def pmps_dm_to_array(pmps, global_=False):
"""Convert PMPS to full array representation of the density matrix
The runtime of this method scales with D**3 instead of D**6 where
D is the rank and D**6 is the scaling of using :func:`pmps_to_mpo`
and :func:`to_array`. This is useful for obtaining reduced states
of a PMPS on non-consecutive sites, as normalizing before using
:func:`pmps_to_mpo` may not be sufficient to reduce the rank
in that case.
.. note:: The resulting array will have dimension-1 physical legs removed.
"""
out = np.ones((1, 1, 1))
# Axes: 0 phys, 1 upper rank, 2 lower rank
for lt in pmps.lt:
out = np.tensordot(out, lt, axes=(1, 0))
# Axes: 0 phys, 1 lower rank, 2 phys, 3 anc, 4 upper rank
out = np.tensordot(out, lt.conj(), axes=((1, 3), (0, 2)))
# Axes: 0 phys, 1 phys, 2 upper rank, 3 phys, 4 lower rank
out = np.rollaxis(out, 3, 2)
# Axes: 0 phys, 1 phys, 2 phys, 3 upper bound, 4 lower rank
out = out.reshape((-1, out.shape[3], out.shape[4]))
# Axes: 0 phys, 1 upper rank, 2 lower rank
out_shape = [dim for dim, _ in pmps.shape for rep in (1, 2) if dim > 1]
out = out.reshape(out_shape)
if global_:
assert len(set(out_shape)) == 1
out = local_to_global(out, sites=len(out_shape) // 2)
return out
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