def __trace_middle_dims(sys, dims, reverse=True):
"""
Get system dimensions for __trace_middle.
Args:
j (int): system to trace over.
dims(list[int]): dimensions of all subsystems.
reverse (bool): if true system-0 is right-most system tensor product.
Returns:
Tuple (dim1, dims2, dims3)
"""
dpre = dims[:sys]
dpost = dims[sys + 1:]
if reverse:
dpre, dpost = (dpost, dpre)
dim1 = int(np.prod(dpre))
dim2 = int(dims[sys])
dim3 = int(np.prod(dpost))
return (dim1, dim2, dim3)
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