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#include <iostream>
#include <random>
#include <Eigen/Eigenvalues>
#include "catch.hpp"
#include "sopt/power_method.h"
TEST_CASE("Power Method") {
using namespace sopt;
typedef t_real Scalar;
auto const N = 10;
Eigen::EigenSolver<Matrix<Scalar>> es;
Matrix<Scalar> A = Matrix<Scalar>::Random(N, N);
es.compute(A.adjoint() * A, true);
auto const eigenvalues = es.eigenvalues();
auto const eigenvectors = es.eigenvectors();
Eigen::DenseIndex index;
(eigenvalues.transpose() * eigenvalues).real().maxCoeff(&index);
auto const eigenvalue = eigenvalues(index);
Vector<t_complex> const eigenvector = eigenvectors.col(index);
// Create input vector close to solution
Vector<t_complex> const input = eigenvector * 1e-4 + Vector<t_complex>::Random(N);
auto const pm = algorithm::PowerMethod<t_complex>().tolerance(1e-12);
SECTION("AtA") {
auto const lt = linear_transform(A.cast<t_complex>());
auto const result = pm.AtA(lt, input);
CHECK(result.good);
CAPTURE(eigenvalue);
CAPTURE(result.magnitude);
CAPTURE(result.eigenvector.transpose() * eigenvector);
CHECK(std::abs(result.magnitude - std::abs(eigenvalue)) < 1e-8);
}
SECTION("A") {
auto const result = pm((A.adjoint() * A).cast<t_complex>(), input);
CHECK(result.good);
CAPTURE(eigenvalue);
CAPTURE(result.magnitude);
CAPTURE(result.eigenvector.transpose() * eigenvector);
CHECK(std::abs(result.magnitude - std::abs(eigenvalue)) < 1e-8);
}
}
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