def get_vind(self, mf):
'''Compute Ax'''
singlet = self.singlet
cell = mf.cell
kpts = mf.kpts
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nkpts = len(mo_occ)
nao, nmo = mo_coeff[0][0].shape
occidxa = [numpy.where(mo_occ[0][k]> 0)[0] for k in range(nkpts)]
occidxb = [numpy.where(mo_occ[1][k]> 0)[0] for k in range(nkpts)]
viridxa = [numpy.where(mo_occ[0][k]==0)[0] for k in range(nkpts)]
viridxb = [numpy.where(mo_occ[1][k]==0)[0] for k in range(nkpts)]
orboa = [mo_coeff[0][k][:,occidxa[k]] for k in range(nkpts)]
orbob = [mo_coeff[1][k][:,occidxb[k]] for k in range(nkpts)]
orbva = [mo_coeff[0][k][:,viridxa[k]] for k in range(nkpts)]
orbvb = [mo_coeff[1][k][:,viridxb[k]] for k in range(nkpts)]
e_ai_a = _get_eai(mo_energy[0], mo_occ[0])
e_ai_b = _get_eai(mo_energy[1], mo_occ[1])
hdiag = numpy.hstack([x.ravel() for x in (e_ai_a + e_ai_b)])
tot_x_a = sum(x.size for x in e_ai_a)
tot_x_b = sum(x.size for x in e_ai_b)
mem_now = lib.current_memory()[0]
max_memory = max(2000, self.max_memory*.8-mem_now)
vresp = _gen_uhf_response(mf, hermi=0, max_memory=max_memory)
def vind(zs):
nz = len(zs)
zs = [_unpack(z, mo_occ) for z in zs]
dmvo = numpy.empty((2,nz,nkpts,nao,nao), dtype=numpy.complex128)
for i in range(nz):
dm1a, dm1b = zs[i]
for k in range(nkpts):
dmvo[0,i,k] = reduce(numpy.dot, (orbva[k], dm1a[k], orboa[k].T.conj()))
dmvo[1,i,k] = reduce(numpy.dot, (orbvb[k], dm1b[k], orbob[k].T.conj()))
v1ao = vresp(dmvo)
v1s = []
for i in range(nz):
dm1a, dm1b = zs[i]
v1as = []
v1bs = []
for k in range(nkpts):
v1a = reduce(numpy.dot, (orbva[k].T.conj(), v1ao[0,i,k], orboa[k]))
v1b = reduce(numpy.dot, (orbvb[k].T.conj(), v1ao[1,i,k], orbob[k]))
v1a += e_ai_a[k] * dm1a[k]
v1b += e_ai_b[k] * dm1b[k]
v1as.append(v1a.ravel())
v1bs.append(v1b.ravel())
v1s += v1as + v1bs
return numpy.hstack(v1s).reshape(nz,-1)
return vind, hdiag
def _gen_hop_uhf_external(mf, verbose=None):
cell = mf.cell
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nkpts = len(mo_occ[0])
occidxa = [numpy.where(mo_occ[0][k]>0)[0] for k in range(nkpts)]
occidxb = [numpy.where(mo_occ[1][k]>0)[0] for k in range(nkpts)]
viridxa = [numpy.where(mo_occ[0][k]==0)[0] for k in range(nkpts)]
viridxb = [numpy.where(mo_occ[1][k]==0)[0] for k in range(nkpts)]
nocca = [len(occidxa[k]) for k in range(nkpts)]
noccb = [len(occidxb[k]) for k in range(nkpts)]
nvira = [len(viridxa[k]) for k in range(nkpts)]
nvirb = [len(viridxb[k]) for k in range(nkpts)]
moa, mob = mo_coeff
orboa = [moa[k][:,occidxa[k]] for k in range(nkpts)]
orbva = [moa[k][:,viridxa[k]] for k in range(nkpts)]
orbob = [mob[k][:,occidxb[k]] for k in range(nkpts)]
orbvb = [mob[k][:,viridxb[k]] for k in range(nkpts)]
h1e = mf.get_hcore()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
fock_ao = h1e + mf.get_veff(cell, dm0)
focka = [reduce(numpy.dot, (moa[k].T.conj(), fock_ao[0][k], moa[k]))
for k in range(nkpts)]
fockb = [reduce(numpy.dot, (mob[k].T.conj(), fock_ao[1][k], mob[k]))
for k in range(nkpts)]
fooa = [focka[k][occidxa[k][:,None],occidxa[k]] for k in range(nkpts)]
fvva = [focka[k][viridxa[k][:,None],viridxa[k]] for k in range(nkpts)]
foob = [fockb[k][occidxb[k][:,None],occidxb[k]] for k in range(nkpts)]
fvvb = [fockb[k][viridxb[k][:,None],viridxb[k]] for k in range(nkpts)]
hdiagab = [fvva[k].diagonal().real[:,None] - foob[k].diagonal().real for k in range(nkpts)]
hdiagba = [fvvb[k].diagonal().real[:,None] - fooa[k].diagonal().real for k in range(nkpts)]
hdiag2 = numpy.hstack([x.ravel() for x in (hdiagab + hdiagba)])
vresp1 = _gen_uhf_response(mf, with_j=False, hermi=0)
def hop_uhf2ghf(x1):
x1ab = []
x1ba = []
ip = 0
for k in range(nkpts):
nv = nvira[k]
no = noccb[k]
x1ab.append(x1[ip:ip+nv*no].reshape(nv,no))
ip += nv * no
for k in range(nkpts):
nv = nvirb[k]
no = nocca[k]
x1ba.append(x1[ip:ip+nv*no].reshape(nv,no))
ip += nv * no
dm1ab = []
dm1ba = []
for k in range(nkpts):
d1ab = reduce(numpy.dot, (orbva[k], x1ab[k], orbob[k].T.conj()))
d1ba = reduce(numpy.dot, (orbvb[k], x1ba[k], orboa[k].T.conj()))
dm1ab.append(d1ab+d1ba.T.conj())
dm1ba.append(d1ba+d1ab.T.conj())
v1ao = vresp1(lib.asarray([dm1ab,dm1ba]))
x2ab = [0] * nkpts
x2ba = [0] * nkpts
for k in range(nkpts):
x2ab[k] = numpy.einsum('pr,rq->pq', fvva[k], x1ab[k])
x2ab[k]-= numpy.einsum('sq,ps->pq', foob[k], x1ab[k])
x2ba[k] = numpy.einsum('pr,rq->pq', fvvb[k], x1ba[k])
x2ba[k]-= numpy.einsum('qs,ps->pq', fooa[k], x1ba[k])
x2ab[k] += reduce(numpy.dot, (orbva[k].T.conj(), v1ao[0][k], orbob[k]))
x2ba[k] += reduce(numpy.dot, (orbvb[k].T.conj(), v1ao[1][k], orboa[k]))
return numpy.hstack([x.real.ravel() for x in (x2ab+x2ba)])
return hop_uhf2ghf, hdiag2
def gen_vind(self, mf):
singlet = self.singlet
cell = mf.cell
kpts = mf.kpts
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nkpts = len(mo_occ)
nao, nmo = mo_coeff[0][0].shape
occidxa = [numpy.where(mo_occ[0][k] > 0)[0] for k in range(nkpts)]
occidxb = [numpy.where(mo_occ[1][k] > 0)[0] for k in range(nkpts)]
viridxa = [numpy.where(mo_occ[0][k] == 0)[0] for k in range(nkpts)]
viridxb = [numpy.where(mo_occ[1][k] == 0)[0] for k in range(nkpts)]
orboa = [mo_coeff[0][k][:, occidxa[k]] for k in range(nkpts)]
orbob = [mo_coeff[1][k][:, occidxb[k]] for k in range(nkpts)]
orbva = [mo_coeff[0][k][:, viridxa[k]] for k in range(nkpts)]
orbvb = [mo_coeff[1][k][:, viridxb[k]] for k in range(nkpts)]
e_ia_a = _get_e_ia(mo_energy[0], mo_occ[0])
e_ia_b = _get_e_ia(mo_energy[1], mo_occ[1])
hdiag = numpy.hstack([x.ravel() for x in (e_ia_a + e_ia_b)])
hdiag = numpy.hstack((hdiag, hdiag))
tot_x_a = sum(x.size for x in e_ia_a)
tot_x_b = sum(x.size for x in e_ia_b)
tot_x = tot_x_a + tot_x_b
mem_now = lib.current_memory()[0]
max_memory = max(2000, self.max_memory * .8 - mem_now)
vresp = _gen_uhf_response(mf, hermi=0, max_memory=max_memory)
def vind(xys):
nz = len(xys)
x1s = [_unpack(x[:tot_x], mo_occ) for x in xys]
y1s = [_unpack(x[tot_x:], mo_occ) for x in xys]
dmov = numpy.empty((2, nz, nkpts, nao, nao),
dtype=numpy.complex128)
for i in range(nz):
xa, xb = x1s[i]
ya, yb = y1s[i]
for k in range(nkpts):
dmx = reduce(numpy.dot,
(orboa[k], xa[k], orbva[k].conj().T))
dmy = reduce(numpy.dot,
(orbva[k], ya[k].T, orboa[k].conj().T))
dmov[0, i, k] = dmx + dmy # AX + BY
dmx = reduce(numpy.dot,
(orbob[k], xb[k], orbvb[k].conj().T))
dmy = reduce(numpy.dot,
(orbvb[k], yb[k].T, orbob[k].conj().T))
dmov[1, i, k] = dmx + dmy # AX + BY
with lib.temporary_env(mf, exxdiv=None):
dmov = dmov.reshape(2 * nz, nkpts, nao, nao)
v1ao = vresp(dmov)
v1ao = v1ao.reshape(2, nz, nkpts, nao, nao)
v1s = []
for i in range(nz):
xa, xb = x1s[i]
ya, yb = y1s[i]
v1xsa = []
v1xsb = []
v1ysa = []
v1ysb = []
for k in range(nkpts):
v1xa = reduce(numpy.dot,
(orboa[k].conj().T, v1ao[0, i, k], orbva[k]))
v1xb = reduce(numpy.dot,
(orbob[k].conj().T, v1ao[1, i, k], orbvb[k]))
v1ya = reduce(
numpy.dot,
(orbva[k].conj().T, v1ao[0, i, k], orboa[k])).T
v1yb = reduce(
numpy.dot,
(orbvb[k].conj().T, v1ao[1, i, k], orbob[k])).T
v1xa += e_ia_a[k] * xa[k]
v1xb += e_ia_b[k] * xb[k]
v1ya += e_ia_a[k] * ya[k]
v1yb += e_ia_b[k] * yb[k]
v1xsa.append(v1xa.ravel())
v1xsb.append(v1xb.ravel())
v1ysa.append(-v1ya.ravel())
v1ysb.append(-v1yb.ravel())
v1s += v1xsa + v1xsb + v1ysa + v1ysb
return numpy.hstack(v1s).reshape(nz, -1)
return vind, hdiag
def _gen_hop_uhf_external(mf, verbose=None):
cell = mf.cell
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nkpts = len(mo_occ[0])
occidxa = [numpy.where(mo_occ[0][k] > 0)[0] for k in range(nkpts)]
occidxb = [numpy.where(mo_occ[1][k] > 0)[0] for k in range(nkpts)]
viridxa = [numpy.where(mo_occ[0][k] == 0)[0] for k in range(nkpts)]
viridxb = [numpy.where(mo_occ[1][k] == 0)[0] for k in range(nkpts)]
nocca = [len(occidxa[k]) for k in range(nkpts)]
noccb = [len(occidxb[k]) for k in range(nkpts)]
nvira = [len(viridxa[k]) for k in range(nkpts)]
nvirb = [len(viridxb[k]) for k in range(nkpts)]
moa, mob = mo_coeff
orboa = [moa[k][:, occidxa[k]] for k in range(nkpts)]
orbva = [moa[k][:, viridxa[k]] for k in range(nkpts)]
orbob = [mob[k][:, occidxb[k]] for k in range(nkpts)]
orbvb = [mob[k][:, viridxb[k]] for k in range(nkpts)]
h1e = mf.get_hcore()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
fock_ao = h1e + mf.get_veff(cell, dm0)
focka = [
reduce(numpy.dot, (moa[k].T.conj(), fock_ao[0][k], moa[k]))
for k in range(nkpts)
]
fockb = [
reduce(numpy.dot, (mob[k].T.conj(), fock_ao[1][k], mob[k]))
for k in range(nkpts)
]
fooa = [focka[k][occidxa[k][:, None], occidxa[k]] for k in range(nkpts)]
fvva = [focka[k][viridxa[k][:, None], viridxa[k]] for k in range(nkpts)]
foob = [fockb[k][occidxb[k][:, None], occidxb[k]] for k in range(nkpts)]
fvvb = [fockb[k][viridxb[k][:, None], viridxb[k]] for k in range(nkpts)]
hdiagab = [
fvva[k].diagonal().reshape(-1, 1) - foob[k].diagonal()
for k in range(nkpts)
]
hdiagba = [
fvvb[k].diagonal().reshape(-1, 1) - fooa[k].diagonal()
for k in range(nkpts)
]
hdiag2 = numpy.hstack([x.ravel() for x in (hdiagab + hdiagba)])
vresp1 = _gen_uhf_response(mf, with_j=False, hermi=0)
def hop_uhf2ghf(x1):
x1ab = []
x1ba = []
ip = 0
for k in range(nkpts):
nv = nvira[k]
no = noccb[k]
x1ab.append(x1[ip:ip + nv * no].reshape(nv, no))
ip += nv * no
for k in range(nkpts):
nv = nvirb[k]
no = nocca[k]
x1ba.append(x1[ip:ip + nv * no].reshape(nv, no))
ip += nv * no
dm1ab = []
dm1ba = []
for k in range(nkpts):
d1ab = reduce(numpy.dot, (orbva[k], x1ab[k], orbob[k].T.conj()))
d1ba = reduce(numpy.dot, (orbvb[k], x1ba[k], orboa[k].T.conj()))
dm1ab.append(d1ab + d1ba.T.conj())
dm1ba.append(d1ba + d1ab.T.conj())
v1ao = vresp1(lib.asarray([dm1ab, dm1ba]))
x2ab = [0] * nkpts
x2ba = [0] * nkpts
for k in range(nkpts):
x2ab[k] = numpy.einsum('pr,rq->pq', fvva[k], x1ab[k])
x2ab[k] -= numpy.einsum('sq,ps->pq', foob[k], x1ab[k])
x2ba[k] = numpy.einsum('pr,rq->pq', fvvb[k], x1ba[k])
x2ba[k] -= numpy.einsum('qs,ps->pq', fooa[k], x1ba[k])
x2ab[k] += reduce(numpy.dot,
(orbva[k].T.conj(), v1ao[0][k], orbob[k]))
x2ba[k] += reduce(numpy.dot,
(orbvb[k].T.conj(), v1ao[1][k], orboa[k]))
return numpy.hstack([x.ravel() for x in (x2ab + x2ba)])
return hop_uhf2ghf, hdiag2
def get_vind(self, mf):
'''Compute Ax'''
singlet = self.singlet
cell = mf.cell
kpts = mf.kpts
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nkpts = len(mo_occ)
nao, nmo = mo_coeff[0][0].shape
occidxa = [numpy.where(mo_occ[0][k]> 0)[0] for k in range(nkpts)]
occidxb = [numpy.where(mo_occ[1][k]> 0)[0] for k in range(nkpts)]
viridxa = [numpy.where(mo_occ[0][k]==0)[0] for k in range(nkpts)]
viridxb = [numpy.where(mo_occ[1][k]==0)[0] for k in range(nkpts)]
orboa = [mo_coeff[0][k][:,occidxa[k]] for k in range(nkpts)]
orbob = [mo_coeff[1][k][:,occidxb[k]] for k in range(nkpts)]
orbva = [mo_coeff[0][k][:,viridxa[k]] for k in range(nkpts)]
orbvb = [mo_coeff[1][k][:,viridxb[k]] for k in range(nkpts)]
e_ia_a = _get_e_ia(mo_energy[0], mo_occ[0])
e_ia_b = _get_e_ia(mo_energy[1], mo_occ[1])
hdiag = numpy.hstack([x.ravel() for x in (e_ia_a + e_ia_b)])
tot_x_a = sum(x.size for x in e_ia_a)
tot_x_b = sum(x.size for x in e_ia_b)
mem_now = lib.current_memory()[0]
max_memory = max(2000, self.max_memory*.8-mem_now)
vresp = _gen_uhf_response(mf, hermi=0, max_memory=max_memory)
def vind(zs):
nz = len(zs)
zs = [_unpack(z, mo_occ) for z in zs]
dmov = numpy.empty((2,nz,nkpts,nao,nao), dtype=numpy.complex128)
for i in range(nz):
dm1a, dm1b = zs[i]
for k in range(nkpts):
dmov[0,i,k] = reduce(numpy.dot, (orboa[k], dm1a[k], orbva[k].conj().T))
dmov[1,i,k] = reduce(numpy.dot, (orbob[k], dm1b[k], orbvb[k].conj().T))
with lib.temporary_env(mf, exxdiv=None):
dmov = dmov.reshape(2*nz,nkpts,nao,nao)
v1ao = vresp(dmov)
v1ao = v1ao.reshape(2,nz,nkpts,nao,nao)
v1s = []
for i in range(nz):
dm1a, dm1b = zs[i]
v1as = []
v1bs = []
for k in range(nkpts):
v1a = reduce(numpy.dot, (orboa[k].conj().T, v1ao[0,i,k], orbva[k]))
v1b = reduce(numpy.dot, (orbob[k].conj().T, v1ao[1,i,k], orbvb[k]))
v1a += e_ia_a[k] * dm1a[k]
v1b += e_ia_b[k] * dm1b[k]
v1as.append(v1a.ravel())
v1bs.append(v1b.ravel())
v1s += v1as + v1bs
return numpy.hstack(v1s).reshape(nz,-1)
return vind, hdiag
def get_vind(self, mf):
singlet = self.singlet
cell = mf.cell
kpts = mf.kpts
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nkpts = len(mo_occ)
nao, nmo = mo_coeff[0][0].shape
occidxa = [numpy.where(mo_occ[0][k]> 0)[0] for k in range(nkpts)]
occidxb = [numpy.where(mo_occ[1][k]> 0)[0] for k in range(nkpts)]
viridxa = [numpy.where(mo_occ[0][k]==0)[0] for k in range(nkpts)]
viridxb = [numpy.where(mo_occ[1][k]==0)[0] for k in range(nkpts)]
orboa = [mo_coeff[0][k][:,occidxa[k]] for k in range(nkpts)]
orbob = [mo_coeff[1][k][:,occidxb[k]] for k in range(nkpts)]
orbva = [mo_coeff[0][k][:,viridxa[k]] for k in range(nkpts)]
orbvb = [mo_coeff[1][k][:,viridxb[k]] for k in range(nkpts)]
e_ia_a = _get_e_ia(mo_energy[0], mo_occ[0])
e_ia_b = _get_e_ia(mo_energy[1], mo_occ[1])
hdiag = numpy.hstack([x.ravel() for x in (e_ia_a + e_ia_b)])
hdiag = numpy.hstack((hdiag, hdiag))
tot_x_a = sum(x.size for x in e_ia_a)
tot_x_b = sum(x.size for x in e_ia_b)
tot_x = tot_x_a + tot_x_b
mem_now = lib.current_memory()[0]
max_memory = max(2000, self.max_memory*.8-mem_now)
vresp = _gen_uhf_response(mf, hermi=0, max_memory=max_memory)
def vind(xys):
nz = len(xys)
x1s = [_unpack(x[:tot_x], mo_occ) for x in xys]
y1s = [_unpack(x[tot_x:], mo_occ) for x in xys]
dmov = numpy.empty((2,nz,nkpts,nao,nao), dtype=numpy.complex128)
for i in range(nz):
xa, xb = x1s[i]
ya, yb = y1s[i]
for k in range(nkpts):
dmx = reduce(numpy.dot, (orboa[k], xa[k] , orbva[k].conj().T))
dmy = reduce(numpy.dot, (orbva[k], ya[k].T, orboa[k].conj().T))
dmov[0,i,k] = dmx + dmy # AX + BY
dmx = reduce(numpy.dot, (orbob[k], xb[k] , orbvb[k].conj().T))
dmy = reduce(numpy.dot, (orbvb[k], yb[k].T, orbob[k].conj().T))
dmov[1,i,k] = dmx + dmy # AX + BY
with lib.temporary_env(mf, exxdiv=None):
dmov = dmov.reshape(2*nz,nkpts,nao,nao)
v1ao = vresp(dmov)
v1ao = v1ao.reshape(2,nz,nkpts,nao,nao)
v1s = []
for i in range(nz):
xa, xb = x1s[i]
ya, yb = y1s[i]
v1xsa = []
v1xsb = []
v1ysa = []
v1ysb = []
for k in range(nkpts):
v1xa = reduce(numpy.dot, (orboa[k].conj().T, v1ao[0,i,k], orbva[k]))
v1xb = reduce(numpy.dot, (orbob[k].conj().T, v1ao[1,i,k], orbvb[k]))
v1ya = reduce(numpy.dot, (orbva[k].conj().T, v1ao[0,i,k], orboa[k])).T
v1yb = reduce(numpy.dot, (orbvb[k].conj().T, v1ao[1,i,k], orbob[k])).T
v1xa+= e_ia_a[k] * xa[k]
v1xb+= e_ia_b[k] * xb[k]
v1ya+= e_ia_a[k] * ya[k]
v1yb+= e_ia_b[k] * yb[k]
v1xsa.append(v1xa.ravel())
v1xsb.append(v1xb.ravel())
v1ysa.append(-v1ya.ravel())
v1ysb.append(-v1yb.ravel())
v1s += v1xsa + v1xsb + v1ysa + v1ysb
return numpy.hstack(v1s).reshape(nz,-1)
return vind, hdiag