import numpy as np
import autograd.numpy as anp
import warnings
from .abstract_function import AbstractFunction
from .utilities import check_input
[docs]class Square(AbstractFunction):
"""Square function (elementwise)
.. math::
f(x)= x^2
with :math:`x: \\mathbb{R}^{n}`.
Args:
fn (AbstractFunction): input function
Raises:
TypeError: input must be a AbstractFunction object
"""
def __init__(self, fn: AbstractFunction):
if not isinstance(fn, AbstractFunction):
raise TypeError("Input must be a AbstractFunction object")
if fn.is_differentiable:
self.differentiable = True
self.fn = fn
self.input_shape = fn.input_shape
self.output_shape = fn.output_shape
self.affine = False
self.quadratic = False # TODO
super().__init__()
def _expression(self):
expression = 'Square({})'.format(self.fn._expression())
return expression
def _to_cvxpy(self):
import cvxpy as cvx
return cvx.square(self.fn._to_cvxpy())
[docs] @check_input
def eval(self, x: np.ndarray) -> np.ndarray:
return anp.power(self.fn.eval(x), 2).reshape(self.output_shape)
def _extend_variable(self, n_var, axis, pos):
return Square(self.fn._extend_variable(n_var, axis, pos))
# @check_input
# def jacobian(self, x: np.ndarray, **kwargs) -> np.ndarray:
# if not self.fn.is_differentiable:
# warnings.warn("Composition of non affine functions. The Jacobian may be not correct.")
# # 2 fn(x) \jac fn(x)
# val = self.fn.eval(x)
# p1 = 2 * np.diag(val.flatten())
# p2 = self.fn.jacobian(x, **kwargs)
# return p1 @ p2