bik?VdZddlZddlmZddlmZmZddlZ ddl m Z ddl mcmZddlmcmZddlmZddlmZddlmZddlmZddlmZmZdd l m!Z"dd l#m$Z$dd l%m&Z&dd l'm(Z(m)Z)dd l*m+Z+GddeZ,ddZ-Gdde,Z.Gdde.Z/Gdde,Z0dZ1dZ2dZ3y)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. N)reduce)ListTuple) AddExpression)AffAtom)conj) deep_flattenreshape)sum) Constraint)DCPError)is_param_affine is_param_free) ExpressioncbeZdZdZdZd fd ZdZdZdee e ffdZ de fdZ de fd Z xZ S) BinaryOperatorzW Base class for expressions involving binary operators. (other than addition) BINARY_OPreturnc.tt| ||yN)superr__init__)selflh_exprh_exp __class__s ^/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/atoms/affine/binary_operators.pyrzBinaryOperator.__init__1s nd,VV<cg}|jD]]}t|ttfr&|j d|j zdz?|j |j _|ddz|j zdz|dzS)N()r )args isinstancer DivExpressionappendnameOP_NAME)r pretty_argsas rr(zBinaryOperator.name4s  -A!m];<""3>C#78""1668,  - 1~#dll2S8;q>IIrc.t|j|S)z3Applies the binary operator to the values. )rOP_FUNCrvaluess rnumericzBinaryOperator.numeric=sdllF++rcvtjj|jd|jdS)z$Default to rules for times. rr#)usignmul_signr$rs rsign_from_argszBinaryOperator.sign_from_argsBs)vvtyy|TYYq\::rc|jdjxr|jdjxs<|jdjxr|jdjS)z%Is the expression imaginary? rr#)r$is_imagis_realr5s rr8zBinaryOperator.is_imagGsd ! $$&A499Q<+?+?+A@ YYq\ ! ! # > ! (<(<(> @rc|jdjxs|jdjxr=|jdjxr|jdj S)z*Is the expression complex valued? rr#)r$ is_complexr8r5s rr;zBinaryOperator.is_complexMsg ! '')FTYYq\-D-D-FD1%%'BDIIaL,@,@,B C DrrN)__name__ __module__ __qualname____doc__r)rr(r0rboolr6r8r; __classcell__rs@rrr)sP G=J, ;dDj 1; @@ DDDrr MulExpressionct||S)zMatrix multiplication.)rD)rrs rmatmulrFTs  ((rceZdZdZdZej ZdZdZ de e dffdZ de fdZde fd Zde fd Zde fd Zde fd Zde fd ZfdZ dde e dfde ej,eeffdZxZS)rDaMatrix multiplication. The semantics of multiplication are exactly as those of NumPy's matmul function, except here multiplication by a scalar is permitted. MulExpression objects can be created by using the '*' operator of the Expression class. Parameters ---------- lh_exp : Expression The left-hand side of the multiplication. rh_exp : Expression The right-hand side of the multiplication. @cv|djdk(s|djdk(r |d|dzS|d|dzS)zMatrix multiplication. rr#)shaper.s rr0zMulExpression.numericlsI !9??b F1IOOr$9!9vay( (!9vay( (rc|jdjdkDs|jdjdkDr tdy)z7Validate that the arguments can be multiplied together.rr#z3Multiplication with N-d arrays is not yet supportedN)r$ndim ValueErrorr5s rvalidate_argumentsz MulExpression.validate_argumentsts> 99Q<  q DIIaL$5$5$9RS S%:rr.ctjj|jdj|jdjS)8Returns the (row, col) shape of the expression. rr#)r2rK mul_shapesr$r5s rshape_from_argszMulExpression.shape_from_argsys7ww!!$))A,"4"4diil6H6HIIrctjjrt|jd}|jd}|j xs|j xs2t |xr t |xst |xr t |S|jdj xs|jdj S)zpMultiplication is convex (affine) in its arguments only if one of the arguments is constant. rr#)r2scopesdpp_scope_activer$ is_constantrr)rxys ris_atom_convexzMulExpression.is_atom_convex~s 88 $ $ & ! A ! A]]_7 >$Q'$Q',>q,A)AA B G \\"  ! **+q0qdiil6H6H6K ]]d D1BMM!##.De LBxEs&I rKc|d}|d}|jdjrtj|||gfS|jdjrtj|||gfSt d)Multiply the linear expressions. Parameters ---------- arg_objs : list LinExpr for each argument. shape : tuple The shape of the resulting expression. data : Additional data required by the atom. Returns ------- tuple (LinOp for objective, list of constraints) rr#3Product of two non-constant expressions is not DCP.)r$rXlumul_expr rmul_exprr rarg_objsrKdatalhsrhss rgraph_implementationz"MulExpression.graph_implementations(qkqk 99Q< # # %KKS%0"5 5 YYq\ % % 'LLc5126 6"# #rr)r=r>r?r@r)opmulr-r0rPrintrTrAr[r^rarerkrprtloLinOprr rrBrCs@rrDrDYs GffG)T JsCxJ LL.%%   ,d, ,d, &R6:#$S#X# rxxj)) *#rceZdZdZdZdfd ZdefdZdefdZdefdZ defdZ d Z d Z de ed ffd Zdefd ZdefdZ dde ed fde ej&eeffdZxZS)multiplyz'Multiplies two expressions elementwise.*rcX|j||\}}tt|||yr) broadcastrrrrlh_exprrh_exprrs rrzmultiply.__init__s)>>'7; h&w8rcy)zIs the atom log-log convex?TrJr5s rrazmultiply.is_atom_log_log_convexrcy)zIs the atom log-log concave?TrJr5s rrez multiply.is_atom_log_log_concaverrcr|jdjxs|jdjxsz|jdjxr|jdjxs<|jdjxr|jdjSNrr#)r$rXrhror5s ris_atom_quasiconvexzmultiply.is_atom_quasiconvexs IIaL $ $ & D$))A,*B*B*DC IIaL " " $ A1)?)?)AC IIaL " " $ A1)?)?)A Crc|jdjxs|jdjxs:td|jDxstd|jDS)Nrr#c3<K|]}|jywr)rh.0args r z0multiply.is_atom_quasiconcave..sM2 #CMMOM2c3<K|]}|jywr)rors rrz0multiply.is_atom_quasiconcave..s92 #CMMO92r)r$rXallr5s ris_atom_quasiconcavezmultiply.is_atom_quasiconcave sp IIaL $ $ & D$))A,*B*B*D2ILM2'+yyM2J225892'+yy9262 2rctj|dr|dj|dStj|dr|dj|dStj|d|dS)z"Multiplies the values elementwise.rr#)rwissparserr|r.s rr0zmultiply.numericsm ;;vay !!9%%fQi0 0 [[ #!9%%fQi0 0;;vay&)4 4rc ,tjtj|jdjtj gtj|jdjtj gy)z.Validate that the arguments are broadcastable.r)dtyper#N)r|remptyr$rKrr5s rrPzmultiply.validate_argumentssV HHTYYq\''rxx| < HHTYYq\''rxx| < r.ctj|jdj|jdjS)z(Call np.broadcast on multiply arguments.rr#)r|broadcast_shapesr$rKr5s rrTzmultiply.shape_from_args"s1""499Q<#5#5tyy|7I7IJJrc|jdjxr|jdjxs<|jdjxr|jdjS)z:Is the expression a positive semidefinite matrix? rr#r$is_psdis_nsdr5s rrzmultiply.is_psd&d ! ##%?$))A,*=*=*?A ! ##%?$))A,*=*=*? Arc|jdjxr|jdjxs<|jdjxr|jdjS)z:Is the expression a negative semidefinite matrix? rr#rr5s rrzmultiply.is_nsd,rrrKc|d}|d}|jdjrtj||gfS|jdjrtj||gfSt d)aMultiply the expressions elementwise. Parameters ---------- arg_objs : list LinExpr for each argument. shape : tuple The shape of the resulting expression. data : Additional data required by the atom. Returns ------- tuple (LinOp for objective, list of exprraints) rr#r)r$rXrrr rs rrzmultiply.graph_implementation2s|(qkqk 99Q< # # %KKS)2. . YYq\ % % 'KKS)2. ."# #rr<r)r=r>r?r@r)rrArarerrr0rPrrrTrrrrrr rrBrCs@rrrs1G9CTC 2d2 5 KsCxKAA AA6:#$S#X# rxxj)) *#rrc"eZdZdZdZej Zdfd ZdZ de fdZ de fdZ de fdZ deed ffd Zde fd Zde fd Zde fd Zde fdZde fdZde fdZde fdZde fdZ ddeed fdeej4eeffdZxZS)r&zSDivision by scalar. Can be created by using the / operator of expression. /rcX|j||\}}tt|||yr)rrr&rrs rrzDivExpression.__init__Zs)>>'7; mT+GW=rctdD]1}tj||s||j||<3t j |d|dS)z*Divides numerator by denominator. rMrr#)rzrwrtoarrayr|divide)rr/is rr0zDivExpression.numeric^sXq 0A{{6!9%"1I--/q  0yyF1I..rcz|jdjxr|jdjSr)r$ is_quadraticrXr5s rrzDivExpression.is_quadraticfs/yy|((*Ityy|/G/G/IIrcz|jdjxr|jdjS)z/Can be a quadratic term if divisor is constant.rr#)r$has_quadratic_termrXr5s rrz DivExpression.has_quadratic_termis/yy|..0OTYYq\5M5M5OOrcz|jdjxr|jdjSr)r$is_qpwarXr5s rrzDivExpression.is_qpwams/yy|##%D$))A,*B*B*DDr.c4|jdjS)rRr)r$rKr5s rrTzDivExpression.shape_from_argspsyy|!!!rc<|jdjS)zeDivision is convex (affine) in its arguments only if the denominator is constant. r#)r$rXr5s rr[zDivExpression.is_atom_convexusyy|''))rc"|jSrr]r5s rr^zDivExpression.is_atom_concave{s""$$rcyr`rJr5s rraz$DivExpression.is_atom_log_log_convex~rbrcy)rdTrJr5s rrez%DivExpression.is_atom_log_log_concaverbrcz|jdjxs|jdjS)Nr#r$rhror5s rrz!DivExpression.is_atom_quasiconvexs/yy|%%'C499Q<+A+A+CCrc"|jSr)rr5s rrz"DivExpression.is_atom_quasiconcaves''))rc|dk(r|jdjS|jdjS)rgrr#rris rrkzDivExpression.is_incr9 !899Q<))+ +99Q<))+ +rc|dk(r|jdjS|jdjS)rnrr#)r$rorhris rrpzDivExpression.is_decrrrrKc>tj|d|dgfS)rrr#)rdiv_expr)rrrKrs rrz"DivExpression.graph_implementations"& HQK!5r::rr<r)r=r>r?r@r)r|rr-rr0rArrrrrrTr[r^rarerrrkrprrrr rrBrCs@rr&r&Qs GiiG>/JdJPDPEE"sCx" ** %%  DTD*d*,d,,d,6:;$S#X; rxxj)) *;rr&cnt|}t|}tt||}t|S)a? Return the standard inner product (or "scalar product") of (x,y). Parameters ---------- x : Expression, int, float, NumPy ndarray, or nested list thereof. The conjugate-linear argument to the inner product. y : Expression, int, float, NumPy ndarray, or nested list thereof. The linear argument to the inner product. Returns ------- expr : Expression The standard inner product of (x,y), conjugate-linear in x. We always have ``expr.shape == ()``. Notes ----- The arguments ``x`` and ``y`` can be nested lists; these lists will be flattened independently of one another. For example, if ``x = [[a],[b]]`` and ``y = [c, d]`` (with ``a,b,c,d`` real scalars), then this function returns an Expression representing ``a * c + b * d``. )r rr cvxpy_sum)rYrZprods rvdotrs04 QAQA DGQ D T?rct||S)z Alias for vdot. )rrYrZs rscalar_productrs 1:rc0tj|}|jdkDr tdtj|}|jdkDr tdt ||j dfd}t |d|j fd}||zS)a+ Return the outer product of (x,y). Parameters ---------- x : Expression, int, float, NumPy ndarray, or nested list thereof. Input is flattened if not already a vector. The linear argument to the outer product. y : Expression, int, float, NumPy ndarray, or nested list thereof. Input is flattened if not already a vector. The transposed-linear argument to the outer product. Returns ------- expr : Expression The outer product of (x,y), linear in x and transposed-linear in y. r#zx must be a 1-d array.zy must be a 1-d array.F)order)r cast_to_constrNrOr rurs routerrs$   #Avvz122  #Avvz122AFFA;c*AAqvv;c*A q5Lr)rrD)4r@operatorr functoolsrtypingrrnumpyr| scipy.sparsesparserwcvxpy.lin_ops.lin_oplin_opslin_oprcvxpy.lin_ops.lin_utils lin_utilsrcvxpy.utilities utilitiesr2cvxpy.atoms.affine.add_exprrcvxpy.atoms.affine.affine_atomrcvxpy.atoms.affine.conjrcvxpy.atoms.affine.reshaper r cvxpy.atoms.affine.sumr rcvxpy.constraints.constraintr cvxpy.errorr %cvxpy.expressions.constants.parameterrrcvxpy.expressions.expressionrrrFrDrr&rrrrJrrrs !!$$52(<33 4(DW(DV) Y#NY#xY#}Y#x`;N`;F@r