def _reorder_kronecker_product(hi, mat, acting_on) -> Tuple[Array, Tuple]:
"""
Reorders the matrix resulting from a kronecker product of several
operators in such a way to sort acting_on.
A conceptual example is the following:
if `mat = Â ⊗ B̂ ⊗ Ĉ` and `acting_on = [[2],[1],[3]`
you will get `result = B̂ ⊗ Â ⊗ Ĉ, [[1], [2], [3]].
However, essentially, A,B,C represent some operators acting on
thei sub-space acting_on[1], [2] and [3] of the hilbert space.
This function also handles any possible set of values in acting_on.
The inner logic uses the Fock.all_states(), number_to_state and
state_to_number to perform the re-ordering.
"""
acting_on_sorted = np.sort(acting_on)
if np.array_equal(acting_on_sorted, acting_on):
return mat, acting_on
# could write custom binary <-> int logic instead of using Fock...
# Since i need to work with bit-strings (where instead of bits i
# have integers, in order to support arbitrary size spaces) this
# is exactly what hilbert.to_number() and viceversa do.
# target ordering binary representation
hi_subspace = Fock(hi.shape[acting_on_sorted[0]] - 1)
for site in acting_on_sorted[1:]:
hi_subspace = hi_subspace * Fock(hi.shape[site] - 1)
hi_unsorted_subspace = Fock(hi.shape[acting_on[0]] - 1)
for site in acting_on[1:]:
hi_unsorted_subspace = hi_unsorted_subspace * Fock(hi.shape[site] - 1)
# find how to map target ordering back to unordered
acting_on_unsorted_ids = np.zeros(len(acting_on), dtype=np.intp)
for (i, site) in enumerate(acting_on):
acting_on_unsorted_ids[i] = np.argmax(site == acting_on_sorted)
# now it is valid that
# acting_on_sorted == acting_on[acting_on_unsorted_ids]
# generate n-bit strings in the target ordering
v = hi_subspace.all_states()
# convert them to origin (unordered) ordering
v_unsorted = v[:, acting_on_unsorted_ids]
# convert the unordered bit-strings to numbers in the target space.
n_unsorted = hi_unsorted_subspace.states_to_numbers(v_unsorted)
# reorder the matrix
mat_sorted = mat[n_unsorted, :][:, n_unsorted]
return mat_sorted, tuple(acting_on_sorted)
def _reorder_matrix(hi, mat, acting_on):
acting_on_sorted = np.sort(acting_on)
if np.all(acting_on_sorted == acting_on):
return mat, acting_on
acting_on_sorted_ids = np.argsort(acting_on)
# could write custom binary <-> int logic instead of using Fock...
# Since i need to work with bit-strings (where instead of bits i
# have integers, in order to support arbitrary size spaces) this
# is exactly what hilbert.to_number() and viceversa do.
# target ordering binary representation
hi_subspace = Fock(hi.shape[acting_on_sorted[0]] - 1)
for site in acting_on_sorted[1:]:
hi_subspace = Fock(hi.shape[site] - 1) * hi_subspace
# find how to map target ordering back to unordered
acting_on_unsorted_ids = np.zeros(len(acting_on), dtype=np.intp)
for (i, site) in enumerate(acting_on):
acting_on_unsorted_ids[i] = np.argmax(site == acting_on_sorted)
# now it is valid that
# acting_on_sorted == acting_on[acting_on_unsorted_ids]
# generate n-bit strings in the target ordering
v = hi_subspace.all_states()
# convert them to origin (unordered) ordering
v_unsorted = v[:, acting_on_unsorted_ids]
# convert the unordered bit-strings to numbers in the target space.
n_unsorted = hi_subspace.states_to_numbers(v_unsorted)
# reorder the matrix
mat_sorted = mat[n_unsorted, :][:, n_unsorted]
return mat_sorted, acting_on_sorted