def eaccsd_diag(eom, imds=None):
if imds is None: imds = eom.make_imds()
t1, t2 = imds.t1, imds.t2
nocc, nvir = t1.shape
foo = imds.eris.foo
fvv = imds.eris.fvv
Hr1 = imds.Lvv.diagonal()
Hr1 = tensor(Hr1)
if eom.partition == 'mp':
jab = fvv.diagonal()[None, :, None]
jab = jab + fvv.diagonal()[None, None, :]
jab = jab - foo.diagonal()[:, None, None]
Hr2 = tensor(jab)
else:
jab = imds.Lvv.diagonal().reshape(1, nvir, 1)
jab = jab + imds.Lvv.diagonal().reshape(1, 1, nvir)
jab = jab - imds.Loo.diagonal().reshape(nocc, 1, 1)
wab = np.einsum("abab->ab", imds.Wvvvv.array)
wjb = np.einsum('jbjb->jb', imds.Wovov.array)
wjb2 = np.einsum('jbbj->jb', imds.Wovvo.array)
wja = np.einsum('jaja->ja', imds.Wovov.array)
jab = jab + wab.reshape(1, nvir, nvir)
jab = jab - wjb.reshape(nocc, 1, nvir)
jab = jab + 2 * wjb2.reshape(nocc, 1, nvir)
jab -= np.einsum('jb,ab->jab', wjb2, np.eye(nvir))
jab = jab - wja.reshape(nocc, nvir, 1)
Hr2 = tensor(jab)
Hr2 -= 2 * lib.einsum('ijab,ijab->jab', t2, imds.Woovv)
Hr2 += lib.einsum('ijab,ijba->jab', t2, imds.Woovv)
vector = eom.amplitudes_to_vector(Hr1, Hr2)
return vector
def ipccsd_diag(eom, imds=None):
if imds is None: imds = eom.make_imds()
t1, t2 = imds.t1, imds.t2
nocc, nvir = t1.shape
foo = imds.eris.foo
fvv = imds.eris.fvv
Hr1 = -imds.Loo.diagonal()
Hr1 = tensor(Hr1)
if eom.partition == 'mp':
ijb = -foo.diagonal().reshape(nocc, 1, 1)
ijb = ijb - foo.diagonal().reshape(1, nocc, 1)
ijb = ijb + fvv.diagonal().reshape(1, 1, nvir)
Hr2 = tensor(ijb)
else:
wij = np.einsum('ijij->ij', imds.Woooo.array)
wjb = np.einsum('jbjb->jb', imds.Wovov.array)
wjb2 = np.einsum('jbbj->jb', imds.Wovvo.array)
wib = np.einsum('ibib->ib', imds.Wovov.array)
ijb = imds.Lvv.diagonal().reshape(1, 1, nvir)
ijb = ijb - imds.Loo.diagonal().reshape(nocc, 1, 1)
ijb = ijb - imds.Loo.diagonal().reshape(1, nocc, 1)
#print(ijb.shape, wjb.shape)
ijb = ijb + wij.reshape(nocc, nocc, 1)
ijb = ijb - wjb.reshape(1, nocc, nvir)
ijb = ijb + 2 * wjb2.reshape(1, nocc, nvir)
ijb = ijb - np.einsum('ij,jb->ijb', np.eye(nocc), wjb2)
ijb = ijb - wib.reshape(nocc, 1, nvir)
Hr2 = tensor(ijb)
Hr2 -= 2. * lib.einsum('ijcb,jibc->ijb', t2, imds.Woovv)
Hr2 += lib.einsum('ijcb,ijbc->ijb', t2, imds.Woovv)
vector = eom.amplitudes_to_vector(Hr1, Hr2)
return vector
def get_range_symten(A,split,l,q=2):
'''
Compute a range that approximates the range of tensor A
Reference: Algorithm 4.4 of https://arxiv.org/abs/0909.4061
args:
A: symtensor
The symtensor whose range we are finding
split: int
The index along which the svd will be done
l: int
The number of vectors to be used (output will be size m x l)
kwargs:
q: int
The number of iterations to perform (default = 2)
returns:
Q: symtensor
An orthonormal tensor whose range
approximates the range of the input tensor A
'''
# Get tensor dimensions
ndiml = split
ndimr = A.ndim-split
# Generate Random Gaussian Matrix
Omega = make_omega(A,split,l)
# Initial Setup
einstr = STR[:ndiml+ndimr]+','\
+STR[ndiml:ndiml+ndimr+1]+'->'\
+STR[:ndiml]+STR[ndiml+ndimr:ndiml+ndimr+1]
Y = einsum(einstr,A,Omega)
Q = orthonormal_ten(Y,ndiml)
#Q = orthonormal_ten_slow(Y,ndiml)
# Loop through iterations
for i in range(q):
# First step
einstr = STR[:ndiml+ndimr]+','\
+STR[:ndiml]+STR[ndiml+ndimr:ndiml+ndimr+1]+'->'\
+STR[ndiml:ndiml+ndimr+1]
Y = einsum(einstr,A,Q)
Q = orthonormal_ten(Y,ndimr)
# Second Step
einstr = STR[:ndiml+ndimr]+','\
+STR[ndiml:ndiml+ndimr+1]+'->'\
+STR[:ndiml]+STR[ndiml+ndimr:ndiml+ndimr+1]
Y = einsum(einstr,A,Q)
Q = orthonormal_ten(Y,ndiml)
# Return Result
return Q
def energy(cc, t1, t2, eris):
log = Logger(cc.stdout, cc.verbose)
nkpts = len(cc.kpts)
e = 2 * lib.einsum('ia,ia', eris.fov, t1)
tau = lib.einsum('ia,jb->ijab', t1, t1)
tau += t2
e += 2 * lib.einsum('ijab,iajb', tau, eris.ovov)
e += -lib.einsum('ijab,ibja', tau, eris.ovov)
if abs(e.imag) > 1e-4:
log.warn('Non-zero imaginary part found in KRCCSD energy %s', e)
return e.real / nkpts
def init_amps(self, eris):
time0 = time.clock(), time.time()
log = Logger(self.stdout, self.verbose)
nocc = self.nocc
nvir = self.nmo - nocc
kpts = self.kpts
nkpts = self.nkpts
gvec = self._scf.cell.reciprocal_vectors()
sym1 = ['+-', [
kpts,
] * 2, None, gvec]
t1 = lib.zeros([nocc, nvir], eris.dtype, sym1)
t2 = eris.ovov.transpose(0, 2, 1, 3).conj() / eris.eijab
self.emp2 = 2 * lib.einsum('ijab,iajb', t2, eris.ovov)
self.emp2 -= lib.einsum('ijab,ibja', t2, eris.ovov)
self.emp2 = self.emp2.real / nkpts
log.info('Init t2, MP2 energy (with fock eigenvalue shift) = %.15g',
self.emp2)
log.timer('init mp2', *time0)
return self.emp2, t1, t2
def rsvd_symten(A,split,k,q=2,nover=2):
'''
Compute the svd of a tensor using the randomized svd algorithm
detailed in https://arxiv.org/abs/0909.4061. Here, we use algorithm
4.4 for step A and algorithm 5.1 for step B
args:
A: symtensor
The matrix whose range we are finding
split: int
The index along which the svd will be done
l: int
The number of vectors to be used (output will be size m x l)
kwargs:
q: int
The number of iterations to perform (default = 2)
nover: int
The number of extra vectors to be used (will be truncated off
at the end)
returns:
Q: symtensor
The resulting unitary U tensor from SVD
R: symtensor
The resulting S*V tensor from SVD
'''
# Do Step A
Q = get_range_symten(A,split,k+nover,q=q)
# Do Step B
ndiml = split
ndimr = A.ndim-split
einstr = STR[:ndiml+1] + ','\
+STR[:ndiml] + STR[ndiml+1:ndiml+ndimr+1] + '->'\
+STR[ndiml:ndiml+ndimr+1]
B = einsum(einstr,Q,A)
# Truncate from l to k
Q = truncate(Q,Q.ndim-1,k)
B = truncate(B,0,k)
# Return Result
return Q,B
def eaccsd_matvec(eom, vector, kshift, imds=None, diag=None):
# Ref: Nooijen and Bartlett, J. Chem. Phys. 102, 3629 (1994) Eqs.(30)-(31)
if imds is None: imds = eom.make_imds()
r1, r2 = eom.vector_to_amplitudes(vector, kshift)
# Eq. (30)
# 1p-1p block
Hr1 = lib.einsum('ac,c->a', imds.Lvv, r1)
# 1p-2p1h block
Hr1 += lib.einsum('ld,lad->a', 2. * imds.Fov, r2)
Hr1 += lib.einsum('ld,lda->a', -imds.Fov, r2)
Hr1 += 2 * lib.einsum('alcd,lcd->a', imds.Wvovv, r2)
Hr1 += -lib.einsum('aldc,lcd->a', imds.Wvovv, r2)
# Eq. (31)
# 2p1h-1p block
Hr2 = lib.einsum('abcj,c->jab', imds.Wvvvo, r1)
# 2p1h-2p1h block
if eom.partition == 'mp':
foo = imds.eris.foo
fvv = imds.eris.fvv
Hr2 += lib.einsum('ac,jcb->jab', fvv, r2)
Hr2 += lib.einsum('bd,jad->jab', fvv, r2)
Hr2 += -lib.einsum('lj,lab->jab', foo, r2)
elif eom.partition == 'full':
Hr2 += eom._eaccsd_diag_matrix2 * r2
else:
Hr2 += lib.einsum('ac,jcb->jab', imds.Lvv, r2)
Hr2 += lib.einsum('bd,jad->jab', imds.Lvv, r2)
Hr2 += -lib.einsum('lj,lab->jab', imds.Loo, r2)
Hr2 += 2 * lib.einsum('lbdj,lad->jab', imds.Wovvo, r2)
Hr2 += -lib.einsum('lbjd,lad->jab', imds.Wovov, r2)
Hr2 += -lib.einsum('lajc,lcb->jab', imds.Wovov, r2)
Hr2 += -lib.einsum('lbcj,lca->jab', imds.Wovvo, r2)
Hr2 += lib.einsum('abcd,jcd->jab', imds.Wvvvv, r2)
tmp = (2 * lib.einsum('klcd,lcd->k', imds.Woovv, r2) -
lib.einsum('kldc,lcd->k', imds.Woovv, r2))
Hr2 += -lib.einsum('k,kjab->jab', tmp, imds.t2)
vector = eom.amplitudes_to_vector(Hr1, Hr2)
return vector
def ipccsd_matvec(eom, vector, kshift, imds=None, diag=None):
# Ref: Nooijen and Snijders, J. Chem. Phys. 102, 1681 (1995) Eqs.(8)-(9)
if imds is None: imds = eom.make_imds()
r1, r2 = eom.vector_to_amplitudes(vector, kshift)
# 1h-1h block
Hr1 = -lib.einsum('ki,k->i', imds.Loo, r1)
#1h-2h1p block
Hr1 += 2 * lib.einsum('ld,ild->i', imds.Fov, r2)
Hr1 += -lib.einsum('kd,kid->i', imds.Fov, r2)
Hr1 += -2 * lib.einsum('klid,kld->i', imds.Wooov, r2)
Hr1 += lib.einsum('lkid,kld->i', imds.Wooov, r2)
# 2h1p-1h block
Hr2 = -lib.einsum('kbij,k->ijb', imds.Wovoo, r1)
# 2h1p-2h1p block
if eom.partition == 'mp':
foo = self.eris.foo
fvv = self.eris.fvv
Hr2 += lib.einsum('bd,ijd->ijb', fvv, r2)
Hr2 += -lib.einsum('ki,kjb->ijb', foo, r2)
Hr2 += -lib.einsum('lj,ilb->ijb', foo, r2)
elif eom.partition == 'full':
Hr2 += self._ipccsd_diag_matrix2 * r2
else:
Hr2 += lib.einsum('bd,ijd->ijb', imds.Lvv, r2)
Hr2 += -lib.einsum('ki,kjb->ijb', imds.Loo, r2)
Hr2 += -lib.einsum('lj,ilb->ijb', imds.Loo, r2)
Hr2 += lib.einsum('klij,klb->ijb', imds.Woooo, r2)
Hr2 += 2 * lib.einsum('lbdj,ild->ijb', imds.Wovvo, r2)
Hr2 += -lib.einsum('kbdj,kid->ijb', imds.Wovvo, r2)
Hr2 += -lib.einsum('lbjd,ild->ijb', imds.Wovov, r2) #typo in Ref
Hr2 += -lib.einsum('kbid,kjd->ijb', imds.Wovov, r2)
tmp = 2 * lib.einsum('lkdc,kld->c', imds.Woovv, r2)
tmp += -lib.einsum('kldc,kld->c', imds.Woovv, r2)
Hr2 += -lib.einsum('c,ijcb->ijb', tmp, imds.t2)
vector = eom.amplitudes_to_vector(Hr1, Hr2)
return vector
backend='numpy')
# put image into symtensor
A = np.array(mpl.image.imread(fname))
shape = A.shape
Aog = A.copy()
Aog2 = A.copy()
Aog3 = A.copy()
A = np.reshape(A, (-1))
nelem = np.prod(ten1.array.shape)
A = A[:nelem]
ten1.array = np.reshape(A, ten1.array.shape)
ten1.enforce_sym()
# Use existing SVD w/o trunc -----------------------------------------------
U, S, V = symsvd(ten1, [[0, 1, 2], [3, 4]])
A2 = einsum('ijkl,lmn->ijkmn', U, einsum('jk,klm->jlm', S, V))
Aog = np.reshape(Aog, (-1))
Aog[:nelem] = np.reshape(A2.array, (-1))
Aog = np.reshape(Aog, shape)
f = plt.figure()
plt.imshow(Aog)
# Use existing SVD w/ trunc -----------------------------------------------
U, S, V = symsvd(ten1, [[0, 1, 2], [3, 4]], truncate_mbd=k)
A2 = einsum('ijkl,lmn->ijkmn', U, einsum('jk,klm->jlm', S, V))
Aog2 = np.reshape(Aog2, (-1))
Aog2[:nelem] = np.reshape(A2.array, (-1))
Aog2 = np.reshape(Aog2, shape)
f = plt.figure()
plt.imshow(Aog2)