函数
Matrix(Index_T r, Index_T c) :m_row(r), m_col(c)//非方阵构造
Matrix(Index_T r, Index_T c, double val ) :m_row(r), m_col(c)// 赋初值val
Matrix(Index_T n) :m_row(n), m_col(n)//方阵构造 Matrix(const Matrix &rhs)//拷贝构造 Matrix &operator=(const Matrix&); //如果类成员有指针必须重写赋值运算符，必须是成员
friend istream &operator>>(istream&, Matrix&);
friend ofstream &operator<<(ofstream &out, Matrix &obj); // 输出到文件
friend ostream &operator<<(ostream&, Matrix&); // 输出到屏幕
friend Matrix &operator<<(Matrix &mat, const double val);
friend Matrix& operator,(Matrix &obj, const double val);
friend Matrix operator+(const Matrix&, const Matrix&);
friend Matrix operator-(const Matrix&, const Matrix&);
friend Matrix operator*(const Matrix&, const Matrix&); //矩阵乘法
friend Matrix operator*(double, const Matrix&); //矩阵乘法
friend Matrix operator*(const Matrix&, double); //矩阵乘法
friend Matrix operator/(const Matrix&, double); //矩阵 除以单数
Matrix multi(const Matrix&); // 对应元素相乘
Matrix mtanh(); // 对应元素相乘
Index_T row()const{ return m_row; }
Index_T col()const{ return m_col; }
Matrix getrow(Index_T index); // 返回第index 行,索引从0 算起
Matrix getcol(Index_T index); // 返回第index 列
Matrix cov(_In_opt_ bool flag = true); //协方差阵 或者样本方差
double det(); //行列式
Matrix solveAb(Matrix &obj); // b是行向量或者列向量
Matrix diag(); //返回对角线元素
//Matrix asigndiag(); //对角线元素
Matrix T()const; //转置
void sort(bool);//true为从小到大
Matrix adjoint();
Matrix inverse();
void QR(_Out_ Matrix&, _Out_ Matrix&)const;
Matrix eig_val(_In_opt_ Index_T _iters = 1000);
Matrix eig_vect(_In_opt_ Index_T _iters = 1000);
double norm1();//1范数
double norm2();//2范数
double mean();// 矩阵均值
double*operator[](Index_T i){ return m_ptr + i*m_col; }//注意this加括号， (*this)[i][j]
void zeromean(_In_opt_ bool flag = true);//默认参数为true计算列
void normalize(_In_opt_ bool flag = true);//默认参数为true计算列
Matrix exponent(double x);//每个元素x次幂
Matrix eye();//对角阵
void maxlimit(double max,double set=0);//对角阵
源码
#include <iostream>
#include <fstream>
#include <stdlib.h>
#include <cmath>
using namespace std;
#ifndef _In_opt_
#define _In_opt_
#endif
#ifndef _Out_
#define _Out_
#endif
typedef unsigned Index_T;
class Matrix
{
private:
Index_T m_row, m_col;
Index_T m_size;
Index_T m_curIndex;
double *m_ptr;//数组指针
public:
Matrix(Index_T r, Index_T c) :m_row(r), m_col(c)//非方阵构造
{
m_size = r*c;
if (m_size>0)
{
m_ptr = new double[m_size];
}
else
m_ptr = NULL;
};
Matrix(Index_T r, Index_T c, double val ) :m_row(r), m_col(c)// 赋初值val
{
m_size = r*c;
if (m_size>0)
{
m_ptr = new double[m_size];
}
else
m_ptr = NULL;
};
Matrix(Index_T n) :m_row(n), m_col(n)//方阵构造
{
m_size = n*n;
if (m_size>0)
{
m_ptr = new double[m_size];
}
else
m_ptr = NULL;
};
Matrix(const Matrix &rhs)//拷贝构造
{
m_row = rhs.m_row;
m_col = rhs.m_col;
m_size = rhs.m_size;
m_ptr = new double[m_size];
for (Index_T i = 0; i<m_size; i++)
m_ptr[i] = rhs.m_ptr[i];
}
~Matrix()
{
if (m_ptr != NULL)
{
delete[]m_ptr;
m_ptr = NULL;
}
}
Matrix &operator=(const Matrix&); //如果类成员有指针必须重写赋值运算符，必须是成员
friend istream &operator>>(istream&, Matrix&);
friend ofstream &operator<<(ofstream &out, Matrix &obj); // 输出到文件
friend ostream &operator<<(ostream&, Matrix&); // 输出到屏幕
friend Matrix &operator<<(Matrix &mat, const double val);
friend Matrix& operator,(Matrix &obj, const double val);
friend Matrix operator+(const Matrix&, const Matrix&);
friend Matrix operator-(const Matrix&, const Matrix&);
friend Matrix operator*(const Matrix&, const Matrix&); //矩阵乘法
friend Matrix operator*(double, const Matrix&); //矩阵乘法
friend Matrix operator*(const Matrix&, double); //矩阵乘法
friend Matrix operator/(const Matrix&, double); //矩阵 除以单数
Matrix multi(const Matrix&); // 对应元素相乘
Matrix mtanh(); // 对应元素相乘
Index_T row()const{ return m_row; }
Index_T col()const{ return m_col; }
Matrix getrow(Index_T index); // 返回第index 行,索引从0 算起
Matrix getcol(Index_T index); // 返回第index 列
Matrix cov(_In_opt_ bool flag = true); //协方差阵 或者样本方差
double det(); //行列式
Matrix solveAb(Matrix &obj); // b是行向量或者列向量
Matrix diag(); //返回对角线元素
//Matrix asigndiag(); //对角线元素
Matrix T()const; //转置
void sort(bool);//true为从小到大
Matrix adjoint();
Matrix inverse();
void QR(_Out_ Matrix&, _Out_ Matrix&)const;
Matrix eig_val(_In_opt_ Index_T _iters = 1000);
Matrix eig_vect(_In_opt_ Index_T _iters = 1000);
double norm1();//1范数
double norm2();//2范数
double mean();// 矩阵均值
double*operator[](Index_T i){ return m_ptr + i*m_col; }//注意this加括号， (*this)[i][j]
void zeromean(_In_opt_ bool flag = true);//默认参数为true计算列
void normalize(_In_opt_ bool flag = true);//默认参数为true计算列
Matrix exponent(double x);//每个元素x次幂
Matrix eye();//对角阵
void maxlimit(double max,double set=0);//对角阵
};
/*
类方法的实现
*/
Matrix Matrix::mtanh() // 对应元素 tanh()
{
Matrix ret(m_row, m_col);
for (Index_T i = 0; i<ret.m_size; i++)
{
ret.m_ptr[i] = tanh(m_ptr[i]);
}
return ret;
}
/*
* 递归调用
*/
double calcDet(Index_T n, double *&aa)
{
if (n == 1)
return aa[0];
double *bb = new double[(n - 1)*(n - 1)];//创建n-1阶的代数余子式阵bb
double sum = 0.0;
for (Index_T Ai = 0; Ai<n; Ai++)
{
for (Index_T Bi = 0; Bi < n - 1; Bi++)//把aa阵第一列各元素的代数余子式存到bb
{
Index_T offset = Bi < Ai ? 0 : 1; //bb中小于Ai的行，同行赋值，等于的错过，大于的加一
for (Index_T j = 0; j<n - 1; j++)
{
bb[Bi*(n - 1) + j] = aa[(Bi + offset)*n + j + 1];
}
}
int flag = (Ai % 2 == 0 ? 1 : -1);//因为列数为0，所以行数是偶数时候，代数余子式为1.
sum += flag* aa[Ai*n] * calcDet(n - 1, bb);//aa第一列各元素与其代数余子式积的和即为行列式
}
delete[]bb;
return sum;
}
Matrix Matrix::solveAb(Matrix &obj)
{
Matrix ret(m_row, 1);
if (m_size == 0 || obj.m_size == 0)
{
cout << "solveAb(Matrix &obj):this or obj is null" << endl;
return ret;
}
if (m_row != obj.m_size)
{
cout << "solveAb(Matrix &obj):the row of two matrix is not equal!" << endl;
return ret;
}
double *Dx = new double[m_row*m_row];
for (Index_T i = 0; i<m_row; i++)
{
for (Index_T j = 0; j<m_row; j++)
{
Dx[i*m_row + j] = m_ptr[i*m_row + j];
}
}
double D = calcDet(m_row, Dx);
if (D == 0)
{
cout << "Cramer法则只能计算系数矩阵为满秩的矩阵" << endl;
return ret;
}
for (Index_T j = 0; j<m_row; j++)
{
for (Index_T i = 0; i<m_row; i++)
{
for (Index_T j = 0; j<m_row; j++)
{
Dx[i*m_row + j] = m_ptr[i*m_row + j];
}
}
for (Index_T i = 0; i<m_row; i++)
{
Dx[i*m_row + j] = obj.m_ptr[i]; //obj赋值给第j列
}
//for( int i=0;i<m_row;i++) //print
//{
// for(int j=0; j<m_row;j++)
// {
// cout<< Dx[i*m_row+j]<<"\t";
// }
// cout<<endl;
//}
ret[j][0] = calcDet(m_row, Dx) / D;
}
delete[]Dx;
return ret;
}
Matrix Matrix::getrow(Index_T index)//返回行
{
Matrix ret(1, m_col); //一行的返回值
for (Index_T i = 0; i< m_col; i++)
{
ret[0][i] = m_ptr[(index) *m_col + i] ;
}
return ret;
}
Matrix Matrix::getcol(Index_T index)//返回列
{
Matrix ret(m_row, 1); //一列的返回值
for (Index_T i = 0; i< m_row; i++)
{
ret[i][0] = m_ptr[i *m_col + index];
}
return ret;
}
Matrix Matrix::exponent(double x)//每个元素x次幂
{
Matrix ret(m_row, m_col);
for (Index_T i = 0; i< m_row; i++)
{
for (Index_T j = 0; j < m_col; j++)
{
ret[i][j]= pow(m_ptr[i*m_col + j],x);
}
}
return ret;
}
void Matrix::maxlimit(double max, double set)//每个元素x次幂
{
for (Index_T i = 0; i< m_row; i++)
{
for (Index_T j = 0; j < m_col; j++)
{
m_ptr[i*m_col + j] = m_ptr[i*m_col + j]>max ? 0 : m_ptr[i*m_col + j];
}
}
}
Matrix Matrix::eye()//对角阵
{
for (Index_T i = 0; i< m_row; i++)
{
for (Index_T j = 0; j < m_col; j++)
{
if (i == j)
{
m_ptr[i*m_col + j] = 1.0;
}
}
}
return *this;
}
void Matrix::zeromean(_In_opt_ bool flag)
{
if (flag == true) //计算列均值
{
double *mean = new double[m_col];
for (Index_T j = 0; j < m_col; j++)
{
mean[j] = 0.0;
for (Index_T i = 0; i < m_row; i++)
{
mean[j] += m_ptr[i*m_col + j];
}
mean[j] /= m_row;
}
for (Index_T j = 0; j < m_col; j++)
{
for (Index_T i = 0; i < m_row; i++)
{
m_ptr[i*m_col + j] -= mean[j];
}
}
delete[]mean;
}
else //计算行均值
{
double *mean = new double[m_row];
for (Index_T i = 0; i< m_row; i++)
{
mean[i] = 0.0;
for (Index_T j = 0; j < m_col; j++)
{
mean[i] += m_ptr[i*m_col + j];
}
mean[i] /= m_col;
}
for (Index_T i = 0; i < m_row; i++)
{
for (Index_T j = 0; j < m_col; j++)
{
m_ptr[i*m_col + j] -= mean[i];
}
}
delete[]mean;
}
}
void Matrix::normalize(_In_opt_ bool flag)
{
if (flag == true) //计算列均值
{
double *mean = new double[m_col];
for (Index_T j = 0; j < m_col; j++)
{
mean[j] = 0.0;
for (Index_T i = 0; i < m_row; i++)
{
mean[j] += m_ptr[i*m_col + j];
}
mean[j] /= m_row;
}
for (Index_T j = 0; j < m_col; j++)
{
for (Index_T i = 0; i < m_row; i++)
{
m_ptr[i*m_col + j] -= mean[j];
}
}
///计算标准差
for (Index_T j = 0; j < m_col; j++)
{
mean[j] = 0;
for (Index_T i = 0; i < m_row; i++)
{
mean[j] += pow(m_ptr[i*m_col + j],2);//列平方和
}
mean[j] = sqrt(mean[j] / m_row); // 开方
}
for (Index_T j = 0; j < m_col; j++)
{
for (Index_T i = 0; i < m_row; i++)
{
m_ptr[i*m_col + j] /= mean[j];//列平方和
}
}
delete[]mean;
}
else //计算行均值
{
double *mean = new double[m_row];
for (Index_T i = 0; i< m_row; i++)
{
mean[i] = 0.0;
for (Index_T j = 0; j < m_col; j++)
{
mean[i] += m_ptr[i*m_col + j];
}
mean[i] /= m_col;
}
for (Index_T i = 0; i < m_row; i++)
{
for (Index_T j = 0; j < m_col; j++)
{
m_ptr[i*m_col + j] -= mean[i];
}
}
///计算标准差
for (Index_T i = 0; i< m_row; i++)
{
mean[i] = 0.0;
for (Index_T j = 0; j < m_col; j++)
{
mean[i] += pow(m_ptr[i*m_col + j], 2);//列平方和
}
mean[i] = sqrt(mean[i] / m_col); // 开方
}
for (Index_T i = 0; i < m_row; i++)
{
for (Index_T j = 0; j < m_col; j++)
{
m_ptr[i*m_col + j] /= mean[i];
}
}
delete[]mean;
}
}
double Matrix::det()
{
if (m_col == m_row)
return calcDet(m_row, m_ptr);
else
{
cout << ("行列不相等无法计算") << endl;
return 0;
}
}
/////////////////////////////////////////////////////////////////////
istream& operator>>(istream &is, Matrix &obj)
{
for (Index_T i = 0; i<obj.m_size; i++)
{
is >> obj.m_ptr[i];
}
return is;
}
ostream& operator<<(ostream &out, Matrix &obj)
{
for (Index_T i = 0; i < obj.m_row; i++) //打印逆矩阵
{
for (Index_T j = 0; j < obj.m_col; j++)
{
out << (obj[i][j]) << "\t";
}
out << endl;
}
return out;
}
ofstream& operator<<(ofstream &out, Matrix &obj)//打印逆矩阵到文件
{
for (Index_T i = 0; i < obj.m_row; i++)
{
for (Index_T j = 0; j < obj.m_col; j++)
{
out << (obj[i][j]) << "\t";
}
out << endl;
}
return out;
}
Matrix& operator<<(Matrix &obj, const double val)
{
*obj.m_ptr = val;
obj.m_curIndex = 1;
return obj;
}
Matrix& operator,(Matrix &obj, const double val)
{
if( obj.m_curIndex == 0 || obj.m_curIndex > obj.m_size - 1 )
{
return obj;
}
*(obj.m_ptr + obj.m_curIndex) = val;
++obj.m_curIndex;
return obj;
}
Matrix operator+(const Matrix& lm, const Matrix& rm)
{
if (lm.m_col != rm.m_col || lm.m_row != rm.m_row)
{
Matrix temp(0, 0);
temp.m_ptr = NULL;
cout << "operator+(): 矩阵shape 不合适,m_col:"
<< lm.m_col << "," << rm.m_col << ". m_row:" << lm.m_row << ", " << rm.m_row << endl;
return temp; //数据不合法时候，返回空矩阵
}
Matrix ret(lm.m_row, lm.m_col);
for (Index_T i = 0; i<ret.m_size; i++)
{
ret.m_ptr[i] = lm.m_ptr[i] + rm.m_ptr[i];
}
return ret;
}
Matrix operator-(const Matrix& lm, const Matrix& rm)
{
if (lm.m_col != rm.m_col || lm.m_row != rm.m_row)
{
Matrix temp(0, 0);
temp.m_ptr = NULL;
cout << "operator-(): 矩阵shape 不合适,m_col:"
<<lm.m_col<<","<<rm.m_col<<". m_row:"<< lm.m_row <<", "<< rm.m_row << endl;
return temp; //数据不合法时候，返回空矩阵
}
Matrix ret(lm.m_row, lm.m_col);
for (Index_T i = 0; i<ret.m_size; i++)
{
ret.m_ptr[i] = lm.m_ptr[i] - rm.m_ptr[i];
}
return ret;
}
Matrix operator*(const Matrix& lm, const Matrix& rm) //矩阵乘法
{
if (lm.m_size == 0 || rm.m_size == 0 || lm.m_col != rm.m_row)
{
Matrix temp(0, 0);
temp.m_ptr = NULL;
cout << "operator*(): 矩阵shape 不合适,m_col:"
<< lm.m_col << "," << rm.m_col << ". m_row:" << lm.m_row << ", " << rm.m_row << endl;
return temp; //数据不合法时候，返回空矩阵
}
Matrix ret(lm.m_row, rm.m_col);
for (Index_T i = 0; i<lm.m_row; i++)
{
for (Index_T j = 0; j< rm.m_col; j++)
{
for (Index_T k = 0; k< lm.m_col; k++)//lm.m_col == rm.m_row
{
ret.m_ptr[i*rm.m_col + j] += lm.m_ptr[i*lm.m_col + k] * rm.m_ptr[k*rm.m_col + j];
}
}
}
return ret;
}
Matrix operator*(double val, const Matrix& rm) //矩阵乘 单数
{
Matrix ret(rm.m_row, rm.m_col);
for (Index_T i = 0; i<ret.m_size; i++)
{
ret.m_ptr[i] = val * rm.m_ptr[i];
}
return ret;
}
Matrix operator*(const Matrix&lm, double val) //矩阵乘 单数
{
Matrix ret(lm.m_row, lm.m_col);
for (Index_T i = 0; i<ret.m_size; i++)
{
ret.m_ptr[i] = val * lm.m_ptr[i];
}
return ret;
}
Matrix operator/(const Matrix&lm, double val) //矩阵除以 单数
{
Matrix ret(lm.m_row, lm.m_col);
for (Index_T i = 0; i<ret.m_size; i++)
{
ret.m_ptr[i] = lm.m_ptr[i]/val;
}
return ret;
}
Matrix Matrix::multi(const Matrix&rm)// 对应元素相乘
{
if (m_col != rm.m_col || m_row != rm.m_row)
{
Matrix temp(0, 0);
temp.m_ptr = NULL;
cout << "multi(const Matrix&rm): 矩阵shape 不合适,m_col:"
<< m_col << "," << rm.m_col << ". m_row:" << m_row << ", " << rm.m_row << endl;
return temp; //数据不合法时候，返回空矩阵
}
Matrix ret(m_row,m_col);
for (Index_T i = 0; i<ret.m_size; i++)
{
ret.m_ptr[i] = m_ptr[i] * rm.m_ptr[i];
}
return ret;
}
Matrix& Matrix::operator=(const Matrix& rhs)
{
if (this != &rhs)
{
m_row = rhs.m_row;
m_col = rhs.m_col;
m_size = rhs.m_size;
if (m_ptr != NULL)
delete[] m_ptr;
m_ptr = new double[m_size];
for (Index_T i = 0; i<m_size; i++)
{
m_ptr[i] = rhs.m_ptr[i];
}
}
return *this;
}
//||matrix||_2 求A矩阵的2范数
double Matrix::norm2()
{
double norm = 0;
for (Index_T i = 0; i < m_size; ++i)
{
norm += m_ptr[i] * m_ptr[i];
}
return (double)sqrt(norm);
}
double Matrix::norm1()
{
double sum = 0;
for (Index_T i = 0; i < m_size; ++i)
{
sum += abs(m_ptr[i]);
}
return sum;
}
double Matrix::mean()
{
double sum = 0;
for (Index_T i = 0; i < m_size; ++i)
{
sum += (m_ptr[i]);
}
return sum/m_size;
}
void Matrix::sort(bool flag)
{
double tem;
for (Index_T i = 0; i<m_size; i++)
{
for (Index_T j = i + 1; j<m_size; j++)
{
if (flag == true)
{
if (m_ptr[i]>m_ptr[j])
{
tem = m_ptr[i];
m_ptr[i] = m_ptr[j];
m_ptr[j] = tem;
}
}
else
{
if (m_ptr[i]<m_ptr[j])
{
tem = m_ptr[i];
m_ptr[i] = m_ptr[j];
m_ptr[j] = tem;
}
}
}
}
}
Matrix Matrix::diag()
{
if (m_row != m_col)
{
Matrix m(0);
cout << "diag():m_row != m_col" << endl;
return m;
}
Matrix m(m_row);
for (Index_T i = 0; i<m_row; i++)
{
m.m_ptr[i*m_row + i] = m_ptr[i*m_row + i];
}
return m;
}
Matrix Matrix::T()const
{
Matrix tem(m_col, m_row);
for (Index_T i = 0; i<m_row; i++)
{
for (Index_T j = 0; j<m_col; j++)
{
tem[j][i] = m_ptr[i*m_col + j];// (*this)[i][j]
}
}
return tem;
}
void Matrix::QR(Matrix &Q, Matrix &R) const
{
//如果A不是一个二维方阵，则提示错误，函数计算结束
if (m_row != m_col)
{
printf("ERROE: QR() parameter A is not a square matrix!\n");
return;
}
const Index_T N = m_row;
double *a = new double[N];
double *b = new double[N];
for (Index_T j = 0; j < N; ++j) //(Gram-Schmidt) 正交化方法
{
for (Index_T i = 0; i < N; ++i) //第j列的数据存到a，b
a[i] = b[i] = m_ptr[i * N + j];
for (Index_T i = 0; i<j; ++i) //第j列之前的列
{
R.m_ptr[i * N + j] = 0; //
for (Index_T m = 0; m < N; ++m)
{
R.m_ptr[i * N + j] += a[m] * Q.m_ptr[m *N + i]; //R[i,j]值为Q第i列与A的j列的内积
}
for (Index_T m = 0; m < N; ++m)
{
b[m] -= R.m_ptr[i * N + j] * Q.m_ptr[m * N + i]; //
}
}
double norm = 0;
for (Index_T i = 0; i < N; ++i)
{
norm += b[i] * b[i];
}
norm = (double)sqrt(norm);
R.m_ptr[j*N + j] = norm; //向量b[]的2范数存到R[j,j]
for (Index_T i = 0; i < N; ++i)
{
Q.m_ptr[i * N + j] = b[i] / norm; //Q 阵的第j列为单位化的b[]
}
}
delete[]a;
delete[]b;
}
Matrix Matrix::eig_val(_In_opt_ Index_T _iters)
{
if (m_size == 0 || m_row != m_col)
{
cout << "矩阵为空或者非方阵！" << endl;
Matrix rets(0);
return rets;
}
//if (det() == 0)
//{
// cout << "非满秩矩阵没法用QR分解计算特征值！" << endl;
// Matrix rets(0);
// return rets;
//}
const Index_T N = m_row;
Matrix matcopy(*this);//备份矩阵
Matrix Q(N), R(N);
/*当迭代次数足够多时,A 趋于上三角矩阵，上三角矩阵的对角元就是A的全部特征值。*/
for (Index_T k = 0; k < _iters; ++k)
{
//cout<<"this:\n"<<*this<<endl;
QR(Q, R);
*this = R*Q;
/* cout<<"Q:\n"<<Q<<endl;
cout<<"R:\n"<<R<<endl; */
}
Matrix val = diag();
*this = matcopy;//恢复原始矩阵；
return val;
}
Matrix Matrix::eig_vect(_In_opt_ Index_T _iters)
{
if (m_size == 0 || m_row != m_col)
{
cout << "矩阵为空或者非方阵！" << endl;
Matrix rets(0);
return rets;
}
if (det() == 0)
{
cout << "非满秩矩阵没法用QR分解计算特征向量！" << endl;
Matrix rets(0);
return rets;
}
Matrix matcopy(*this);//备份矩阵
Matrix eigenValue = eig_val(_iters);
Matrix ret(m_row);
const Index_T NUM = m_col;
double eValue;
double sum, midSum, diag;
Matrix copym(*this);
for (Index_T count = 0; count < NUM; ++count)
{
//计算特征值为eValue，求解特征向量时的系数矩阵
*this = copym;
eValue = eigenValue[count][count];
for (Index_T i = 0; i < m_col; ++i)//A-lambda*I
{
m_ptr[i * m_col + i] -= eValue;
}
//cout<<*this<<endl;
//将 this为阶梯型的上三角矩阵
for (Index_T i = 0; i < m_row - 1; ++i)
{
diag = m_ptr[i*m_col + i]; //提取对角元素
for (Index_T j = i; j < m_col; ++j)
{
m_ptr[i*m_col + j] /= diag; //【i,i】元素变为1
}
for (Index_T j = i + 1; j<m_row; ++j)
{
diag = m_ptr[j * m_col + i];
for (Index_T q = i; q < m_col; ++q)//消去第i+1行的第i个元素
{
m_ptr[j*m_col + q] -= diag*m_ptr[i*m_col + q];
}
}
}
//cout<<*this<<endl;
//特征向量最后一行元素置为1
midSum = ret.m_ptr[(ret.m_row - 1) * ret.m_col + count] = 1;
for (int m = m_row - 2; m >= 0; --m)
{
sum = 0;
for (Index_T j = m + 1; j < m_col; ++j)
{
sum += m_ptr[m * m_col + j] * ret.m_ptr[j * ret.m_col + count];
}
sum = -sum / m_ptr[m * m_col + m];
midSum += sum * sum;
ret.m_ptr[m * ret.m_col + count] = sum;
}
midSum = sqrt(midSum);
for (Index_T i = 0; i < ret.m_row; ++i)
{
ret.m_ptr[i * ret.m_col + count] /= midSum; //每次求出一个列向量
}
}
*this = matcopy;//恢复原始矩阵；
return ret;
}
Matrix Matrix::cov(bool flag)
{
//m_row 样本数，column 变量数
if (m_col == 0)
{
Matrix m(0);
return m;
}
double *mean = new double[m_col]; //均值向量
for (Index_T j = 0; j<m_col; j++) //init
{
mean[j] = 0.0;
}
Matrix ret(m_col);
for (Index_T j = 0; j<m_col; j++) //mean
{
for (Index_T i = 0; i<m_row; i++)
{
mean[j] += m_ptr[i*m_col + j];
}
mean[j] /= m_row;
}
Index_T i, k, j;
for (i = 0; i<m_col; i++) //第一个变量
{
for (j = i; j<m_col; j++) //第二个变量
{
for (k = 0; k<m_row; k++) //计算
{
ret[i][j] += (m_ptr[k*m_col + i] - mean[i])*(m_ptr[k*m_col + j] - mean[j]);
}
if (flag == true)
{
ret[i][j] /= (m_row-1);
}
else
{
ret[i][j] /= (m_row);
}
}
}
for (i = 0; i<m_col; i++) //补全对应面
{
for (j = 0; j<i; j++)
{
ret[i][j] = ret[j][i];
}
}
return ret;
}
/*
* 返回代数余子式
*/
double CalcAlgebraicCofactor( Matrix& srcMat, Index_T ai, Index_T aj)
{
Index_T temMatLen = srcMat.row()-1;
Matrix temMat(temMatLen);
for (Index_T bi = 0; bi < temMatLen; bi++)
{
for (Index_T bj = 0; bj < temMatLen; bj++)
{
Index_T rowOffset = bi < ai ? 0 : 1;
Index_T colOffset = bj < aj ? 0 : 1;
temMat[bi][bj] = srcMat[bi + rowOffset][bj + colOffset];
}
}
int flag = (ai + aj) % 2 == 0 ? 1 : -1;
return flag * temMat.det();
}
/*
* 返回伴随阵
*/
Matrix Matrix::adjoint()
{
if (m_row != m_col)
{
return Matrix(0);
}
Matrix adjointMat(m_row);
for (Index_T ai = 0; ai < m_row; ai++)
{
for (Index_T aj = 0; aj < m_row; aj++)
{
adjointMat.m_ptr[aj*m_row + ai] = CalcAlgebraicCofactor(*this, ai, aj);
}
}
return adjointMat;
}
Matrix Matrix::inverse()
{
double detOfMat = det();
if (detOfMat == 0)
{
cout << "行列式为0，不能计算逆矩阵。" << endl;
return Matrix(0);
}
return adjoint()/detOfMat;
}
原文链接: https://www.cnblogs.com/MrLiuZF/p/13437739.html
欢迎关注
微信关注下方公众号，第一时间获取干货硬货；公众号内回复【pdf】免费获取数百本计算机经典书籍
原创文章受到原创版权保护。转载请注明出处：https://www.ccppcoding.com/archives/201146
非原创文章文中已经注明原地址，如有侵权，联系删除
关注公众号【高性能架构探索】，第一时间获取最新文章
转载文章受原作者版权保护。转载请注明原作者出处！
