import numpy as np
import autograd.numpy as anp
import warnings
from .abstract_function import AbstractFunction
from .utilities import check_input
[docs]class Exp(AbstractFunction):
"""Exponential function (elementwise)
.. math::
f(x)=e^x
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 not fn.is_differentiable:
warnings.warn(
'Composition with a nondifferentiable function will lead to an\
error when asking for a subgradient')
else:
self.differentiable = True
self.fn = fn
self.input_shape = fn.input_shape
self.output_shape = fn.output_shape
self.affine = False
self.quadratic = False
super().__init__()
def _expression(self):
expression = 'Exp({})'.format(self.fn._expression())
return expression
def _to_cvxpy(self):
import cvxpy as cvx
return cvx.exp(self.fn._to_cvxpy())
def _extend_variable(self, n_var, axis, pos):
return Exp(self.fn._extend_variable(n_var, axis, pos))
[docs] @check_input
def eval(self, x: np.ndarray) -> np.ndarray:
return anp.exp(self.fn.eval(x)).reshape(self.output_shape)
@check_input
def _alternative_jacobian(self, x: np.ndarray, **kwargs) -> np.ndarray:
warnings.simplefilter("error")
if not self.fn.is_differentiable:
warnings.warn("Composition of non affine functions. The Jacobian may be not correct.")
# e^{g(x)} \jac g(x)
val = self.fn.eval(x).flatten()
try:
p1 = np.diag(np.exp(val))
except RuntimeWarning:
# check for overflows
p2 = np.diag(val)
for idx, value in enumerate(val):
if value > 600:
p1[idx, idx] = np.nan_to_num(np.inf)
else:
p1[idx, idx] = np.exp(value)
p2 = self.fn.jacobian(x, **kwargs)
return p1 @ p2