def orthog(q, qs, **kwargs):
"Orthonormalize vector q to set of vectors qs"
nbasis, nvec = qs.shape
north = kwargs.get('north', nvec)
#if north==-1: north = nvec
#north = min(north,nvec)
for i in xrange(north):
olap = dot(q, qs[:, i])
q -= olap * qs[:, i]
norm = sqrt(dot(q, q))
return norm
def orthog(q,qs,**kwargs):
"Orthonormalize vector q to set of vectors qs"
nbasis,nvec = qs.shape
north = kwargs.get('north',nvec)
#if north==-1: north = nvec
#north = min(north,nvec)
for i in xrange(north):
olap = dot(q,qs[:,i])
q -= olap*qs[:,i]
norm = sqrt(dot(q,q))
return norm
def orthogonalize(orbs,S):
nbf,norb = orbs.shape
Smax = 0
for i in xrange(norb):
for j in xrange(i):
Sij = dot(orbs[:,j],dot(S,orbs[:,i]))
Smax = max(Smax,abs(Sij))
orbs[:,i] -= Sij*orbs[:,j]
Sii = dot(orbs[:,i],dot(S,orbs[:,i]))
orbs[:,i] /= sqrt(Sii)
print "Max orthogonalized element = ",Smax
return
def get_energy(self,b):
self.iter += 1
ba = b[:self.nbf]
bb = b[self.nbf:]
self.Hoepa = get_Hoep(ba,self.H0,self.Gij)
self.Hoepb = get_Hoep(bb,self.H0,self.Gij)
self.orbea,self.orbsa = geigh(self.Hoepa,self.S)
self.orbeb,self.orbsb = geigh(self.Hoepb,self.S)
if self.etemp:
self.Da,entropya = mkdens_fermi(2*self.nalpha,self.orbea,self.orbsa,
self.etemp)
self.Db,entropyb = mkdens_fermi(2*self.nbeta,self.orbeb,self.orbsb,
self.etemp)
self.entropy = 0.5*(entropya+entropyb)
else:
self.Da = mkdens(self.orbsa,0,self.nalpha)
self.Db = mkdens(self.orbsb,0,self.nbeta)
self.entropy=0
J = getJ(self.Ints,self.Da+self.Db)
Ka = getK(self.Ints,self.Da)
Kb = getK(self.Ints,self.Db)
self.Fa = self.h + J - Ka
self.Fb = self.h + J - Kb
self.energy = 0.5*(trace2(self.h+self.Fa,self.Da) +
trace2(self.h+self.Fb,self.Db))\
+ self.Enuke + self.entropy
if self.iter == 1 or self.iter % 10 == 0:
logging.debug("%4d %10.5f %10.5f" % (self.iter,self.energy,dot(b,b)))
return self.energy
def get_exx_energy(b,nbf,nel,nocc,ETemp,Enuke,S,h,Ints,H0,Gij,**opts):
"""Computes the energy for the OEP/HF functional
Options:
return_flag 0 Just return the energy
1 Return energy, orbe, orbs
2 Return energy, orbe, orbs, F
"""
return_flag = opts.get('return_flag',0)
Hoep = get_Hoep(b,H0,Gij)
orbe,orbs = geigh(Hoep,S)
if ETemp:
efermi = get_efermi(nel,orbe,ETemp)
occs = get_fermi_occs(efermi,orbe,ETemp)
D = mkdens_occs(orbs,occs)
entropy = get_entropy(occs,ETemp)
else:
D = mkdens(orbs,0,nocc)
F = get_fock(D,Ints,h)
energy = trace2(h+F,D)+Enuke
if ETemp: energy += entropy
iref = nel/2
gap = 627.51*(orbe[iref]-orbe[iref-1])
logging.debug("EXX Energy, B, Gap: %10.5f %10.5f %10.5f"
% (energy,sqrt(dot(b,b)),gap))
#logging.debug("%s" % orbe)
if return_flag == 1:
return energy,orbe,orbs
elif return_flag == 2:
return energy,orbe,orbs,F
return energy
def get_exx_energy(b, nbf, nel, nocc, ETemp, Enuke, S, h, Ints, H0, Gij,
**opts):
"""Computes the energy for the OEP/HF functional
Options:
return_flag 0 Just return the energy
1 Return energy, orbe, orbs
2 Return energy, orbe, orbs, F
"""
return_flag = opts.get('return_flag', 0)
Hoep = get_Hoep(b, H0, Gij)
orbe, orbs = geigh(Hoep, S)
if ETemp:
efermi = get_efermi(nel, orbe, ETemp)
occs = get_fermi_occs(efermi, orbe, ETemp)
D = mkdens_occs(orbs, occs)
entropy = get_entropy(occs, ETemp)
else:
D = mkdens(orbs, 0, nocc)
F = get_fock(D, Ints, h)
energy = trace2(h + F, D) + Enuke
if ETemp: energy += entropy
iref = nel / 2
gap = 627.51 * (orbe[iref] - orbe[iref - 1])
logging.debug("EXX Energy, B, Gap: %10.5f %10.5f %10.5f" %
(energy, sqrt(dot(b, b)), gap))
#logging.debug("%s" % orbe)
if return_flag == 1:
return energy, orbe, orbs
elif return_flag == 2:
return energy, orbe, orbs, F
return energy
def get_energy(self, b):
self.iter += 1
ba = b[:self.nbf]
bb = b[self.nbf:]
self.Hoepa = get_Hoep(ba, self.H0, self.Gij)
self.Hoepb = get_Hoep(bb, self.H0, self.Gij)
self.orbea, self.orbsa = geigh(self.Hoepa, self.S)
self.orbeb, self.orbsb = geigh(self.Hoepb, self.S)
if self.etemp:
self.Da, entropya = mkdens_fermi(2 * self.nalpha, self.orbea,
self.orbsa, self.etemp)
self.Db, entropyb = mkdens_fermi(2 * self.nbeta, self.orbeb,
self.orbsb, self.etemp)
self.entropy = 0.5 * (entropya + entropyb)
else:
self.Da = mkdens(self.orbsa, 0, self.nalpha)
self.Db = mkdens(self.orbsb, 0, self.nbeta)
self.entropy = 0
J = getJ(self.Ints, self.Da + self.Db)
Ka = getK(self.Ints, self.Da)
Kb = getK(self.Ints, self.Db)
self.Fa = self.h + J - Ka
self.Fb = self.h + J - Kb
self.energy = 0.5*(trace2(self.h+self.Fa,self.Da) +
trace2(self.h+self.Fb,self.Db))\
+ self.Enuke + self.entropy
if self.iter == 1 or self.iter % 10 == 0:
logging.debug("%4d %10.5f %10.5f" %
(self.iter, self.energy, dot(b, b)))
return self.energy
def getF(self, F, D):
n, m = F.shape
err = matrixmultiply(F,matrixmultiply(D,self.S)) -\
matrixmultiply(self.S,matrixmultiply(D,F))
err = ravel(err)
maxerr = max(abs(err))
if maxerr < self.errcutoff and not self.started:
if VERBOSE: print "Starting DIIS: Max Err = ", maxerr
self.started = 1
if not self.started:
# Do simple averaging until DIIS starts
if self.Fold:
Freturn = 0.5 * F + 0.5 * self.Fold
else:
Freturn = F
self.Fold = F
return Freturn
elif not self.errold:
Freturn = 0.5 * F + 0.5 * self.Fold
self.errold = err
return Freturn
a = zeros((3, 3), 'd')
b = zeros(3, 'd')
a[0, 0] = dot(self.errold, self.errold)
a[1, 0] = dot(self.errold, err)
a[0, 1] = a[1, 0]
a[1, 1] = dot(err, err)
a[:, 2] = -1
a[2, :] = -1
a[2, 2] = 0
b[2] = -1
c = solve(a, b)
# Handle a few special cases:
alpha = c[1]
print alpha, c
#if alpha < 0: alpha = 0
#if alpha > 1: alpha = 1
F = (1 - alpha) * self.Fold + alpha * F
self.errold = err
self.Fold = F
return F
def getF(self, F, D):
n, m = F.shape
err = matrixmultiply(F, matrixmultiply(D, self.S)) - matrixmultiply(self.S, matrixmultiply(D, F))
err = ravel(err)
maxerr = max(abs(err))
if maxerr < self.errcutoff and not self.started:
if VERBOSE:
print "Starting DIIS: Max Err = ", maxerr
self.started = 1
if not self.started:
# Do simple averaging until DIIS starts
if self.Fold:
Freturn = 0.5 * F + 0.5 * self.Fold
else:
Freturn = F
self.Fold = F
return Freturn
elif not self.errold:
Freturn = 0.5 * F + 0.5 * self.Fold
self.errold = err
return Freturn
a = zeros((3, 3), "d")
b = zeros(3, "d")
a[0, 0] = dot(self.errold, self.errold)
a[1, 0] = dot(self.errold, err)
a[0, 1] = a[1, 0]
a[1, 1] = dot(err, err)
a[:, 2] = -1
a[2, :] = -1
a[2, 2] = 0
b[2] = -1
c = solve(a, b)
# Handle a few special cases:
alpha = c[1]
print alpha, c
# if alpha < 0: alpha = 0
# if alpha > 1: alpha = 1
F = (1 - alpha) * self.Fold + alpha * F
self.errold = err
self.Fold = F
return F
def getK(Ints,D):
"Form the exchange operator corresponding to a density matrix D"
nbf = D.shape[0]
D1d = reshape(D,(nbf*nbf,)) #1D version of Dens
K = zeros((nbf,nbf),'d')
for i in xrange(nbf):
for j in xrange(i+1):
if sorted:
temp = kints[i,j]
else:
temp = fetch_kints(Ints,i,j,nbf)
K[i,j] = dot(temp,D1d)
K[j,i] = K[i,j]
return K
def get2JmK(Ints,D):
"Form the 2J-K integrals corresponding to a density matrix D"
nbf = D.shape[0]
D1d = reshape(D,(nbf*nbf,)) #1D version of Dens
G = zeros((nbf,nbf),'d')
for i in xrange(nbf):
for j in xrange(i+1):
if sorted:
temp = 2*jints[i,j]-kints[i,j]
else:
temp = 2*fetch_jints(Ints,i,j,nbf)-fetch_kints(Ints,i,j,nbf)
G[i,j] = dot(temp,D1d)
G[j,i] = G[i,j]
return G
def getJ(Ints,D):
"Form the Coulomb operator corresponding to a density matrix D"
nbf = D.shape[0]
D1d = reshape(D,(nbf*nbf,)) #1D version of Dens
J = zeros((nbf,nbf),'d')
for i in xrange(nbf):
for j in xrange(i+1):
if sorted:
temp = jints[i,j]
else:
temp = fetch_jints(Ints,i,j,nbf)
J[i,j] = dot(temp,D1d)
J[j,i] = J[i,j]
return J
def getF(self, F, D):
n, m = F.shape
err = matrixmultiply(F,matrixmultiply(D,self.S)) -\
matrixmultiply(self.S,matrixmultiply(D,F))
err = ravel(err)
maxerr = max(abs(err))
self.maxerr = maxerr
if maxerr < self.errcutoff and not self.started:
if VERBOSE: print "Starting DIIS: Max Err = ", maxerr
self.started = 1
if not self.started:
# Do simple averaging until DIIS starts
if self.Fold != None:
Freturn = 0.5 * F + 0.5 * self.Fold
self.Fold = F
else:
self.Fold = F
Freturn = F
return Freturn
self.Fs.append(F)
self.Errs.append(err)
nit = len(self.Errs)
a = zeros((nit + 1, nit + 1), 'd')
b = zeros(nit + 1, 'd')
for i in xrange(nit):
for j in xrange(nit):
a[i, j] = dot(self.Errs[i], self.Errs[j])
for i in xrange(nit):
a[nit, i] = a[i, nit] = -1.0
b[i] = 0
#mtx2file(a,'A%d.dat' % nit)
a[nit, nit] = 0
b[nit] = -1.0
# The try loop makes this a bit more stable.
# Thanks to John Kendrick!
try:
c = solve(a, b)
except:
self.Fold = F
return F
F = zeros((n, m), 'd')
for i in xrange(nit):
F += c[i] * self.Fs[i]
return F
def getF(self, F, D):
n, m = F.shape
err = matrixmultiply(F, matrixmultiply(D, self.S)) - matrixmultiply(self.S, matrixmultiply(D, F))
err = ravel(err)
maxerr = max(abs(err))
self.maxerr = maxerr
if maxerr < self.errcutoff and not self.started:
if VERBOSE:
print "Starting DIIS: Max Err = ", maxerr
self.started = 1
if not self.started:
# Do simple averaging until DIIS starts
if self.Fold != None:
Freturn = 0.5 * F + 0.5 * self.Fold
self.Fold = F
else:
self.Fold = F
Freturn = F
return Freturn
self.Fs.append(F)
self.Errs.append(err)
nit = len(self.Errs)
a = zeros((nit + 1, nit + 1), "d")
b = zeros(nit + 1, "d")
for i in range(nit):
for j in range(nit):
a[i, j] = dot(self.Errs[i], self.Errs[j])
for i in range(nit):
a[nit, i] = a[i, nit] = -1.0
b[i] = 0
# mtx2file(a,'A%d.dat' % nit)
a[nit, nit] = 0
b[nit] = -1.0
# The try loop makes this a bit more stable.
# Thanks to John Kendrick!
try:
c = solve(a, b)
except:
self.Fold = F
return F
F = zeros((n, m), "d")
for i in range(nit):
F += c[i] * self.Fs[i]
return F
def get_energy(self,b):
self.iter += 1
self.Hoep = get_Hoep(b,self.H0,self.Gij)
self.orbe,self.orbs = geigh(self.Hoep,self.S)
if self.etemp:
self.D,self.entropy = mkdens_fermi(self.nel,self.orbe,self.orbs,
self.etemp)
else:
self.D = mkdens(self.orbs,0,self.nclosed)
self.entropy=0
self.F = get_fock(self.D,self.Ints,self.h)
self.energy = trace2(self.h+self.F,self.D)+self.Enuke + self.entropy
if self.iter == 1 or self.iter % 10 == 0:
logging.debug("%4d %10.5f %10.5f" % (self.iter,self.energy,dot(b,b)))
return self.energy
def get_energy(self, b):
self.iter += 1
self.Hoep = get_Hoep(b, self.H0, self.Gij)
self.orbe, self.orbs = geigh(self.Hoep, self.S)
if self.etemp:
self.D, self.entropy = mkdens_fermi(self.nel, self.orbe, self.orbs,
self.etemp)
else:
self.D = mkdens(self.orbs, 0, self.nclosed)
self.entropy = 0
self.F = get_fock(self.D, self.Ints, self.h)
self.energy = trace2(self.h + self.F,
self.D) + self.Enuke + self.entropy
if self.iter == 1 or self.iter % 10 == 0:
logging.debug("%4d %10.5f %10.5f" %
(self.iter, self.energy, dot(b, b)))
return self.energy
def dot1d(a, b):
return dot(ravel(a), ravel(b))
def dot1d(a, b):
return dot(ravel(a), ravel(b))