bidZddlZddlmZddlZddlmZddl m Z ddl m Z ddlmZddlmZddlmZdd lmZGd d eZGd d eZGddeZddefdZddefdZy)aD Copyright 2013 Steven Diamond, 2017 Robin Verschueren 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. N)Tuple)linalg)psd_wrap)Atom) Expression) is_sparse)sparse_choleskyc eZdZy)CvxPyDomainErrorN)__name__ __module__ __qualname__P/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/atoms/quad_form.pyr r srr ceZdZdZdfd ZdZdfd ZdeeeffdZ defdZ defdZ defd Z defd Z defd Zdefd Zdefd ZdefdZdefdZdefdZdZdeedffdZxZS)QuadFormTreturnc.tt| ||y)z"Atom representing :math:`x^T P x`.N)superr__init__)selfxP __class__s rrzQuadForm.__init__&s h&q!,rcZ|dj|d}|jdjr7tjtj|dj |}n,tjtj |d|}tj|S)Nr)dotargs is_complexnpconjT transposereal)rvaluesprodquads rnumericzQuadForm.numeric*szay}}VAY' 99Q< " " $66"''&),..5D66",,vay148Dwwt}rcFtt| |jdjd}|jdjd|k7s |jdj|df|ffvr t d|jdj s t dy)Nrr.Invalid dimensions for arguments to quad_form.z4Quadratic form matrices must be symmetric/Hermitian.)rrvalidate_argumentsrshape ValueError is_hermitian)rnrs rr,zQuadForm.validate_arguments2s h02 IIaL  q ! 99Q<  a A %1););QFQD>)QMN Nyy|((*ST T+rcB|j|jfS)zCReturns sign (is positive, is negative) of the expression. )is_atom_convexis_atom_concavers rsign_from_argszQuadForm.sign_from_args:s!##%t';';'=>>rcd|jd}|jxr|jS)zIs the atom convex? r)r is_constantis_psdrrs rr2zQuadForm.is_atom_convex?( IIaL}}-188:-rcd|jd}|jxr|jS)zIs the atom concave? r)rr7is_nsdr9s rr3zQuadForm.is_atom_concaveEr:rcy)z$Is the atom log-log convex? Trr4s ris_atom_log_log_convexzQuadForm.is_atom_log_log_convexKrcy)z%Is the atom log-log concave? Frr4s ris_atom_log_log_concavez QuadForm.is_atom_log_log_concavePrc|jdjxr|jdjxs<|jdjxr|jdjS)z;Is the composition non-decreasing in argument idx? rrr is_nonneg is_nonposridxs ris_incrzQuadForm.is_incrUd ! &&(ETYYq\-C-C-EG ! &&(ETYYq\-C-C-E Grc|jdjxr|jdjxs<|jdjxr|jdjS)z;Is the composition non-increasing in argument idx? rrrDrGs ris_decrzQuadForm.is_decr[rJrcy)zIs the atom quadratic? Trr4s r is_quadraticzQuadForm.is_quadraticar?rcy)z!Always a quadratic term. Trr4s rhas_quadratic_termzQuadForm.has_quadratic_termfr?rcy)z&Is the atom piecewise linear? Frr4s ris_pwlzQuadForm.is_pwlkrBrct|jjd|jdd|jddS)N(rz, r))rr rr4s rnamez QuadForm.nameps/#~~66#yy|#yy|- -rctj|d}tj|d}|tj|jz|z}t j |j dgjgS)NrrF)order)r!arrayr"r#sp csc_arrayravel)rr&rrDs r_gradzQuadForm._gradusg HHVAY  HHVAY    " aggCg0124455r.ctSN)tupler4s rshape_from_argszQuadForm.shape_from_args{s wrrN)r r r_allow_complexrr)r,rboolr5r2r3r>rArIrLrNrPrRstrrVr_intrc __classcell__rs@rrr#sN-U?dDj 1? .. ..   GdG GdG d D  -c- 6 sCxrrceZdZdZdfd ZdZdZdefdZdefdZ defdZ defd Z de e d ffd Zde eeffd Zdefd ZxZS)SymbolicQuadFormzM Symbolic form of QuadForm when quadratic matrix is not known (yet). rcd||_tt||||jd|_y)Nr)original_expressionrrlrrr)rrrexprrs rrzSymbolicQuadForm.__init__s,#'  .q!41rc|jgSra)rnr4s rget_datazSymbolicQuadForm.get_datas(())rctra)NotImplementedError)rr&s rr_zSymbolicQuadForm._grads !##rc6|jjSra)rnr3r4s rr3z SymbolicQuadForm.is_atom_concave''7799rc6|jjSra)rnr2r4s rr2zSymbolicQuadForm.is_atom_convex''6688rc8|jj|Sra)rnrLrGs rrLzSymbolicQuadForm.is_decr''//44rc8|jj|Sra)rnrIrGs rrIzSymbolicQuadForm.is_incrryr.c6|jjSra)rnrcr4s rrcz SymbolicQuadForm.shape_from_argsrurc6|jjSra)rnr5r4s rr5zSymbolicQuadForm.sign_from_argsrwrcy)NTrr4s rrNzSymbolicQuadForm.is_quadraticsrrd)r r r__doc__rrqr_rfr3r2rLrIrrhrcr5rNrirjs@rrlrls| *$::995d55d5:sCx:9dDj 19drrl check_finitect|rS t|\}}}|dkDrd||ddftjdfSdtjd|dd|ffStj|||\}} ||}|dvrN| jjj} ddd } | | tj| jz}ttj |} | dk(r|} n|| z } | |kD}| | k}tj"|r*tj"|rt%j&d | dd|ftj(| |z}| dd|ftj(| | z}| ||fS#tt f$r'tj |j}YewxYw) a Compute a matrix decomposition. Compute sgn, scale, M such that P = sgn * scale * dot(M, M.T). The strategy of determination of eigenvalue negligibility follows the pinvh contributions from the scikit-learn project to scipy. Parameters ---------- P : matrix or ndarray A real symmetric positive or negative (semi)definite input matrix cond, rcond : float, optional Cutoff for small eigenvalues. Singular values smaller than rcond * largest_eigenvalue are considered negligible. If None or -1, suitable machine precision is used (default). lower : bool, optional Whether the array data is taken from the lower or upper triangle of P. The default is to take it from the lower triangle. check_finite : bool, optional Whether to check that the input matrix contains only finite numbers. The default is True; disabling may give a performance gain but may result in problems (crashes, non-termination) if the inputs contain infinities or NaNs. Returns ------- scale : float induced matrix 2-norm of P M1, M2 : 2d ndarray A rectangular ndarray such that P = scale * (dot(M1, M1.T) - dot(M2, M2.T)) rg?N)rr)lowerr)Ng@@g.A)fdz8Forming a nonconvex expression quad_form(x, indefinite).)rr r!emptyr.ModuleNotFoundErrorrZtodenseLAeighdtypecharrfinfoepsmaxabsoluteanywarningswarnsqrt)rcondrcondrrsignLpwVtfactorscalew_scaledmaskpmasknM1M2s r decomp_quadrsD| &(+JD!QaxAadGRXXf%555BHHV,a1g55 771E =DAq  z GGLL   %ay288A;??*  A E zu9 tOE u E vve} PQ 1e8rwwx/ /B 1e8rww/0 0B "b=//0 &%A &s2FF2GG assume_PSDcttj||f\}}|jdk(rH|jd|jdk7s)t |jdd|jdk7r t d|jr |jj|z|zS|jr|r t|}t||St d)z Alias for :math:`x^T P x`. Parameters ---------- x : vector argument. P : matrix argument. assume_PSD : P is assumed to be PSD without checking. rr)rr+z8At least one argument to quad_form must be non-variable.) mapr cast_to_constndimr-r Exceptionr7r# conjugaterr)rrrs r quad_formrs z''!Q 0DAq 66Q;!''!* 2c!''46H6KqwwWXz6YHII}}ss}}"Q&&   A1~ F  r)NNTT)F)r~rtypingrnumpyr! scipy.sparsesparser[scipyrrcvxpy.atoms.affine.wrapsrcvxpy.atoms.atomrcvxpy.expressions.expressionr cvxpy.interface.matrix_utilitiesrcvxpy.utilities.linalgr rr rrlrfrrrrrrsm -!362 y YtYx"t"JADAH  r