biJdZddlmZddlZddlmZddlm Z Gdde Z y)a, Copyright 2013 Steven Diamond 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. )TupleN)AtomceZdZdZdZdfd ZdZdZdee dffdZ dee e ffd Z de fd Z de fd Zde fd Zde fd ZxZS)normNucz Sum of the singular values. Treturnc,tt| |y)N)superr__init__)selfA __class__s O/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/atoms/norm_nuc.pyr znormNuc.__init__s gt%a(cHtjj|ddS)zMReturns the nuclear norm (i.e. the sum of the singular values) of A. rnuc)nplinalgnorm)r valuess rnumericznormNuc.numeric!syy~~fQi//rctjj|dd\}}}|j|}t j |j dgjgS)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. rF) full_matricesF)order)rrsvddotsp csc_arrayravelT)r rU_VDs r_gradz normNuc._grad&sW))--q -?1a EE!H aggCg0124455r.ctS)z8Returns the (row, col) shape of the expression. )tupler s rshape_from_argsznormNuc.shape_from_args6s wrcy)zCReturns sign (is positive, is negative) of the expression. )TFr(s rsign_from_argsznormNuc.sign_from_args;srcy)zIs the atom convex? Tr+r(s ris_atom_convexznormNuc.is_atom_convex@srcy)zIs the atom concave? Fr+r(s ris_atom_concaveznormNuc.is_atom_concaveErcy)z;Is the composition non-decreasing in argument idx? Fr+r idxs ris_incrznormNuc.is_incrJr1rcy)z;Is the composition non-increasing in argument idx? Fr+r3s ris_decrznormNuc.is_decrOr1r)rN)__name__ __module__ __qualname____doc___allow_complexr rr%rintr)boolr,r.r0r5r7 __classcell__)r s@rrrsuN)0 6 sCx dDj 1   d drr) r;typingrnumpyr scipy.sparsesparsercvxpy.atoms.atomrrr+rrrEs$ !9d9r