polarcbo.objectives.Himmelblau

class polarcbo.objectives.Himmelblau(factor=1.0)

Bases: objective

Himmelblau’s function

Himmelblau’s function is a multimodal function with 4 global minima at \((3,2)\), \((-2.805118,3.131312)\), \((-3.779310,-3.283186)\), and \((3.584428,-1.848126)\). The function is defined as

\[f(x,y) = (x^2 + y - 11)^2 + (x + y^2 - 7)^2\]

See Himmelblau’s function.

Parameters:

factor (float, optional) – The factor by which the input is multiplied. The default is 1.0.

Examples

>>> import numpy as np
>>> from polarcbo.objectives import Himmelblau
>>> x = np.array([[1,2], [3,4], [5,6]])
>>> f = Himmelblau()
>>> f(x)
array([  68.,  148., 1556.])

__call__(x)

Call method for classes that inherit from objective

Parameters:

x (array_like, shape (J, d)) – For a system of \(J\) particles, the i-th row of this array x[i,:] represents the position of the i-th particle.

Returns:

y – The value of the objective function at the positions x.

Return type:

array_like, shape (J,)