beale.py

import numpy as np
from numpy import exp, sqrt, cos, pi, sin

from base_function import BaseFunction

class Beale(BaseFunction):
    target_E = 0.
    target_coords = np.array([3., 0.5])
    xmin = np.array([-4.5,-4.5])
    xmax = np.array([4.5,4.5])
    def getEnergy(self, coords):
        x, y = coords
        return (1.5 - x + x*y)**2 + (2.25 - x + x * y**2)**2 + (2.625 - x + x * y**3)**2
        
    def getEnergyGradient(self, coords):
        E = self.getEnergy(coords)
        x, y = coords
        dx = 2. * (1.5 - x + x*y) * (-1. + y) + 2. * (2.25 - x + x * y**2) * (-1. + y**2) + 2. * (2.625 - x + x * y**3) * (-1. + y**3)
        dy = 2. * (1.5 - x + x*y) * (x) +       2. * (2.25 - x + x * y**2) * (2. * y * x) + 2. * (2.625 - x + x * y**3) * (3. * x * y**2)
        return E, np.array([dx, dy])
        

    
if __name__ == "__main__":
    f = Beale()
    f.test_potential(f.target_coords)
    print ""
    f.test_potential(f.get_random_configuration())
    f.test_potential(np.array([1.,1.]), print_grads=True)
    
    from base_function import makeplot2d
    v = 3.
    makeplot2d(f, nx=30)