bii\ddlZddlmZddlmZddlmZddlm Z dZ dZ Gdd Z y) N)sparse SuppFuncAtom)Variable)CONVEX_ATTRIBUTEScddlm}ddlm}ddlm}|||||}|j d\}}}|d} | j|j} tj| | |jz} |d} tj| jd ft } d | | <| d d | f}| d d | f}tj ||g } |d }|d}| ||fS)a Return (A, b, K) so that {x : x satisfies constraints} can be written as {x : exists y where A @ [x; y] + b in K}. Parameters ---------- x: cvxpy.Variable constraints: list of cvxpy.constraints.constraint.Constraint Each Constraint object must be DCP-compatible. Notes ----- This function DOES NOT work when ``x`` has attributes, like ``PSD=True``, ``diag=True``, ``symmetric=True``, etc... r)sum)Minimize)ProblemSCS)solverA)shapedtypeTNbdims)cvxpy.atoms.affine.sumr cvxpy.problems.objectiver cvxpy.problems.problemr get_problem_data var_offsetsidnparangesizezerosrboolrhstack)x constraintsr r r probdatachaininvdatainvx_offset x_indicesr x_selectorA_xA_otherrKs T/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/transforms/suppfunc.py scs_conicliftr/ s$+1. 8CF#[ 1D  000>D% "+Cqtt$H (Hqvv$56I S A T:J Jy AzM CJ;G W~ &&A S A V A a7Nc6|jrd}|dz }t||j}tj|||j z}||j z }g}|j D]1}tj|||z}|j|||z }3g}|jD]:}||dzzdz} |jtj||| z|| z }<d|jz} tj||| z} || ||d} | S)a  Parse a ConeDims object, as returned from SCS's apply function. Return a dictionary which gives row-wise information for the affine operator returned from SCS's apply function. Parameters ---------- K : cvxpy.reductions.solvers.conic_solver.ConeDims Returns ------- selectors : dict Keyed by strings, which specify cone types. Values are numpy arrays, or lists of numpy arrays. The numpy arrays give row indices of the affine operator (A, b) returned by SCS's apply function. z8SuppFunc doesn't yet support feasible sets represented zwith power cone constraints.r)nonnegexpsocpsd) p3dNotImplementedErrorzerorrr4r6appendr7r5) r-msgidx nonneg_idxssoc_idxsr6idxspsd_idxsr7veclenexpsizeexp_idxs selectorss r.scs_cone_selectorsrF2s#$ uuI --!#&& &&C))Cqxx0K188OCHuuyycCi( s HuuaA% #sV|45 v !%%iGyycGm,H I r0c0eZdZdZdZdefdZddZdZy) SuppFunca Given a list of CVXPY Constraint objects :math:`\texttt{constraints}` involving a real CVXPY Variable :math:`\texttt{x}`, consider the convex set .. math:: S = \{ v : \text{it's possible to satisfy all } \texttt{constraints} \text{ when } \texttt{x.value} = v \}. This object represents the *support function* of :math:`S`. This is the convex function .. math:: y \mapsto \max\{ \langle y, v \rangle : v \in S \}. The support function is a fundamental object in convex analysis. It's extremely useful for expressing dual problems using `Fenchel duality `_. Parameters ---------- x : Variable This variable cannot have any attributes, such as PSD=True, nonneg=True, symmetric=True, etc... constraints : list[Constraint] Usually, these are constraints over :math:`\texttt{x}`, and some number of auxiliary CVXPY Variables. It is valid to supply :math:`\texttt{constraints = []}`. Examples -------- If :math:`\texttt{h = cp.SuppFunc(x, constraints)}`, then you can use :math:`\texttt{h}` just like any other scalar-valued atom in CVXPY. For example, if :math:`\texttt{x}` was a CVXPY Variable with :math:`\texttt{x.ndim == 1}`, you could do the following: .. code:: z = cp.Variable(shape=(10,)) A = np.random.standard_normal((x.size, 10)) c = np.random.rand(10) objective = h(A @ z) - c @ z prob = cp.Problem(cp.Minimize(objective), []) prob.solve() Notes ----- You are allowed to use CVXPY Variables other than :math:`\texttt{x}` to define :math:`\texttt{constraints}`, but the set :math:`S` only consists of objects (vectors or matrices) with the same shape as :math:`\texttt{x}`. It's possible for the support function to take the value :math:`+\infty` for a fixed vector :math:`\texttt{y}`. This is an important point, and it's one reason why support functions are actually formally defined with the supremum ":math:`\sup`" rather than the maximum ":math:`\max`". For more information on support functions, check out `this Wikipedia page `_. cHtts tdtfdtDr td|D]+}|j }t |dkDs"td|_||_d|_ d|_ d|_ |jy)Nz?The first argument must be an unmodified cvxpy Variable object.c3<K|]}j|ywN) attributes).0attrr!s r. z$SuppFunc.__init__..s@dq||D!@sz7The first argument cannot have any declared attributes.rz=Convex sets described with Parameter objects are not allowed.) isinstancer ValueErroranyr parameterslenr!r"_A_b_K_sels_compute_conic_repr_of_set)selfr!r"con con_paramss ` r.__init__zSuppFunc.__init__s!X&^_ _ @.?@ @VW W bC)J:" !`aa b&  '')r0returnct||}|S)z Return an atom representing max{ cvxpy.vec(y) @ cvxpy.vec(x) : x in S } where S is the convex set associated with this SuppFunc object. r)rYy sigma_at_ys r.__call__zSuppFunc.__call__s"!T* r0Nct|jdk(rt}|dk(g}n |j}t|j|\}}}t |}||_||_||_y)Nrr) rTr"rr/r!rFrUrVrW)rYdummyconstrsrrr-K_selss r.rXz#SuppFunc._compute_conic_repr_of_setsg t A %JEzlG&&G01a#A& r0cH|j|j|jfSrK)rUrVrW)rYs r.conic_repr_of_setzSuppFunc.conic_repr_of_setsww--r0)r]N) __name__ __module__ __qualname____doc__r\rrarXrgr0r.rHrHas#:x* \  .r0rH) numpyrscipyrcvxpy.atoms.suppfuncrcvxpy.expressions.variabler cvxpy.reductions.cvx_attr2constrrr/rFrHrlr0r.rrs,-/>&R,^e.e.r0