bi xdZddlmZmZddlZddlmZddl m Z d de dee dee fdZ d dee dee fd Z y) a6 Copyright 2022, adapted from Convex.jl. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. )OptionalTupleN)Atomjdimsaxisctjdgdgdgff}tjdgdgdgff}t|D]\}}||k(rWtjdg|gdgff|df}tj||j}tj||}btj |} tj|| }tj|| }||z|zS)aHelper function for partial trace. Parameters ---------- expr : :class:`~cvxpy.expressions.expression.Expression` The 2D expression to take the partial trace of. j : int Term in the partial trace sum. dims : tuple of ints. A tuple of integers encoding the dimensions of each subsystem. axis : int The index of the subsystem to be traced out from the tensor product that defines expr. g?r)shape)sp coo_matrix enumeratekronT eye_array) exprrrrabi_axisdimveye_mats [/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/atoms/affine/partial_trace.py_termrs& usQCj)*A usQCj)*A"4$  T> saS1#J/Qx@A133A1 All3'G7#A7#A$ t8a<c tj|}|jdks|jd|jdk7r t d|dks|t |k\rt dt |d|d|jdt j|k7r t dtt||Dcgc]}t||||c}Scc}w) a8 Assumes :math:`\texttt{expr} = X_1 \otimes \cdots \otimes X_n` is a 2D Kronecker product composed of :math:`n = \texttt{len(dims)}` implicit subsystems. Letting :math:`k = \texttt{axis}`, the returned expression represents the *partial trace* of :math:`\texttt{expr}` along its :math:`k^{\text{th}}` implicit subsystem: .. math:: \text{tr}(X_k) (X_1 \otimes \cdots \otimes X_{k-1} \otimes X_{k+1} \otimes \cdots \otimes X_n). Parameters ---------- expr : :class:`~cvxpy.expressions.expression.Expression` The 2D expression to take the partial trace of. dims : tuple of ints. A tuple of integers encoding the dimensions of each subsystem. axis : int The index of the subsystem to be traced out from the tensor product that defines expr. rr z.partial_trace only supports 2-d square arrays.z/Invalid axis argument, should be between 0 and z, got .zBDimension of system doesn't correspond to dimension of subsystems.) r cast_to_constndimr ValueErrorlennpprodsumranger)rrrrs r partial_tracer':s*   d #D yy1} 1 A6IJJ ax43t9$=c$i[tfTU V   zz!} %]^^ E$t*4EFqdAtT*F GGFsC)r)__doc__typingrrnumpyr# scipy.sparsesparser cvxpy.atoms.atomrintrr'rrr0sY#!3eCj DHeCjH Hr