class LJTest(unittest.TestCase):
def setUp(self):
self.natoms = 10
self.coords = np.random.uniform(-1,1.,3*self.natoms) * self.natoms**(-1./3)
self.pot = LJ()
self.E = self.pot.getEnergy(self.coords)
self.Egrad, self.grad = self.pot.getEnergyGradient(self.coords)
import itertools
self.ilist = [] #np.zeros([self.natoms*(self.natoms-1)/2, 2])
k = 0
for i in range(self.natoms):
for j in range(i):
k += 1
self.ilist.append( [i,j] )
self.ilist = np.array(self.ilist)
#print self.ilist
def test_grad_e(self):
self.assertAlmostEqual(self.E, self.Egrad, 7)
def test_lists_e(self):
e = self.pot.getEnergyList(self.coords, self.ilist)
self.assertAlmostEqual(self.E, e, 7)
def test_lists_eg(self):
e, g = self.pot.getEnergyGradientList(self.coords, self.ilist)
self.assertAlmostEqual(self.E, e, 7)
gdiffmax = np.max(np.abs( g-self.grad )) / np.max(np.abs(self.grad))
self.assertLess(gdiffmax, 1e-7)
class LJTest(unittest.TestCase):
def setUp(self):
self.natoms = 10
self.coords = np.random.uniform(-1, 1., 3 * self.natoms) * self.natoms ** (-1. / 3)
self.pot = LJ()
self.E = self.pot.getEnergy(self.coords)
self.Egrad, self.grad = self.pot.getEnergyGradient(self.coords)
self.ilist = [] # np.zeros([self.natoms*(self.natoms-1)/2, 2])
k = 0
for i in range(self.natoms):
for j in range(i):
k += 1
self.ilist.append([i, j])
self.ilist = np.array(self.ilist)
# print self.ilist
def test_grad_e(self):
self.assertAlmostEqual(self.E, self.Egrad, 7)
def test_lists_e(self):
e = self.pot.getEnergyList(self.coords, self.ilist)
self.assertAlmostEqual(self.E, e, 7)
def test_lists_eg(self):
e, g = self.pot.getEnergyGradientList(self.coords, self.ilist)
self.assertAlmostEqual(self.E, e, 7)
gdiffmax = np.max(np.abs(g - self.grad)) / np.max(np.abs(self.grad))
self.assertLess(gdiffmax, 1e-7)
def test():
natoms = 100
tol = 1e-6
from pele.potentials.lj import LJ
pot = LJ()
X = getInitialCoords(natoms, pot)
X += np.random.uniform(-1,1,[3*natoms]) * 0.3
#do some steepest descent steps so we don't start with a crazy structure
#from optimize.quench import _steepest_descent as steepestDescent
#ret = steepestDescent(X, pot.getEnergyGradient, iprint = 1, dx = 1e-4, nsteps = 100, gtol = 1e-3, maxstep = .5)
#X = ret[0]
#print X
Xinit = np.copy(X)
e, g = pot.getEnergyGradient(X)
print "energy", e
lbfgs = BFGS(X, pot, maxstep = 0.1)
ret = lbfgs.run(100, tol = tol, iprint=1)
print "done", ret[1], ret[2], ret[3]
print "now do the same with scipy lbfgs"
from pele.optimize import lbfgs_scipy as quench
ret = quench(Xinit, pot.getEnergyGradient, tol = tol)
print ret[1], ret[2], ret[3]
print "now do the same with scipy bfgs"
from pele.optimize import bfgs as oldbfgs
ret = oldbfgs(Xinit, pot.getEnergyGradient, tol = tol)
print ret[1], ret[2], ret[3]
print "now do the same with old gradient + linesearch"
gpl = GradientPlusLinesearch(Xinit, pot, maxstep = 0.1)
ret = gpl.run(100, tol = 1e-6)
print ret[1], ret[2], ret[3]
class TestLJAfterQuench(unittest.TestCase):
"""do the tests after a short quench so that the energies are not crazy large
"""
def setUp(self):
from pele.optimize import mylbfgs
self.natoms = 10
self.coords = np.random.uniform(-1, 1., 3 * self.natoms) * self.natoms ** (-1. / 3)
self.pot = LJ()
ret = mylbfgs(self.coords, self.pot, tol=2.)
self.coords = ret.coords
self.E = self.pot.getEnergy(self.coords)
self.Egrad, self.grad = self.pot.getEnergyGradient(self.coords)
def test_gradient(self):
e0 = self.pot.getEnergy(self.coords)
e, g, hess = self.pot.getEnergyGradientHessian(self.coords)
gnum = self.pot.NumericalDerivative(self.coords)
maxg = np.max(np.abs(g))
maxgdiff = np.max(np.abs(g - gnum))
self.assertAlmostEqual(e0, e, 5)
self.assertLess(maxgdiff / maxg, 1e-5)
def test_hessian(self):
e, g, hess = self.pot.getEnergyGradientHessian(self.coords)
nhess = self.pot.NumericalHessian(self.coords, eps=1e-8)
# print "hess", hess
# print "numerical", nhess
# diff = hess - nhess
maxhess = np.max(np.abs(hess))
maxdiff = np.max(np.abs(hess - nhess))
# print "diff", hess[:2,:2] - nhess[:2,:2]
# print maxhess, maxdiff, maxdiff / maxhess
# print "diff", (hess[:2,:2] - nhess[:2,:2])/maxhess
# print "diff", (hess - nhess)/maxhess
# print np.max(np.abs((hess-nhess)/nhess))
self.assertLess(maxdiff / maxhess, 1e-5)
def testpot1():
from pele.potentials.lj import LJ
import itertools
pot = LJ()
a = 1.12 #2.**(1./6.)
theta = 60./360*np.pi
coords = [ 0., 0., 0., \
-a, 0., 0., \
-a/2, a*np.cos(theta), 0., \
-a/2, -a*np.cos(theta), 0.1 \
]
natoms = len(coords)/3
c = np.reshape(coords, [-1,3])
for i, j in itertools.combinations(range(natoms), 2):
r = np.linalg.norm(c[i,:] - c[j,:])
print i, j, r
e, g = pot.getEnergyGradient(coords)
print "initial E", e
print "initial G", g, np.linalg.norm(g)
eigpot = LowestEigPot(coords, pot)
vec = np.random.rand(len(coords))
e, g = eigpot.getEnergyGradient(vec)
print "eigenvalue", e
print "eigenvector", g
if True:
e, g, hess = pot.getEnergyGradientHessian(coords)
print "shape hess", np.shape(hess)
print "hessian", hess
u, v = np.linalg.eig(hess)
print "max imag value", np.max(np.abs(u.imag))
print "max imag vector", np.max(np.abs(v.imag))
u = u.real
v = v.real
print "eigenvalues", u
for i in range(len(u)):
print "eigenvalue", u[i], "eigenvector", v[:,i]
#find minimum eigenvalue, vector
imin = 0
umin = 10.
for i in range(len(u)):
if np.abs(u[i]) < 1e-10: continue
if u[i] < umin:
umin = u[i]
imin = i
print "lowest eigenvalue ", umin, imin
print "lowest eigenvector", v[:,imin]
from pele.optimize import lbfgs_py as quench
ret = quench(vec, eigpot.getEnergyGradient, iprint=10, tol = 1e-5, maxstep = 1e-3, \
rel_energy = True)
print ret
print "lowest eigenvalue "
print umin, imin
print "lowest eigenvector"
print v[:,imin]
print "now the estimate"
print ret[1]
print ret[0]
