def tensor_contract(qobj, *pairs):
"""Contracts a qobj along one or more index pairs.
Note that this uses dense representations and thus
should *not* be used for very large Qobjs.
Parameters
----------
pairs : tuple
One or more tuples ``(i, j)`` indicating that the
``i`` and ``j`` dimensions of the original qobj
should be contracted.
Returns
-------
cqobj : Qobj
The original Qobj with all named index pairs contracted
away.
"""
# Record and label the original dims.
dims = qobj.dims
dims_idxs = enumerate_flat(dims)
tensor_dims = dims_to_tensor_shape(dims)
# Convert to dense first, since sparse won't support the reshaping we need.
qtens = qobj.data.toarray()
# Reshape by the flattened dims.
qtens = qtens.reshape(tensor_dims)
# Contract out the indices from the flattened object.
# Note that we need to feed pairs through dims_idxs_to_tensor_idxs
# to ensure that we are contracting the right indices.
qtens = _tensor_contract_dense(qtens,
*dims_idxs_to_tensor_idxs(dims, pairs))
# Remove the contracted indexes from dims so we know how to
# reshape back.
# This concerns dims, and not the tensor indices, so we need
# to make sure to use the original dims indices and not the ones
# generated by dims_to_* functions.
contracted_idxs = deep_remove(dims_idxs, *flatten(list(map(list, pairs))))
contracted_dims = unflatten(flatten(dims), contracted_idxs)
# We don't need to check for tensor idxs versus dims idxs here,
# as column- versus row-stacking will never move an index for the
# vectorized operator spaces all the way from the left to the right.
l_mtx_dims, r_mtx_dims = map(np.product, map(flatten, contracted_dims))
# Reshape back into a 2D matrix.
qmtx = qtens.reshape((l_mtx_dims, r_mtx_dims))
# Return back as a qobj.
return Qobj(qmtx, dims=contracted_dims, superrep=qobj.superrep)
def tensor_contract(qobj, *pairs):
"""Contracts a qobj along one or more index pairs.
Note that this uses dense representations and thus
should *not* be used for very large Qobjs.
Parameters
----------
pairs : tuple
One or more tuples ``(i, j)`` indicating that the
``i`` and ``j`` dimensions of the original qobj
should be contracted.
Returns
-------
cqobj : Qobj
The original Qobj with all named index pairs contracted
away.
"""
# Record and label the original dims.
dims = qobj.dims
dims_idxs = enumerate_flat(dims)
tensor_dims = dims_to_tensor_shape(dims)
# Convert to dense first, since sparse won't support the reshaping we need.
qtens = qobj.data.toarray()
# Reshape by the flattened dims.
qtens = qtens.reshape(tensor_dims)
# Contract out the indices from the flattened object.
# Note that we need to feed pairs through dims_idxs_to_tensor_idxs
# to ensure that we are contracting the right indices.
qtens = _tensor_contract_dense(qtens, *dims_idxs_to_tensor_idxs(dims, pairs))
# Remove the contracted indexes from dims so we know how to
# reshape back.
# This concerns dims, and not the tensor indices, so we need
# to make sure to use the original dims indices and not the ones
# generated by dims_to_* functions.
contracted_idxs = deep_remove(dims_idxs, *flatten(list(map(list, pairs))))
contracted_dims = unflatten(flatten(dims), contracted_idxs)
# We don't need to check for tensor idxs versus dims idxs here,
# as column- versus row-stacking will never move an index for the
# vectorized operator spaces all the way from the left to the right.
l_mtx_dims, r_mtx_dims = map(np.product, map(flatten, contracted_dims))
# Reshape back into a 2D matrix.
qmtx = qtens.reshape((l_mtx_dims, r_mtx_dims))
# Return back as a qobj.
return Qobj(qmtx, dims=contracted_dims, superrep=qobj.superrep)
def _implicit_tensor_dimensions(dimensions):
"""
Total flattened size and operator dimensions for operator creation routines
that automatically perform tensor products.
Parameters
----------
dimensions : (int) or (list of int) or (list of list of int)
First dimension of an operator which can create an implicit tensor
product. If the type is `int`, it is promoted first to `[dimensions]`.
From there, it should be one of the two-elements `dims` parameter of a
`qutip.Qobj` representing an `oper` or `super`, with possible tensor
products.
Returns
-------
size : int
Dimension of backing matrix required to represent operator.
dimensions : list
Dimension list in the form required by ``Qobj`` creation.
"""
if not isinstance(dimensions, list):
dimensions = [dimensions]
flat = flatten(dimensions)
if not all(isinstance(x, numbers.Integral) and x >= 0 for x in flat):
raise ValueError("All dimensions must be integers >= 0")
return np.prod(flat), [dimensions, dimensions]
def test_dims_idxs_to_tensor_idxs():
# Dims for a superoperator acting on linear operators on C^2 x C^3.
dims = [[[2, 3], [2, 3]], [[2, 3], [2, 3]]]
# Should swap the input and output subspaces of the left and right dims.
assert_equal(
dims_idxs_to_tensor_idxs(dims, list(range(len(flatten(dims))))),
[2, 3, 0, 1, 6, 7, 4, 5])
def test_dims_idxs_to_tensor_idxs():
# Dims for a superoperator acting on linear operators on C^2 x C^3.
dims = [[[2, 3], [2, 3]], [[2, 3], [2, 3]]]
# Should swap the input and output subspaces of the left and right dims.
assert_equal(
dims_idxs_to_tensor_idxs(dims, list(range(len(flatten(dims))))),
[2, 3, 0, 1, 6, 7, 4, 5]
)
def test_deep_map(base, mapping):
"""
Test the deep mapping. To simplify generation of edge-cases, this tests
against an equivalent (but slower) operation of flattening and unflattening
the list. We can get false negatives if the `flatten` or `unflatten`
functions are broken, but other tests should catch those.
"""
# This function might not need to be public, and consequently might not
# need to be tested here.
labels = enumerate_flat(base)
expected = unflatten([mapping(x) for x in flatten(base)], labels)
assert deep_map(mapping, base) == expected
def tensor_swap(q_oper, *pairs):
"""Transposes one or more pairs of indices of a Qobj.
Note that this uses dense representations and thus
should *not* be used for very large Qobjs.
Parameters
----------
pairs : tuple
One or more tuples ``(i, j)`` indicating that the
``i`` and ``j`` dimensions of the original qobj
should be swapped.
Returns
-------
sqobj : Qobj
The original Qobj with all named index pairs swapped with each other
"""
dims = q_oper.dims
tensor_pairs = dims_idxs_to_tensor_idxs(dims, pairs)
data = q_oper.data.toarray()
# Reshape into tensor indices
data = data.reshape(dims_to_tensor_shape(dims))
# Now permute the dims list so we know how to get back.
flat_dims = flatten(dims)
perm = list(range(len(flat_dims)))
for i, j in pairs:
flat_dims[i], flat_dims[j] = flat_dims[j], flat_dims[i]
for i, j in tensor_pairs:
perm[i], perm[j] = perm[j], perm[i]
dims = unflatten(flat_dims, enumerate_flat(dims))
# Next, permute the actual indices of the dense tensor.
data = data.transpose(perm)
# Reshape back, using the left and right of dims.
data = data.reshape(list(map(np.prod, dims)))
return Qobj(inpt=data, dims=dims, superrep=q_oper.superrep)
def tensor_swap(q_oper, *pairs):
"""Transposes one or more pairs of indices of a Qobj.
Note that this uses dense representations and thus
should *not* be used for very large Qobjs.
Parameters
----------
pairs : tuple
One or more tuples ``(i, j)`` indicating that the
``i`` and ``j`` dimensions of the original qobj
should be swapped.
Returns
-------
sqobj : Qobj
The original Qobj with all named index pairs swapped with each other
"""
dims = q_oper.dims
tensor_pairs = dims_idxs_to_tensor_idxs(dims, pairs)
data = q_oper.data.toarray()
# Reshape into tensor indices
data = data.reshape(dims_to_tensor_shape(dims))
# Now permute the dims list so we know how to get back.
flat_dims = flatten(dims)
perm = list(range(len(flat_dims)))
for i, j in pairs:
flat_dims[i], flat_dims[j] = flat_dims[j], flat_dims[i]
for i, j in tensor_pairs:
perm[i], perm[j] = perm[j], perm[i]
dims = unflatten(flat_dims, enumerate_flat(dims))
# Next, permute the actual indices of the dense tensor.
data = data.transpose(perm)
# Reshape back, using the left and right of dims.
data = data.reshape(list(map(np.prod, dims)))
return Qobj(inpt=data, dims=dims, superrep=q_oper.superrep)
def test_flatten(self, base, flat):
assert flatten(base) == flat
def test_dims_idxs_to_tensor_idxs(self, indices):
test_indices = list(range(len(flatten(indices.base))))
assert (dims_idxs_to_tensor_idxs(indices.base,
test_indices) == indices.permutation)
def test_unflatten():
l = [[[10, 20, 30], [40, 50, 60]], [[70, 80, 90], [100, 110, 120]]]
labels = enumerate_flat(l)
assert unflatten(flatten(l), labels) == l
def test_flatten():
l = [[[0], 1], 2]
assert_equal(flatten(l), [0, 1, 2])
def test_unflatten():
l = [[[10, 20, 30], [40, 50, 60]], [[70, 80, 90], [100, 110, 120]]]
labels = enumerate_flat(l)
assert unflatten(flatten(l), labels) == l
def test_flatten():
l = [[[0], 1], 2]
assert_equal(flatten(l), [0, 1, 2])