bixndZddlZddlZddlmZddlmZmZmZm Z ddl Z ddl Z ddlmZddlmZddlmcmZddlmcmZddl mZddlmZmZmZddlm Z ddlm!Z!dd l"m#Z#d Z$d a%d Z&d Z'dZ(dZ)dZ*e jVde jXde jZde j\de j^de j`de jbde jdde jfde jhde jjde jlde jndi Z8dZ9Gdd ejtZ;y)!a, Copyright 2013 Steven Diamond Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. Nwraps)ListLiteralOptionalTuple)error)PSDEquality Inequality)cvxtypes)scopes)size_from_shapec.tfd}|S)zCasts the second argument of a binary operator as an Expression. Args: binary_op: A binary operator in the Expression class. Returns: A wrapped binary operator that can handle non-Expression arguments. c8|j|}||S)zLA wrapped binary operator that can handle non-Expression arguments. ) cast_to_const)selfother binary_ops W/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/expressions/expression.pycast_opz_cast_other..cast_op.s"""5)u%%r)rrs` r _cast_otherr$s# 9&& Nrak This use of ``*`` has resulted in matrix multiplication. Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1. Use ``*`` for matrix-scalar and vector-scalar multiplication. Use ``@`` for matrix-matrix and matrix-vector multiplication. Use ``multiply`` for elementwise multiplication. This code path has been hit %s times so far. z You're calling a NumPy function on a CVXPY expression. This is prone to causing errors or code that doesn't behave as expected. Consider using one of the functions documented here: https://www.cvxpy.org/tutorial/functions/index.html z You're trying to mutate a CVXPY expression inplace. This is prone to errors or code that doesn't behave as expected. Consider alternatives. For example, replace x += 1 with x = x + 1 z You're calling the built-in abs function on a CVXPY expression. This is not supported. Consider using the abs function provided by CVXPY. a" You didn't specify the order of the FUNC_NAME expression. The default order used in CVXPY is Fortran ('F') order. This default will change to match NumPy's default order ('C') in a future version of CVXPY. To suppress this warning, please specify the order explicitly. c$|j|SN)__radd__ras rr _s a 0rc$|j|Sr)__rsub__rs rr r `T]]1%5rc$|j|Sr)__rmul__rs rr r ar#rc$|j|Sr)__rdiv__rs rr r bs4==#3rc$|j|Sr) __rmatmul__rs rr r cs4#3#3A#6rc$|j|Sr)__rpow__rs rr r ds$--"2rc$|j|Sr) __rlshift__rs rr r est'7'7':rc$|j|Sr) __rrshift__rs rr r fs(8(8(;rc$|j|Sr)__eq__rs rr r gs$++a.rc$|j|Sr)__ge__rs rr r jst{{1~rc$|j|Sr)__le__rs rr r ks$++a.rc$|j|Sr)__gt__rs rr r lsQrc$|j|Sr)__lt__rs rr r msDKKNrz Expression | np.typing.ArrayLikeceZdZdZdZeejdee jfdZ dee jfdZ eejdZ eejdZdefdZdefd Zejdefd Zed Zedeefd Zedefd ZedefdZej2defdZej2defdZejdefdZejdefdZej2dqdedefdZdefdZ ej2defdZ!ejdefdZ"ejdefdZ#dqdedefdZ$ejdrdedefdZ%defdZ&defdZ'defdZ(ej2defd Z)defd!Z*defd"Z+defd#Z,defd$Z-defd%Z.defd&Z/defd'Z0defd(Z1defd)Z2edefd*Z3ej2defd+Z4ejdefd,Z5ejdefd-Z6eejde7e8d.ffd/Z9defd0Z:eejdefd1Z;ejdefd2Zdsd6e?d7fd8Z@defd9ZAdefd:ZBdefd;ZCdtd<ZDedtd=ZEedtd>ZFd?eGddfd@ZHdAeGddfdBZIeJdtdCZKeJdudDZLeJdvdEZMeNdFeOddfdGZPeNdFeOddfdHZQeNdFeOddfdIZReNdFeOddfdJZSeNdFeOddfdKZTeNdFeOddfdLZUeNdFeOddfdMZVeNdFeOddfdNZWeNdFeOddfdOZXeNdFeOddfdPZYeNdFeOddfdQZZeNdFeOddfdRZ[dtdSZ\eNdFeOde]fdTZ^eNdFeOde]fdUZ_eNdFeOde]fdVZ`eNdFeOde]fdWZade8fdXZbeNdFeOdecfdYZdeNdFeOdeefdZZfdFeOfd[ZgeNdFeOdeefd\ZhdFeOfd]Zid^Zjd_Zkdtd`ZldtdaZmdwdtdcZndsddddtdeZodsddddtdfZpdsddddtdgZqdsddddtdhZrdsddddtdiZsdsd6e?d7ddfdjZtdsdbddkdtdlZudsddddtdmZvdtdnZwdbdodtdpZxy5)x ExpressionzA mathematical expression in a convex optimization problem. 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Returns ------- dict A map of variable to SciPy CSC sparse matrix; None if a variable value is missing. r?rAs rgradzExpression.grads "##rct)zolist : The constraints describing the closure of the region where the expression is finite. r?rAs rdomainzExpression.domains "##rc"|jS)z>Returns a string showing the mathematical expression. )namerAs r__str__zExpression.__str__syy{rcVd|jd|jd|jdS)z@Returns a string with information about the expression. z Expression(z, )) curvaturesignshaperAs r__repr__zExpression.__repr__s#,0>>+/99+/::7 7rct)z;str : The string representation of the expression. r?rAs rrKzExpression.name "##rc|S)zExpression : returns itself.rAs rexprzExpression.exprs  rc |jtjf|jtjf|j tj f|jtjf|jtjf|jtjf|jtjf|jtj f|j"tj$f|j&tj(f|j*tj,fg }|Dcgc]\}}|s|}}}|stj.gS|Scc}}w)z:List : Returns a list of the curvatures of the expression.) is_constantsCONSTANT is_affineAFFINE is_convexCONVEX is_concaveCONCAVEis_log_log_constantLOG_LOG_CONSTANTis_log_log_affineLOG_LOG_AFFINEis_log_log_convexLOG_LOG_CONVEXis_log_log_concaveLOG_LOG_CONCAVEis_quasilinear QUASILINEARis_quasiconvex QUASICONVEXis_quasiconcave QUASICONCAVEUNKNOWN)r curvatures conditionrOs rrqzExpression.curvaturess   qzz * ^^QXX & ^^QXX & __aii (  % %q'9'9 :  # #Q%5%5 6  # #Q%5%5 6  $ $a&7&7 8  !-- 0  !-- 0  ! !1>> 2  =GV$8Iy)+iV VII; Ws 1EEc|jrtj}|S|jrtj}|S|j rtj }|S|jrtj}|S|jrtj}|S|jrtj}|S|jrtj}|S|jrtj }|S|j#rtj$}|S|j'rtj(}|Stj*}|S)z/str : The curvature of the expression. )rYrZr[r\r]r^r_r`rardrerfrgrhrirjrkrlrmrnrorpr curvature_strs rrOzExpression.curvaturesI    JJM*)^^ HHM&%^^ HHM"!__ IIM # # %,,M # # %,,M $ $ &--M "MMM  "MMM   ! ! #NNMIIMrc6|jrtj}|S|jrtj}|S|j rtj }|S|jrtj}|Stj}|S)z7str : The log-log curvature of the expression. ) rbrZrcrdrerfrgrhrirprts rlog_log_curvaturezExpression.log_log_curvatures  # # %..M # # %,,M  # # %,,M   $ $ &--MIIMrcZd|jvxstd|jDS)z$Is the expression constant? rc3<K|]}|jywrrY).0args r z)Expression.is_constant..s&4"%COO &4s)rQallargsrAs rrYzExpression.is_constants1DJJ4#&4)-&4#4 4rcj|jxs"|jxr|jSz"Is the expression affine? )rYr^r`rAs rr\zExpression.is_affines+!Mdnn&6&L4??;LMrct)z"Is the expression convex? r?rAs rr^zExpression.is_convexrTrct)z#Is the expression concave? r?rAs rr`zExpression.is_concave rTrFdppc|r@tj5|jxs|jcdddS|jxs|jS#1swY+xYw)aqChecks whether the Expression is DCP. Parameters ---------- dpp : bool, optional If True, enforce the disciplined parametrized programming (DPP) ruleset; only relevant when the problem involves Parameters. Returns ------- bool True if the Expression is DCP, False otherwise. N)r dpp_scoper^r`rrs ris_dcpzExpression.is_dcps\ !!# =~~'<4??+< = =~~44??#44 = = "A%%A.c |jsyt|tjtjfr|j S|j duxr"tj|j dkDS)zFIs the expression log-log constant, ie, elementwise positive? FNr) rY isinstancer constant parameteris_posrBnpr~rAs rrbzExpression.is_log_log_constant'se! dX..0(2D2D2FG H;;= ::T)DbffTZZ!^.D Drcj|jxs"|jxr|jSr)rbrfrhrAs rrdzExpression.is_log_log_affine2s6((*L**,J1H1H1J Mrct)z*Is the expression log-log convex? r?rAs rrfzExpression.is_log_log_convex9rTrct)z+Is the expression log-log concave? r?rAs rrhzExpression.is_log_log_concave?rTrc|r@tj5|jxs|jcdddS|jxs|jS#1swY+xYw)zChecks whether the Expression is log-log DCP. Returns ------- bool True if the Expression is log-log DCP, False otherwise. N)rrrfrhrs ris_dgpzExpression.is_dgpEsi !!# M--/L43J3J3L M M%%'D4+B+B+DD M Mrcontextct)zBThe expression is a disciplined parameterized expression. r?)rrs ris_dppzExpression.is_dppRrTrc"|jSr)r^rAs rrlzExpression.is_quasiconvexXs~~rc"|jSr)r`rAs rrnzExpression.is_quasiconcave[s  rcF|jxr|jSrrlrnrAs rrjzExpression.is_quasilinear^s""$?)=)=)??rcF|jxs|jS)zChecks whether the Expression is DQCP. Returns ------- bool True if the Expression is DQCP, False otherwise. rrAs ris_dqcpzExpression.is_dqcpas!""$>(<(<(>>rcF|jxr|jS)z.Is the expression a Hermitian matrix? )is_real is_symmetricrAs r is_hermitianzExpression.is_hermitianls 64#4#4#67rcy)z:Is the expression a positive semidefinite matrix? FrVrAs ris_psdzExpression.is_psdqrcy)z:Is the expression a negative semidefinite matrix? FrVrAs ris_nsdzExpression.is_nsdwrrc"|jS)z%Is the expression quadratic? rzrAs r is_quadraticzExpression.is_quadratic}!!rc"|jS)aDoes the affine head of the expression contain a quadratic term? 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FrVrAs ris_skew_symmetriczExpression.is_skew_symmetricsrc"|jS)z,Is the expression piecewise linear? rzrAs ris_pwlzExpression.is_pwlrrcF|jxs|jS)z9Is the expression quadratic of piecewise affine? )rrrAs ris_qpwazExpression.is_qpwas  "3dkkm3rc|jrtj}|S|jrtj}|S|j rtj }|Stj}|S)z)str: The sign of the expression. )is_zerorZZERO is_nonnegNONNEG is_nonposNONPOSrp)rsign_strs rrPzExpression.signse <<>vvH ^^ xxH  ^^ xxHyyHrcF|jxr|jS)z$Is the expression all zero? )rrrAs rrzExpression.is_zeros~~4DNN$44rct)z$Is the expression positive? r?rAs rrzExpression.is_nonnegrTrct)z$Is the expression negative? r?rAs rrzExpression.is_nonposrTr.ct)z+tuple : The expression dimensions. r?rAs rrQzExpression.shaperCrc$|j S)z!Is the Leaf real valued? ) is_complexrAs rrzExpression.is_reals??$$$rct)zIs the Leaf imaginary? r?rAs ris_imagzExpression.is_imagrCrct)z$Is the Leaf complex valued? r?rAs rrzExpression.is_complexrTrc,t|jS)z7int : The number of entries in the expression. )rrQrAs rsizezExpression.sizestzz**rc,t|jS)zBint : The number of dimensions in the expression's shape. )lenrQrAs rndimzExpression.ndims4::rNorder)FCNc|2tjdd}tj|td}|dvsJt j ||S)zi Vectorizes the expression. order: column-major ('F') or row-major ('C') order. FUNC_NAMEflattenr)rr)DEFAULT_ORDER_DEPRECATION_MSGreplacewarningswarn FutureWarningr vec)rrflatten_order_warnings rrzExpression.flattensT =$A$I$I+W`$a ! MM/ ?E """x||~dE**rc:td|jDS)zIs the expression a scalar?c3&K|] }|dk( yw)rNrV)r{ds rr}z'Expression.is_scalar..s.a16.s)r~rQrAs rrzExpression.is_scalars.4::...rcv|jdkxs)|jdk(xrt|jdk(S)z)Is the expression a column or row vector?r)rminrQrAs r is_vectorzExpression.is_vectors/yyA~J$))q."IS_5IJrcp|jdk(xr&|jddkDxr|jddkDS)zIs the expression a matrix?rrr)rrQrAs r is_matrixzExpression.is_matrixs4yyA~I$**Q-!"3I 1 8IIrct|trt|dk(r|Stj|rt j ||St j||S)z2Return a slice/index into the expression. r)rtuplerkuis_special_slicer special_indexindex)rkeys r __getitem__zExpression.__getitem__sY c5 !c#h!mK   %+8))+D#6 6#8>>#D#. .rcX|jdkr|Stj|S)z6Expression : The transpose of the expression. r)rr transposerAs rTz Expression.Ts* 99>K'8%%'- -rc|jr |jStj|jS)z@Expression : The conjugate-transpose of the expression. )rrr conjrAs rHz Expression.Hs/ <<>66M"8==?4(** *rpowerc8tj||S)zRaise expression to a power. Parameters ---------- power : float The power to which to raise the expression. Returns ------- Expression The expression raised to ``power``. )r r)rrs r__pow__zExpression.__pow__"s x~~e,,rbasectd)NzCVXPY currently does not support variables on the right side of **. Consider using the identity that a**x = cp.exp(cp.multiply(np.log(a), x)).r?)rrs rr+zExpression.__rpow__1s!#23 3rc,tj|S)z If expr_like is an Expression, return it. Otherwise, cast expr_like to a Constant. This is a wrapper around the misleadingly-named `Expression.cast_to_const` function. )r;r) expr_likes rcastzExpression.cast7s'' 22rct|tr"|D]}t|tstdt|tr|St j |S)z1Converts a non-Expression to a Constant. zzThe input must be a single CVXPY Expression, not a list. Combine Expressions using atoms such as bmat, hstack, and vstack.)rlistr; ValueErrorr r)rWelems rrzExpression.cast_to_constAsa dD ! dJ/$\  "$ 3tR9L9J9J9LT9RRrctj|}tj|}|jr1|js!tj||j }ne|jr1|js!tj||j }n$|jr|jr||fS|j dk(r`|j dk(rPtdDcgc](}t|j ||j |*}}|j ddk(r2|j d|dkrtj|ddf|z}|j ddk(r2|j d|dkrtj|ddf|z}|j ddk(r2|j d|dkr|tjd|dfz}|j ddk(r2|j d|dkr|tjd|dfz}||fS|j dk\s(|j dk\s|j |j k7rttj|j |j }|j |k7rtj||}|j |k7rtj||}||fScc}w)zBroadcast the binary operator.rrr) r;rrcppromoterQrrangemaxronesbroadcast_shapes broadcast_to)lh_exprrh_expridims output_shapes r broadcastzExpression.broadcastNs{**73**73    w'8'8':jj'--8G    ):):)<jj'--8G    W%6%6%8G# # <<1 !2EJ1XNC a('--*:;NDN}}Q1$q)9DG)C''47A,/'9}}Q1$q)9DG)C''47A,/'9}}Q1$q)9DG)C!BGGQQL$99}}Q1$q)9DG)C!BGGQQL$99 \\Q ',,!"3w||w||7S..w}}gmmLL}} ,//'<@}} ,//'<@%Os>-K0rct|tjr|jr|S|j ||\}}tj ||gSz*Expression : Sum two expressions. )rr rrradd_exprrrs r__add__zExpression.__add__qsR eX..0 1emmoKnnT51 e"x  "D%=11rclt|tjr|jr|S||zSr )rr rrr s rrzExpression.__radd__zs. eX..0 1emmoKt|rc|| zSz8Expression : The difference of two expressions. rVr s r__sub__zExpression.__sub__suf}rc ||z SrrVr s rr"zExpression.__rsub__t|rc|jdk(s|jdk(rtj||S|jd|jdk7r;|js|jrtj||S|j s9|j s)t j rtjdtj5tjdtdttz}tj|ttj|ttdz a d d d tj||S#1swY$xYw) z5Expression : The product of two expressions. rVrzForming a nonconvex expression.alwaysT)appendrN)rQr elmul_exprrrYr warnings_enabledrrcatch_warnings simplefilter UserWarning__STAR_MATMUL_WARNING____STAR_MATMUL_COUNT__DeprecationWarning matmul_expr)rrmsgs r__mul__zExpression.__mul__s. :: u{{b0 )8&&(u5 5 ZZ^u{{1~ -!U__%6)8&&(u5 5 $$&%*;*;*=))+MM"CD((* +%%h DI-0EE c;/ c#56%*%  +*8'')$6 6 + +s 1A'E;;Fc|jdk(s|jdk(r tdt|tjr_|j d|urN|j s>|j dj r!ddlm}|||j dStj||S)z?Expression : Matrix multiplication of two expressions. rV0Scalar operands are not allowed, use '*' insteadrr) quad_form) rQrrr r rrYcvxpy.expressions.cvxtypesr%)rrr%s r __matmul__zExpression.__matmul__s :: u{{b0OP P dH002 3yy|u$U->->-@TYYq\E]E]E_@"y{5$))A,77%x##%dE22rc$|j|S)8Expression : One expression divided by another. )__div__r s r __truediv__zExpression.__truediv__s||E""rc |j||\}}|js)|js|j|jk(rtj||St d|jd|jd)r)z"Incompatible shapes for division (z / rN)rrrQr div_exprrr s rr*zExpression.__div__sqnnT51 e NN  1ekkTZZ6O&8$$&tU3 3!ZZ67 7rc ||z Sz5Expression : Called for Number / Expression. rVr s rr'zExpression.__rdiv__rrc ||z Sr/rVr s r __rtruediv__zExpression.__rtruediv__rrc ||zS)z5Expression : Called for Number * Expression. rVr s rr%zExpression.__rmul__rrc|jdk(s|jdk(r tdtj||S)z5Expression : Called for matrix @ Expression. rVr$)rQrr r r s rr)zExpression.__rmatmul__s? :: u{{b0OP P%x##%eT22rc6tj|S)z5Expression : The negation of the expression. )r neg_exprrAs r__neg__zExpression.__neg__s#x  "4((rct||z Sz:PSD : Creates a positive semidefinite inequality. r r s r __rshift__zExpression.__rshift__4%<  rct||z Sr8r9r s rr/zExpression.__rrshift__54<  rct||z Sz:PSD : Creates a negative semidefinite inequality. r9r s r __lshift__zExpression.__lshift__r=rct||z Sr?r9r s rr-zExpression.__rlshift__r;rct|Sr)idrAs r__hash__zExpression.__hash__ s $xrct||S)z;Equality : Creates a constraint ``self == other``. )r r s rr1zExpression.__eq__se$$rct||S)zIInequality : Creates an inequality constraint ``self <= other``. r r s rr5zExpression.__le__s$&&rctdNz$Strict inequalities are not allowed.r?r s rr9zExpression.__lt__!"HIIrct||SrrGr s rr3zExpression.__ge__s%&&rctdrIr?r s rr7zExpression.__gt__!rJrc t|}|ik(r!t|dk(r|d|ur |||dS|jdhk(rUt|dk(rG|d|ur@t|dtr-t|ddk(r|d|ddurt t t t#t$rYt twxYw)Nrrrout) __BINARY_EXPRESSION_UFUNCS__rkeysrr RuntimeError__INPLACE_MUTATION_ERROR__KeyError__NUMPY_UFUNC_ERROR__)rufuncmethodrkwargs ufunc_handlers r__array_ufunc__zExpression.__array_ufunc__$s 8?M|INGtO$T47335')INGtOve}e4u &!+Gve}Q//"#=>> 011  011 s.B)A)B)) CCc ttr) TypeError __ABS_ERROR__rAs r__abs__zExpression.__abs__8s  &&rcddlm}||Sz0 Equivalent to `cp.conj(self)`. r)rcvxpyrrrs rrzExpression.conj; Dzrcddlm}||Sr_r`rbs r conjugatezExpression.conjugateBrcrrc ddlm}|||S)z8 Equivalent to `cp.cumsum(self, axis)`. r)cumsum)rarg)raxisrgs rrgzExpression.cumsumIs !dD!!r)keepdimsc"ddlm}||||S)z? Equivalent to `cp.max(self, axis, keepdims)`. r)r)rar)rrhrimax_s rrzExpression.maxP &D$))rc"ddlm}||||S)z@ Equivalent to `cp.mean(self, axis, keepdims)`. r)mean)rarn)rrhrirns rrnzExpression.meanW D$))rc"ddlm}||||S)z? Equivalent to `cp.min(self, axis, keepdims)`. r)r)rar)rrhrimin_s rrzExpression.min^rlrc"ddlm}||||S)z@ Equivalent to `cp.prod(self, axis, keepdims)`. r)prod)rars)rrhrirss rrszExpression.proderorc"ddlm}||||S)z? Equivalent to `cp.ptp(self, axis, keepdims)`. r)ptp)raru)rrhrirus rruzExpression.ptpls 4x((rc|2tjdd}tj|td}ddlm}||||S)zA Equivalent to `cp.reshape(self, shape, order)`. rreshaperr)rw)rrrrrrarw)rrQrreshape_order_warningrws rrwzExpression.reshapessC =$A$I$I+W`$a ! MM/ ?E!tUE**r)ddofric&ddlm}|||||S)z? Equivalent to `cp.std(self, axis, keepdims)`. r)std)rhryri)rar{)rrhryrir{s rr{zExpression.std~s 4dAArc"ddlm}||||S)z? Equivalent to `cp.sum(self, axis, keepdims)`. r)sum)rar})rrhrisum_s rr}zExpression.sumrlrcddlm}||S)z1 Equivalent to `cp.trace(self)`. r)trace)rar)rrs rrzExpression.traces T{rryc"ddlm}|||S)z/ Equivalent to `cp.var(self)`. r)varr)rar)rryrs rrzExpression.vars 4d##r)F)dcpr)r=r;)rWr;)rr;rr;)r)y__name__ __module__ __qualname____doc____array_priority__propertyabcabstractmethodrrndarrayrBrErGrIstrrLrRrKrWrrqrOrwperf compute_onceboolrYr\r^r`rrbrdrfrhrrrlrnrjrrrrrrrrrrrPrrrrintrQrrrrrrrrrrrrrfloatrr+ staticmethodrrrrExpressionLiker rrr"r"r'r+r*r'r1r%r)r6r r:r/r@r-rDr r1r r5r9r3r7rYr]rrergrrnrrsrurwr{r}rrrVrrr;r;ts $x +$$ Xbjj1  $ $$$  7#7 $c$$  DI(36 3   4T44  N4NN  $4$$  $D$$  5$5455& ET E M4MM  $4$$  $D$$ E$ E4 E $c$d$$   !!@@ ???8d8   "d" "D" d 4 "" 44 c   555  $4$$  $4$$ $uS#X$$ %% $$$  $D$$ +c++ c +W^4 +/4/K4KJ4J /..++ -U -| -3U3|3 33 S S    D2^2 22n^  n 7^7 77B33<33 ##L## 7^7 77n .\ n 33L33) !!3!! !!C!! !!3!! !!C!! #%N%x%% 'N'z'' JNJ'N'z''JNJ2('"***%****%*)) +GN$; +| +BQB**$rr;)rs$  11&&0077&"1&   0 5 5 3 6 2 : ; 0 5 8 / 2 &4d $d $r