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#include <iostream>
#include <random>
#include <ctime>
#include <chrono>
#include <algorithm>
using namespace std;
void rref(std::vector<std::vector<double>> & vec);
void matrixPrint(const std::vector<std::vector<double>> & V);
void luDecomp(vector<vector<double>> & A,vector<vector<double>> & L,vector<vector<double>> & U);
;
int main() {
typedef std::chrono::high_resolution_clock myclock;
myclock::time_point beginning = myclock::now();
int n;
cout<<"size of matrix?"; cin>>n;
std::vector<int> x (n);
std::vector<int> b (n);
std::vector<int> xcomp (n);
std::vector<int> temp (n);
myclock::duration d = myclock::now() - beginning;
unsigned seed2 = d.count();
cout<<seed2<<endl;
minstd_rand0 generator (seed2);
uniform_int_distribution<int> distribution(-9999999,9999999);
vector<vector<double>> V(n, vector<double>(n));
vector<vector<double>> L(n, vector<double>(n));
vector<vector<double>> U(n, vector<double>(n));
V={{3,6,-3},{-1,0,11},{1,1,-2}};
x={5,68,45};
b={288,490,-17};
//commenting the above and uncommenting the below fills my vector of vectors, //but y and x vecors refuse to change, they remain at 0 and the vectors will not take any new values assigned
/* for(int r = 0; r < n; r++)
{
for(int c = 0; c < n; c++)
{
double val=double(distribution(generator))/10000;
V[r][c]=val;
}
}
for(int c = 0; c < n; c++)
{
double val=double(distribution(generator))/10000;
b[c]=val;
}
cout<<"Original Random Matrix"<<endl;
matrixPrint(V);
cout<<"random b";
for (int i=0; i<V.size();i++)
{
cout <<b[i]<<",";
}
cout<<endl;
*/
//init U and L
for(int i=0; i<U.size();i++)
{
U[i][i]=1;
L[i][0]=V[i][0];
}
matrixPrint(V);
luDecomp(V,L,U);
cout<<"umatrix"<<endl;
matrixPrint(U);
cout<<"Lmatrix"<<endl;
matrixPrint(L);
//backsolve
temp[0]=b[0]/L[0][0];
for(int r=1;r<L.size();r++)
{
double sum=0;
for (int c=0;c<r;c++)
{
sum=sum+L[r][c]*temp[c];
}
temp[r]=(b[r]-sum)/L[r][r];
cout <<",";
}
cout<<"yvec"<<endl;
for (int i=0; i<U.size();i++)
{
cout <<temp[i]<<",";
}
cout<<endl;
//forward solve
xcomp[U.size()-1]=temp[U.size()-1];
for(int r=U.size()-1;r>0-1;r--)
{
double sum =0;
for(int c=U.size()-1;c>r;c--)
{
sum=sum+xcomp[c]*U[r][c];
}
xcomp[r]=temp[r]-sum;
}
cout<<"xvec"<<endl;
for (int i=0; i<U.size();i++)
{
cout <<xcomp[i]<<",";
}
cout<<endl;
return 0;
}
void luDecomp(vector<vector<double>> & A, vector<vector<double>> & L, vector<vector<double>> & U) {
for (int c = 0; c < U.size(); c++) {
U[0][c] = A[0][c] / A[0][0];
}
//calc column c values
for (int c=1;c<U.size();c++)
{
//calc L[c][r] then [c][r+1]... so on
for (int r=1; r<U.size();r++) {
double sum = 0;
//i is the iterative value from 0 to end of row/column
for (int i = 0; i < U.size(); i++) {
sum = sum + L[r][i] * U[i][c];
}
L[r][c] = A[r][c] - sum;
}
//Calc rows
for (int col=c+1;col<U.size();col++)
{
double sum =0;
for (int i = 0; i < U.size(); i++) {
sum = sum + L[c][i]*U[i][col];
}
U[c][col] =(A[c][col]-sum)/L[c][c];
}
}
}
//prints the matrix
void matrixPrint(const vector<vector<double>> & matrix)
{
for(int r=0; r<matrix.size(); r++)
{
for(int c=0; c<matrix[0].size(); c++)
{
//print element A[r][c]
cout<<"["<<r<<"]["<<c<<"]="<<matrix[r][c]<<" ";
}
cout<<endl;
}
cout<<endl;
}
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