import numpy as np
import autograd.numpy as anp
import warnings
from typing import Union
from .abstract_function import AbstractFunction
from .utilities import check_input
from .norm import Norm
[docs]class SquaredNorm(AbstractFunction):
"""Squared norm (supporte norms are 1, 2, inf)
.. math::
f(x)=\\|x\\|^2
with :math:`x: \\mathbb{R}^{n}`.
Args:
fn (AbstractFunction): input function
order (int, optional): order of the norm. Can be 1, 2 or np.inf. Defaults to 2.
Raises:
TypeError: input must be a function object
NotImplementedError: only 1, 2 and inf norms are currently supported
"""
def __init__(self, fn: AbstractFunction, order: Union[int, float]=None, axis: int=None):
if not isinstance(fn, AbstractFunction):
raise TypeError("Input must be a AbstractFunction object")
# if not fn.is_differentiable:
# warnings.warn(
# 'Composition with a nondifferentiable function will lead to an\
# error when asking for a subgradient')
# if not fn.is_affine:
# warnings.warn(
# 'Composition with a non affine function will lead to an error \
# when asking for a subgradient')
self.fn = fn
if order not in [1, 2, np.inf, None]:
raise NotImplementedError
if order == 2:
self.differentiable = True
self.order = order
self.axis = axis
self.input_shape = fn.input_shape
self.output_shape = (1, 1)
self.affine = False
self.quadratic = False # TODO
super().__init__()
def _expression(self):
expression = 'SquaredNorm({})'.format(self.fn._expression())
return expression
def _to_cvxpy(self):
import cvxpy as cvx
return cvx.square(cvx.norm(self.fn._to_cvxpy()))
[docs] @check_input
def eval(self, x: np.ndarray) -> np.ndarray:
# TODO: order
return anp.power(anp.linalg.norm(self.fn.eval(x), ord=self.order, axis=self.axis), 2).reshape(self.output_shape)
def _extend_variable(self, n_var, axis, pos):
return SquaredNorm(self.fn._extend_variable(n_var, axis, pos), self.order, self.axis)
@check_input
def _alternative_jacobian(self, x: np.ndarray, **kwargs) -> np.ndarray:
if self.order in [1, 2, np.inf, None]:
if not self.fn.is_differentiable:
warnings.warn("Composition of nondifferentiable functions. The Jacobian may be not correct.")
# raise ValueError(
# "Composition of nondifferentiable functions. \
# No subgradients available.")
if not self.fn.is_affine:
warnings.warn("Composition of non affine functions. The Jacobian may be not correct.")
# raise ValueError(
# "Composition of non affine function. \
# No subgradients available.")
if self.order in [2, None]:
return 2 * self.fn.eval(x).transpose() @ self.fn.jacobian(x, **kwargs)
else:
norm = Norm(self.fn, order=self.order)
return 2 * norm.jacobian(x, **kwargs) * \
np.linalg.norm(self.fn.eval(x), ord=self.order)
else:
raise NotImplementedError