矩阵三角分解（LU+高斯+平方根+求解方法+求逆）

#include <iostream>
#include <iomanip>
#include <vector>
#include <math.h>
using namespace std;
typedef vector<vector<double>> Matrix;
void dispMatrix(Matrix m);       //输出矩阵值
void dispRes(vector<double> r);  //输出解向量
void normlize(Matrix &m, int i); //行列式第i行归一
Matrix eye(int n);               //返回一个n阶单位矩阵
vector<double> solve(Matrix a, Matrix L, Matrix U);
Matrix LU(Matrix &m, Matrix &U);       //分解n*n
vector<double> LUsolve(Matrix a);      //对n*n的矩阵分解并求出解
Matrix LU1(Matrix &m, Matrix &U);      //分解n*m
Matrix colesky(Matrix a);              //a是正定对称矩阵 n*n
vector<double> coleskySolve(Matrix a); //对与平方根法分解结果进行求解
Matrix OSR(Matrix a, Matrix &T);       //optimized square root改进平方根
vector<double> OSR_solve(Matrix a);
Matrix transpos(Matrix m); //求矩阵的转置
Matrix multi(Matrix a, Matrix b);
Matrix Inv(Matrix a); //对矩阵求逆
//TODO:改进平方根 求逆
int main()
{
   
    ios::sync_with_stdio("false");
    int n;
    cin >> n;
    Matrix M1(n, vector<double>(n, 0));
    for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++) //这里需要注意是输入n*n 还是n*n+1 根据需要改写
            cin >> M1[i][j];
    // dispMatrix(M1);
    Matrix m = Inv(M1);

    // dispMatrix(d);

    /* 
    case1:n*n
     dispRes(LUsolve(M1));
     case2:n*m
    Matrix U(n, vector<double>(n + 1, 0));
    Matrix L = LU1(M1, U, n);

     */
    system("pause");
    return 0;
}

Matrix OSR(Matrix a, Matrix &T)
{
   
    int n = (int)a.size();
    Matrix L = eye(n);
    T[0][0] = a[0][0];
    for (int i = 1; i < n; i++)
    {
   
        for (int j = 0; j < i; j++)
        {
   
            T[i][j] = a[i][j];
            for (int k = 0; k <= j - 1; k++)
                T[i][j] -= T[i][k] * L[j][k];
            L[i][j] = T[i][j] / T[j][j];
        }
        T[i][i] = a[i][i];
        for (int k = 0; k <= i - 1