def test_associativity(self):
N,S=2,0.5
a,b,c,d=np.random.random((N,N)),np.random.random((N,N)),np.random.random((N,N)),np.random.random((N,N))
p4_2_2=QuantumNumbers.kron([QuantumNumbers.kron([SQNS(S)]*2,signs=(+1,-1))]*2,signs=(+1,+1)).sorted(history=True)[1]
p41111=QuantumNumbers.kron([SQNS(S)]*4,signs=(+1,-1,+1,-1)).sorted(history=True)[1]
tmp1,tmp2=np.kron(a,b),np.kron(c,d)
m1=hm.reorder(np.kron(tmp1,tmp2),permutation=p4_2_2)
m2=hm.reorder(np.kron(np.kron(np.kron(a,b),c),d),permutation=p41111)
self.assertAlmostEqual(nl.norm(m2-m1),0.0,delta=10**-14)
def reorder(self, *args):
'''
Reorder a dimension of a tensor with a permutation and optionally set a new qns for this dimension.
Usage: ``tensor.reorder((axis,permutation,<qns>),(axis,permutation,<qns>),...)``
* axis: int/Label
The axis of the dimension to be reordered.
* permutation: 1d ndarray of int
The permutation array.
* qns: QuantumNumbers, optional
The new quantum number collection of the dimension if good quantum numbers are used.
Returns
-------
DTensor
The reordered tensor.
Notes
-----
If `qns` is not passed, the new qns will be automatically set according to the permutation array.
'''
result, qnon = copy(self), self.qnon
for arg in args:
assert len(arg) in (2, 3)
axis, permutation = arg[0], arg[1]
if permutation is not None:
axis = self.axis(axis) if isinstance(axis, Label) else axis
label = result.labels[axis]
result.labels[axis] = label.replace(
qns=arg[2] if len(arg) == 3 else label.qns.
reorder(permutation) if qnon else len(permutation))
result.data = hm.reorder(result.data,
axes=[axis],
permutation=permutation)
return result
def split(self,*args):
'''
Split a label into small ones with an optional permutation.
Usage: ``tensor.split((old,news,<permutation>),(old,news,<permutation>),...)``
* old: Label/int
The label/axis to be split.
* news: list of Label
The new labels.
* permutation: 1d ndarray of int, optional
The permutation of the quantum number collection of the old label.
Returns
-------
DTensor
The new tensor.
'''
table={(self.axis(arg[0]) if isinstance(arg[0],Label) else arg[0]):i for i,arg in enumerate(args)}
shape,labels,axes,permutations=(),[],[],[]
for axis,dim,label in zip(range(self.ndim),self.shape,self.labels):
if axis in table:
arg=args[table[axis]]
assert len(arg) in (2,3)
shape+=tuple(new.dim for new in arg[1])
labels.extend(arg[1])
axes.append(axis)
permutations.append(arg[2] if len(arg)==3 else None)
else:
shape+=(dim,)
labels.append(label)
data=self.data
for axis,permutation in zip(axes,permutations):
data=hm.reorder(data,axes=[axis],permutation=permutation)
return DTensor(data.reshape(shape),labels=labels)
def reorder(self,*args):
'''
Reorder a dimension of a tensor with a permutation and optionally set a new qns for this dimension.
Usage: ``tensor.reorder((axis,permutation,<qns>),(axis,permutation,<qns>),...)``
* axis: int/Label
The axis of the dimension to be reordered.
* permutation: 1d ndarray of int
The permutation array.
* qns: QuantumNumbers, optional
The new quantum number collection of the dimension if good quantum numbers are used.
Returns
-------
DTensor
The reordered tensor.
Notes
-----
If `qns` is not passed, the new qns will be automatically set according to the permutation array.
'''
result,qnon=copy(self),self.qnon
for arg in args:
assert len(arg) in (2,3)
axis,permutation=arg[0],arg[1]
if permutation is not None:
axis=self.axis(axis) if isinstance(axis,Label) else axis
label=result.labels[axis]
result.labels[axis]=label.replace(qns=arg[2] if len(arg)==3 else label.qns.reorder(permutation) if qnon else len(permutation))
result.data=hm.reorder(result.data,axes=[axis],permutation=permutation)
return result
def fedspcom(blocks, omega):
'''
This function composes the zero-temperature single-particle Green's function of a fermionic system from its blocks.
Parameters
----------
blocks : list of BGF
The blocks of the Green's function.
omega : number
The frequency.
Returns
-------
2d ndarray
The composed Green's function.
'''
assert len(blocks) in (2, 4)
if len(blocks) == 2:
return blocks[0].gf(omega).T + blocks[1].gf(omega)
else:
gfdw, indsdw = blocks[0].gf(omega).T + blocks[1].gf(
omega), blocks[0].indices
gfup, indsup = blocks[2].gf(omega).T + blocks[3].gf(
omega), blocks[2].indices
return HM.reorder(HM.block_diag(gfdw, gfup),
axes=[0, 1],
permutation=np.argsort(
np.concatenate((indsdw, indsup))))
def merge(self, *args):
'''
Merge some continuous and ascending labels of a tensor into a new one with an optional permutation.
Usage: ``tensor.merge((olds,new,<permutation>),(olds,new,<permutation>),...)``
* olds: list of Label/int
The old labels/axes to be merged.
* new: Label
The new label.
* permutation: 1d ndarray of int, optional
The permutation of the quantum number collection of the new label.
Returns
-------
DTensor
The new tensor.
'''
permutations = {}
keep = OrderedDict([(i, i) for i in xrange(self.ndim)])
labels = OrderedDict([(i, label)
for i, label in enumerate(self.labels)])
for arg in args:
assert len(arg) in (2, 3)
olds, new, permutation = (arg[0], arg[1],
None) if len(arg) == 2 else arg
axes = np.array([
self.axis(old) if isinstance(old, Label) else old
for old in olds
])
if len(axes) != max(axes) - min(axes) + 1 or not all(
axes[1:] > axes[:-1]):
raise ValueError(
'DTensor merge error: the axes to be merged should be continuous and ascending, please call transpose first.'
)
permutations[new] = permutation
keep[axes[0]] = slice(axes[0], axes[-1] + 1)
labels[axes[0]] = new
for axis in axes[1:]:
keep.pop(axis)
labels.pop(axis)
data = self.data.reshape(
tuple(
np.product(self.data.shape[ax]
) if isinstance(ax, slice) else self.data.shape[ax]
for ax in keep.itervalues()))
labels = labels.values()
for label, permutation in permutations.iteritems():
data = hm.reorder(data,
axes=[labels.index(label)],
permutation=permutation)
return DTensor(data, labels=labels)
def qnsort(self,history=False):
'''
Sort the quantum numbers of all the dimensions of the tensor.
Returns
-------
list of 1d ndarray, optional
The permutation arrays of the dimensions of the tensor.
Returned only when ``history`` is True.
'''
permutations=[]
for axis,label in enumerate(self.labels):
assert label.qnon
qns,permutation=(label.qns,None) if label.qns.form=='C' else label.qns.sorted(history=True)
self.data=hm.reorder(self.data,axes=[axis],permutation=permutation)
self.labels[axis]=label.replace(qns=qns)
if history: permutations.append(permutation)
if history: return permutations
def fedspcom(blocks,omega):
'''
This function composes the zero-temperature single-particle Green's function of a fermionic/hard-core-bosonic system from its blocks.
Parameters
----------
blocks : list of BGF
The blocks of the Green's function.
omega : number
The frequency.
Returns
-------
2d ndarray
The composed Green's function.
'''
assert len(blocks) in (2,4)
if len(blocks)==2:
return blocks[0].gf(omega).T+blocks[1].gf(omega)
else:
gfdw,indsdw=blocks[0].gf(omega).T+blocks[1].gf(omega),blocks[0].indices
gfup,indsup=blocks[2].gf(omega).T+blocks[3].gf(omega),blocks[2].indices
return HM.reorder(HM.blockdiag(gfdw,gfup),axes=[0,1],permutation=np.argsort(np.concatenate((indsdw,indsup))))
def merge(self,*args):
'''
Merge some continuous and ascending labels of a tensor into a new one with an optional permutation.
Usage: ``tensor.merge((olds,new,<permutation>),(olds,new,<permutation>),...)``
* olds: list of Label/int
The old labels/axes to be merged.
* new: Label
The new label.
* permutation: 1d ndarray of int, optional
The permutation of the quantum number collection of the new label.
Returns
-------
DTensor
The new tensor.
'''
permutations={}
keep=OrderedDict([(i,i) for i in range(self.ndim)])
labels=OrderedDict([(i,label) for i,label in enumerate(self.labels)])
for arg in args:
assert len(arg) in (2,3)
olds,new,permutation=(arg[0],arg[1],None) if len(arg)==2 else arg
axes=np.array([self.axis(old) if isinstance(old,Label) else old for old in olds])
if len(axes)!=max(axes)-min(axes)+1 or not all(axes[1:]>axes[:-1]):
raise ValueError('DTensor merge error: the axes to be merged should be continuous and ascending, please call transpose first.')
permutations[new]=permutation
keep[axes[0]]=slice(axes[0],axes[-1]+1)
labels[axes[0]]=new
for axis in axes[1:]:
keep.pop(axis)
labels.pop(axis)
data=self.data.reshape(tuple(np.product(self.data.shape[ax]) if isinstance(ax,slice) else self.data.shape[ax] for ax in keep.values()))
labels=list(labels.values())
for label,permutation in permutations.items():
data=hm.reorder(data,axes=[labels.index(label)],permutation=permutation)
return DTensor(data,labels=labels)
def random(labels,ttype='D',dtype=np.float64):
'''
Construct a random block-structured tensor.
Parameters
----------
labels : list of Label
The labels of the random tensor.
ttype : 'D'/'S', optional
Tensor type. 'D' for dense and 'S' for sparse.
dtype : np.float64, np.complex128, optional
The data type of the random tensor.
Returns
-------
DTensor/STensor
A random block-structured tensor.
'''
assert ttype in 'DS' and dtype in (np.float32,np.float64,np.complex64,np.complex128)
np.random.seed()
if next(iter(labels)).qnon:
paxes,plbls,maxes,mlbls=[],[],[],[]
for axis,label in enumerate(labels):
(paxes if label.flow==1 else maxes).append(axis)
(plbls if label.flow==1 else mlbls).append(label)
traxes=np.argsort(list(it.chain(paxes,maxes)))
if ttype=='D':
plabel,ppermutation=Label.union(plbls,'__TENSOR_RANDOM_D_+__',+1,mode=1)
mlabel,mpermutation=Label.union(mlbls,'__TENSOR_RANDOM_D_-__',-1,mode=1)
data=np.zeros((plabel.dim,mlabel.dim),dtype=dtype)
pod,mod=plabel.qns.toordereddict(),mlabel.qns.toordereddict()
for qn in filter(lambda key: key in pod,mod):
bshape=(pod[qn].stop-pod[qn].start,mod[qn].stop-mod[qn].start)
data[pod[qn],mod[qn]]=np.random.random(bshape)
if dtype in (np.complex64,np.complex128):
data[pod[qn],mod[qn]]+=1j*np.random.random(bshape)
for axis,permutation in [(0,np.argsort(ppermutation)),(1,np.argsort(mpermutation))]:
data=hm.reorder(data,axes=[axis],permutation=permutation)
data=data.reshape(tuple(label.dim for label in it.chain(plbls,mlbls))).transpose(*traxes)
result=DTensor(data,labels=labels)
else:
plabel,precord=Label.union(plbls,'__TENSOR_RANDOM_S_+__',+1,mode=2)
mlabel,mrecord=Label.union(mlbls,'__TENSOR_RANDOM_S_-__',-1,mode=2)
data={}
ods=[label.qns.toordereddict(protocol=QuantumNumbers.COUNTS) for label in labels]
pod,mod=plabel.qns.toordereddict(),mlabel.qns.toordereddict()
for qn in filter(lambda key: key in pod,mod):
for pqns,mqns in it.product(precord[qn],mrecord[qn]):
qns=tuple(it.chain(pqns,mqns))
qns=tuple(qns[axis] for axis in traxes)
data[qns]=np.zeros(tuple(od[qn] for od,qn in zip(ods,qns)),dtype=dtype)
data[qns][...]=np.random.random(data[qns].shape)
if dtype in (np.complex64,np.complex128):
data[qns][...]+=1j*np.random.random(data[qns].shape)
result=STensor(data,labels=labels)
else:
assert ttype=='D'
data=np.zeros(tuple(label.dim for label in labels),dtype=dtype)
data[...]=np.random.random(data.shape)
if dtype in (np.complex64,np.complex128):
data[...]+=1j*np.random.random(data.shape)
result=DTensor(data,labels=labels)
return result