#!/usr/bin/env python3
import torch
from torch import Tensor
ALPHA = [1.0, 1.2, 3.0, 3.2]
A = [
[10, 3, 17, 3.5, 1.7, 8],
[0.05, 10, 17, 0.1, 8, 14],
[3, 3.5, 1.7, 10, 17, 8],
[17, 8, 0.05, 10, 0.1, 14],
]
P = [
[1312, 1696, 5569, 124, 8283, 5886],
[2329, 4135, 8307, 3736, 1004, 9991],
[2348, 1451, 3522, 2883, 3047, 6650],
[4047, 8828, 8732, 5743, 1091, 381],
]
GLOBAL_MAXIMIZER = [0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573]
GLOBAL_MAXIMUM = 3.32237
[docs]def neg_hartmann6(X: Tensor) -> Tensor:
r"""Negative Hartmann6 test function.
Six-dimensional function (typically evaluated on `[0, 1]^6`)
`H(x) = - sum_{i=1}^4 ALPHA_i exp( - sum_{j=1}^6 A_ij (x_j - P_ij)**2 )`
H has a 6 local minima and a global minimum at
`z = (0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573)`
with `H(z) = -3.32237`
Args:
X: A Tensor of size `6` or `k x 6` (k batch evaluations).
Returns:
`-H(X)`, the negative value of the standard Hartmann6 function.
"""
batch = X.ndimension() > 1
X = X if batch else X.unsqueeze(0)
inner_sum = torch.sum(X.new(A) * (X.unsqueeze(1) - 0.0001 * X.new(P)) ** 2, dim=2)
H = -torch.sum(X.new(ALPHA) * torch.exp(-inner_sum), dim=1)
result = -H
return result if batch else result.squeeze(0)
