Source code for secml.optim.constraints.c_constraint_l2

.. module:: CConstraintL2
   :synopsis: L2 Constraint

.. moduleauthor:: Battista Biggio <>

from secml.optim.constraints import CConstraint
from secml.array import CArray

[docs]class CConstraintL2(CConstraint): """L2 Constraint. Parameters ---------- center : scalar or CArray, optional Center of the constraint. Use an array to specify a different value for each dimension. Default 0. radius : scalar, optional The semidiagonal of the constraint. Default 1. Attributes ---------- class_type : 'l2' """ __class_type = 'l2' def __init__(self, center=0, radius=1): # Setting the value of the center (array or scalar) = center # Setting the radius of the L2 ball (fixed) self.radius = radius @property def center(self): """Center of the constraint.""" return self._center @center.setter def center(self, value): """Center of the constraint.""" self._center = CArray(value) @property def radius(self): """Radius of the constraint.""" return self._radius @radius.setter def radius(self, value): """Radius of the constraint.""" self._radius = float(value) def _constraint(self, x): """Returns the value of the constraint for the sample x. The constraint value y is given by: y = ||x - center||_2 - radius Parameters ---------- x : CArray Input sample. Returns ------- float Value of the constraint. """ return float((x - - self.radius) def _projection(self, x): """Project x onto feasible domain / within the given constraint. Parameters ---------- x : CArray Input sample. Returns ------- CArray Projected x onto feasible domain if constraint is violated. """ # define tolerance and project onto radius-tol # to ensure that numerical errors do not violate the projection tol = 1e-6 sub = (self._radius-tol) * (x - sub_l2 = (x - if sub_l2 != 0: # Avoid division by 0 sub /= sub_l2 out = self._center + sub return out.tosparse() if x.issparse else out def _gradient(self, x): """Returns the gradient of c(x) in x. Parameters ---------- x : CArray Input sample. Returns ------- CArray The gradient of the constraint computed on x. """ sub = (x - # Avoid division by 0 return sub if sub.norm() == 0 else sub / sub.norm()