biXrdZddlmZmZddlZddlmZddl m Z ddl m Z ddl mZddlmZGd d eZy) a0 Copyright 2023, 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. )ListTupleN)linalg)entropy)settings)Atom) ConstraintceZdZdZeej dZddee e fddffd Z dZ ddZ dee e ffd Zde fd Zdee d ffd Zde fd Zde fdZde fdZdZdZdeefdZxZS)quantum_rel_entraw An approximation of the quantum relative entropy between systems with (possibly un-normalized) density matrices :math:`X` and :math`Y:` .. math:: \operatorname{tr}\left( X ( \log X - \log Y ) \right). The approximation uses a quadrature scheme described in https://arxiv.org/abs/1705.00812. Parameters ---------- X : Expression or numeric A PSD matrix Y : Expression or numeric A PSD matrix quad_approx : Tuple[int, int] quad_approx[0] is the number of quadrature nodes and quad_approx[1] is the number of scaling points in the quadrature scheme from https://arxiv.org/abs/1705.00812. Notes ----- This function does not assume :math:`\operatorname{tr}(X)=\operatorname{tr}(Y)=1,` which would be required for most uses of this function in the context of quantum information. gư> quad_approxreturnNc<||_tt|||yN)r superr __init__)selfXYr __class__s W/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/atoms/quantum_rel_entr.pyrzquantum_rel_entr.__init__7s& .q!4c|\}}t|dr$t|dr|j}|j}||jjzdz }||jjzdz }t j |\}}t j |\}}|jt j|jj|zdzz}t j||j ks#t j||j krt jSd||dk<d||dk<t| } |t j|z} | | z S)Nvaluer) hasattrrconjTLAeighnpabsanyEVAL_TOLinfrlog) rvaluesrrw1Vw2Wur1r2s rnumericzquantum_rel_entr.numeric;s"1 1g 71g#6AA ^q  ^q  A A DD266!&&(**q.)Q. . 66"& '266" ~2E+F66MBrAvJBrAvJbk\ ^Rrc|jdjr|jdjs tdy)Nrz9The arguments to quantum_rel_entr must both be hermitian.)args is_hermitian ValueErrorrs rvalidate_argumentsz#quantum_rel_entr.validate_argumentsOs? ! ))+ ! 0I0I0KK 1Lrcy)zCReturns sign (is positive, is negative) of the expression. )FFr4s rsign_from_argszquantum_rel_entr.sign_from_argsUsrcy)zIs the atom convex? Tr7r4s ris_atom_convexzquantum_rel_entr.is_atom_convexZsr.ctS)z-Returns the shape of the expression. )tupler4s rshape_from_argsz quantum_rel_entr.shape_from_args_s wrcy)zIs the atom concave? Fr7r4s ris_atom_concavez quantum_rel_entr.is_atom_concavedrcy)z;Is the composition non-decreasing in argument idx? Fr7ridxs ris_incrzquantum_rel_entr.is_incrir@rcy)z;Is the composition non-increasing in argument idx? Fr7rBs ris_decrzquantum_rel_entr.is_decrnr@rc|jgSr)r r4s rget_datazquantum_rel_entr.get_datass  !!rct)a+Gives the (sub/super)gradient of the atom w.r.t. each argument. Matrix expressions are vectorized, so the gradient is a matrix. Args: values: A list of numeric values for the arguments. Returns: A list of SciPy CSC sparse matrices or None. )NotImplementedError)rr&s r_gradzquantum_rel_entr._gradvs "##rcJ|jddz |jddz gS)z?Returns constraints describing the domain of the node. rr0)r1r4s r_domainzquantum_rel_entr._domains) ! !499Q<1#455r))rN)r N)__name__ __module__ __qualname____doc__minr ATOM_EVAL_TOLr#rintrr.r5boolr8r:r=r?rDrFrHrKrr rM __classcell__)rs@rr r s28))40H5%S/5t5( dDj 1  sCx  d d " $6j)6rr )rRtypingrrnumpyr scipyrr scipy.statsrcvxpyrcvxpy.atoms.atomrcvxpy.constraints.constraintr r r7rrr_s/!3k6tk6r