代码说明：
①模仿Matlab的思想对矩阵进行操作
②利用(double*) data动态分配内存来保存矩阵的的元素
主要功能（持续更新）：
运行实例：
Matrix.h（持续更新）：
#include <iostream>
#include <iomanip>
#include <random>
using namespace std;
void swap( double& a, double& b )
{
double tmp = a;
a = b;
b = tmp;
}
class Matrix {
private:
int row = 0;
int col = 0;
double* data = nullptr; //存储数据
static int precision; //设置小数位数
public:
inline int getRow() const; //行
inline int getCol() const; //列
inline double& getValue( int i, int j ); //获取值(返回左值引用)
inline void setValue( const double* a ); //利用数组设置元素
inline void random( int low, int high ); //随机元素[low,high]
static void setPrecision( int a ); //设置输出时的小数位数
Matrix( const Matrix& a ); //拷贝构造函数
Matrix( int r, int c ); //构造1(行,列)
Matrix( int r, int c, const double* a ); //构造2(行,列,元素初始化)
~Matrix(); //析构函数
Matrix& operator = ( const Matrix& a ); //赋值运算符重载
friend bool operator == ( const Matrix& a, const Matrix& b ); //判断相等
friend istream& operator >> ( istream& input, Matrix& a ); //输入
friend ostream& operator << ( ostream& output, const Matrix& a ); //输出
friend Matrix operator + ( const Matrix& a, const Matrix& b ); // +
friend Matrix operator - ( const Matrix& a, const Matrix& b ); // -
friend Matrix operator * ( const Matrix& a, const Matrix& b ); // 矩阵乘法
friend Matrix operator * ( const Matrix& a, double b ); // 数乘1
friend Matrix operator * ( double b, const Matrix& a ); // 数乘2
void swapRow( int i0, int i1 ); //交换两行
void linearChange( int des, double times, int src ); //des += times*src
int legalify( int col ); //使基准行合法
double det(); //行列式(高斯消元法)
Matrix operator ^ ( int b ); //矩阵快速幂(log b)
Matrix triu(); //上三角矩阵(高斯消元法)
Matrix inv(); //求逆(高斯-亚当思想) 【0.01秒内可求100阶】
Matrix tran(); //转置
static Matrix eye( int n ); //返回一个n阶单位阵
};
int Matrix::precision = 4;
int Matrix::getRow() const {
return row;
}
int Matrix::getCol() const {
return col;
}
double& Matrix::getValue( int i, int j ) {
if (1 <= i && i <= row && 1 <= j && j <= col)
return data[(i - 1) * col + j - 1];
else
{
cerr << "引用非法数据" << endl;
return data[0];
}
}
Matrix::Matrix( const Matrix & a ) {
row = a.row;
col = a.col;
data = new double[row * col];
memcpy( data, a.data, sizeof( double ) * row * col );
}
Matrix::Matrix( int r, int c ) {
row = r;
col = c;
data = new double[r * c];
memset( data, 0, r * c * sizeof( double ) );
}
Matrix::Matrix( int r, int c, const double* a )
{
row = r;
col = c;
setValue( a );
}
Matrix::~Matrix()
{
if (data != nullptr)
delete[] data;
}
Matrix& Matrix::operator = ( const Matrix & a )
{
row = a.row;
col = a.col;
if (data != nullptr) delete[] data;
data = new double[row*col];
memcpy( data, a.data, sizeof( double ) * row * col );
return *this;
}
void Matrix::setValue( const double* a ) {
if (data != nullptr) delete[]data;
data = new double[row*col];
memcpy( data, a, sizeof( double ) * row * col );
}
inline void Matrix::random( int low, int high )
{
default_random_engine e;
uniform_real_distribution<double> u( low, high );
for (int i = 0; i < row * col; ++i)
data[i] = u( e );
}
inline void Matrix::setPrecision( int a )
{
precision = a;
}
bool operator == ( const Matrix& a, const Matrix& b ) {
if (a.row != b.row || a.col != b.col)
return false;
//判断是否相等
for (int i = 0; i < a.row * a.col; ++i)
if (a.data[i] != b.data[i])
return false;
return true;
}
istream& operator >> ( istream& input, Matrix& a )
{
for (int i = 0; i < a.row * a.col; ++i)
input >> a.data[i];
return input;
}
ostream& operator << ( ostream& output, const Matrix& a )
{
for (int i = 1; i <= a.row * a.col; ++i)
{
output << fixed << setprecision( Matrix::precision ) << (a.data[i - 1] == 0 ? 0.0 : a.data[i - 1]) << " ";
if (i % a.col == 0) output << endl;
}
return output;
}
Matrix operator + ( const Matrix& a, const Matrix& b ) {
if (a.row != b.row || a.col != b.col) {
cerr << ("类型不同，无法相加") << endl;
return Matrix( 0, 0 );
}
Matrix temp( a.col, a.row );
for (int i = 0; i < a.row * a.col; ++i)
temp.data[i] = a.data[i] + b.data[i];
return temp;
}
Matrix operator - ( const Matrix& a, const Matrix& b ) {
if (a.row != b.row || a.col != b.col) {
cerr << ("类型不同，无法相减") << endl;
return Matrix( 0, 0 );
}
Matrix temp( a );
for (int i = 0; i < a.row * a.col; ++i)
temp.data[i] -= b.data[i];
return temp;
}
Matrix operator * ( const Matrix& a, const Matrix& b ) {
if (a.col != b.row) {
cerr << ("类型不符，无法相乘") << endl;
return Matrix( 0, 0 );
}
Matrix temp( a.row, b.col );
for (int i = 1; i <= a.row; ++i)
{
for (int j = 1; j <= b.col; ++j)
for (int k = 1; k <= a.row; ++k)
temp.data[(i - 1) * temp.col + j - 1] += a.data[(i - 1) * a.col + k - 1] * b.data[(k - 1) * b.col + j - 1];
}
return temp;
}
Matrix operator * ( const Matrix& a, double b )
{
Matrix tmp( a );
for (int i = 0; i < tmp.row * tmp.col; ++i)
tmp.data[i] *= b;
return tmp;
}
Matrix operator * ( double b, const Matrix& a )
{
Matrix tmp( a );
for (int i = 0; i < tmp.row * tmp.col; ++i)
tmp.data[i] *= b;
return tmp;
}
void Matrix::swapRow( int i0, int i1 )
{
for (int j = 1; j <= col; ++j)
swap( getValue( i0, j ), getValue( i1, j ) );
}
void Matrix::linearChange( int des, double times, int src ) //des += times src
{
for (int j = 1; j <= col; ++j)
getValue( des, j ) += times * getValue( src, j );
}
int Matrix::legalify( int col )
{
if (getValue( col, col ) != 0) return 1; //若基准行的基准数不为0，返回1
for (int legal_row = col + 1; legal_row <= row; ++legal_row) //若基准行的基准数为0,则向下寻找非0的行
{
if (getValue( legal_row, col ) != 0)
{
swapRow( legal_row, col ); //若找到，交换两行，并改变行列式符号
return -1;
}
}
return 0; //若没找到，返回0
}
double Matrix::det()
{
Matrix tmp( *this );
if (tmp.row != tmp.col)
{
cout << "此矩阵无行列式" << endl;
return -1.0;
}
double times, res = 1, flag; //times为线性系数,flag为符号位
for (int j = 1; j < col; ++j)
{
flag = tmp.legalify( j );
if (flag == 0) return 0.0; //若此列全为0,则直接进入下一列
res *= flag;
for (int i = j + 1; i <= row; ++i)
{
if (tmp.getValue( i, j ) == 0) continue;
times = -tmp.getValue( i, j ) / tmp.getValue( j, j );
tmp.linearChange( i, times, j ); //线性变换, 使目标行的目标值为0
}
}
for (int i = 1; i <= row; ++i)
res *= tmp.getValue( i, i );
return res == 0 ? 0.0 : res;
}
Matrix Matrix::operator ^ ( int b )
{
if (col != row)
{
cerr << "不是方阵，无法求幂";
return Matrix( row, col );
}
if (b == 0) return Matrix::eye( row );
if (b < 0) return inv() ^ (-b);
Matrix base( *this );
Matrix res( Matrix::eye( row ) );
while (b)
{
if (b & 1) res = res * base;
base = base * base;
b >>= 1;
}
return res;
}
Matrix Matrix::triu()
{
double times;
Matrix tmp( *this );
for (int j = 1; j < row; ++j)
{
tmp.legalify( j ); //若此列全为0,则直接进入下一列
for (int i = j + 1; i <= row; ++i)
{
if (tmp.getValue( i, j ) == 0) continue;
times = -tmp.getValue( i, j ) / tmp.getValue( j, j );
tmp.linearChange( i, times, j ); //线性变换, 使目标行的目标值为0
}
}
return tmp;
}
Matrix Matrix::inv()
{
if (row != col || det() == 0) //注：未考虑 广义逆矩阵
{
cerr << "无逆矩阵" << endl;
return Matrix( 0, 0 );
}
//配置AE
Matrix AE( row, 2 * col );
for (int i = 1; i <= row; ++i)
for (int j = 1; j <= col; ++j)
AE.getValue( i, j ) = getValue( i, j );
for (int i = 1; i <= row; ++i)
AE.getValue( i, row + i ) = 1;
AE = AE.triu(); //A化为上三角
double times;
for (int j = col; j > 1; --j)
for (int i = j - 1; i >= 1; --i)
{
times = -AE.getValue( i, j ) / AE.getValue( j, j ); //A化为对角矩阵
AE.linearChange( i, times, j );
}
for (int i = 1; i <= AE.row; ++i) //对角矩阵化为E
{
times = AE.getValue( i, i );
if (times == 1) continue;
for (int j = 1; j <= AE.col; ++j)
AE.getValue( i, j ) /= times;
}
Matrix inver( row, col );
for (int i = 1; i <= row; ++i)
for (int j = 1; j <= col; ++j)
inver.getValue( i, j ) = AE.getValue( i, j + col );
return inver;
}
Matrix Matrix::tran()
{
Matrix t( col, row );
for (int i = 1; i <= t.row; ++i)
for (int j = 1; j <= t.row; ++j)
t.getValue( i, j ) = getValue( j, i );
return t;
}
Matrix Matrix::eye( int n )
{
Matrix e( n, n );
for (int i = 1; i <= n; ++i)
e.getValue( i, i ) = 1;
return e;
}参考资料：