class Rosenbrock(BaseFunction):
target_E = 0.
target_coords = np.array([1., 1.])
xmin = np.array([-10.,-10.])
xmax = np.array([10.,10.])
def getEnergy(self, coords):
x, y = coords
return 100. * (y - x**2)**2 + (x-1)**2
def getEnergyGradient(self, coords):
E = self.getEnergy(coords)
x, y = coords
dx = -400. * (y - x**2) * x + 2. * (x-1)
dy = 200. * (y - x**2)
return E, np.array([dx, dy])
if __name__ == "__main__":
f = Rosenbrock()
f.test_potential(f.target_coords)
print ""
f.test_potential(f.get_random_configuration())
from base_function import makeplot2d
v = 3.
xmin = np.array([0.,0.])
xmax = np.array([1.2,1.5])
makeplot2d(f, xmin=-xmax, xmax=xmax, nx=30)
if x > 0: return 1.
elif x < 0: return -1.
else: return 0.
def getEnergyGradient_2(self, coords):
"""there is a bug here. it doesn't pass the test"""
E = self.getEnergy(coords)
x, y = coords
dEdy = (-sin(sqrt(abs(47. + 0.5 * x + y))) +
(x * cos(sqrt(abs(-47. + x - y))) * -1. *
self.dabs(-47. + x - y)) / (2. * sqrt(abs(-47. + x - y))) +
(0.5 * (-47. - y) * cos(sqrt(abs(47. + 0.5 * x + y))) *
self.dabs(47. + 0.5 * x + y)) / sqrt(abs(47. + 0.5 * x + y)))
dEdx = (-sin(sqrt(abs(-47. + x - y))) -
(x * cos(sqrt(abs(-47. + x - y))) * self.dabs(-47. + x - y)) /
(2. * sqrt(abs(-47. + x - y))) +
(0.25 * (-47. - y) * cos(sqrt(abs(47. + 0.5 * x + y))) * 0.5 *
self.dabs(47. + 0.5 * x + y)) / sqrt(abs(47. + 0.5 * x + y)))
grad = np.array([dEdx, dEdy])
print "grad", grad
return E, grad
if __name__ == "__main__":
f = EggHolder()
# f.test_potential(f.get_random_configuration())
from base_function import makeplot2d
makeplot2d(EggHolder())
class Levi(BaseFunction):
target_E = 0.
xmin = np.array([-10.,-10.])
xmax = np.array([10.,10.])
def getEnergy(self, coords):
x, y = coords
E = sin(3.*pi*x)**2 + (x-1.)**2 * (1. + sin(3*pi*y)**2) \
+ (y-1.)**2 * (1. + sin(2*pi*y)**2)
return E
def getEnergyGradient(self, coords):
x, y = coords
E = self.getEnergy(coords)
dEdx = 2.*3.*pi* cos(3.*pi*x) * sin(3.*pi*x) + 2.*(x-1.) * (1. + sin(3*pi*y)**2)
dEdy = (x-1.)**2 * 2.*3.*pi* cos(3.*pi*y) * sin(3.*pi*y) + 2. * (y-1.) * (1. + sin(2*pi*y)**2) \
+ (y-1.)**2 * 2.*2.*pi * cos(2.*pi*y) * sin(2.*pi*y)
return E, np.array([dEdx, dEdy])
if __name__ == "__main__":
f = Levi()
f.test_potential(f.get_random_configuration())
from base_function import makeplot2d
makeplot2d(f)
x, y = coords
dEdy = (-sin(sqrt(abs(47. + 0.5*x + y))) +
(x*cos(sqrt(abs(-47. + x - y)))
* -1.*self.dabs(-47. + x - y))/
(2.*sqrt(abs(-47. + x - y)))
+
(0.5*(-47. - y)*cos(sqrt(abs(47. + 0.5*x + y)))
* self.dabs(47. + 0.5*x + y)
)/sqrt(abs(47. + 0.5*x + y)))
dEdx = (
-sin(sqrt(abs(-47. + x - y)))
-
(x*cos(sqrt(abs(-47. + x - y)))
*self.dabs(-47. + x - y))/
(2.*sqrt(abs(-47. + x - y)))
+
(0.25*(-47. - y)*cos(sqrt(abs(47. + 0.5*x + y)))
*0.5*self.dabs(47. + 0.5*x + y)
)/sqrt(abs(47. + 0.5*x + y)))
grad = np.array([dEdx, dEdy])
print "grad", grad
return E, grad
if __name__ == "__main__":
f = EggHolder()
# f.test_potential(f.get_random_configuration())
from base_function import makeplot2d
makeplot2d(EggHolder())
"""derivative of absolute value"""
if x < 0: return -1.
elif x > 0: return 1.
else: return 0.
def getEnergyGradient(self, coords):
x, y = coords
R = sqrt(x**2 + y**2)
g = 1. - R / pi
f = sin(x)* cos(y) * exp(abs(g))
E = -abs(f)
dRdx = x / R
dgdx = - dRdx / pi
dfdx = cos(x) * cos(y) * exp(abs(g)) + f * self.dabs(g) * dgdx
dEdx = - self.dabs(f) * dfdx
dRdy = y / R
dgdy = - dRdy / pi
dfdy = -sin(x) * sin(y) * exp(abs(g)) + f * self.dabs(g) * dgdy
dEdy = - self.dabs(f) * dfdy
return E, np.array([dEdx, dEdy])
if __name__ == "__main__":
f = HolderTable()
f.test_potential(f.get_random_configuration())
from base_function import makeplot2d
makeplot2d(f)
class Rosenbrock(BaseFunction):
target_E = 0.
target_coords = np.array([1., 1.])
xmin = np.array([-10., -10.])
xmax = np.array([10., 10.])
def getEnergy(self, coords):
x, y = coords
return 100. * (y - x**2)**2 + (x - 1)**2
def getEnergyGradient(self, coords):
E = self.getEnergy(coords)
x, y = coords
dx = -400. * (y - x**2) * x + 2. * (x - 1)
dy = 200. * (y - x**2)
return E, np.array([dx, dy])
if __name__ == "__main__":
f = Rosenbrock()
f.test_potential(f.target_coords)
print ""
f.test_potential(f.get_random_configuration())
from base_function import makeplot2d
v = 3.
xmin = np.array([0., 0.])
xmax = np.array([1.2, 1.5])
makeplot2d(f, xmin=-xmax, xmax=xmax, nx=30)
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)
from numpy import exp, cos, sqrt, pi
import numpy as np
from base_function import BaseFunction
from pygmin.systems import BaseSystem
class Bulkin(BaseFunction):
xmin = np.array([-15.,-3.])
xmax = np.array([-5.,3.])
target_E = 0.
def getEnergy(self, coords):
x, y = coords
E = 100. * sqrt(abs(y - 0.01 * x**2)) + 0.01 * abs(x + 10.)
return E
def get_random_configuration(self):
x = np.random.uniform(-13,-8, 1)
y = np.random.uniform(-4,-4, 1)
return np.array([x,y]).flatten()
class BukinSystem(BaseSystem):
def get_potential(self):
return Bulkin()
if __name__ == "__main__":
from base_function import makeplot2d
makeplot2d(Bulkin())
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)
