def bump_ij(c, i, n, env):
# [i+1,n,i+1] <- [i,1,i] + [i,n,i] + [i,n+1,i] + [i,n+2,i] + [i,n,i-1] + [i,n+1,i-1] + [i-1,n,i-1]
b, binv = env['b'], env['binv']
if n == 0 and c.force_orth:
c[i + 1, n, i + 1] = c.eye.copy()
return c
tmp = c[i, n + 2, i].copy()
tmp -= lib.hermi_sum(c.cb(i, n + 1, i - 1, env))
tmp -= lib.hermi_sum(c.mc(i, n + 1, i, env).T.conj())
tmp += lib.hermi_sum(np.dot(c[i, 1, i], c.cb(i, n, i - 1, env)))
tmp += np.dot(b[i - 1], c.cb(i - 1, n, i - 1, env))
tmp += np.dot(c.mc(i, n, i, env), c[i, 1, i].T.conj())
c[i + 1, n, i + 1] = np.dot(np.dot(binv.T.conj(), tmp), binv)
return c
def contract2(self, vPuv):
''' Contract the auxbasis and one AO basis indices with multiplicand vPuv, as when computing the exchange matrix of Hartree--Fock.
Args:
vPuv : np.ndarray of shape (nao, nao, naux) stored in row-major order. The FIRST index is contracted
with self ; the output of contract1 must be TRANSPOSED ON THE FIRST 2 INDICES in order to generate
the vk matrix
Returns:
vk : np.ndarray of shape (nao, nao)
'''
if self.ndim == 3: return self.pack_mo()
if not self.flags['F_CONTIGUOUS']: self = self.naux_fast()
if self.nent_max is None: self.get_sparsity_()
nao = self.nmo[0]
vk = np.zeros((nao, nao), dtype=self.dtype)
wrk = np.zeros((lib.num_threads(), self.nent_max, self.naux),
dtype=self.dtype)
libsint.SINT_SDCDERI_VK(
self.ctypes.data_as(ctypes.c_void_p),
vPuv.ctypes.data_as(ctypes.c_void_p),
vk.ctypes.data_as(ctypes.c_void_p),
wrk.ctypes.data_as(ctypes.c_void_p),
self.iao_sort.ctypes.data_as(ctypes.c_void_p),
self.iao_nent.ctypes.data_as(ctypes.c_void_p),
self.iao_entlist.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(nao), ctypes.c_int(self.naux),
ctypes.c_int(self.nent_max))
wrk = None
vk = lib.hermi_sum(vk, inplace=True)
vk[np.diag_indices(nao)] /= 2
return vk
def test_transpose_sum(self):
a = numpy.random.random((3, 400, 400))
self.assertAlmostEqual(
abs(a[0] + a[0].T - lib.hermi_sum(a[0])).max(), 0, 12)
self.assertAlmostEqual(
abs(a + a.transpose(0, 2, 1) - lib.hermi_sum(a, (0, 2, 1))).max(),
0, 12)
self.assertAlmostEqual(
abs(a + a.transpose(0, 2, 1) -
lib.hermi_sum(a, (0, 2, 1), inplace=True)).max(), 0, 12)
a = numpy.random.random((3, 400, 400)) + numpy.random.random(
(3, 400, 400)) * 1j
self.assertAlmostEqual(
abs(a[0] + a[0].T.conj() - lib.hermi_sum(a[0])).max(), 0, 12)
self.assertAlmostEqual(
abs(a + a.transpose(0, 2, 1).conj() -
lib.hermi_sum(a, (0, 2, 1))).max(), 0, 12)
self.assertAlmostEqual(
abs(a + a.transpose(0, 2, 1) -
lib.hermi_sum(a, (0, 2, 1), hermi=3)).max(), 0, 12)
self.assertAlmostEqual(
abs(a + a.transpose(0, 2, 1).conj() -
lib.hermi_sum(a, (0, 2, 1), inplace=True)).max(), 0, 12)
a = numpy.random.random((400, 400))
b = a + a.T.conj()
c = lib.transpose_sum(a)
self.assertAlmostEqual(abs(b - c).max(), 0, 12)
a = (a * 1000).astype(numpy.int32)
b = a + a.T
c = lib.transpose_sum(a)
self.assertAlmostEqual(abs(b - c).max(), 0, 12)
self.assertTrue(c.dtype == numpy.int32)
def test_transpose_sum(self):
a = numpy.random.random((3,400,400))
self.assertAlmostEqual(abs(a[0]+a[0].T - lib.hermi_sum(a[0])).max(), 0, 12)
self.assertAlmostEqual(abs(a+a.transpose(0,2,1) - lib.hermi_sum(a,(0,2,1))).max(), 0, 12)
self.assertAlmostEqual(abs(a+a.transpose(0,2,1) - lib.hermi_sum(a,(0,2,1), inplace=True)).max(), 0, 12)
a = numpy.random.random((3,400,400)) + numpy.random.random((3,400,400)) * 1j
self.assertAlmostEqual(abs(a[0]+a[0].T.conj() - lib.hermi_sum(a[0])).max(), 0, 12)
self.assertAlmostEqual(abs(a+a.transpose(0,2,1).conj() - lib.hermi_sum(a,(0,2,1))).max(), 0, 12)
self.assertAlmostEqual(abs(a+a.transpose(0,2,1) - lib.hermi_sum(a,(0,2,1),hermi=3)).max(), 0, 12)
self.assertAlmostEqual(abs(a+a.transpose(0,2,1).conj() - lib.hermi_sum(a,(0,2,1),inplace=True)).max(), 0, 12)
a = numpy.random.random((400,400))
b = a + a.T.conj()
c = lib.transpose_sum(a)
self.assertAlmostEqual(abs(b-c).max(), 0, 12)
def compute_b(i, env, cond_tol=10, maxiter=20, method='eig'):
c, b, t, nmo = env['c'], env['b'], env['t'], env['nmo']
if i == 0:
b2 = t[0]
else:
b2 = c[i, 2, i].copy()
#b2 -= lib.hermi_sum(np.dot(c[i,1,i-1], b[i-1].T.conj()))
b2 -= lib.hermi_sum(c.cb(i, 1, i - 1, env))
b2 -= np.dot(c[i, 1, i], c[i, 1, i].T.conj())
if i > 1:
b2 += np.dot(b[i - 1], b[i - 1].T.conj())
tol = 10 * np.finfo(c.dtype).eps
if method == 'eig':
w, v = np.linalg.eigh(b2)
w[w < tol] = tol
bi = np.dot(v * w[None]**0.5, v.T)
binv = np.dot(v * w[None]**-0.5, v.T)
elif method == 'chol' or method == 'chol-iter':
bi = cholesky(force_posdef(b2, tol=tol)).T.conj()
binv = inv(bi)
elif method == 'shifted-chol' or method == 'shifted-chol-iter':
# https://arxiv.org/pdf/1809.11085.pdf
shift = np.finfo(dtype).eps
shift *= 11 * (nmo * (nmo + (nmo // 2)**3) + nmo * (nmo + 1))
shift *= np.trace(b2)
shift = np.dot(shift, np.eye(nmo))
bi = cholesky(force_posdef(b2, tol=tol)).T.conj()
binv = inv(bi)
if method.endswith('iter'):
n = 0
b2_next = b2
while np.linalg.cond(b2_next) > cond_tol and n < maxiter:
b2_next = np.dot(np.dot(binv.T.conj(), b2), binv)
b_next = cholesky(force_posdef(b2_next, tol=tol)).T.conj()
bi = np.dot(b_next, bi)
binv = inv(bi)
n += 1
return bi, binv
def incore(eri, dms, hermi=0, with_j=True, with_k=True):
assert (eri.dtype == numpy.double)
eri = numpy.asarray(eri, order='C')
dms = numpy.asarray(dms, order='C')
dms_shape = dms.shape
nao = dms_shape[-1]
dms = dms.reshape(-1, nao, nao)
n_dm = dms.shape[0]
vj = vk = None
if with_j:
vj = numpy.zeros((n_dm, nao, nao))
if with_k:
vk = numpy.zeros((n_dm, nao, nao))
dmsptr = []
vjkptr = []
fjkptr = []
npair = nao * (nao + 1) // 2
if eri.ndim == 2 and npair * npair == eri.size: # 4-fold symmetry eri
fdrv = getattr(libcvhf, 'CVHFnrs4_incore_drv')
if with_j:
# 'ijkl,kl->ij'
fvj = _fpointer('CVHFics4_kl_s2ij')
# or
## 'ijkl,ij->kl'
#fvj = _fpointer('CVHFics4_ij_s2kl')
for i, dm in enumerate(dms):
dmsptr.append(dm.ctypes.data_as(ctypes.c_void_p))
vjkptr.append(vj[i].ctypes.data_as(ctypes.c_void_p))
fjkptr.append(fvj)
if with_k:
# 'ijkl,il->jk'
fvk = _fpointer('CVHFics4_il_s1jk')
# or
## 'ijkl,jk->il'
#fvk = _fpointer('CVHFics4_jk_s1il')
for i, dm in enumerate(dms):
dmsptr.append(dm.ctypes.data_as(ctypes.c_void_p))
vjkptr.append(vk[i].ctypes.data_as(ctypes.c_void_p))
fjkptr.append(fvk)
elif eri.ndim == 1 and npair * (npair +
1) // 2 == eri.size: # 8-fold symmetry eri
fdrv = getattr(libcvhf, 'CVHFnrs8_incore_drv')
if with_j:
fvj = _fpointer('CVHFics8_tridm_vj')
tridms = lib.pack_tril(lib.hermi_sum(dms, axes=(0, 2, 1)))
idx = numpy.arange(nao)
tridms[:, idx * (idx + 1) // 2 + idx] *= .5
for i, tridm in enumerate(tridms):
dmsptr.append(tridm.ctypes.data_as(ctypes.c_void_p))
vjkptr.append(vj[i].ctypes.data_as(ctypes.c_void_p))
fjkptr.append(fvj)
if with_k:
if hermi == 1:
fvk = _fpointer('CVHFics8_jk_s2il')
else:
fvk = _fpointer('CVHFics8_jk_s1il')
for i, dm in enumerate(dms):
dmsptr.append(dm.ctypes.data_as(ctypes.c_void_p))
vjkptr.append(vk[i].ctypes.data_as(ctypes.c_void_p))
fjkptr.append(fvk)
else:
raise RuntimeError('Array shape not consistent: DM %s, eri %s' %
(dms_shape, eri.shape))
n_ops = len(dmsptr)
fdrv(eri.ctypes.data_as(ctypes.c_void_p),
(ctypes.c_void_p * n_ops)(*dmsptr),
(ctypes.c_void_p * n_ops)(*vjkptr), ctypes.c_int(n_ops),
ctypes.c_int(nao), (ctypes.c_void_p * n_ops)(*fjkptr))
if with_j:
for i in range(n_dm):
lib.hermi_triu(vj[i], 1, inplace=True)
vj = vj.reshape(dms_shape)
if with_k:
if hermi != 0:
for i in range(n_dm):
lib.hermi_triu(vk[i], hermi, inplace=True)
vk = vk.reshape(dms_shape)
return vj, vk
def get_blocks(self):
"""Get on- and off-diagonal blocks of the block tridiagonalised
Hamiltonian.
"""
α = np.zeros((self.niter+1, self.norb, self.norb), dtype=self.dtype)
β = np.zeros((self.niter, self.norb, self.norb), dtype=self.dtype)
v = V(self.zero)
βsq = self.moments[0]
β[0] = self.mat_sqrt(βsq)
βinv = self.mat_isqrt(βsq)
for i in range(self.nmom):
v[1, i, 1] = np.linalg.multi_dot((
βinv.T.conj(),
self.moments[i],
βinv,
))
def vb(i, n, j):
return np.dot(v[i, n, j], β[j].T.conj())
def av(i, n, j):
return np.dot(v[i, 1, i], v[i, n, j])
for i in range(1, self.niter):
βsq = (
+ v[i, 2, i]
- lib.hermi_sum(vb(i, 1, i-1))
- np.dot(v[i, 1, i], v[i, 1, i].T.conj())
)
if i > 1:
βsq += np.dot(β[i-1], β[i-1].T.conj())
β[i] = self.mat_sqrt(βsq)
βinv = self.mat_isqrt(βsq)
for n in range(2 * (self.niter-i)):
if n != (2 * (self.niter-i) - 1):
r = (
+ v[i, n+1, i]
- vb(i, n, i-1).T.conj()
- av(i, n, i)
)
v[i+1, n, i] = np.dot(βinv.T.conj(), r)
r = (
+ v[i, n+2, i]
- lib.hermi_sum(vb(i, n+1, i-1))
- lib.hermi_sum(av(i, n+1, i))
+ lib.hermi_sum(np.dot(v[i, 1, i], vb(i, n, i-1)))
+ np.dot(β[i-1], vb(i-1, n, i-1))
+ np.dot(av(i, n, i), v[i, 1, i].T.conj())
)
v[i+1, n, i+1] = np.linalg.multi_dot((βinv.T.conj(), r, βinv))
for i in range(self.niter+1):
α[i] = v[i, 1, i]
return α, β