def setLehmannTermsDynamicFermionic(self, dynamicObservable):
for statePair, operatorPair in dynamicObservable.operatorPairs.items():
operator1 = operatorPair[0]
operator2 = operatorPair[1]
if type(operator1) != ndarray:
operator1 = operator1.toarray()
operator2 = operator2.toarray()
e = self.getEnergyEigenvalues()
ve = self.getEnergyEigenstates().toarray()
fockstates = range(self.fockspaceSize)
n_inds_p = array(scatter_list(fockstates))
nominators_p = []
denominators_p = []
for n in n_inds_p:
n_op1 = ve[:,n].dot(operator1)
op2_n = operator2.dot(ve[:,n])
expn = exp(-self.beta*e[n])
for m in fockstates:
if dynamicObservable.species == 'bosonic':
if equals(e[n], e[m]):
continue
el1 = n_op1.dot(ve[:,m])
if not equals(el1, 0):
el2 = ve[:,m].dot(op2_n)
if not equals(el2, 0):
expm = exp(-self.beta*e[m])
el = el1*el2
nominators_p.append([])
nominators_p[-1].append(expn*el)
nominators_p[-1].append(expm*el)
denominators_p.append(e[n]-e[m])
dynamicObservable.lehmannNominators.update({statePair: allgather_list(nominators_p)})
dynamicObservable.lehmannDenominators.update({statePair: allgather_list(denominators_p)})
dynamicObservable.partitionFunction = self.getPartitionFunction()
def setZeroFrequencyTerms(self, dynamicObservable):
for statePair, operatorPair in dynamicObservable.operatorPairs.items():
operator1 = operatorPair[0]
operator2 = operatorPair[1]
if type(operator1) != ndarray:
operator1 = operator1.toarray()
operator2 = operator2.toarray()
e = self.getEnergyEigenvalues()
ve = self.getEnergyEigenstates().toarray()
fockstates = range(self.fockspaceSize)
n_inds_p = array(scatter_list(fockstates))
zeroFrequencyTerms_p = []
for n in n_inds_p:
n_op1 = ve[:,n].dot(operator1)
op2_n = operator2.dot(ve[:,n])
expn = exp(-self.beta*e[n])
for m in fockstates:
if equals(e[n], e[m]):
el1 = n_op1.dot(ve[:,m])
if not equals(el1, 0):
el2 = ve[:,m].dot(op2_n)
if not equals(el2, 0):
el = el1*el2
zeroFrequencyTerms_p.append(-self.beta*expn*el)
dynamicObservable.zeroFrequencyTerms.update({statePair: allgather_list(zeroFrequencyTerms_p)})
def setLehmannSumStatic(self, staticObservable):
assert type(staticObservable) == StaticObservable, 'StaticObservable expected.'
e = self.getEnergyEigenvalues()
ve = self.getEnergyEigenstates().toarray()
z = self.getPartitionFunction()
fockstates = range(self.fockspaceSize)
for index, matrix in staticObservable.operators.items():
if type(matrix) != ndarray:
m = matrix.toarray()
else:
m = matrix
n_inds_p = array(scatter_list(fockstates))
terms_p = list()
for n in n_inds_p:
el = ve[:,n].dot(m.dot(ve[:,n]))
expn = exp(-self.beta*e[n])
if not equals(el, 0) and not equals(expn, 0):
terms_p.append(expn * el)
staticObservable.expectationValue.update({index: sumScatteredLists(terms_p)/z})
def __eq__(self, other):
if isnan(self.w) and isnan(other.w):
return bool(
equals(self.red, other.red)
and equals(self.green, other.green)
and equals(self.blue, other.blue)
)
else:
return bool(
equals(self.x, other.x)
and equals(self.y, other.y)
and equals(self.z, other.z)
and equals(self.w, other.w)
)
def embedV(subspaceVectors, blocksizes):
fockspaceSize = nsum(blocksizes)
assert fockspaceSize == len(subspaceVectors), 'embedding will fail'
iBlock = 0
iBlockOrigin = 0
vectors = zeros([len(subspaceVectors), fockspaceSize])
x = list()
y = list()
data = list()
for i, v in enumerate(subspaceVectors):
for j, vj in enumerate(v):
if not equals(vj, 0):
y.append(j + iBlockOrigin) # TODO understand row/col exchange
x.append(i)
data.append(vj)
if i == iBlockOrigin + blocksizes[iBlock] - 1:
iBlockOrigin += blocksizes[iBlock]
iBlock += 1
return coo_matrix((data, (x,y)), [fockspaceSize]*2)
def step_impl(context):
assert equals(context.reflectance, 0.48873)
def step_impl(context):
assert equals(context.xs[0].t, 6.80798)
def step_impl(context):
assert equals(context.xs[1].t, 7.08872)
def step_impl(context):
assert equals(context.xs[1].t, 49.44994)
def step_impl(context):
assert equals(context.xs[0].t, 0.35355)
def step_impl(context):
assert equals(context.xs[0].t, 4.55006)
def step_impl(context):
assert equals(context.xs[1].t, 8.66025)
def __init__(
self,
dim,
depth,
heads=8,
cross_attend=False,
only_cross=False,
position_infused_attn=True,
custom_layers=None,
sandwich_coef=None,
residual_attn=False,
pre_norm=True,
causal=False,
use_scalenorm=True,
#dim_out=None,
**kwargs):
super().__init__()
self.dim = dim
self.depth = depth
self.layers = nn.ModuleList([])
self.dim_out = dim
self.pia_pos_emb = FixedPositionalEmbedding(dim) if position_infused_attn else \
None
# To do: Implement relative position bias
# To do: Implement residual attention
self.pre_norm = pre_norm
# ScaleNorm from paper: https://arxiv.org/abs/1910.05895
norm_class = ScaleNorm if use_scalenorm else nn.LayerNorm
norm_fn = partial(norm_class, dim)
ff_kwargs, kwargs = groupby_prefix_and_trim('ff_', kwargs)
attn_kwargs, _ = groupby_prefix_and_trim('attn_', kwargs)
if cross_attend and not only_cross:
default_block = ('a', 'c', 'f'
) # Attention -> cross -> Feedforward
elif cross_attend and only_cross:
default_block = ('c', 'f') # Cross -> Feedforward
else:
default_block = ('a', 'f') # Attention -> Feedforward
if exists(custom_layers):
layer_types = custom_layers
elif exists(sandwich_coef):
# TO DO
pass
else:
layer_types = default_block * depth
self.layer_types = layer_types
self.num_attn_layers = len(list(filter(equals('a'), layer_types)))
for layer_type in self.layer_types:
if layer_type == 'a':
layer = Attention(dim,
heads=heads,
causal=causal,
**attn_kwargs)
elif layer_type == 'c':
layer = Attention(dim, heads=heads, **attn_kwargs)
elif layer_type == 'f':
layer = FeedForward(dim, **ff_kwargs)
else:
raise Exception(f'invalid layer type {layer_type}')
self.layers.append(nn.ModuleList([norm_fn(), layer, Residual()]))
def step_impl(context):
assert equals(context.c.pixel_size, 0.01)
def __eq__(self, other):
if (equals(self.matrix[0][0], other.matrix[0][0])
and equals(self.matrix[0][1], other.matrix[0][1])
and equals(self.matrix[0][2], other.matrix[0][2])
and equals(self.matrix[0][3], other.matrix[0][3])
and equals(self.matrix[1][0], other.matrix[1][0])
and equals(self.matrix[1][1], other.matrix[1][1])
and equals(self.matrix[1][2], other.matrix[1][2])
and equals(self.matrix[1][3], other.matrix[1][3])
and equals(self.matrix[2][0], other.matrix[2][0])
and equals(self.matrix[2][1], other.matrix[2][1])
and equals(self.matrix[2][2], other.matrix[2][2])
and equals(self.matrix[2][3], other.matrix[2][3])
and equals(self.matrix[3][0], other.matrix[3][0])
and equals(self.matrix[3][1], other.matrix[3][1])
and equals(self.matrix[3][2], other.matrix[3][2])
and equals(self.matrix[3][3], other.matrix[3][3])):
return True
else:
return False
