Matrix.h

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#ifndef _Matrix_H
#define _Matrix_H
 
#include <stdlib.h>
#include <string.h>
#include <iostream>
#include <iomanip>
#include <initializer_list>
 
typedef std::initializer_list<double> MatIniLst; // 初始化列表
 
class Matrix
{
    // ---- 成员变量 ----
private:
    int miRow = 0;           // 行数
    int miCol = 0;           // 列数
    double *mpBuf = nullptr; // 存储矩阵
    // ---- 静态成员变量 ----
    static int iPrecise; // 控制流输出的显示精度
 
public:
    // ---- 构造析构函数 ----
 
    explicit Matrix();
 
    Matrix(double num);
 
    Matrix(const MatIniLst &lst);
 
    Matrix(const std::initializer_list<MatIniLst> &lst);
 
    explicit Matrix(const std::initializer_list<MatIniLst> &lst, int col);
 
    explicit Matrix(double *p, int row, int col, int count);
 
    Matrix(const Matrix &tmp);
 
    Matrix(Matrix &&tmp) noexcept;
 
    ~Matrix();
 
    // ---- 静态成员函数 ----
 
    static Matrix eye(int row);
 
    static Matrix eye(int row, int col);
 
    static Matrix ones(int row);
 
    static Matrix ones(int row, int col);
 
    static Matrix zeros(int row);
 
    static Matrix zeros(int row, int col);
 
    static Matrix diag(Matrix mat);
 
    static Matrix randMatrix(int n);
 
    static Matrix randMatrix(int row, int col);
 
    static void setPrecise(int precise);
 
    // ---- 运算符重载 ----
 
    Matrix &operator=(const Matrix &tmp);
 
    Matrix &operator=(Matrix &&tmp) noexcept;
 
    friend Matrix operator+(const Matrix &lMat, const Matrix &rMat);
 
    friend Matrix operator-(const Matrix &lMat, const Matrix &rMat);
 
    friend Matrix operator*(const Matrix &lMat, const Matrix &rMat);
 
    friend Matrix operator*(const double &lFactor, const Matrix &rMat);
 
    friend Matrix operator*(const Matrix &lMat, const double &rFactor);
 
    friend Matrix operator/(const Matrix &lMat, const Matrix &rMat);
 
    friend Matrix operator/(const double &lFactor, const Matrix &rMat);
 
    friend Matrix operator/(const Matrix &lMat, const double &rFactor);
 
    friend Matrix operator+(const Matrix &lMat, const double &rNum);
 
    friend Matrix operator+(const double &lNum, const Matrix &rMat);
 
    friend Matrix operator-(const Matrix &lMat, const double &rNum);
 
    friend Matrix operator-(const double &lNum, const Matrix &rMat);
 
    Matrix &operator+=(const Matrix &tmp);
 
    Matrix &operator+=(const double &num);
 
    Matrix &operator-=(const Matrix &tmp);
 
    Matrix &operator-=(const double &num);
 
    friend bool operator==(const Matrix &lMat, const Matrix &rMat);
    friend bool operator!=(const Matrix &lMat, const Matrix &rMat);
 
    friend Matrix operator-(const Matrix &Mat);
    friend Matrix operator+(const Matrix &Mat);
 
    Matrix &operator++();
 
    Matrix operator++(int);
 
    Matrix &operator--();
 
    Matrix operator--(int);
 
    double *operator[](int num);
    const double *operator[](int num) const;
 
    friend std::ostream &operator<<(std::ostream &os, const Matrix &tmp);
 
public:
    int getRow() const;
 
    int getCol() const;
 
    Matrix add(const Matrix &tmp) const;
 
    Matrix sub(const Matrix &tmp) const;
 
    Matrix rMultiple(const Matrix &tmp) const;
 
    Matrix sMultiple(const double &factor) const;
 
    Matrix transpose() const;
 
    bool det(double &result) const;
 
    Matrix gauss() const;
 
    Matrix inverse() const;
 
    int rank() const;
 
    bool isSizeValidity();
 
    bool isSquareMatrix() const;
 
    bool isEmptyMatrix() const;
 
    void rowAdd(int des, int src, double factor);
 
    bool rowExchange(int des, int src);
 
    void rowMultiply(int des, double factor);
 
    static Matrix lrMerge(Matrix &left, Matrix &right);
 
    static Matrix udMerge(Matrix &up, Matrix &down);
 
    Matrix getBlock(int startRowId, int startColId, int blockRow, int blockCol) const;
 
    Matrix &setBlock(int startRowId, int startColId, const Matrix &block);
 
    Matrix hessenberg(Matrix &Q) const;
 
    void qrDecom(Matrix &Q, Matrix &R) const;
 
    Matrix eigen() const;
 
private:
    static signed char sgn(double num);
 
    Matrix merge(Matrix &right) const;
 
    Matrix lrDivide(int col) const;
 
    bool qrDecom4Hessenberg(Matrix &Q, Matrix &R) const;
};
 
#endif // !_Matrix