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Add (full) reorthogonalization step to applyExp #322

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Add (full) reorthogonalization step to applyExp #322

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40 changes: 32 additions & 8 deletions itensor/iterativesolvers.h
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Original file line number Diff line number Diff line change
Expand Up @@ -964,7 +964,20 @@ assembleLanczosVectors(std::vector<ITensor> const& lanczos_vectors,
for(int i=1; i<(int)lanczos_vectors.size(); ++i)
phi += norm*linear_comb(i)*lanczos_vectors[i];
}


// function to reorthogonalize and add new Lanczos vector, modified Gram-Schmidt
inline double
reorthAddLanczosVector(std::vector<ITensor>& lanczos_vectors,
ITensor w)
{
for (const auto& v :lanczos_vectors )
w -= eltC(dag(v) * w) * v;

double beta = norm(w);
lanczos_vectors.emplace_back(w / beta);
return beta;
}

template<typename BigMatrixT, typename ElT>
void
applyExp(BigMatrixT const& H, ITensor& phi,
Expand All @@ -974,7 +987,8 @@ applyExp(BigMatrixT const& H, ITensor& phi,
auto max_iter = args.getInt("MaxIter",30);
auto debug_level = args.getInt("DebugLevel",-1);
auto beta_tol = args.getReal("NormCutoff",1e-7);

auto doReorth = args.getBool("DoReorthogonalization",true); // default true

// Initialize Lanczos vectors
ITensor v1 = phi;
ITensor v0;
Expand All @@ -997,13 +1011,15 @@ applyExp(BigMatrixT const& H, ITensor& phi,
H.product(v1, w);

double avnorm = norm(w);
if (iter > 0) // Modified Gram-Schmidt
w -= beta * v0;
double alpha = real(eltC(dag(w) * v1));
bigTmat(iter, iter) = alpha;
w -= alpha * v1;
if (iter > 0)
w -= beta * v0;
//if (iter > 0) // Classical Gram-Schmidt
//w -= beta * v0;
v0 = v1;
beta = norm(w);
//beta = norm(w); // will calculate later

// check for Lanczos sequence exhaustion
if (std::abs(beta) < beta_tol)
Expand All @@ -1017,9 +1033,17 @@ applyExp(BigMatrixT const& H, ITensor& phi,
}

// update next lanczos vector
v1 = w;
v1 /= beta;
lanczos_vectors.push_back(v1);
if (doReorth)
{
beta = reorthAddLanczosVector(lanczos_vectors, w);
v1 = lanczos_vectors.back();
}
else
{
beta = norm(w);
v1 = w/beta;
lanczos_vectors.push_back(v1);
}
bigTmat(iter+1, iter) = beta;
bigTmat(iter, iter+1) = beta;

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