C++实现的线性代数矩阵计算(一)

/**
* 线性代数矩阵计算
* 实现功能：行列向量获取，子矩阵获取，转置矩阵获取，
* 行列式计算，转置伴随矩阵获取，逆矩阵计算
*
* Copyright 2011 Shi Y.M. All Rights Reserved
*/

#ifndef MATICAL_TMATRIX_H_INCLUDED
#define MATICAL_TMATRIX_H_INCLUDED

#include

namespace matical
{

template
class TMatrix
{
private:
T * m_Elems;
int m_Rows;
int m_Cols;

public:
typedef T ElemType;

public:

TMatrix() : m_Elems(NULL), m_Rows(0), m_Cols(0) {}
TMatrix(int rows, int cols) : m_Rows(rows), m_Cols(cols) {
m_Elems = new ElemType[m_Rows * m_Cols];
memset(m_Elems, 0, sizeof(ElemType) * m_Rows * m_Cols);
}
// 生成n阶方阵
TMatrix(int n) : m_Rows(n), m_Cols(n){
m_Elems = new ElemType[m_Rows * m_Cols];
memset(m_Elems, 0, sizeof(ElemType) * m_Rows * m_Cols);
}

TMatrix(const TMatrix& m) : m_Rows(m.Rows()), m_Cols(m.Cols()) {
m_Elems = new ElemType[m_Rows * m_Cols];
memcpy(m_Elems, m.m_Elems, sizeof(ElemType) * m_Rows * m_Cols);
}
virtual ~TMatrix() {
if ( m_Elems ) delete[] m_Elems;
m_Elems = NULL;
m_Rows = 0;
m_Cols = 0;
}

public:

int Rows() const { return m_Rows;}
int Cols() const { return m_Cols;}

// 是否为方阵
bool IsSquare() const { return ( m_Rows > 0 && (m_Rows == m_Cols)); }

// 取行向量
TMatrix Row(int row) const {
TMatrix m(1, m_Cols);
for(int i = 0; i < m_Cols; i++) {
m(0, i) = (*this)(row, i);
}
return m;
}

// 取列向量
TMatrix Col(int col) const {
TMatrix m(m_Rows, 1);
for(int i = 0; i < m_Rows; i++) {
m(i, 0) = (*this)(i, col);
}
return m;
}

public:

// 将当前矩阵设置为单位矩阵
void Identity() {
for(int r = 0; r < this->m_Rows; r++) {
for(int c = 0; c < this->m_Cols; c++) {
if ( r == c ) (*this)(r, c) = 1;
else (*this)(r, c) = 0;
}
}
return ;
}

// 当前矩阵设置为零矩阵
void Zero() {
int sz = m_Rows * m_Cols;
for (int i = 0; i < sz; i++ ) m_Elems[i] = 0;
return ;
}

// 获取指定范围的子矩阵，rrow>=lrow, rcol>=lcol
TMatrix SubMatrix(int lrow, int lcol, int rrow, int rcol) const {
TMatrix m(rrow - lrow + 1, rcol - lcol + 1);
for ( int r = 0; r < m.m_Rows; r++) {
for (int c = 0; c < m.m_Cols; c++) {
m(r, c ) = (*this)(r + lrow, c + lcol);
}
}
return m;
}

// 获取当前矩阵元素(row, col)的子矩阵（去掉元素（row,col）所在的行和列）
TMatrix SubMatrixEx(int row, int col) const {
int rr = 0;
int cc = 0;
TMatrix m(this->m_Rows - 1, this->m_Cols - 1);
for ( int r = 0; r < m.m_Rows; r++, rr++) {
if ( r == row) rr++;
cc = 0;
for (int c = 0; c < m.m_Cols; c++, cc++) {
if ( c == col ) cc++;
m(r, c) = (*this)(rr, cc);
}
}
return m;
}

// 计算当前矩阵的转置矩阵
TMatrix Transpose() const {
printf("Transpose\n");
TMatrix m(this->m_Cols, this->m_Rows);
for (int r = 0; r < m.m_Rows; r++ ) {
for ( int c = 0; c < m.m_Cols; c++ ) {
m(r, c) = (*this)(c, r);
}
}
return m;
}

// 计算当前矩阵的行列式(递归方式), 计算行列式的矩阵，须是n阶方阵
ElemType Det() const {
ElemType det = 0;
if ( m_Rows == 1) {
det = (*this)(0, 0);
} else if ( m_Rows == 2) {
det = (*this)(0, 0) * (*this)(1, 1) - (*this)(0 ,1) * (*this)(1, 0);
} else {
for (int r = 0; r < m_Rows; r++) {
TMatrix m = this->SubMatrixEx(r, 0);
if ( r % 2 ) det += (-1) * (*this)(r, 0) * m.Det();
else det += (*this)(r, 0) * m.Det();
}
}
return det;
}

// 计算当前矩阵