biD dZddlmZmZddlZddlmZddl m Z d de de dee dee fd Z d dee d fdee fd Z y) a1 Copyright 2022, the CVXPY authors. 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)Atomijdimsaxisc>tjdgdgdgff}t|D]l\}}||k(r7tjdg|g|gff||f}tj||}Btj|} tj|| }n||z|zS)aHelper function for partial transpose. Parameters ---------- expr : :class:`~cvxpy.expressions.expression.Expression` The 2D expression to take the partial transpose of. i : int Term in the partial transpose sum. j : int Term in the partial transpose sum. dims : tuple of ints. A tuple of integers encoding the dimensions of each subsystem. axis : int The index of the subsystem to be transposed from the tensor product that defines expr. g?r)shape)sp coo_matrix enumeratekron eye_array) exprrrrr ai_axisdimveye_mats _/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/atoms/affine/partial_transpose.py_termrs* usQCj)*A"4$  T> saS1#J/SzBA1 All3'G7#A $ t8a<.ctj|}|jdks|jd|jdk7r t d|dks|t |k\rt dt |d|d|jdt j|k7r t dtt||Dcgc]$}t||D]}t|||||&c}}Scc}}w) a& Assumes :math:`\texttt{expr} = X_1 \otimes ... \otimes X_n` is a 2D Kronecker product composed of :math:`n = \texttt{len(dims)}` implicit subsystems. Letting :math:`k = \texttt{axis}`, the returned expression is a *partial transpose* of :math:`\texttt{expr}`, with the transpose applied to its :math:`k^{\text{th}}` implicit subsystem: .. math:: X_1 \otimes ... \otimes X_k^T \otimes ... \otimes X_n. Parameters ---------- expr : :class:`~cvxpy.expressions.expression.Expression` The 2D expression to take the partial transpose of. dims : tuple of ints. A tuple of integers encoding the dimensions of each subsystem. axis : int The index of the subsystem to be transposed from the tensor product that defines expr. rr z2partial_transpose only supports 2-d square arrays.z/Invalid axis argument, should be between 0 and z, got .zBDimension of system doesn't correspond to dimension of subsystems.) r cast_to_constndimr ValueErrorlennpprodsumranger)rrr rrs rpartial_transposer&;s*   d #D yy1} 1 A6MNN ax43t9$=c$i[tfTU V   zz!} %]^^ /4T$Z/@*+%PTUYPZJ[EFdAq$%% s)C4 )r)__doc__typingrrnumpyr" scipy.sparsesparser cvxpy.atoms.atomrintrr&rrr/sa$#!33eCj @ %S/ # r