线性回归方程对数形式,cramer法则解方程组

f毕竟数学多用分数，所以修改了原程序：

程序

Source.cpp

#include <iostream>#include <conio.h>#include <Windows.h>#include "Det.h"#include "Fraction.h"using namespace std;int main(){int num;unsigned m = 0;deque<deque<double>> mat;deque<deque<deque<double>>> D;// instructioncout << "Please input like this:n"<< "a_11 * x_1 + a_12 * x_2 + ... + a_1n * x_n = b_1n"<< "a_21 * x_1 + a_22 * x_2 + ... + a_2n * x_n = b_2n"<< "...n"<< "a_n1 * x_1 + a_n2 * x_2 + ... + a_nn * x_n = b_n"<< "n" << endl;// inputwhile (1){deque<double> row;while (cin >> num){row.push_back(num);if (getchar() == 'n') break;}mat.push_back(row);m = (row.size() > m) ? row.size() : m;if (mat.size() >= m - 1) break;}// hide the Console CursorHANDLE hOut = GetStdHandle(STD_OUTPUT_HANDLE);CONSOLE_CURSOR_INFO cci;GetConsoleCursorInfo(hOut, &cci);cci.bVisible = FALSE;SetConsoleCursorInfo(hOut, &cci);// calculate & printfor (unsigned i = 0; i < m; i++){deque<deque<double>> temp = mat; // D[m - 1][m]for (unsigned j = 0; j != m - 1; j++){if (i) temp[j][i - 1] = mat[j][m - 1];temp[j].pop_back();}D.push_back(temp);}double D0 = det_is(D[0]);if (D0 != 0){cout << "n-------------------------------------------------------------------------n"<< "By default you view the solution in the FRACTION form.n"<< "You can switch to DECIMAL by any keyboard press except Enter.n"<< "Press Enter to end the program.n"<< "-------------------------------------------------------------------------n" << endl;for (unsigned i = 1; i < m; i++){cout << "x_" << i << " = " << decimal_to_fraction(det_is(D[i]) / D0) << endl;}while (1){if (_kbhit()){if (_getch() != 'r') // not Enter{// return to the front of the line (r)// cover the initial input by pressing the keyboardcout << "rtrn-------------------------------------------------------------------------n" << endl;for (unsigned i = 1; i < m; i++){cout << "x_" << i << " = " << det_is(D[i]) / D0 << endl;}}cout << "n-------------------------------------------------------------------------" << endl;break;}}}else{cout << "n-------------------------------------------------------------------------" << endl;cout << "nNo finite solution!" << endl;cout << "n-------------------------------------------------------------------------" << endl;}return 0;}

Fraction.h

#ifndef _FRACTION_#define _FRACTION_#include <string>#include <vector>std::string decimal_to_fraction(double n){std::string fra = "";std::string sgn = (n >= 0) ? "" : "-";n = fabs(n);double epsilon = 1E-10;if (n - static_cast<int>(n) < epsilon){fra = std::to_string(static_cast<int>(n));return fra;}else if (n - static_cast<int>(n) > 1 - epsilon){fra = std::to_string(static_cast<int>(n) + 1);return fra;}else{std::vector<int> denominator;for (int i = 2; i <= 100000; i++)denominator.push_back(i);for (auto c : denominator) // every number within 100000{if (c * n - static_cast<int>(c * n) < epsilon){fra = sgn + std::to_string(static_cast<int>(c * n)) + "/" + std::to_string(c);return fra;}if (c * n - static_cast<int>(c * n) > 1 - epsilon){fra = sgn + std::to_string(static_cast<int>(c * n) + 1) + "/" + std::to_string(c);return fra;}}}return std::to_string(n);}#endif // !_FRACTION_

Det.h
见我的博客【C++ 程序】行列式。

输出示例

分析输出分数原理：判断分数值与小数值相差不超过一个极小的值，此处即epsilon。特别注意负数时候的情况！r回车，回到一行最前端。（事实上Enter=rn，不过C++中n就是rn）其他详见我的博客【C++ 程序】解线性方程组（Cramer法则）。