def testOrthog(self):
from PyQuante.LA2 import CanOrth, SymOrth, CholOrth, simx
from PyQuante.NumWrap import eigh
solver = SCF(h2, method="HF")
h, S = solver.h, solver.S
X1 = CanOrth(S)
X2 = SymOrth(S)
X3 = CholOrth(S)
h1 = simx(h, X1)
ha = simx(h, X2)
h3 = simx(h, X3)
e1, v1 = eigh(h1)
e2, v2 = eigh(ha)
e3, v3 = eigh(h3)
self.assertAlmostEqual(e1[0], e2[0], 6)
self.assertAlmostEqual(e1[0], e3[0], 6)
def inertial(self):
"Transform to inertial coordinates"
from PyQuante.NumWrap import zeros, eigh
rcom = self.com()
print "Translating to COM: ", rcom
self.translate(-rcom)
I = zeros((3, 3), 'd')
for atom in self:
m = atom.mass()
x, y, z = atom.pos()
x2, y2, z2 = x * x, y * y, z * z
I[0, 0] += m * (y2 + z2)
I[1, 1] += m * (x2 + z2)
I[2, 2] += m * (x2 + y2)
I[0, 1] -= m * x * y
I[1, 0] = I[0, 1]
I[0, 2] -= m * x * z
I[2, 0] = I[0, 2]
I[1, 2] -= m * y * z
I[2, 1] = I[1, 2]
E, U = eigh(I)
print "Moments of inertial ", E
self.urotate(U)
print "New coordinates: "
print self
return
def lanczos_minmax(F, S=None, **kwargs):
"Estimate the min/max evals of F using a few iters of Lanczos"
doS = S is not None
niter = kwargs.get('niter', settings.DMPLanczosMinmaxIters)
N = F.shape[0]
niter = min(N, niter)
x = zeros(N, 'd')
x[0] = 1
q = x
avals = []
bvals = []
if doS:
r = matrixmultiply(S, q)
else:
r = q
beta = sqrt(matrixmultiply(q, r))
wold = zeros(N, 'd')
for i in xrange(niter):
w = r / beta
v = q / beta
r = matrixmultiply(F, v)
r = r - wold * beta
alpha = matrixmultiply(v, r)
avals.append(alpha)
r = r - w * alpha
if doS:
q = solve(S, r)
else:
q = r
beta = sqrt(matrixmultiply(q, r))
bvals.append(beta)
wold = w
E, V = eigh(tridiagmat(avals, bvals))
return min(E), max(E)
def testOrthog(self):
from PyQuante.LA2 import CanOrth, SymOrth, CholOrth, simx
from PyQuante.NumWrap import eigh
solver = SCF(h2,method="HF")
h,S = solver.h, solver.S
X1 = CanOrth(S)
X2 = SymOrth(S)
X3 = CholOrth(S)
h1 = simx(h,X1)
ha = simx(h,X2)
h3 = simx(h,X3)
e1,v1 = eigh(h1)
e2,v2 = eigh(ha)
e3,v3 = eigh(h3)
self.assertAlmostEqual(e1[0],e2[0],6)
self.assertAlmostEqual(e1[0],e3[0],6)
def inertial(self):
"Transform to inertial coordinates"
from PyQuante.NumWrap import zeros,eigh
rcom = self.com()
print "Translating to COM: ",rcom
self.translate(-rcom)
I = zeros((3,3),'d')
for atom in self:
m = atom.mass()
x,y,z = atom.pos()
x2,y2,z2 = x*x,y*y,z*z
I[0,0] += m*(y2+z2)
I[1,1] += m*(x2+z2)
I[2,2] += m*(x2+y2)
I[0,1] -= m*x*y
I[1,0] = I[0,1]
I[0,2] -= m*x*z
I[2,0] = I[0,2]
I[1,2] -= m*y*z
I[2,1] = I[1,2]
E,U = eigh(I)
print "Moments of inertial ",E
self.urotate(U)
print "New coordinates: "
print self
return
def lanczos_minmax(F,S=None,**kwargs):
"Estimate the min/max evals of F using a few iters of Lanczos"
doS = S is not None
niter = kwargs.get('niter',8)
N = F.shape[0]
niter = min(N,niter)
x = zeros(N,'d')
x[0] = 1
q = x
avals = []
bvals = []
if doS:
r = matrixmultiply(S,q)
else:
r = q
beta = sqrt(matrixmultiply(q,r))
wold = zeros(N,'d')
for i in xrange(niter):
w = r/beta
v = q/beta
r = matrixmultiply(F,v)
r = r - wold*beta
alpha = matrixmultiply(v,r)
avals.append(alpha)
r = r-w*alpha
if doS:
q = solve(S,r)
else:
q = r
beta = sqrt(matrixmultiply(q,r))
bvals.append(beta)
wold = w
E,V = eigh(tridiagmat(avals,bvals))
return min(E),max(E)
def geigh(H,A,**opts):
"""\
Generalized eigenproblem using a symmetric matrix H.
"""
X = SymOrthCutoff(A)
val,vec = eigh(simx(H,X))
vec = matrixmultiply(X,vec)
return val,vec
def geigh(H, A, **opts):
"""\
Generalized eigenproblem using a symmetric matrix H.
"""
X = SymOrthCutoff(A)
val, vec = eigh(simx(H, X))
vec = matrixmultiply(X, vec)
return val, vec
def update(self, **kwargs):
from PyQuante.Ints import getJ, getK
from PyQuante.LA2 import geigh, mkdens
from PyQuante.rohf import ao2mo
from PyQuante.hartree_fock import get_energy
from PyQuante.NumWrap import eigh, matrixmultiply
if self.orbs is None:
self.orbe, self.orbs = geigh(self.h, self.S)
Da = mkdens(self.orbs, 0, self.nalpha)
Db = mkdens(self.orbs, 0, self.nbeta)
Ja = getJ(self.ERI, Da)
Jb = getJ(self.ERI, Db)
Ka = getK(self.ERI, Da)
Kb = getK(self.ERI, Db)
Fa = self.h + Ja + Jb - Ka
Fb = self.h + Ja + Jb - Kb
energya = get_energy(self.h, Fa, Da)
energyb = get_energy(self.h, Fb, Db)
self.energy = (energya + energyb) / 2 + self.Enuke
Fa = ao2mo(Fa, self.orbs)
Fb = ao2mo(Fb, self.orbs)
# Building the approximate Fock matrices in the MO basis
F = 0.5 * (Fa + Fb)
K = Fb - Fa
# The Fock matrix now looks like
# F-K | F + K/2 | F
# ---------------------------------
# F + K/2 | F | F - K/2
# ---------------------------------
# F | F - K/2 | F + K
# Make explicit slice objects to simplify this
do = slice(0, self.nbeta)
so = slice(self.nbeta, self.nalpha)
uo = slice(self.nalpha, self.norbs)
F[do, do] -= K[do, do]
F[uo, uo] += K[uo, uo]
F[do, so] += 0.5 * K[do, so]
F[so, do] += 0.5 * K[so, do]
F[so, uo] -= 0.5 * K[so, uo]
F[uo, so] -= 0.5 * K[uo, so]
self.orbe, mo_orbs = eigh(F)
self.orbs = matrixmultiply(self.orbs, mo_orbs)
return
def update(self,**opts):
from PyQuante.Ints import getJ,getK
from PyQuante.LA2 import geigh,mkdens
from PyQuante.rohf import ao2mo
from PyQuante.hartree_fock import get_energy
from PyQuante.NumWrap import eigh,matrixmultiply
if self.orbs is None:
self.orbe,self.orbs = geigh(self.h, self.S)
Da = mkdens(self.orbs,0,self.nalpha)
Db = mkdens(self.orbs,0,self.nbeta)
Ja = getJ(self.ERI,Da)
Jb = getJ(self.ERI,Db)
Ka = getK(self.ERI,Da)
Kb = getK(self.ERI,Db)
Fa = self.h+Ja+Jb-Ka
Fb = self.h+Ja+Jb-Kb
energya = get_energy(self.h,Fa,Da)
energyb = get_energy(self.h,Fb,Db)
self.energy = (energya+energyb)/2 + self.Enuke
Fa = ao2mo(Fa,self.orbs)
Fb = ao2mo(Fb,self.orbs)
# Building the approximate Fock matrices in the MO basis
F = 0.5*(Fa+Fb)
K = Fb-Fa
# The Fock matrix now looks like
# F-K | F + K/2 | F
# ---------------------------------
# F + K/2 | F | F - K/2
# ---------------------------------
# F | F - K/2 | F + K
# Make explicit slice objects to simplify this
do = slice(0,self.nbeta)
so = slice(self.nbeta,self.nalpha)
uo = slice(self.nalpha,self.norbs)
F[do,do] -= K[do,do]
F[uo,uo] += K[uo,uo]
F[do,so] += 0.5*K[do,so]
F[so,do] += 0.5*K[so,do]
F[so,uo] -= 0.5*K[so,uo]
F[uo,so] -= 0.5*K[uo,so]
self.orbe,mo_orbs = eigh(F)
self.orbs = matrixmultiply(self.orbs,mo_orbs)
return
def SymOrthCutoff(S, scut=1e-5):
"""Symmetric orthogonalization of the real symmetric matrix S.
This is given by Ut(1/sqrt(lambda))U, where lambda,U are the
eigenvalues/vectors.
Only eigenvectors with eigenvalues greater that a cutoff are kept.
This approximation is useful in cases where the basis set has
linear dependencies.
"""
val, vec = eigh(S)
n = vec.shape[0]
shalf = identity(n, 'd')
for i in range(n):
if val[i] > scut:
shalf[i, i] /= sqrt(val[i])
else:
shalf[i, i] = 0.
X = simx(shalf, vec, 'T')
return X
def SymOrthCutoff(S,scut=1e-5):
"""Symmetric orthogonalization of the real symmetric matrix S.
This is given by Ut(1/sqrt(lambda))U, where lambda,U are the
eigenvalues/vectors.
Only eigenvectors with eigenvalues greater that a cutoff are kept.
This approximation is useful in cases where the basis set has
linear dependencies.
"""
val,vec = eigh(S)
n = vec.shape[0]
shalf = identity(n,'d')
for i in range(n):
if val[i] > scut:
shalf[i,i] /= sqrt(val[i])
else:
shalf[i,i] = 0.
X = simx(shalf,vec,'T')
return X
def ocbse(orbs,h,Hs,f,a,b,noccsh):
# Need to write this so that we don't need the orbs 3 times!
nsh = len(noccsh)
nbf = norb = h.shape[0]
orbe = zeros(norb,'d')
for ish in xrange(nsh):
orbs_in_shell = get_orbs_in_shell(ish,noccsh,norb)
F = get_os_fock(ish,nsh,f,a,b,h,Hs)
# form the orbital space of all of the orbs in ish plus the virts
T = orbs.take(orbs_in_shell,1)
#print "take worked? ",(T==get_orbs(orbs,orbs_in_shell)).all()
# Transform to MO space
Fmo = ao2mo(F,T)
mo_orbe,mo_orbs = eigh(Fmo)
T = matrixmultiply(T,mo_orbs)
# Insert orbital energies into the right place
update_orbe(orbs_in_shell,orbe,mo_orbe)
update_orbs(orbs_in_shell,orbs,T)
return orbe,orbs
def davidson(A, nroots, **kwargs):
etol = kwargs.get('etol', settings.DavidsonEvecTolerance
) # tolerance on the eigenval convergence
ntol = kwargs.get('ntol', settings.DavidsonNormTolerance
) # tolerance on the vector norms for addn
n, m = A.shape
ninit = max(nroots, 2)
B = zeros((n, ninit), 'd')
for i in xrange(ninit):
B[i, i] = 1.
nc = 0 # number of converged roots
eigold = 1e10
for iter in xrange(n):
if nc >= nroots: break
D = matrixmultiply(A, B)
S = matrixmultiply(transpose(B), D)
m = len(S)
eval, evec = eigh(S)
bnew = zeros(n, 'd')
for i in xrange(m):
bnew += evec[i, nc] * (D[:, i] - eval[nc] * B[:, i])
for i in xrange(n):
denom = max(eval[nc] - A[i, i],
1e-8) # Maximum amplification factor
bnew[i] /= denom
norm = orthog(bnew, B)
bnew = bnew / norm
if abs(eval[nc] - eigold) < etol:
nc += 1
eigold = eval[nc]
if norm > ntol: B = appendColumn(B, bnew)
E = eval[:nroots]
nv = len(evec)
V = matrixmultiply(B[:, :nv], evec)
return E, V
def davidson(A,nroots,**kwargs):
etol = kwargs.get('etol',settings.DavidsonEvecTolerance) # tolerance on the eigenval convergence
ntol = kwargs.get('ntol',settings.DavidsonNormTolerance) # tolerance on the vector norms for addn
n,m = A.shape
ninit = max(nroots,2)
B = zeros((n,ninit),'d')
for i in xrange(ninit): B[i,i] = 1.
nc = 0 # number of converged roots
eigold = 1e10
for iter in xrange(n):
if nc >= nroots: break
D = matrixmultiply(A,B)
S = matrixmultiply(transpose(B),D)
m = len(S)
eval,evec = eigh(S)
bnew = zeros(n,'d')
for i in xrange(m):
bnew += evec[i,nc]*(D[:,i] - eval[nc]*B[:,i])
for i in xrange(n):
denom = max(eval[nc]-A[i,i],1e-8) # Maximum amplification factor
bnew[i] /= denom
norm = orthog(bnew,B)
bnew = bnew / norm
if abs(eval[nc]-eigold) < etol:
nc += 1
eigold = eval[nc]
if norm > ntol: B = appendColumn(B,bnew)
E = eval[:nroots]
nv = len(evec)
V = matrixmultiply(B[:,:nv],evec)
return E,V
#Form Hcore
Hcore = KE + Vext
#calculate two electron integrals
elecRepulsion = Ints.get2ints(basisSet)
#Section 3############################
#Calculate Transformation Matrix X from Overlap matrix
X = linalg.SymOrth(S)
#Section 4############################
#guess density matrix from Core Hamiltonian
#diagnolize Hamiltonian and transform hamiltonian to get guess orbitals
eVal, eVec = eigh(linalg.simx(Hcore, X))
#transform orbitals from AO to MO basis
orbitals = matrixmultiply(Hcore, X)
#guess Density from guess orbitals and number of closed electron shells
D = HF.mkdens(orbitals, 0, molecule.get_closedopen()[0])
#Start of SCF Procedures############################
#init variables for SCF
cycle = 0
energy = [float("-inf")]
while (cycle < maxCycle):
#while max. number of cycles not reached
#continues with SCF iterations
def solve_fock(self):
from PyQuante.NumWrap import eigh
from PyQuante.LA2 import mkdens
self.orbea,self.orbsa = eigh(self.Fa)
self.orbeb,self.orbsb = eigh(self.Fb)
def solve_fock(self):
from PyQuante.NumWrap import eigh
self.orbe,self.orbs = eigh(self.F)
def rohf(atoms,**opts):
"""\
rohf(atoms,**opts) - Restriced Open Shell Hartree Fock
atoms A Molecule object containing the molecule
"""
ConvCriteria = opts.get('ConvCriteria',1e-5)
MaxIter = opts.get('MaxIter',40)
DoAveraging = opts.get('DoAveraging',True)
averaging = opts.get('averaging',0.95)
verbose = opts.get('verbose',True)
bfs = opts.get('bfs',None)
if not bfs:
basis_data = opts.get('basis_data',None)
bfs = getbasis(atoms,basis_data)
nbf = len(bfs)
integrals = opts.get('integrals', None)
if integrals:
S,h,Ints = integrals
else:
S,h,Ints = getints(bfs,atoms)
nel = atoms.get_nel()
nalpha,nbeta = atoms.get_alphabeta()
S,h,Ints = getints(bfs,atoms)
orbs = opts.get('orbs',None)
if orbs is None:
orbe,orbs = geigh(h,S)
norbs = nbf
enuke = atoms.get_enuke()
eold = 0.
if verbose: print "ROHF calculation on %s" % atoms.name
if verbose: print "Nbf = %d" % nbf
if verbose: print "Nalpha = %d" % nalpha
if verbose: print "Nbeta = %d" % nbeta
if verbose: print "Averaging = %s" % DoAveraging
print "Optimization of HF orbitals"
for i in xrange(MaxIter):
if verbose: print "SCF Iteration:",i,"Starting Energy:",eold
Da = mkdens(orbs,0,nalpha)
Db = mkdens(orbs,0,nbeta)
if DoAveraging:
if i:
Da = averaging*Da + (1-averaging)*Da0
Db = averaging*Db + (1-averaging)*Db0
Da0 = Da
Db0 = Db
Ja = getJ(Ints,Da)
Jb = getJ(Ints,Db)
Ka = getK(Ints,Da)
Kb = getK(Ints,Db)
Fa = h+Ja+Jb-Ka
Fb = h+Ja+Jb-Kb
energya = get_energy(h,Fa,Da)
energyb = get_energy(h,Fb,Db)
eone = (trace2(Da,h) + trace2(Db,h))/2
etwo = (trace2(Da,Fa) + trace2(Db,Fb))/2
energy = (energya+energyb)/2 + enuke
print i,energy,eone,etwo,enuke
if abs(energy-eold) < ConvCriteria: break
eold = energy
Fa = ao2mo(Fa,orbs)
Fb = ao2mo(Fb,orbs)
# Building the approximate Fock matrices in the MO basis
F = 0.5*(Fa+Fb)
K = Fb-Fa
# The Fock matrix now looks like
# F-K | F + K/2 | F
# ---------------------------------
# F + K/2 | F | F - K/2
# ---------------------------------
# F | F - K/2 | F + K
# Make explicit slice objects to simplify this
do = slice(0,nbeta)
so = slice(nbeta,nalpha)
uo = slice(nalpha,norbs)
F[do,do] -= K[do,do]
F[uo,uo] += K[uo,uo]
F[do,so] += 0.5*K[do,so]
F[so,do] += 0.5*K[so,do]
F[so,uo] -= 0.5*K[so,uo]
F[uo,so] -= 0.5*K[uo,so]
orbe,mo_orbs = eigh(F)
orbs = matrixmultiply(orbs,mo_orbs)
if verbose:
print "Final ROHF energy for system %s is %f" % (atoms.name,energy)
return energy,orbe,orbs
def solve_fock(self):
from PyQuante.NumWrap import eigh
self.orbe, self.orbs = eigh(self.F)
def solve_fock(self):
from PyQuante.NumWrap import eigh
from PyQuante.LA2 import mkdens
self.orbea, self.orbsa = eigh(self.Fa)
self.orbeb, self.orbsb = eigh(self.Fb)