bi]"dZddlmZmZmZddlZddlmZ ddl m Z ddl m Z ddlmZddlmZddlmZmZmZdd eeefd ed efd ZGd de 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 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. )ListTupleUnionN)AxisAtom)norm1)norm_inf) Constraint)pow_highpow_midpow_negpkeepdims max_denomc|dk(rt|||S|tjddfvrt|||St |||||S)a#Factory function for a mathematical p-norm. Parameters ---------- p : numeric type or string The type of norm to construct; set this to np.inf or 'inf' to construct an infinity norm. Returns ------- Atom A norm1, norm_inf, or Pnorm object. axisrinfInf)r rrr)rnprrPnorm)xr rrrs L/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/atoms/pnorm.pypnormrsO AvQTH55 rvvue$ $x88Q!$YOOc eZdZdZdZ ddedededdffd Zd Zdfd Z de eeffd Z defd Z defd Z defdZdefdZdefdZdefdZdefdZdZdefdZdeefdZdZdZxZS)raGThe vector p-norm, for p not equal to 1 or infinity. If given a matrix variable, ``pnorm`` will treat it as a vector, and compute the p-norm of the concatenated columns. Only accepts p values that are not equal to 1 or infinity; the norm1 and norm_inf classes handle those norms. For :math:`p > 1`, the p-norm is given by .. math:: \|x\|_p = \left(\sum_i |x_i|^p \right)^{1/p}, with domain :math:`x \in \mathbf{R}^n`. For :math:`p < 1,\ p \neq 0`, the p-norm is given by .. math:: \|x\|_p = \left(\sum_i x_i^p \right)^{1/p}, with domain :math:`x \in \mathbf{R}^n_+`. - Note that the "p-norm" is actually a **norm** only when :math:`p > 1`. For these cases, it is convex. - The expression is not defined when :math:`p = 0`. - Otherwise, when :math:`p < 1`, the expression is concave, but it is not a true norm. .. note:: Generally, ``p`` cannot be represented exactly, so a rational, i.e., fractional, **approximation** must be made. Internally, ``pnorm`` computes a rational approximation to the reciprocal :math:`1/p` with a denominator up to ``max_denom``. The resulting approximation can be found through the attribute ``pnorm.p``. The approximation error is given by the attribute ``pnorm.approx_error``. Increasing ``max_denom`` can give better approximations. When ``p`` is an ``int`` or ``Fraction`` object, the approximation is usually **exact**. Parameters ---------- x : cvxpy.Variable The value to take the norm of. p : int, float, or Fraction We require that :math:`p > 1`, but :math:`p \neq \infty`. See the norm1 and norm_inf classes for these norms, or use the pnorm function wrapper to instantiate them. max_denom : int The maximum denominator considered in forming a rational approximation for ``p``. axis : 0 or 1 The axis to apply the norm to. Returns ------- Expression An Expression representing the norm. TNr rrreturnc|dkrt||\|_}nd|cxkrdkrnnt||\|_}nl|dkDrt||\|_}nR|dk(r t d|dk(s|dk(s|t j k(r t dt dj|tt|j|z |_ ||_ tt|;|||y) Nrrz.Use the norm1 class to instantiate a one norm.rrz7Use the norm_inf class to instantiate an infinity norm.z Invalid p: {}r)r r r r ValueErrorrrformatfloatabs approx_error original_psuperr__init__)selfrr rrr_ __class__s rr&zPnorm.__init__ys q59-IDFA YQY9-IDFA U I.IDFA !VMN N %Z1:bff./ /_33A67 7!#dffqj/2 eT#AD8#Drc|j'tj|dj}ntj|d}|jdkr)tj |dkrtj S|jdkrtj |dk(rytjj|t|j|j|jS)z!Returns the p-norm of x. rrgr) rrarrayflattenr anyrlinalgnormr!rr'valuess rnumericz Pnorm.numerics 99 XXfQi(002FXXfQi(F 66A:"&&!,FF7N 66A:"&&1-yy~~feDFFm$))'+}}6 6rctt| |j|jdk7r t d|jdkr)|j djr t dyy)Nz-The axis parameter is only supported for p=2.rrz,pnorm(x, p) cannot have x complex for p < 1.)r%rvalidate_argumentsrr rargs is_complex)r'r)s rr5zPnorm.validate_argumentssg eT-/ 99 TVVq[?A A 66A:$))A,113KL L4:rcy)zCReturns sign (is positive, is negative) of the expression. )TFr's rsign_from_argszPnorm.sign_from_argssrc |jdkDS)zIs the atom convex? rr r:s ris_atom_convexzPnorm.is_atom_convexvvzrc |jdkS)zIs the atom concave? rr=r:s ris_atom_concavezPnorm.is_atom_concaver?rcy)z$Is the atom log-log convex? Tr9r:s ris_atom_log_log_convexzPnorm.is_atom_log_log_convexsrcy)z%Is the atom log-log concave? Fr9r:s ris_atom_log_log_concavezPnorm.is_atom_log_log_concaverc|jdkxs.|jdkDxr|jdjS)z;Is the composition non-decreasing in argument idx? rr)r r6 is_nonnegr'idxs ris_incrz Pnorm.is_incrs5vvzFdffqjETYYq\-C-C-EFrc^|jdkDxr|jdjS)z;Is the composition non-increasing in argument idx? rr)r r6 is_nonposrIs ris_decrz Pnorm.is_decrs(vvz6diil4466rcy)z&Is the atom piecewise linear? Fr9r:s ris_pwlz Pnorm.is_pwlrFrc2|j|jgS)N)r rr:s rget_datazPnorm.get_datas ""rc|jjd|jdjd|jdS)N(rz, ))r)__name__r6namer r:s rrWz Pnorm.names4#~~66#yy|002#vv' 'rch|jdkr"|jdk7r|jddk\gSgS)z?Returns constraints describing the domain of the node. rr)r r6r:s r_domainz Pnorm._domains4 66A:$&&A+IIaLA%& &Irc$|j|S)a+Gives the (sub/super)gradient of the atom w.r.t. each argument. Matrix expressions are vectorized, so the gradient is a matrix. Args: values: A list of numeric values for the arguments. Returns: A list of SciPy CSC sparse matrices or None. ) _axis_gradr0s r_gradz Pnorm._gradsv&&rc,|j}|jdkrtj|dkryt j |dfd}tj |jd}tjj|t|j}t|jdz }tj||}|dk(r |jdkDr|jSy|jdkDr@tj|tjtj||z}ntj||}tj||}tj ||jdfS)a Gives the (sub/super)gradient of the atom w.r.t. a column argument. Matrix expressions are vectorized, so the gradient is a matrix. Args: value: A numeric value for a column. Returns: A NumPy ndarray or None. rrNfloat64)dtypeF)order)sizer rr-sp csc_arrayasarrayravelr.r/r!powertodensesignr"dividereshape)r'valuerowsD_null denominatorexp nominatorfracs r _column_gradzPnorm._column_grads$zz 66A:"&&!,tQiy9 5!''c'2iinnUE$&&M: DFFQJhh{C0 ! vvz~~'' 66A:"&&-)EEI,IyyK0zz$A//rr4NFi)rN)rV __module__ __qualname____doc___allow_complexintboolr&r2r5rr;r>rArCrErKrNrPrRstrrWrr rYr\rs __classcell__)r)s@rrr2sCHN+/:>ESEE47ECGE(6 MdDj 1     GdG 7d7  #'c' j) '!0rrrt)rwtypingrrrnumpyr scipy.sparsesparserccvxpy.atoms.axis_atomrcvxpy.atoms.norm1rcvxpy.atoms.norm_infrcvxpy.constraints.constraintr cvxpy.utilities.power_toolsr r r ryr{rzrrr9rrrs_&%*#)3BBPc3hP$PSVP,[0H[0r