def feasible(self, x):
"""Feasibility of the constraint.
From the interface "Constraint".
Parameters
----------
x : Numpy array. The variable to check for feasibility.
Examples
--------
>>> import numpy as np
>>> from parsimony.functions.penalties import LInf
>>>
>>> np.random.seed(42)
>>> x = np.random.rand(10, 1) * 2.0 - 1.0
>>> linf = LInf(c=0.618)
>>> linf.feasible(x)
False
>>> linf.feasible(linf.proj(x))
True
"""
if self.penalty_start > 0:
x_ = x[self.penalty_start:, :]
else:
x_ = x
return maths.normInf(x_) <= self.c
def f(self, x):
"""Function value.
From the interface "Function".
Parameters
----------
x : Numpy array. The point at which to evaluate the function.
Example
-------
>>> import numpy as np
>>> from parsimony.functions.penalties import LInf
>>> import parsimony.utils.maths as maths
>>>
>>> np.random.seed(42)
>>> x = np.random.rand(10, 1)
>>> linf = LInf(l=1.1)
>>> linf.f(x) - 1.1 * maths.normInf(x)
0.0
"""
if self.penalty_start > 0:
x_ = x[self.penalty_start:, :]
else:
x_ = x
return self.l * (maths.normInf(x_) - self.c)
def proj(self, x):
"""The corresponding projection operator.
From the interface "ProjectionOperator".
Examples
--------
>>> import numpy as np
>>> from parsimony.functions.penalties import LInf
>>>
>>> np.random.seed(42)
>>> x = np.random.rand(10, 1) * 2.0 - 1.0
>>> linf = LInf(c=0.618)
>>> linf.proj(x)
array([[-0.25091976],
[ 0.618 ],
[ 0.46398788],
[ 0.19731697],
[-0.618 ],
[-0.618 ],
[-0.618 ],
[ 0.618 ],
[ 0.20223002],
[ 0.41614516]])
"""
if self.penalty_start > 0:
x_ = x[self.penalty_start:, :]
else:
x_ = x
if maths.normInf(x_) <= self.c:
return x
y = np.copy(x_)
y[y > self.c] = self.c
y[y < -self.c] = -self.c
# Put the unregularised variables back.
if self.penalty_start > 0:
y = np.vstack((x[:self.penalty_start, :],
y))
return y