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// Example reported in Issue #115
// https://github.com/yixuan/spectra/issues/115
#include <iostream>
#include <Eigen/Core>
#include <Eigen/SparseCore>
#include <Spectra/SymGEigsSolver.h>
#include <Spectra/MatOp/SparseCholesky.h>
#include "catch.hpp"
using namespace Spectra;
using Matrix = Eigen::MatrixXd;
using Vector = Eigen::VectorXd;
using SpMat = Eigen::SparseMatrix<double>;
using TriVec = std::vector<Eigen::Triplet<double>>;
using OpType = SparseSymMatProd<double>;
using BOpType = SparseCholesky<double>;
// (Highest) Eigenvalues of: ([A] + lam [B])x = 0
// A := M, (pos. semi definite)
// B := [C + shift*M] (pos. definite)
// -> f = sqrt(1/lam - s)/2pi
void run_test(SpMat& M, SpMat& C, double shift, int nef, int ncv)
{
SpMat A = M;
SpMat B = C + shift * M;
INFO("A =\n " << Matrix(A));
INFO("B =\n " << Matrix(B));
OpType op(A);
BOpType Bop(B);
REQUIRE(Bop.info() == CompInfo::Successful);
SymGEigsSolver<OpType, BOpType, GEigsMode::Cholesky> eigs(op, Bop, nef, ncv);
eigs.init();
int nconv = eigs.compute(SortRule::LargestMagn);
int niter = eigs.num_iterations();
int nops = eigs.num_operations();
INFO("nconv = " << nconv);
INFO("niter = " << niter);
INFO("nops = " << nops);
REQUIRE(eigs.info() == CompInfo::Successful);
Vector evals = eigs.eigenvalues();
Vector lam = 1 / (eigs.eigenvalues().array()) - shift;
Matrix evecs = eigs.eigenvectors();
Matrix resid = A.template selfadjointView<Eigen::Lower>() * evecs -
B.template selfadjointView<Eigen::Lower>() * evecs * evals.asDiagonal();
const double err = resid.array().abs().maxCoeff();
INFO("evals = " << evals.transpose());
INFO("lam = " << lam.transpose());
INFO("U'BU =\n " << evecs.transpose() * B * evecs);
INFO("||AU - BUD||_inf = " << err);
REQUIRE(err == Approx(0.0).margin(1e-9));
}
TEST_CASE("Example #115, case 1", "[example_115]")
{
TriVec C_tri = {
{0, 0, 1.1807575e+08},
{1, 1, 304744.5},
{1, 5, -152372.25},
{2, 2, 304744.5},
{2, 4, 152372.25},
{3, 3, 15403.85},
{4, 2, 152372.25},
{4, 4, 101581.5},
{5, 1, -152372.25},
{5, 5, 101581.5},
};
TriVec M_tri = {
{0, 0, 1000.0},
{1, 1, 1000.0},
{2, 2, 1000.0},
};
SpMat C(6, 6);
C.setFromTriplets(C_tri.begin(), C_tri.end());
SpMat M(6, 6);
M.setFromTriplets(M_tri.begin(), M_tri.end());
const double shift = 1.0e5;
run_test(M, C, shift, 4, 5);
}
TEST_CASE("Example #115, case 2", "[example_115]")
{
TriVec C_tri = {
{0, 0, 2.361515e+08},
{1, 1, 609489.01},
{2, 2, 609489.01},
{3, 3, 30807.7},
{4, 4, 203163},
{5, 5, 203163},
{6, 0, -1.1807575e+08},
{0, 6, -1.1807575e+08},
{6, 6, 1.1807575e+08},
{7, 1, -304744.5},
{1, 7, -304744.5},
{7, 5, -152372.25},
{5, 7, -152372.25},
{7, 7, 304744.5},
{8, 2, -304744.5},
{2, 8, -304744.5},
{8, 4, 152372.25},
{4, 8, 152372.25},
{8, 8, 304744.5},
{9, 3, -15403.85},
{3, 9, -15403.85},
{9, 9, 15403.85},
{10, 2, -152372.25},
{2, 10, -152372.25},
{10, 4, 50790.751},
{4, 10, 50790.751},
{10, 8, 152372.25},
{8, 10, 152372.25},
{10, 10, 101581.5},
{11, 1, 152372.25},
{1, 11, 152372.25},
{11, 5, 50790.751},
{5, 11, 50790.751},
{11, 7, -152372.25},
{7, 11, -152372.25},
{11, 11, 101581.5},
};
TriVec M_tri = {
{0, 0, 1000.0},
{1, 1, 1000.0},
{2, 2, 1000.0},
};
SpMat C(12, 12);
C.setFromTriplets(C_tri.begin(), C_tri.end());
SpMat M(12, 12);
M.setFromTriplets(M_tri.begin(), M_tri.end());
const double shift = 1.0e5;
run_test(M, C, shift, 5, 8);
}
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