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force hermicity to the block alpha and force diagonal of the block beta to be real

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This commit is contained in:
Yong-Chull Jang 2017-12-29 23:26:17 -05:00
parent bfc0306a43
commit 44b218a595
1 changed files with 42 additions and 19 deletions
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61
lib/algorithms/iterative/ImplicitlyRestartedBlockLanczos.h
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@ -106,6 +106,18 @@ public:
normalize(w); normalize(w);
} }
void orthogonalize_blockhead(Field& w, std::vector<Field>& evec, int k, int Nu)
{
typedef typename Field::scalar_type MyComplex;
MyComplex ip;
for(int j=0; j<k; ++j){
ip = innerProduct(evec[j*Nu],w);
w = w - ip * evec[j*Nu];
}
normalize(w);
}
/* Rudy Arthur's thesis pp.137 /* Rudy Arthur's thesis pp.137
------------------------ ------------------------
Require: M > K P = M − K † Require: M > K P = M − K †
@ -438,7 +450,8 @@ private:
if (b>0) { if (b>0) {
for (int u=0; u<Nu; ++u) { for (int u=0; u<Nu; ++u) {
for (int k=L-Nu; k<L; ++k) { //for (int k=L-Nu; k<L; ++k) {
for (int k=L-Nu+u; k<L; ++k) {
w[u] = w[u] - evec[k] * conjugate(lme[u][k]); w[u] = w[u] - evec[k] * conjugate(lme[u][k]);
//clog << "ckpt A (k= " << k+1 << ")" << '\n'; //clog << "ckpt A (k= " << k+1 << ")" << '\n';
//clog << "lme = " << lme[u][k] << '\n'; //clog << "lme = " << lme[u][k] << '\n';
@ -449,14 +462,25 @@ private:
} }
// 4. αk:=(vk,wk) // 4. αk:=(vk,wk)
//for (int u=0; u<Nu; ++u) {
// for (int k=L; k<R; ++k) {
// lmd[u][k] = innerProduct(evec[k],w[u]); // lmd = transpose of alpha
// }
// lmd[u][L+u] = real(lmd[u][L+u]); // force diagonal to be real
//}
for (int u=0; u<Nu; ++u) { for (int u=0; u<Nu; ++u) {
for (int k=L; k<R; ++k) { for (int k=L+u; k<R; ++k) {
lmd[u][k] = innerProduct(evec[k],w[u]); // lmd = transpose of alpha lmd[u][k] = innerProduct(evec[k],w[u]); // lmd = transpose of alpha
lmd[k-L][u+L] = conjugate(lmd[u][k]); // force hermicity
} }
lmd[u][L+u] = real(lmd[u][L+u]); // force diagonal to be real lmd[u][L+u] = real(lmd[u][L+u]); // force diagonal to be real
//clog << "ckpt B (k= " << L+u << ")" << '\n';
//clog << "lmd = " << lmd[u][L+u] << std::endl;
} }
//for (int u=0; u<Nu; ++u) {
// for (int k=L; k<L+u+1; ++k) {
// clog << "ckpt B: alphaT[" << u+L << "," << k << "] = " << lmd[u][k]
// << ", alphaT - conj(alphaT) = " << lmd[u][k] - conjugate(lmd[k-L][u+L]) << std::endl;
// }
//}
// 5. wk:=wk−αkvk // 5. wk:=wk−αkvk
for (int u=0; u<Nu; ++u) { for (int u=0; u<Nu; ++u) {
@ -469,7 +493,7 @@ private:
// In block version, the steps 6 and 7 in Lanczos construction is // In block version, the steps 6 and 7 in Lanczos construction is
// replaced by the QR decomposition of new basis block. // replaced by the QR decomposition of new basis block.
// It results block version beta and orthonormal block basis. // It results block version beta and orthonormal block basis.
// Here, QR decomposition is done by using Gram-Schmidt // Here, QR decomposition is done by using Gram-Schmidt.
for (int u=0; u<Nu; ++u) { for (int u=0; u<Nu; ++u) {
for (int k=L; k<R; ++k) { for (int k=L; k<R; ++k) {
lme[u][k] = 0.0; lme[u][k] = 0.0;
@ -483,23 +507,14 @@ private:
} }
for (int u=0; u<Nu; ++u) { for (int u=0; u<Nu; ++u) {
for (int v=0; v<Nu; ++v) { //for (int v=0; v<Nu; ++v) {
for (int v=u; v<Nu; ++v) {
lme[u][L+v] = innerProduct(w[u],w_copy[v]); lme[u][L+v] = innerProduct(w[u],w_copy[v]);
} }
lme[u][L+u] = real(lme[u][L+u]); // force diagonal to be real
} }
lme[0][L] = beta; //lme[0][L] = beta;
#if 0
for (int u=0; u<Nu; ++u) {
for (int k=L+u; k<R; ++k) {
if (lme[u][k] < tiny) {
clog <<" In block "<< b << ",";
std::cout <<" beta[" << u << "," << k-L << "] = ";
std::cout << lme[u][k] << std::endl;
}
}
}
#else
for (int u=0; u<Nu; ++u) { for (int u=0; u<Nu; ++u) {
clog << "norm2(w[" << u << "])= "<< norm2(w[u]) << std::endl; clog << "norm2(w[" << u << "])= "<< norm2(w[u]) << std::endl;
for (int k=L+u; k<R; ++k) { for (int k=L+u; k<R; ++k) {
@ -508,14 +523,22 @@ private:
std::cout << lme[u][k] << std::endl; std::cout << lme[u][k] << std::endl;
} }
} }
#endif
// re-orthogonalization for numerical stability // re-orthogonalization for numerical stability
if (b>0) { if (b>0) {
for (int u=0; u<Nu; ++u) { for (int u=0; u<Nu; ++u) {
orthogonalize(w[u],evec,R); orthogonalize(w[u],evec,R);
} }
for (int u=1; u<Nu; ++u) {
orthogonalize(w[u],w,u);
} }
}
//if (b>0) {
// orthogonalize_blockhead(w[0],evec,b,Nu);
// for (int u=1; u<Nu; ++u) {
// orthogonalize(w[u],w,u);
// }
//}
if (b < Nm/Nu-1) { if (b < Nm/Nu-1) {
for (int u=0; u<Nu; ++u) { for (int u=0; u<Nu; ++u) {