C++矩阵类的编写，基于运算符重载

#include "MATRIX.h" Mtx::Mtx(int m1, int n1) { if (m1 <= 0 || n1 <= 0) { cout << "错误：二维数组的维数不得为0或负数！\n"; system("pause"); exit(0); } m = m1; n = n1; M = new double*[m1]; for (int i = 0; i < m1; ++i) M[i] = new double[n1]; } Mtx::Mtx(const Mtx& M1) { setMtx(M1.M, M1.m, M1.n); } Mtx::Mtx(double **M1, int m1, int n1) { setMtx(M1, m1, n1); } Mtx::~Mtx() { for (int i = 0; i < m; ++i) delete[] M[i]; delete[] M; } void Mtx::setMtx(double **M1, int m1, int n1) { if (m1 <= 0 || n1 <= 0) { cout << "错误：二维数组的维数不得为0或负数！\n"; system("pause"); exit(0); } m = m1; n = n1; M = new double*[m1]; for (int i = 0; i < m1; ++i) { M[i] = new double[n1]; for (int j = 0; j < n1; ++j) M[i][j] = M1[i][j]; } } void swap(double &a, double &b) { double c; c = a; a = b; b = c; } Mtx Mtx::inv() { double Mmax, **M1; int i, j, k, *Mrow, *Mcol; Mtx M2(m, n); M1 = new double*[m]; for (i = 0; i < m; ++i) { M1[i] = new double[n]; for (j = 0; j < n; ++j) M1[i][j] = M[i][j]; } Mrow = new int[m]; Mcol = new int[n]; if (m != n) { cout << "错误：矩阵不是方阵，无法求逆！\n"; cout << "当前对象的维数是： " << m << " * " << n << endl; system("pause"); exit(0); } for (k = 0; k < m; ++k) { Mmax = 0.; //找到右下角(m-k)*(m-k)矩阵的主元，及其所在行列 for (i = k; i<m; ++i) for (j = k; j < n; ++j) if (fabs(M1[i][j]) > Mmax) { //cout << i << j << endl; Mmax = fabs(M1[i][j]); Mrow[k] = i; Mcol[k] = j; } if (fabs(Mmax) < 1.E-7) { cout << "错误：矩阵奇异，无法求逆！\n"; cout << "当前对象的秩是： " << k << endl; system("pause"); exit(0); } //将当前的主元变换到k*k位置 //cout << Mrow[k] << Mcol[k] << endl; if (Mrow[k] != k) for (j = 0; j < n; ++j) swap(M1[k][j], M1[Mrow[k]][j]); if (Mcol[k] != k) for (i = 0; i < m; ++i) swap(M1[i][k], M1[i][Mcol[k]]); //将k*k元素，即主元变成1，再将k列其它元素全部化为零，记此变化为左乘Pk：Pk*M1 M1[k][k] = 1 / M1[k][k]; for (i = 0; i < m; ++i) if (i != k) M1[i][k] = -M1[i][k] * M1[k][k]; for (i = 0; i < m; ++i) for (j = 0; j < n; ++j) if (i != k&&j != k) M1[i][j] += M1[i][k] * M1[k][j]; for (j = 0; j < n; ++j) if (j != k) M1[k][j] *= M1[k][k]; } //当k执行到最后一次的时候，M1变成的由Pk组成的矩阵，再对其进行从后往前的列行交换返回到原本的情况，就是M1的逆矩阵 for (k = m - 1; k >= 0; --k) { if (Mcol[k] != k) for (j = 0; j < n; ++j) swap(M1[k][j], M1[Mcol[k]][j]); if (Mrow[k] != k) for (i = 0; i < m; ++i) swap(M1[i][k], M1[i][Mrow[k]]); } M2 = M1; for (int i = 0; i < m; ++i) delete[] M1[i]; delete[] M1; delete[] Mrow; delete[] Mcol; return M2; } Mtx Mtx::tran() { Mtx M2(n, m); for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) M2.M[j][i] = M[i][j]; return M2; } Mtx& Mtx::operator=(const Mtx& M1) { setMtx(M1.M, M1.m, M1.n); return *this; } Mtx& Mtx::operator=(double **M1) { if (m == 0 || n == 0) cout << "错误：矩阵维数未初始化！\n"; setMtx(M1, m, n); return *this; } Mtx operator+(const Mtx& M1, const Mtx& M2) { if (M1.m != M2.m || M1.n != M2.n) { cout << "错误：维数不一致！\n"; cout << "当前对象的维数是： " << M1.m << " * " << M1.n << endl; cout << "另一个对象的维数是： " << M2.m << " * " << M2.n << endl; system("pause"); exit(0); } Mtx M3(M1.m, M1.n); for (int i = 0; i < M1.m; ++i) for (int j = 0; j < M1.n; ++j) M3.M[i][j] = M1.M[i][j] + M2.M[i][j]; return M3; } Mtx& Mtx::operator+=(const Mtx& M1) { if (m != M1.m || n != M1.n) { cout << "错误：维数不一致！\n"; cout << "当前对象的维数是： " << m << " * " << n << endl; cout << "另一个对象的维数是： " << M1.m << " * " << M1.n << endl; system("pause"); exit(0); } for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) M[i][j] += M1.M[i][j]; return *this; } Mtx operator-(const Mtx& M1, const Mtx& M2) { if (M1.m != M2.m || M1.n != M2.n) { cout << "错误：维数不一致！\n"; cout << "当前对象的维数是： " << M1.m << " * " << M1.n << endl; cout << "另一个对象的维数是： " << M2.m << " * " << M2.n << endl; system("pause"); exit(0); } Mtx M3(M1.m, M1.n); for (int i = 0; i < M1.m; ++i) for (int j = 0; j < M1.n; ++j) M3.M[i][j] = M1.M[i][j] - M2.M[i][j]; return M3; } Mtx& Mtx::operator-=(const Mtx& M1) { if (m != M1.m || n != M1.n) { cout << "错误：维数不一致！\n"; cout << "当前对象的维数是： " << m << " * " << n << endl; cout << "另一个对象的维数是： " << M1.m << " * " << M1.n << endl; system("pause"); exit(0); } for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) M[i][j] -= M1.M[i][j]; return *this; } Mtx operator*(const Mtx& M1, const Mtx& M2) { if (M1.n != M2.m) { cout << "错误：矩阵乘法的维数不匹配！\n"; cout << "当前对象的维数是： " << M1.m << " * " << M1.n << endl; cout << "另一个对象的维数是： " << M2.m << " * " << M2.n << endl; system("pause"); exit(0); } Mtx M3(M1.m, M2.n); for (int i = 0; i < M1.m; ++i) for (int j = 0; j < M2.n; ++j) { M3.M[i][j] = 0.; for (int k = 0; k < M1.n; k++) M3.M[i][j] += M1.M[i][k] * M2.M[k][j]; } return M3; } double& Mtx::operator[](int mn) { int m1 = mn / n; int n1 = mn % n; return M[m1][n1]; } const double& Mtx::operator[](int mn) const { int m1 = mn / n; int n1 = mn % n; return M[m1][n1]; } ostream& operator<< (ostream& os, const Mtx& M1) { for (int i = 0; i<M1.m; ++i) { for (int j = 0; j<M1.n; ++j) cout << setw(8) << M1.M[i][j] << " "; cout << endl; } cout << endl; return os; } istream& operator<< (istream& is, Mtx& M1) { for (int i = 0; i<M1.m; i++) for (int j = 0; j<M1.n; j++) cin >> M1.M[i][j]; cout << endl; return is; }