bi9dZddlmZmZddlZddlmZddl m Z ddl m Z ddlmZddlmZddlmZmZmZmZdefd ZGd d e Zy) 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 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. )ListTupleN) Elementwise) Constraint)cvxtypes) is_power2pow_highpow_midpow_negreturnc>t|tjSN) isinstancerconstant)ps X/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/atoms/elementwise/power.py _is_constrs a**, --c*eZdZdZddeddffd ZejdZde e e ffdZ de fdZ de fd Z d Zde fd Zde fd Zde ffd Zde fdZde fdZde fdZde fdZde fdZde fdZdZdeefdZdZdddZdefdZxZ S)powera Elementwise power function :math:`f(x) = x^p`. If ``expr`` is a CVXPY expression, then ``expr**p`` is equivalent to ``power(expr, p)``. For DCP problems, the exponent `p` must be a numeric constant. For DGP problems, `p` can also be a scalar Parameter. Specifically, the atom is given by the cases .. math:: \begin{array}{ccl} p = 0 & f(x) = 1 & \text{constant, positive} \\ p = 1 & f(x) = x & \text{affine, increasing, same sign as $x$} \\ p = 2,4,8,\ldots &f(x) = |x|^p & \text{convex, signed monotonicity, positive} \\ p < 0 & f(x) = \begin{cases} x^p & x > 0 \\ +\infty & x \leq 0 \end{cases} & \text{convex, decreasing, positive} \\ 0 < p < 1 & f(x) = \begin{cases} x^p & x \geq 0 \\ -\infty & x < 0 \end{cases} & \text{concave, increasing, positive} \\ p > 1,\ p \neq 2,4,8,\ldots & f(x) = \begin{cases} x^p & x \geq 0 \\ +\infty & x < 0 \end{cases} & \text{convex, increasing, positive}. \end{array} .. note:: For DCP problems, ``power`` assumes ``p`` has a rational representation with a small denominator. **Approximations** are employed when this is not the case. Specifically, ``power`` computes a rational approximation to ``p`` with a denominator up to ``max_denom``. Increasing ``max_denom`` can give better approximations. When ``p`` is an ``int`` or ``Fraction`` object, the approximation is usually *exact*. No such approximation is used for DGP problems. CVXPY supports exponential cone and power cone constraints. Such constraints could be used to handle the ``power`` atom in DCP problems without relying on approximations. Such an approach would also result in fewer variables than the current method, even when the current method is an exact reformulation. If you're interested in helping enhance CVXPY with this ability, please get in touch with us and check out `GitHub Issue 1222 `_! .. note:: The final domain, sign, monotonicity, and curvature of the ``power`` atom are determined by the rational approximation to ``p``, **not** the input parameter ``p``. For example, >>> from cvxpy import Variable, power >>> x = Variable() >>> g = power(x, 1.001) >>> g.p Fraction(1001, 1000) >>> g Expression(CONVEX, POSITIVE, (1, 1)) results in a convex atom with implicit constraint :math:`x \geq 0`, while >>> g = power(x, 1.0001) >>> g.p 1 >>> g Expression(AFFINE, UNKNOWN, (1, 1)) results in an affine atom with no constraint on ``x``. - When :math:`p > 1` and ``p`` is not a power of two, the monotonically increasing version of the function with full domain, .. math:: f(x) = \begin{cases} x^p & x \geq 0 \\ 0 & x < 0 \end{cases} can be formed with the composition ``power(pos(x), p)``. - The symmetric version with full domain, .. math:: f(x) = |x|^p can be formed with the composition ``power(abs(x), p)``. Parameters ---------- x : cvxpy.Variable p : int, float, Fraction, or Parameter. Scalar power. ``p`` may be a Parameter in DGP programs, but not in DCP programs. max_denom : int The maximum denominator considered in forming a rational approximation of ``p``; only relevant when solving as a DCP program. max_denomr Ncr||_tjj||_t |jtj s=t |jtjstdt|||_ d|_ t |jtj rt |jtjs |j}n|jj}|dkDrt||\}}n2d|cxkrdkrnnt||\}}n|dkrt||\}}|dk(rd}d}|dk(rd}d}|c|_ |_t#t%|j|z |_t(t*|[|y)NzDThe exponent `p` must be either a Constant or a Parameter; received r)_p_origr expression cast_to_constrrr parameter ValueErrortyper p_rationalvaluer r r wfloatabs approx_errorsuperr__init__)selfxrrr" __class__s rr'zpower.__init__sm $$&44Q74668#4#4#674668#5#5#7867;Aw@ @" dffh//1 2dllH,?,?,ABLLFFLL1u9-1Qq),1Qq),1 AvAv&' #DOTV %c$//A*=&> ?D  eT#A&rcntj|dt|jjSNr)nprr#rr!)r(valuess rnumericz power.numerics$xxq 5#677rc|jjdk(r:|jdj|jdj fSy)zCReturns sign (is positive, is negative) of the expression. rr)TF)rr!args is_nonneg is_nonposr(s rsign_from_argszpower.sign_from_argssF 66<<1 IIaL**,diil.D.D.FG G!rct|jxr4|jjdkxs|jjdk\S)zIs the atom convex? rrrrr!r4s ris_atom_convexzpower.is_atom_convexs7 Mdfflla&7&L466<<1;LMrcxt|jxr$d|jjcxkxrdkScS)zIs the atom concave? rrr7r4s ris_atom_concavezpower.is_atom_concaves0  ;Q$&&,,%;!%;;%;;rcr|jdj|jjzSr,)r1 parametersrr4s rr<zpower.parameterss- yy|&&(466+<+<+>>>rctjjr>|jd}|j}|j xr|j Sy)z$Is the atom log-log convex? rT)uscopesdpp_scope_activer1rr<)r(r)rs ris_atom_log_log_convexzpower.is_atom_log_log_convexsI 88 $ $ & ! AA 91<<>: :rc"|jS)z%Is the atom log-log concave? )rAr4s ris_atom_log_log_concavezpower.is_atom_log_log_concaves**,,rct|jxr|jjdk(xstt|S)z$Is the expression constant? r)rrr!r&r is_constant)r(r*s rrEzpower.is_constants5$&&!7dfflla&7\E% A A 9?@ @!eAFAilIIaLA%& &Irc2|j|jgSr)rrr4s rget_datazpower.get_datas dnn--rcf| |j}t|d|j|jS)aReturns a shallow copy of the power atom. Parameters ---------- args : list, optional The arguments to reconstruct the atom. If args=None, use the current args of the atom. Returns ------- power atom r)r1rrr)r(r1 id_objectss rcopyz power.copys- <99DT!WdllDNN;;rc|jjd|jdjd|jj dS)N(rz, ))r*__name__r1namerr!r4s rrqz power.names8#~~66#yy|002#vv||- -r)i)NN)r r)!rp __module__ __qualname____doc__intr'r numpy_numericr/rboolr5r8r:r<rArCrErIrKrOrSrUrXrerrrgrirlstrrq __classcell__)r*s@rrrsbH-'-'t-'^88!dDj 1!NN<<?$,-- ]T] d"d" .d .D$ . .$ #DJj) .<"-c-rr)rttypingrrnumpyr- scipy.sparsesparser]cvxpy.utilities utilitiesr>#cvxpy.atoms.elementwise.elementwisercvxpy.constraints.constraintrcvxpy.expressionsrcvxpy.utilities.power_toolsrr r r rwrrrrrsA ;3&MM.D.G-KG-r