Source code for nubo.test_functions.sumsquares

import torch
from nubo.test_functions import TestFunction
from torch import Tensor
from typing import Optional

[docs] class SumSquares(TestFunction): r""" :math:`d`-dimensional Sum Squares function. The Sum Squares function is bowl-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 [-10, 10]^d`. .. math:: f(\boldsymbol x) = \sum_{i=1}^d i x_i^2. 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([[-10.0, ] * 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 Sum-of-Squares 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) y = torch.sum(ii * x**2, dim=-1) # 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