bifdZddlmZmZddlZddlmZddl m Z ddl m Z ddl mZGdd e Zy) a0 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. )ListTupleN)linalg)entr)Atom) ConstraintceZdZdZddeedfddffd ZdZddZdee e ffd Z de fd Z deedffd Z de fd Z de fd Zde fdZdZdZdeefdZxZS)von_neumann_entraE Represents the von Neumann Entropy of the positive-definite matrix :math:`X,` .. math:: -\operatorname{tr}(X \log X). Mathematically, this is equivalent to .. math:: \texttt{von_neumann_entr}(X) = -\textstyle\sum_{i=1}^n \lambda_i \log \lambda_i where :math:`\lambda_{i}` are the eigenvalues of :math:`X.` Parameters ---------- X : Expression or numeric A PSD matrix quad_approx : Tuple[int,...] This is either an empty tuple (default) or a 2-tuple. If a 2-tuple, then this atom is approximately canonicalized. The approximations replace ExpCone constraints with SOC constraints based on a quadrature scheme from https://arxiv.org/abs/1705.00812; quad_approx[0] is the number of quadrature nodes and quad_approx[1] is the number of scaling points in the quadrature scheme. Notes ----- This function does not assume :math:`\operatorname{tr}(X)=1,` which would be required for most uses of this function in the context of quantum information theory. quad_approx.returnNc:||_tt||yN)r superr __init__)selfXr __class__s W/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/atoms/von_neumann_entr.pyrzvon_neumann_entr.__init__:s& .q1c|d}t|dr |j}tj|}t j t |}|S)Nrvalue)hasattrrLAeigvalshnpsumr)rvaluesNwvals rnumericzvon_neumann_entr.numeric>sA 1I 1g A KKNffT!Wo rc|jdjs*td|jdjdy)z&Verify that the argument is Hermitian.rz The argument z to von_neumann_entr must be a Hermitian matrix. If you know for a fact that the input is Hermitian, wrap it with the hermitian_wrap atom before calling von_neumann_entr. N)args is_hermitian ValueErrornamers rvalidate_argumentsz#von_neumann_entr.validate_argumentsFsNyy|((*"iil//123 +rcy)zCReturns sign (is positive, is negative) of the expression. )FFr's rsign_from_argszvon_neumann_entr.sign_from_argsQsrcy)zIs the atom convex? Fr*r's ris_atom_convexzvon_neumann_entr.is_atom_convexVrctS)z-Returns the shape of the expression. )tupler's rshape_from_argsz von_neumann_entr.shape_from_args[s wrcy)zIs the atom concave? Tr*r's ris_atom_concavez von_neumann_entr.is_atom_concave`srcy)z;Is the composition non-decreasing in argument idx? Fr*ridxs ris_incrzvon_neumann_entr.is_increr.rcy)z;Is the composition non-increasing in argument idx? Fr*r5s ris_decrzvon_neumann_entr.is_decrjr.rc|jgSr)r r's rget_datazvon_neumann_entr.get_dataos  !!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)rrs r_gradzvon_neumann_entr._gradrs "##rc(|jddz gS)z?Returns constraints describing the domain of the node. r)r#r's r_domainzvon_neumann_entr._domains ! !""r)r*)r N)__name__ __module__ __qualname____doc__rintrr!r(boolr+r-r1r3r7r9r;r>rrr@ __classcell__)rs@rr r s>2uS#X22 dDj 1  sCx  d d "$$#j)#rr )rDtypingrrnumpyrscipyrr scipy.specialrcvxpy.atoms.atomrcvxpy.constraints.constraintrr r*rrrNs,!3m#tm#r