def lanczos(t,
y,
npsi,
nel,
nmodes,
nspfs,
npbfs,
psistart,
psiend,
ham,
uopips,
copips,
spfovs,
nvecs=5,
return_evecs=True):
"""
"""
# thing to store A tensors
V = np.zeros(nvecs, np.ndarray)
# TODO
V[0] = A / norm(nel, A)
T = np.zeros((nvecs, nvecs))
# form krylov vectors and tridiagonal matrix
for i in range(nvecs - 1):
V[i + 1] = cmfeom_coeffs(t, y, npsi, nel, nmodes, nspfs, npbfs,
psistart, psiend, ham.huelterms,
ham.hcelterms, uopips, copips, spfovs)
#V[i+1] = matel(nel,nmodes,nspfs,npbfs,uopips,copips,ham.huelterms,
# ham.hcelterms,spfovs,V[i])
# compute alpha
# TODO
T[i, i] = inner(nel, V[i], V[i + 1]).real
if i > 0:
V[i + 1] += -T[i, i] * V[i] - T[i - 1, i] * V[i - 1]
else:
V[i + 1] += -T[i, i] * V[i]
# normalize previous vector
# TODO
nvprev = norm(nel, V[i + 1])
V[i + 1] /= nvprev
# compute beta
T[i, i + 1] = nvprev
T[i + 1, i] = T[i, i + 1]
Vtmp = cmfeom_coeffs(t, y, npsi, nel, nmodes, nspfs, npbfs, psistart,
psiend, ham.huelterms, ham.hcelterms, uopips, copips,
spfovs)
# TODO
T[-1, -1] = inner(nel, V[-1], Vtmp)
#T[-1,-1] = inner(nel,V[-1], matel(nel,nmodes,nspfs,npbfs,uopips,copips,
# ham.huelterms,ham.hcelterms,spfovs,V[-1])).real
if return_evecs:
return T, V
else:
return T
def arnoldi(A, nel, nmodes, nspfs, npbfs, ham, uopips, copips, spfovs, nvecs=5,
return_evecs=True):
"""
"""
# thing to store A tensors
V = np.zeros(nvecs, np.ndarray)
V[0] = A/norm(nel,A)
# form krylov subspace and upper hessenberg matrix
T = np.zeros((nvecs,nvecs), dtype=complex)
for j in range(nvecs-1):
w = matel(nel,nmodes,nspfs,npbfs,uopips,copips,ham.huelterms,
ham.hcelterms,spfovs,V[i])
for i in range(j+1):
T[i,j] = inner(nel, w, V[i])
w -= T[i,j]*V[i]
if j < nvecs-1:
T[j+1,j] = norm(nel,w)
V[j+1] = w/T[j+1,j]
return T , V
def arnoldi(y,
ham,
uopips,
copips,
spfovs,
nvecs=5,
v0=None,
return_evecs=True):
"""
"""
# get wavefunction info
nel = y.nel
nmodes = y.nmodes
nspfs = y.nspfs
npbfs = y.npbfs
spfstart = y.spfstart
spfend = y.spfend
A = y.A
# thing to store A tensors
V = np.zeros(nvecs, np.ndarray)
V[0] = A / norm(nel, A)
# form krylov subspace and upper hessenberg matrix
T = np.zeros((nvecs, nvecs), dtype=complex)
for j in range(nvecs - 1):
w = matel(nel, nmodes, nspfs, npbfs, uopips, copips, ham.huelterms,
ham.hcelterms, spfovs, V[j])
for i in range(j + 1):
T[i, j] = inner(nel, w, V[i])
w -= T[i, j] * V[i]
if j < nvecs - 1:
T[j + 1, j] = norm(nel, w)
V[j + 1] = w / T[j + 1, j]
return T, V
def lanczos(A, nel, nmodes, nspfs, npbfs, ham, uopips, copips, spfovs, nvecs=5,
return_evecs=True):
"""
"""
# thing to store A tensors
V = np.zeros(nvecs, np.ndarray)
V[0] = A/norm(nel,A)
T = np.zeros((nvecs,nvecs))
# form krylov vectors and tridiagonal matrix
for i in range(nvecs-1):
V[i+1] = matel(nel,nmodes,nspfs,npbfs,uopips,copips,ham.huelterms,
ham.hcelterms,spfovs,V[i])
#np.set_printoptions(threshold=np.inf)
#print(V[i+1])
#raise ValueError
# compute alpha
T[i,i] = inner(nel,V[i],V[i+1]).real
if i>0:
V[i+1] += -T[i,i]*V[i] - T[i-1,i]*V[i-1]
else:
V[i+1] += -T[i,i]*V[i]
# normalize previous vector
nvprev = norm(nel,V[i+1])
V[i+1] /= nvprev
# compute beta
T[i,i+1] = nvprev
T[i+1,i] = T[i,i+1]
Vtmp = matel(nel,nmodes,nspfs,npbfs,uopips,copips,ham.huelterms,
ham.hcelterms,spfovs,V[-1])
T[-1,-1] = inner(nel,V[-1], Vtmp).real
if return_evecs:
return T , V
else:
return T