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Calculate.h
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Calculate.h
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#pragma once
#include<iostream>
#include<fstream>
#include<string>
#include<stdlib.h>
using namespace std;
//菜单函数
void menu()
{
cout << " 选择菜单" << endl;
cout << "______________________________" << endl << endl;
cout << "1.利用克莱姆法则求解线性方程组." << endl << endl;
cout << "2.矩阵乘法." << endl << endl;
cout << "3.矩阵求逆." << endl << endl;
cout << "4.行列式求值." << endl;
cout << "______________________________" << endl << endl;
cout << "请输入您的选择:" << endl;
}
//行列式计算函数
double det(double** a, int n)
{
if (n == 1)
return a[0][0];
double** b = new double* [n - 1];
for (int i = 0; i < n - 1; i++)
b[i] = new double[n - 1];
int mov = 0;//判断余子式行是否移动
double sum = 0.0;//sum为行列式的值
for (int arow = 0; arow < n; arow++) // a的行数把矩阵a[n][n]赋值到b[n-1][n-1]
{
for (int brow = 0; brow < n - 1; brow++)//把a阵第一列各元素的代数余子式存到b
{
mov = arow > brow ? 0 : 1; //b中小于arow的行,直接赋值,等于和大于的加一
//把a的第(brow + mov)行第(j+1)的元素赋值到b 的第brow行第j列的元素
for (int j = 0; j < n - 1; j++)
{
b[brow][j] = a[brow + mov][j + 1];
}
}
int flag = (arow % 2 == 0 ? 1 : -1);//因为列数为0,所以行数是偶数时候,代数余子式系数为1.
sum += flag * a[arow][0] * det(b, n - 1);//a第一列各元素与其代数余子式积的和即为行列式
}
delete[]b;
return sum;
}
//将常数项代入到第k列的行列式
double calcud(double** m, double* c, int k, int n)
{
double d = 0;
double** temp = NULL;
temp = new double* [n];
for (int i = 0; i < n; i++)
temp[i] = new double[n];
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
temp[i][j] = m[i][j];
}
}
for (int j = 0; j < n; j++)
{
temp[j][k] = c[j];
}
d = det(temp, n);
delete[] temp;
return d;
}
//克拉默法则求解
void cramer()
{
int n;
system("cls");
cout << "请输入未知数个数:" << endl;
cin >> n;
double** m;
double* c;
c = new double[n];
m = new double* [n];
for (int i = 0; i < n; i++)
m[i] = new double[n];
cout << "请输入系数矩阵:" << endl;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
cin >> m[i][j];
}
}
if (det(m, n) == 0)
{
cout << "系数行列式为零,不能用克拉默法则计算!" << endl;
}
else
{
cout << "请输入右端常数项:" << endl;
for (int i = 0; i < n; i++)
{
cin >> c[i];
}
for (int i = 0; i < n; i++)
{
cout << "X" << i + 1 << " = " << calcud(m, c, i, n) / det(m, n) << endl;
}
}
delete[]m;
system("pause");
system("cls");
}
//矩阵类
class Matrix
{
public:
double** matrix;
int row, col;
};
//输入矩阵
Matrix input()
{
Matrix m;
cout << "请输入矩阵行数:";
cin >> m.row;
cout << "请输入矩阵列数:";
cin >> m.col;
m.matrix = (double**)malloc(m.row * sizeof(double*));
for (int i = 0; i < m.row; i++)
m.matrix[i] = (double*)malloc(m.col * sizeof(double));
cout << "输入你的矩阵:" << endl;
for (int i = 0; i < m.row; i++)
{
for (int j = 0; j < m.col; j++)
{
cin >> m.matrix[i][j];
}
}
return m;
}
//输出矩阵
void output(Matrix m)
{
cout << "矩阵输出为:" << endl;
for (int i = 0; i < m.row; i++)
{
for (int j = 0; j < m.col; j++)
{
cout << m.matrix[i][j] << ' ';
}
cout << endl;
}
}
//矩阵行列相乘相加
double M(Matrix m1, Matrix m2, int i, int j)
{
double m = 0;
for (int k = 0; k < m1.col; k++)
m = m + m1.matrix[i][k] * m2.matrix[k][j];
return m;
}
//矩阵乘法
void mul(Matrix m1, Matrix m2)
{
if (m1.col == m2.row)
{
Matrix z;
z.row = m1.row;
z.col = m2.col;
z.matrix = (double**)malloc(z.row * sizeof(double*));
for (int i = 0; i < z.row; i++)
z.matrix[i] = (double*)malloc(z.col * sizeof(double));
for (int i = 0; i < m1.row; i++)
for (int j = 0; j < m2.col; j++)
z.matrix[i][j] = M(m1, m2, i, j);
cout << "相乘后";
output(z);
}
else
cout << "行列不符,不能相乘!" << endl;
}
void cal()
{
system("cls");
Matrix x, y;
cout << "请输入矩阵A:" << endl;
x = input();
cout << "请输入矩阵B:" << endl;
y = input();
mul(x, y);
system("pause");
system("cls");
}
//求余子式
double cofactor(double** m, int k, int h, int n)
{
double d = 0;
double** temp = NULL;
temp = new double* [n-1];
for (int i = 0; i < n-1; i++)
temp[i] = new double[n-1];
int movr = 0;//行的移动
int movc = 0;//列的移动
for (int i = 0; i < n-1; i++)
{
movr = k > i ? 0 : 1;
for (int j = 0; j < n-1; j++)
{
movc = h > j ? 0 : 1;
temp[i][j] = m[i + movr][j+movc];
}
}
d = det(temp, n-1);
delete[] temp;
return d;
}
void Inverse()
{
int n;
system("cls");
cout << "请输入矩阵阶数:" << endl;
cin >> n;
double** m;
double** b;
m = new double* [n];
for (int i = 0; i < n; i++)
m[i] = new double[n];
b = new double* [n];
for (int i = 0; i < n; i++)
b[i] = new double[n];
cout << "请输入矩阵:" << endl;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
cin >> m[i][j];
}
}
if (det(m, n) == 0)
{
cout << "行列式为0,不能求逆!" << endl;
}
else if (n == 1)
{
cout << "矩阵逆为:" << endl;
cout << m[0][0];
}
else
{
double x = 1;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
x = (i + j + 2) % 2 == 0 ? 1 : -1;
b[j][i] = x * cofactor(m, i, j, n) / det(m, n);
if (x * cofactor(m, i, j, n) / det(m, n) == 0)
b[j][i] = 0;
}
}
cout << "矩阵的逆为:" << endl;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
cout << b[i][j] << " ";
}
cout << endl;
}
}
delete[]m;
delete[]b;
system("pause");
system("cls");
}
void Det()
{
int n;
system("cls");
cout << "请输入行列式阶数:" << endl;
cin >> n;
double** m;
m = new double* [n];
for (int i = 0; i < n; i++)
m[i] = new double[n];
cout << "请输入行列式:" << endl;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
cin >> m[i][j];
}
}
cout << "\n\nA = " << det(m, n) << endl;
system("pause");
system("cls");
}