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Build analytic vector to include in plot

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This commit is contained in:
Janita Willumsen 2023-09-25 13:10:34 +02:00
parent 3b1c42cf2d
commit 4f2a49a0ff
1 changed files with 51 additions and 5 deletions
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56
src/main.cpp
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@ -19,6 +19,22 @@
#include "matrix.hpp" #include "matrix.hpp"
#include "jacobi.hpp" #include "jacobi.hpp"
// void analytical_eigenvec(arma::mat &analytic, int N)
// {
// arma::vec analytic_vec = arma::vec(N);
// for (int i=0; i < N; i++) {
// for (int j=0; j < N; j++) {
// analytic_vec(j) = std::sin(((j+1.)*(i+1.)*M_PI) / (N+1.));
// }
// analytic_vec = arma::normalise(analytic_vec);
// // Flip the sign of the analytic vector if they are different
// if (analytic_vec(0)*v(0) < 0.) {
// analytic_vec *= -1;
// }
// }
// }
void write_transformation_dense(int N) void write_transformation_dense(int N)
{ {
@ -87,6 +103,7 @@ void write_eigenvec(int N)
// Create tridiagonal matrix // Create tridiagonal matrix
arma::mat A = create_symmetric_tridiagonal(N, a, d); arma::mat A = create_symmetric_tridiagonal(N, a, d);
arma::mat analytic = arma::mat(N, N);
arma::vec eigval; arma::vec eigval;
arma::mat eigvec; arma::mat eigvec;
@ -96,15 +113,38 @@ void write_eigenvec(int N)
// Solve using Jacobi rotation method // Solve using Jacobi rotation method
jacobi_eigensolver(A, 10e-14, eigval, eigvec, 100000, iters, converged); jacobi_eigensolver(A, 10e-14, eigval, eigvec, 100000, iters, converged);
// Build analytic eigenvectors
arma::vec v, analytic_vec = arma::vec(N);
for (int i=0; i < N; i++) {
v = eigvec.col(i);
for (int j=0; j < N; j++) {
analytic_vec(j) = std::sin(((j+1.)*(i+1.)*M_PI) / (N+1.));
}
analytic_vec = arma::normalise(analytic_vec);
// Flip the sign of the analytic vector if they are different
if (analytic_vec(0)*v(0) < 0.) {
analytic_vec *= -1;
}
analytic.col(i) = analytic_vec;
}
std::ofstream ofile; std::ofstream ofile;
// Create file based on matrix size, and write header line to file // Create file based on matrix size, and write header line to file
ofile.open("../latex/output/eigenvector_" + std::to_string(N) + ".csv"); ofile.open("../latex/output/eigenvector_" + std::to_string(N) + ".csv");
ofile << "x,Vector 1,Vector 2,Vector 3" << std::endl; ofile << "x,"
<< "Vector 1,Vector 2,Vector 3,"
<< "Analytic 1,Analytic 2,Analytic 3" << std::endl;
// Add boundary value for x=0 // Add boundary value for x=0
ofile << scientific_format(0., 16) << "," ofile << scientific_format(0., 16) << ","
<< scientific_format(0., 16) << "," << scientific_format(0., 16) << ","
<< scientific_format(0., 16) << "," << scientific_format(0., 16) << ","
<< scientific_format(0., 16) << ","
<< scientific_format(0., 16) << ","
<< scientific_format(0., 16) << ","
<< scientific_format(0., 16) << std::endl; << scientific_format(0., 16) << std::endl;
// Add x-value and element i of each eigenvector to same line // Add x-value and element i of each eigenvector to same line
@ -113,12 +153,18 @@ void write_eigenvec(int N)
ofile << scientific_format(x, 16)<< "," ofile << scientific_format(x, 16)<< ","
<< scientific_format(eigvec(i,0), 16) << "," << scientific_format(eigvec(i,0), 16) << ","
<< scientific_format(eigvec(i,1), 16) << "," << scientific_format(eigvec(i,1), 16) << ","
<< scientific_format(eigvec(i,2), 16) << std::endl; << scientific_format(eigvec(i,2), 16) << ","
<< scientific_format(analytic(i,0), 16) << ","
<< scientific_format(analytic(i,1), 16) << ","
<< scientific_format(analytic(i,2), 16) << std::endl;
} }
// Add boundary value for x=1 // Add boundary value for x=1
ofile << scientific_format(1., 16) << "," ofile << scientific_format(1., 16) << ","
<< scientific_format(0., 16) << "," << scientific_format(0., 16) << ","
<< scientific_format(0., 16) << "," << scientific_format(0., 16) << ","
<< scientific_format(0., 16) << ","
<< scientific_format(0., 16) << ","
<< scientific_format(0., 16) << ","
<< scientific_format(0., 16) << std::endl; << scientific_format(0., 16) << std::endl;
ofile.close(); ofile.close();
} }
@ -126,8 +172,8 @@ void write_eigenvec(int N)
int main() int main()
{ {
write_transformation_tridiag(100); // write_transformation_tridiag(100);
write_transformation_dense(100); // write_transformation_dense(100);
write_eigenvec(6); write_eigenvec(6);
write_eigenvec(100); write_eigenvec(100);
return 0; return 0;