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P3.cpp
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P3.cpp
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#define EIGEN_STACK_ALLOCATION_LIMIT 0
#include<bits/stdc++.h>
#include<math.h>
#include<Eigen/Eigen>
#include<iomanip>
using namespace std;
using namespace Eigen;
int main()
{
const int gridSize=8; //only for square matrix
double delta=(double)1/gridSize;
const int matSize=pow(gridSize-1,2);
Matrix<double,matSize,matSize> mat;
mat.setZero();
for(int i=0;i<matSize;i++)
{
for(int j=0;j<matSize;j++)
{
if(i==j)
{
mat(i,j)=-4/pow(delta,2);
}
else if(j==i+1 && i%(gridSize-1)!=(gridSize-2))
{
mat(i,j)=1/pow(delta,2);
}
else if(j==i-1 && i%(gridSize-1)!=0)
{
mat(i,j)=1/pow(delta,2);
}
else if(j==i+(gridSize-1))
{
mat(i,j)=1/pow(delta,2);
}
else if(j==i-(gridSize-1))
{
mat(i,j)=1/pow(delta,2);
}
}
}
Matrix<double,matSize,1> Y_BC,X_BC;
Y_BC.setZero();
X_BC.setZero();
for(int i=0;i<matSize;i++)
{
if(abs((i-0)<gridSize-1))
{
Y_BC(i,0)=(40-10*((i+1)*delta))/pow(delta,2);
}
else if(abs(i-(matSize-1))<gridSize-1)
{
Y_BC(i,0)=(40-10*(((i%(gridSize-1))+1)*delta))/pow(delta,2);
}
}
for(int i=0;i<matSize;i++)
{
if(i%(gridSize-1)==0)
{
X_BC(i,0)=40/pow(delta,2);
}
else if(i%(gridSize-1)==gridSize-2)
{
X_BC(i,0)=30/pow(delta,2);
}
}
Matrix<double,matSize,1> sol_0,ans;
sol_0.setZero();
ans.setZero();
ans=mat.colPivHouseholderQr().solve(sol_0-Y_BC-X_BC);
Matrix<double,gridSize+1,gridSize+1> actuallResult;
actuallResult.setZero();
for(int i=0;i<gridSize+1;i++)
{
for(int j=0;j<gridSize+1;j++)
{
if(j==0)
{
actuallResult(i,j)=40;
}
else if(j==gridSize)
{
actuallResult(i,j)=30;
}
else if(i==0 || i==gridSize)
{
actuallResult(i,j)=40-10*(j*delta);
}
else
{
actuallResult(i,j)=ans((i-1)*(gridSize-1)+(j-1),0);
}
}
}
cout<<actuallResult;
return 0;
}