Ackley Function

get_ipython().ast_node_interactivity = 'all'
import os
import matplotlib.pyplot as plt
import numpy as np
import matplotlib
import math
import numba
matplotlib.rcParams['figure.dpi'] = 150

def make_ackley(dimensions, a=20, b=0.2, c=2 * 3.14):
    @numba.njit
    def inner(*args):
        assert len(args) == dimensions
        x = 0
        for d in args:
            x += d ** 2
        x *= 1 / dimensions
        x = math.sqrt(x)
        x *= -b
        result = -a * math.exp(x)
        
        x = 0
        for d in args:
            x += math.cos(d * c)
        x *= 1 / dimensions
        result -= math.exp(x)
        
        result += a
        result -= math.exp(1)
        
        return result
    return inner

ackley_1d = make_ackley(1)

graph = [ackley_1d(x) for x in np.arange(-40, 40, 0.001)]

plt.plot(np.arange(-40, 40, 0.001), graph)

[<matplotlib.lines.Line2D at 0x7fb3345a8a30>]

ackley_2d = make_ackley(2)

RES = 10
graph = np.zeros((80 * RES, 80 * RES))

for x in range(80 * RES):
    for y in range(80 * RES):
        graph[y][x] = ackley_2d((x / RES) - 40, (y / RES) - 40)

plt.imshow(graph)
plt.colorbar()

<matplotlib.image.AxesImage at 0x7fb32a3046a0>

<matplotlib.colorbar.Colorbar at 0x7fb3221cf7c0>

ackley_2d = make_ackley(2)

gx = []
gy = []
gz = []

for x in np.arange(-40, 40, 0.5):
    for y in np.arange(-40, 40, 0.5):
        gx.append(x)
        gy.append(y)
        gz.append(ackley_2d(x, y))

fig = plt.figure()
ax = fig.add_subplot(projection='3d')
_ = ax.plot_trisurf(gx, gy, gz)