import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize


def eggholder(x):
    return (-(x[1] + 47) * np.sin(np.sqrt(abs(x[0]/2 + (x[1]  + 47))))
            -x[0] * np.sin(np.sqrt(abs(x[0] - (x[1]  + 47)))))

bounds = [(-512, 512), (-512, 512)]

x = np.arange(-512, 513)
y = np.arange(-512, 513)
xgrid, ygrid = np.meshgrid(x, y)
xy = np.stack([xgrid, ygrid])

results = dict()
results['shgo'] = optimize.shgo(eggholder, bounds)
results['DA'] = optimize.dual_annealing(eggholder, bounds)
results['DE'] = optimize.differential_evolution(eggholder, bounds)
results['shgo_sobol'] = optimize.shgo(eggholder, bounds, n=256, iters=5,
                                      sampling_method='sobol')

fig = plt.figure(figsize=(4.5, 4.5))
ax = fig.add_subplot(111)
im = ax.imshow(eggholder(xy), interpolation='bilinear', origin='lower',
               cmap='gray')
ax.set_xlabel('x')
ax.set_ylabel('y')

def plot_point(res, marker='o', color=None):
    ax.plot(512+res.x[0], 512+res.x[1], marker=marker, color=color, ms=10)

plot_point(results['DE'], color='c')  # differential_evolution - cyan
plot_point(results['DA'], color='w')  # dual_annealing.        - white

# SHGO produces multiple minima, plot them all (with a smaller marker size)
plot_point(results['shgo'], color='r', marker='+')
plot_point(results['shgo_sobol'], color='r', marker='x')
for i in range(results['shgo_sobol'].xl.shape[0]):
    ax.plot(512 + results['shgo_sobol'].xl[i, 0],
            512 + results['shgo_sobol'].xl[i, 1],
            'ro', ms=2)

ax.set_xlim([-4, 514*2])
ax.set_ylim([-4, 514*2])

fig.tight_layout()
plt.show()