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Necessary code for Harmonic KS added

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This commit is contained in:
Chulwoo Jung
2025-12-03 19:38:45 -05:00
parent 985ab70f85
commit 17e3799bcc
1 changed files with 54 additions and 33 deletions
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87
Grid/algorithms/iterative/KrylovSchur.h
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@@ -376,47 +376,32 @@ class KrylovSchur {
// Rearrange Schur matrix so wanted evals are on top left (like MATLAB's ordschur)
std::cout << GridLogMessage << "Reordering Schur eigenvalues" << std::endl;
schur.schurReorder(Nk);
std::cout << GridLogMessage << "Shifted Schur eigenvalues" << std::endl;
std::cout << GridLogMessage << "Reordering Schur eigenvalues" << std::endl;
schurS.schurReorder(Nk);
Eigen::MatrixXcd Q = schur.getMatrixQ();
Qt = Q.adjoint(); // TODO should Q be real?
Eigen::MatrixXcd S = schur.getMatrixS();
// std::cout << GridLogDebug << "Schur decomp holds after reorder? " << schur.checkDecomposition() << std::endl;
Eigen::MatrixXcd Q_s = schurS.getMatrixQ();
Eigen::MatrixXcd Qt_s = Q_s.adjoint(); // TODO should Q be real?
Eigen::MatrixXcd S_s = schurS.getMatrixS();
std::cout << GridLogMessage << "*** ROTATING TO SCHUR BASIS *** " << std::endl;
// Rotate Krylov basis, b vector, redefine Rayleigh quotient and evecs, and truncate.
Rayleigh = schur.getMatrixS();
b = Q * b; // b^\dag = b^\dag * Q^\dag <==> b = Q*b
// basisRotate(basis, Q, 0, Nm, 0, Nm, Nm);
// basisRotate(evecs, Q, 0, Nm, 0, Nm, Nm);
if(shift){
Field w(Grid);
ComplexD coeff;
for (int j = 0; j < Nm; j++) {
Linop.Op(basis[j], w);
// Linop.Op(basis[i], w);
for (int k = 0; k < Nm; k++) {
coeff = innerProduct(basis[k], w); // coeff = h_{ij}. Note that since {vi} is ONB it's OK to subtract it off after.
std::cout << GridLogMessage << " Btilde "<<k<<" "<<j<<" "<<Btilde(k,j)<<" "<<coeff << std::endl;
// Rayleigh(j, i) = coeff;
// w -= coeff * basis[j];
}
coeff = innerProduct(utilde, w); // coeff = h_{ij}. Note that since {vi} is ONB it's OK to subtract it off after.
std::cout << GridLogMessage << " utilde "<<j<<" "<<coeff << std::endl;
}
std::cout << GridLogMessage << "Shifted Schur eigenvalues" << std::endl;
schurS.schurReorder(_Nk);
Btilde = schurS.getMatrixS();
Eigen::VectorXcd b_s = b;
b_s = Q_s * b_s; // b^\dag = b^\dag * Q^\dag <==> b = Q*b
Eigen::MatrixXcd Q_s = schurS.getMatrixQ();
Eigen::MatrixXcd Qt_s = Q_s.adjoint(); // TODO should Q be real?
Eigen::MatrixXcd S_s = schurS.getMatrixS();
// std::cout << GridLogDebug << "Schur deco
std::cout << GridLogMessage << "Shifted part done " << std::endl;
}
std::vector<Field> basis2;
@@ -427,15 +412,10 @@ if(shift){
constructUR(basis2, basis, Qt, Nm);
basis = basis2;
// std::vector<Field> evecs2;
// constructUR(evecs2, evecs, Qt, Nm);
// constructRU(evecs2, evecs, Q, Nm);
// evecs = evecs2;
// littleEvecs = littleEvecs * Q.adjoint(); // TODO try this and see if it works
// littleEvecs = Q * littleEvecs; // TODO try this and see if it works
// std::cout << GridLogDebug << "Ritz vectors rotated correctly? " << checkEvecRotation() << std::endl;
std::vector<Field> basis_s;
constructUR(basis_s, basis, Qt_s, Nm);
// basis = basis2_s;
// checkKSDecomposition();
std::cout << GridLogMessage << "*** TRUNCATING FOR RESTART *** " << std::endl;
@@ -443,21 +423,62 @@ if(shift){
Eigen::MatrixXcd RayTmp = Rayleigh(Eigen::seqN(0, Nk), Eigen::seqN(0, Nk));
Rayleigh = RayTmp;
RayTmp = Btilde(Eigen::seqN(0, Nk), Eigen::seqN(0, Nk));
Btilde = RayTmp;
std::vector<Field> basisTmp = std::vector<Field> (basis.begin(), basis.begin() + Nk);
basis = basisTmp;
std::vector<Field> basisTmp_s = std::vector<Field> (basis_s.begin(), basis_s.begin() + Nk);
basis_s = basisTmp_s;
Eigen::VectorXcd btmp = b.head(Nk);
b = btmp;
Eigen::VectorXcd btmp_s = b_s.head(Nk);
b_s = btmp_s;
std::cout << GridLogDebug << "Rayleigh after truncation: " << std::endl << Rayleigh << std::endl;
checkKSDecomposition();
// Compute eigensystem of Rayleigh. Note the eigenvectors correspond to the sorted eigenvalues.
computeEigensystem(Rayleigh);
std::cout << GridLogMessage << "Eigenvalues (first Nk sorted): " << std::endl << evals << std::endl;
computeEigensystem(Btilde);
std::cout << GridLogMessage << "Shifted Eigenvalues (first Nk sorted): " << std::endl << evals << std::endl;
if(shift){
Field w(Grid);
Eigen::MatrixXcd ghat=g;
ghat = - Q_s*g;
Field uhat(Grid);
uhat=utilde;
for (int j = 0; j<Nk; j++){
utilde -= basis_s[j]*ghat(j);
}
RealD gamma = std::sqrt(norm2(utilde)); // beta_k = ||f_k|| determines convergence.
uhat = (1/gamma) * uhat;
Eigen::MatrixXcd Bhat = S_s;
Eigen::MatrixXcd btemp = b;
Bhat += ghat*b_s.adjoint();
ComplexD coeff;
for (int j = 0; j < Nk; j++) {
Linop.Op(basis_s[j], w);
for (int k = 0; k < Nm; k++) {
coeff = innerProduct(basis_s[k], w); // coeff = h_{ij}. Note that since {vi} is ONB it's OK to subtract it off after.
std::cout << GridLogMessage << " Bhat "<<k<<" "<<j<<" "<<Bhat(k,j)<<" "<<coeff << std::endl;
}
coeff = innerProduct(basis_s[j], uhat); // coeff = h_{ij}. Note that since {vi} is ONB it's OK to subtract it off after.
std::cout << GridLogMessage << " uhat "<<j<<" "<<coeff << std::endl;
}
}
// check convergence and return if needed.
int Nconv = converged();
std::cout << GridLogMessage << "Number of evecs converged: " << Nconv << std::endl;