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Another try at block Harmonic KS. Still not working

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This commit is contained in:
Chulwoo Jung
2026-04-09 21:13:41 -04:00
parent 99be36c891
commit aecc50869c
2 changed files with 57 additions and 22 deletions
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Grid/algorithms/iterative/HarmonicBlockKrylovSchur.h
+54 -18
View File
@@ -234,6 +234,41 @@ public:
// ---- Truncate to Nk ----
int Nkeep = Nk;
// ---- Option B: corrected restart starting block -------------------------
//
// In standard Krylov-Schur, Q diagonalises H itself, so Q H Q^H = S is
// upper triangular and the off-diagonal coupling block H_dk = S[Nkeep:,:Nkeep] = 0.
// Truncation is therefore exact.
//
// Here Q diagonalises Hhat (not H), so H_new = Q H Q^H is generally dense.
// The off-diagonal block
//
// H_dk = H_new[Nkeep:, :Nkeep] (size (N-Nkeep) x Nkeep)
//
// is non-zero, and the true KS relation after truncation is:
//
// A V_k = V_k H_k + V_disc H_dk + F B_k^H
//
// If we restart from F only, the V_disc H_dk term is lost.
//
// Fix: include the V_disc coupling in the new starting block:
//
// G[t] = F[t] + sum_{s=Nkeep}^{N-1} basis[s] * H(s, t), t = 0..Nblock-1
//
// G[:,t] is the t-th column of (V_disc H_dk + F B_k^H) restricted to the
// first Nblock columns of H_dk. Since F ⊥ V_k and V_disc ⊥ V_k, G is
// automatically orthogonal to the retained subspace.
//
// This must be computed BEFORE basis[Nkeep:] and H[Nkeep:, :] are discarded.
std::vector<Field> G(Nblock, Field(Grid_));
for (int t = 0; t < Nblock; t++) {
G[t] = F[t];
for (int s = Nkeep; s < N; s++)
G[t] += basis[s] * H(s, t);
}
blockQR(G); // orthonormalise within G (G is already ⊥ to basis[0:Nkeep])
CMat Htmp = H(Eigen::seqN(0, Nkeep), Eigen::seqN(0, Nkeep));
H = CMat::Zero(N, N);
H(Eigen::seqN(0, Nkeep), Eigen::seqN(0, Nkeep)) = Htmp;
@@ -249,10 +284,10 @@ public:
std::cout << GridLogMessage
<< "HarmonicBlockKrylovSchur: beta_k = " << beta_k << std::endl;
// Restart from the residual block F (unchanged from last Arnoldi step).
// Note: for a Hermitian operator the correct H rows H[i,j] for i >= Nkeep+Nblock,
// j < Nkeep are filled via Hermitian symmetry inside blockArnoldiStep.
startBlock = F;
// Use corrected starting block G (not bare F).
// G encodes the coupling from the discarded basis vectors V_disc through
// H_dk[:,0:Nblock], restoring the exact KS relation to first order.
startBlock = G;
if (doVerify) {
std::string lbl = "iter " + std::to_string(iter) + " after restart+truncation";
@@ -454,25 +489,26 @@ private:
blockOrthonormalise(V0);
for (auto& v : V0) basis.push_back(v);
} else {
// Append residual block (startBlock = F_old) to basis.
// The truncated KS relation after restart is:
// Append the new starting block to the retained basis.
//
// A V_k = V_k S_k + F_old B_old^dag (*)
// Standard KS (startBlock = F):
// The exact truncated relation is A V_k = V_k H_k + F B_k^dag,
// so the coupling rows are H[Nkeep+t, j] = conj(B_k[j,t]).
//
// where V_k = basis[0:Nkeep], S_k is stored in H[0:Nkeep,0:Nkeep],
// B_old = B[0:Nkeep,:], F_old = startBlock.
//
// Once F_old is appended as basis[Nkeep:Nkeep+Nblock], (*) becomes
// a statement about the extended H matrix:
//
// H[Nkeep+t, j] = (B_old^dag)[t,j] = conj(B_old[j,t])
// for t=0..Nblock-1, j=0..Nkeep-1
//
// These "restart coupling rows" must be set before Arnoldi continues.
// Harmonic KS Option B (startBlock = G, where G = F + V_disc H_dk[:,0:Nblock]):
// The exact coupling rows are H[Nkeep+t, j] = <G[t], A V_k[:,j]>,
// which differs from conj(B_k[j,t]) because G ≠ F.
// For a Hermitian operator these preset rows are overwritten by the
// Hermitian symmetry fill inside blockArnoldiStep (via explicit inner
// products), so the approximate preset below does no harm.
// For a non-Hermitian operator the preset is approximate; a more
// expensive fix would compute <G[t], A V_k[:,j]> explicitly here.
int Nkeep = startIdx * Nblock;
for (auto& v : startBlock) basis.push_back(v);
// Fill restart coupling rows into H
// Fill restart coupling rows into H (exact for standard KS; approximate
// for harmonic KS with Option-B starting block, but overwritten by
// Hermitian symmetry fill for Hermitian operators).
for (int t = 0; t < Nblock; t++)
for (int j = 0; j < Nkeep; j++)
H(Nkeep + t, j) = std::conj(B(j, t));
examples/Example_krylov_schur.cc
+3 -4
View File
@@ -349,8 +349,8 @@ int main (int argc, char ** argv)
RealD shift=1.5;
#if 0
KrylovSchur KrySchur (Dwilson, UGrid, resid,EvalImNormSmall);
KrySchur(src[0], maxIter, Nm, Nk, Nstop);
// KrySchur(src[0], maxIter, Nm, Nk, Nstop,&shift);
// KrySchur(src[0], maxIter, Nm, Nk, Nstop);
KrySchur(src[0], maxIter, Nm, Nk, Nstop,&shift);
std::cout << GridLogMessage << "KrylovSchur evec.size= " << KrySchur.evecs.size()<< std::endl;
#else
int Nblock=4;
@@ -360,9 +360,8 @@ int main (int argc, char ** argv)
// KrylovSchur KrySchur (Dwilson, UGrid, resid,EvalImNormSmall);
// KrySchur(src, maxIter, Nm, Nk, Nstop,true,if_verify);
BlockKrylovSchur KrySchur (Dwilson, UGrid, resid,EvalImNormSmall);
KrySchur(src, maxIter, Nm, Nk, Nstop,Nblock,true,if_verify);
// HarmonicBlockKrylovSchur KrySchur (Dwilson, UGrid, resid,shift,EvalImNormSmall);
// KrySchur(src, maxIter, Nm, Nk, Nstop,Nblock,true);
KrySchur(src, maxIter, Nm, Nk, Nstop,Nblock,true,if_verify);
std::cout << GridLogMessage << "BlockKrylovSchur evec.size= " << KrySchur.evecs.size()<< std::endl;
#endif