import torch
from nubo.test_functions import TestFunction
from torch import Tensor
from typing import Optional
[docs]
class Zakharov(TestFunction):
r"""
:math:`d`-dimensional Zakharov function.
The Zakharov function is plate-shaped and has one global minimum
:math:`f(\boldsymbol x^*) = 0` at :math:`\boldsymbol x^* = (0, ..., 0)`.
It is usually evaluated on the hypercube
:math:`\boldsymbol x \in [-5, 10]^d`.
.. math::
f(\boldsymbol x) = \sum_{i=1}^d x_i^2 + \left( \sum_{i=1}^d 0.5 i x_i \right)^2 + \left( \sum_{i=1}^d 0.5 i x_i \right)^4.
Attributes
----------
dims : ``int``
Number of input dimensions.
noise_std : ``float``
Standard deviation of Gaussian noise.
minimise : ``bool``
Minimisation problem if true, maximisation problem if false.
bounds : ``torch.Tensor``
(size 2 x `dims`) Bounds of input space.
optimum : ``dict``
Contains inputs and output of global maximum.
"""
def __init__(self,
dims: int,
noise_std: Optional[float]=0.0,
minimise: Optional[bool]=True) -> None:
"""
Parameters
----------
dims : ``int``
Number of input dimensions.
noise_std : ``float``, optional
Standard deviation of Gaussian noise, default is 0.0.
minimise : ``bool``, optional
Minimisation problem if true (default), maximisation problem if
false.
"""
self.dims = dims
self.bounds = Tensor([[-5.0, ] * dims, [10.0, ] * dims])
self.optimum = {"inputs": Tensor([[0.0, ] * dims]), "ouput": Tensor([[0.0]])}
self.noise_std = noise_std
self.minimise = minimise
[docs]
def eval(self, x: Tensor) -> Tensor:
"""
Compute output of Zakharov function for some test points `x`.
Parameters
----------
x : ``torch.Tensor``
(size n x `dims`) Test points.
"""
# compute output
ii = torch.arange(1, self.dims+1)
term_1 = torch.sum(x**2, dim=-1)
term_2 = torch.sum(0.5 * ii * x, dim=-1)
y = term_1 + term_2**2 + term_2**4
# turn into maximisation problem
if not self.minimise:
y = -y
# add noise
noise = torch.normal(mean=0, std=self.noise_std, size=y.size())
f = y + noise
return f