582
ostringstream oss;
583
oss<<"In double Matrix::operator()(int i,int j) const.i "<<i<<" out of bounds.Please check it";
584
throw oss.str();
585
}
586
if(j<0 || j>= m_col)
587
{
588
ostringstream oss;
589
oss<<"In double Matrix::operator()(int i,int j) const.j "<<j<<" out of bounds.Please check it";
590
throw oss.str();
591
}
592
593
return m_data[i][j];
594
}
595
596
//to string 化为标准串
597
string Matrix::ToString() const
598
{
599
ostringstream oss;
600
for(int i=0;i<m_row;i++)
601
{
602
copy(m_data[i],m_data[i]+m_col,ostream_iterator<double>(oss," "));
603
oss<<"\n";
604
}
605
606
return oss.str();
607
}
608
609
// outputt stream function 输出
610
611
ostream& operator<<(ostream& os,const Matrix& m)
612
{
613
for(int i=0;i<m.m_row;i++)
614
{
615
copy(m.m_data[i],m.m_data[i]+m.m_col,ostream_iterator<double>(os," "));
616
os<<'\n';
617
}
618
return os;
619
}
620
621
// input stream function 输入
622
istream& operator>>(istream& is,Matrix& m)
623
{
624
for(int i=0;i<m.m_row;i++)
625
{
626
for(int j=0;j<m.m_col;j++)
627
{
628
is>>m.m_data[i][j];
629
}
630
}
631
return is;
632
}
633
634
635
// reallocation method
636
637
// public method for resizing matrix
638
639
// logical equal-to operator
640
641
// logical no-equal-to operator
642
643
// combined addition and assignment operator
644
645
// combined subtraction and assignment operator
646
647
// combined scalar multiplication and assignment operator
648
649
650
// combined matrix multiplication and assignment operator
651
652
// combined scalar division and assignment operator
653
654
// combined power and assignment operator
655
656
// unary negation operator
657
658
// binary addition operator
659
660
// binary subtraction operator
661
662
// binary scalar multiplication operator
663
664
// binary scalar multiplication operator
665
666
// binary matrix multiplication operator
667
668
// binary scalar division operator
669
670
671
// binary scalar division operator
672
673
// binary matrix division operator
674
675
// binary power operator
676
677
// unary transpose operator
678
679
// unary Inverse operator
680
681
// Inverse function
682
683
// solve simultaneous equation
684
685
// set zero to all elements of this matrix
686
687
// set this matrix to unity
688
689
// private partial pivoting method
690
691
// calculate the determinant of a matrix
692
693
// calculate the norm of a matrix
694
695
// calculate the condition number of a matrix
696
697
// calculate the cofactor of a matrix for a given element
698
699
// calculate adjoin of a matrix
700
701
// Determine if the matrix is singular
702
703
// Determine if the matrix is diagonal
704
705
// Determine if the matrix is scalar
706
707
// Determine if the matrix is a unit matrix
708
709
// Determine if this is a null matrix
710
711
// Determine if the matrix is symmetric
712
713
// Determine if the matrix is skew-symmetric
714
// Determine if the matrix is upper triangular
715
716
// Determine if the matrix is lower triangular

2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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15
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16
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17
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18
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19
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20
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21
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22
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23
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24
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25
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26
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27
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28
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29
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30
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31
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32
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33
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34
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35
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36
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37
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38
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39
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40
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41
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42
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43
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44
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45
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46
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47
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48
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49
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50
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340
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341
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342
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357
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358
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359
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360
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361
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362
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363
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364
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365
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366
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367
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368
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369
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370
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371
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372
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373
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374
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375
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376
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377
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378
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379
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380
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381
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382
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383
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384
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385
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386
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387
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388
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389
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390
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391
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392
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393
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394
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395
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396
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397
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398
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399
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400
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401
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402
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403
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404
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405
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406
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407
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408
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409
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410
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411
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412
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413
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414
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415
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416
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417
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418
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419
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420
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421
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422
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423
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424
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425
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426
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427
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428
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429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486

487

488

489

490

491

492

493

494

495

496

497

498

499

500

501

502

503

504

505

506

507

508

509

510

511

512

513

514

515

516

517

518

519

520

521

522

523

524

525

526

527

528

529

530

531

532

533

534

535

536

537

538

539

540

541

542

543

544

545

546

547

548

549

550

551

552

553

554

555

556

557

558

559

560

561

562

563

564

565

566

567

568

569

570

571

572

573

574

575

576

577

578

579

580

581

582

583

584

585

586

587

588

589

590

591

592

593

594

595

596

597

598

599

600

601

602

603

604

605

606

607

608

609

610

611

612

613

614

615

616

617

618

619

620

621

622

623

624

625

626

627

628

629

630

631

632

633

634

635

636

637

638

639

640

641

642

643

644

645

646

647

648

649

650

651

652

653

654

655

656

657

658

659

660

661

662

663

664

665

666

667

668

669

670

671

672

673

674

675

676

677

678

679

680

681

682

683

684

685

686

687

688

689

690

691

692

693

694

695

696

697

698

699

700

701

702

703

704

705

706

707

708

709

710

711

712

713

714

715

716

另有标准C语言版本。