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This commit is contained in:
Chulwoo Jung
2025-12-08 21:08:14 -05:00
parent 504b85dfc0
commit 88611659a3
2 changed files with 155 additions and 12 deletions
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Grid/algorithms/iterative/KrylovSchur.h
+154 -11
View File
@@ -289,10 +289,11 @@ class KrylovSchur {
RitzFilter ritzFilter; // how to sort evals
public:
RealD *shift;
KrylovSchur(LinearOperatorBase<Field> &_Linop, GridBase *_Grid, RealD _Tolerance, RitzFilter filter = EvalReSmall)
: Linop(_Linop), Grid(_Grid), Tolerance(_Tolerance), ritzFilter(filter), u(_Grid), MaxIter(-1), Nm(-1), Nk(-1), Nstop (-1),
evals (0), ritzEstimates (), evecs (), ssq (0.0), rtol (0.0), beta_k (0.0), approxLambdaMax (0.0)
evals (0), ritzEstimates (), evecs (), ssq (0.0), rtol (0.0), beta_k (0.0), approxLambdaMax (0.0),shift(NULL)
{
u = Zero();
};
@@ -315,7 +316,12 @@ class KrylovSchur {
* - Permutes the Rayleigh quotient according to the eigenvalues.
* - Truncate the Krylov-Schur expansion.
*/
void operator()(const Field& v0, int _maxIter, int _Nm, int _Nk, int _Nstop, bool doubleOrthog = true) {
void operator()(const Field& v0, int _maxIter, int _Nm, int _Nk, int _Nstop, RealD *_shift=NULL, bool doubleOrthog = true) {
// RealD shift_=1.;
// shift = &shift_;
if(_shift) shift = _shift;
MaxIter = _maxIter;
Nm = _Nm; Nk = _Nk;
Nstop = _Nstop;
@@ -342,11 +348,129 @@ class KrylovSchur {
arnoldiIteration(startVec, Nm, start, doubleOrthog);
startVec = u; // original code
start = Nk;
std::cout << GridLogMessage << "b after Arnoldi " << b << std::endl;
// checkKSDecomposition();
RealD gamma;
Field uhat(Grid);
Eigen::MatrixXcd Btilde;
std::vector<Field> basis2_s;
Eigen::VectorXcd b_s;
#if 1
if (shift){
if(1){
Field w(Grid);
ComplexD coeff,coeff2;
for (int j = 0; j < Nm; j++) {
Linop.Op(basis[j], w);
for (int k = 0; k < Nm; k++) {
coeff2 = innerProduct(basis[k], basis[j]);
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 << " Rayleigh "<<k<<" "<<j<<" "<<Rayleigh (k,j)<<" "<<coeff << " <k|j> = " << coeff2 << std::endl;
}
coeff = innerProduct(basis[j], u); // coeff = h_{ij}. Note that since {vi} is ONB it's OK to subtract it off after.
std::cout << GridLogMessage << " u "<<j<<" "<<coeff << std::endl;
}
}
Eigen::MatrixXcd temp = Rayleigh;
for (int m=0;m<Nm;m++) temp(m,m) -= *shift;
Eigen::MatrixXcd RayleighS = temp.inverse(); // (B-tI)^-1
Eigen::MatrixXcd temp2 = RayleighS*temp;
std::cout << GridLogMessage << "Shift inverse check: shift= "<<*shift<<" "<< temp2 <<std::endl;
temp2=RayleighS.adjoint(); //(B-tI)^-1*
Eigen::VectorXcd g = temp2*b; //g = (B-tI)^-1* * b
Btilde= Rayleigh + g*(b.adjoint());
Field utilde(Grid);
utilde = u;
for (int j = 0; j<Nm; j++){
utilde -= basis[j]*g(j);
}
ComplexSchurDecomposition schurS (Btilde, false, ritzFilter);
std::cout << GridLogMessage << "Shifted Schur eigenvalues" << std::endl;
schurS.schurReorder(Nk);
Eigen::MatrixXcd Q_s = schurS.getMatrixQ();
Eigen::MatrixXcd Qt_s = Q_s.adjoint(); // TODO should Q be real?
#if 0
std::cout << GridLogMessage << "Q_s" << Q_s <<std::endl;
std::cout << GridLogMessage << "Qt_s" << Qt_s <<std::endl;
Eigen::MatrixXcd temp4= Q_s*Qt_s;
std::cout << GridLogMessage << "Q_s*Qt_s" << temp4 << std::endl;
temp4 = Btilde;
std::cout << GridLogMessage << "Btilde" << temp4<< std::endl;
temp4 = temp4*Qt_s;
std::cout << GridLogMessage << "Btilde*Qt_s" << temp4<< std::endl;
temp4 = Q_s*temp4;
std::cout << GridLogMessage << "Q_s*Btilde*Qt_s" << temp4<< std::endl;
#endif
Eigen::MatrixXcd S_s = schurS.getMatrixS();
Btilde=schurS.getMatrixS();
b_s= b;
b_s=Q_s*b; // Q is Qt in SlepC, b_s=bhat
constructUR(basis2_s, basis, Qt_s, Nm);
// Eq.(41)
Eigen::MatrixXcd RayTmp_s = Btilde(Eigen::seqN(0, Nk), Eigen::seqN(0, Nk));
Btilde = RayTmp_s;
std::vector<Field> basisTmp_s = std::vector<Field> (basis2_s.begin(), basis2_s.begin() + Nk);
basis2_s = basisTmp_s;
Eigen::VectorXcd btmp_s = b_s.head(Nk);
b_s = btmp_s;
Eigen::VectorXcd ghat = g;
ghat = -Q_s * g;
Eigen::VectorXcd gtmp_s = ghat.head(Nk);
ghat = gtmp_s;
uhat = utilde;
for (int j = 0; j<Nk; j++){
uhat -= basis2_s[j]*ghat(j);
}
gamma = std::sqrt(norm2(uhat));
uhat *= 1.0/gamma;
std::cout << GridLogMessage << " gamma "<<gamma << std::endl;
Btilde += ghat*(b_s.adjoint());
b_s *=gamma;
// Eq.(44)
if(1){
Field w(Grid);
ComplexD coeff,coeff2;
for (int j = 0; j < Nk; j++) {
Linop.Op(basis2_s[j], w);
for (int k = 0; k < Nk; k++) {
coeff2 = innerProduct(basis2_s[k], basis2_s[j]);
coeff = innerProduct(basis2_s[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 << " <k|j> = " << coeff2 << std::endl;
}
coeff = innerProduct(basis2_s[j], uhat); // coeff = h_{ij}. Note that since {vi} is ONB it's OK to subtract it off after.
coeff2 = innerProduct(uhat,w);
std::cout << GridLogMessage << " uhat "<<j<<" "<<coeff << " w "<< coeff2 << " b " << b_s (j) << " ghat "<<ghat(j)<< std::endl;
}
}
}
#endif
// Perform a Schur decomposition on Rayleigh
// ComplexSchurDecomposition schur (Rayleigh, false);
ComplexSchurDecomposition schur (Rayleigh, false, ritzFilter);
std::cout << GridLogDebug << "Schur decomp holds? " << schur.checkDecomposition() << std::endl;
@@ -373,16 +497,23 @@ class KrylovSchur {
// }
constructUR(basis2, basis, Qt, Nm);
basis = basis2;
if(0){
Field w(Grid);
// 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;
ComplexD coeff,coeff2;
for (int j = 0; j < Nm; j++) {
Linop.Op(basis[j], w);
for (int k = 0; k < Nm; k++) {
coeff2 = innerProduct(basis[k], basis[j]);
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 << " Stilde "<<k<<" "<<j<<" "<<Rayleigh(k,j)<<" "<<coeff << " <k|j> = " << coeff2 << std::endl;
}
coeff = innerProduct(basis[j], u); // coeff = h_{ij}. Note that since {vi} is ONB it's OK to subtract it off after.
std::cout << GridLogMessage << " u"<<j<<" "<<coeff << std::endl;
}
}
// checkKSDecomposition();
std::cout << GridLogMessage << "*** TRUNCATING FOR RESTART *** " << std::endl;
@@ -399,12 +530,24 @@ class KrylovSchur {
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;
if(shift){
Rayleigh = Btilde;
basis= basis2_s;
b = b_s;
beta_k = gamma;
u= uhat;
checkKSDecomposition();
computeEigensystem(Rayleigh);
std::cout << GridLogMessage << "Eigenvalues (first Nk sorted): " << std::endl << evals << std::endl;
}
// check convergence and return if needed.
int Nconv = converged();
std::cout << GridLogMessage << "Number of evecs converged: " << Nconv << std::endl;
examples/Example_krylov_schur.cc
+1 -1
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@@ -540,7 +540,7 @@ int main (int argc, char ** argv)
// Hacked, really EvalImagSmall
KrylovSchur KrySchur (Dwilson, UGrid, resid,EvalImNormSmall);
// BlockKrylovSchur KrySchur (HermOp2, UGrid, Nu, resid,EvalNormSmall);
RealD shift=1.;
RealD shift=0.;
KrySchur(src[0], maxIter, Nm, Nk, Nstop,&shift);
std::cout << GridLogMessage << "evec.size= " << KrySchur.evecs.size()<< std::endl;