def setUp(self):
from pygmin.landscape import DoubleEndedConnect
from pygmin.landscape._graph import create_random_database
from pygmin.systems import LJCluster
# from pygmin.mindist import minPermDistStochastic, MinDistWrapper
# from pygmin.potentials import LJ
nmin = 10
natoms = 13
sys = LJCluster(natoms)
pot = sys.get_potential()
mindist = sys.get_mindist()
db = create_random_database(nmin=nmin, natoms=natoms, nts=nmin / 2)
min1, min2 = list(db.minima())[:2]
connect = DoubleEndedConnect(min1,
min2,
pot,
mindist,
db,
use_all_min=True,
merge_minima=True,
max_dist_merge=1e100)
self.connect = connect
self.db = db
self.natoms = natoms
def test():
from pygmin.systems import LJCluster
natoms = 13
system = LJCluster(natoms)
db = system.create_database()
# get some minima
bh = system.get_basinhopping(database=db, outstream=None)
bh.run(100)
manager = ConnectManager(db, clust_min=2)
for i in range(4):
min1, min2 = manager.get_connect_job(strategy="random")
print "connecting", min1._id, min2._id
connect = system.get_double_ended_connect(min1, min2, db, verbosity=0)
connect.connect()
print "\n\ntesting untrap"
for i in range(10):
min1, min2 = manager.get_connect_job(strategy="untrap")
print min1._id, min2._id
print "\n\ntesting combine"
for i in range(5):
min1, min2 = manager.get_connect_job(strategy="combine")
print min1._id, min2._id
print "\n\ntesting gmin"
for i in range(5):
min1, min2 = manager.get_connect_job(strategy="gmin")
print min1._id, min2._id
def test():
from pygmin.systems import LJCluster
natoms = 13
system = LJCluster(natoms)
db = system.create_database()
# get some minima
bh = system.get_basinhopping(database=db, outstream=None)
bh.run(100)
manager = ConnectManager(db, clust_min=2)
for i in range(4):
min1, min2 = manager.get_connect_job(strategy="random")
print "connecting", min1._id, min2._id
connect = system.get_double_ended_connect(min1, min2, db, verbosity=0)
connect.connect()
print "\n\ntesting untrap"
for i in range(10):
min1, min2 = manager.get_connect_job(strategy="untrap")
print min1._id, min2._id
print "\n\ntesting combine"
for i in range(5):
min1, min2 = manager.get_connect_job(strategy="combine")
print min1._id, min2._id
print "\n\ntesting gmin"
for i in range(5):
min1, min2 = manager.get_connect_job(strategy="gmin")
print min1._id, min2._id
def setUp(self):
from pygmin.landscape import DoubleEndedConnect
from pygmin.landscape._graph import create_random_database
from pygmin.systems import LJCluster
# from pygmin.mindist import minPermDistStochastic, MinDistWrapper
# from pygmin.potentials import LJ
nmin = 10
natoms=13
sys = LJCluster(natoms)
pot = sys.get_potential()
mindist = sys.get_mindist()
db = create_random_database(nmin=nmin, natoms=natoms, nts=nmin/2)
min1, min2 = list(db.minima())[:2]
connect = DoubleEndedConnect(min1, min2, pot, mindist, db, use_all_min=True,
merge_minima=True, max_dist_merge=1e100)
self.connect = connect
self.db = db
self.natoms = natoms
def guessts(coords1, coords2, pot):
from pygmin.optimize import lbfgs_py as quench
# from pygmin.mindist.minpermdist_stochastic import minPermDistStochastic as mindist
from pygmin.transition_states import NEB
from pygmin.systems import LJCluster
ret1 = quench(coords1, pot.getEnergyGradient)
ret2 = quench(coords2, pot.getEnergyGradient)
coords1 = ret1[0]
coords2 = ret2[0]
natoms = len(coords1) / 3
system = LJCluster(natoms)
mindist = system.get_mindist()
dist, coords1, coords2 = mindist(coords1, coords2)
print "dist", dist
print "energy coords1", pot.getEnergy(coords1)
print "energy coords2", pot.getEnergy(coords2)
from pygmin.transition_states import InterpolatedPath
neb = NEB(InterpolatedPath(coords1, coords2, 20), pot)
#neb.optimize(quenchParams={"iprint" : 1})
neb.optimize(iprint=-30, nsteps=100)
neb.MakeAllMaximaClimbing()
#neb.optimize(quenchParams={"iprint": 30, "nsteps":100})
for i in xrange(len(neb.energies)):
if (neb.isclimbing[i]):
coords = neb.coords[i, :]
return pot, coords, neb.coords[0, :], neb.coords[-1, :]
def guessts(coords1, coords2, pot):
from pygmin.optimize import lbfgs_py as quench
# from pygmin.mindist.minpermdist_stochastic import minPermDistStochastic as mindist
from pygmin.transition_states import NEB
from pygmin.systems import LJCluster
ret1 = quench(coords1, pot.getEnergyGradient)
ret2 = quench(coords2, pot.getEnergyGradient)
coords1 = ret1[0]
coords2 = ret2[0]
natoms = len(coords1)/3
system = LJCluster(natoms)
mindist = system.get_mindist()
dist, coords1, coords2 = mindist(coords1, coords2)
print "dist", dist
print "energy coords1", pot.getEnergy(coords1)
print "energy coords2", pot.getEnergy(coords2)
from pygmin.transition_states import InterpolatedPath
neb = NEB(InterpolatedPath(coords1, coords2, 20), pot)
#neb.optimize(quenchParams={"iprint" : 1})
neb.optimize(iprint=-30, nsteps=100)
neb.MakeAllMaximaClimbing()
#neb.optimize(quenchParams={"iprint": 30, "nsteps":100})
for i in xrange(len(neb.energies)):
if(neb.isclimbing[i]):
coords = neb.coords[i,:]
return pot, coords, neb.coords[0,:], neb.coords[-1,:]
class TestMinimizers(unittest.TestCase):
def setUp(self):
from pygmin.systems import LJCluster
natoms = 31
self.system = LJCluster(natoms)
self.pot = self.system.get_potential()
# get a partially minimized structure
x0 = self.system.get_random_configuration()
ret = lbfgs_py(x0, self.pot, tol=1e-1)
self.x0 = ret.coords.copy()
self.E0 = ret.energy
ret = lbfgs_py(self.x0, self.pot, tol=1e-7)
self.x = ret.coords.copy()
self.E = ret.energy
def check_attributes(self, res):
self.assertTrue(hasattr(res, "energy"))
self.assertTrue(hasattr(res, "coords"))
self.assertTrue(hasattr(res, "nsteps"))
self.assertTrue(hasattr(res, "nfev"))
self.assertTrue(hasattr(res, "rms"))
self.assertTrue(hasattr(res, "grad"))
self.assertTrue(hasattr(res, "success"))
def test_lbfgs_py(self):
res = lbfgs_py(self.x0, self.pot, tol=1e-7)
self.assertTrue(res.success)
self.assertAlmostEqual(self.E, res.energy, 4)
self.check_attributes(res)
def test_mylbfgs(self):
res = mylbfgs(self.x0, self.pot, tol=1e-7)
self.assertTrue(res.success)
self.assertAlmostEqual(self.E, res.energy, 4)
self.check_attributes(res)
def test_fire(self):
res = fire(self.x0, self.pot, tol=1e-7)
self.assertTrue(res.success)
self.assertAlmostEqual(self.E, res.energy, 4)
self.check_attributes(res)
def test_lbfgs_scipy(self):
res = lbfgs_scipy(self.x0, self.pot, tol=1e-7)
self.assertTrue(res.success)
self.assertAlmostEqual(self.E, res.energy, 4)
self.check_attributes(res)
def test_bfgs_scipy(self):
res = bfgs_scipy(self.x0, self.pot, tol=1e-7)
self.assertTrue(res.success)
self.assertAlmostEqual(self.E, res.energy, 4)
self.check_attributes(res)
class TestMinimizers(unittest.TestCase):
def setUp(self):
from pygmin.systems import LJCluster
natoms = 31
self.system = LJCluster(natoms)
self.pot = self.system.get_potential()
# get a partially minimized structure
x0 = self.system.get_random_configuration()
ret = lbfgs_py(x0, self.pot, tol=1e-1)
self.x0 = ret.coords.copy()
self.E0 = ret.energy
ret = lbfgs_py(self.x0, self.pot, tol=1e-7)
self.x = ret.coords.copy()
self.E = ret.energy
def check_attributes(self, res):
self.assertTrue(hasattr(res, "energy"))
self.assertTrue(hasattr(res, "coords"))
self.assertTrue(hasattr(res, "nsteps"))
self.assertTrue(hasattr(res, "nfev"))
self.assertTrue(hasattr(res, "rms"))
self.assertTrue(hasattr(res, "grad"))
self.assertTrue(hasattr(res, "success"))
def test_lbfgs_py(self):
res = lbfgs_py(self.x0, self.pot, tol=1e-7)
self.assertTrue(res.success)
self.assertAlmostEqual(self.E, res.energy, 4)
self.check_attributes(res)
def test_mylbfgs(self):
res = mylbfgs(self.x0, self.pot, tol=1e-7)
self.assertTrue(res.success)
self.assertAlmostEqual(self.E, res.energy, 4)
self.check_attributes(res)
def test_fire(self):
res = fire(self.x0, self.pot, tol=1e-7)
self.assertTrue(res.success)
self.assertAlmostEqual(self.E, res.energy, 4)
self.check_attributes(res)
def test_lbfgs_scipy(self):
res = lbfgs_scipy(self.x0, self.pot, tol=1e-7)
self.assertTrue(res.success)
self.assertAlmostEqual(self.E, res.energy, 4)
self.check_attributes(res)
def test_bfgs_scipy(self):
res = bfgs_scipy(self.x0, self.pot, tol=1e-7)
self.assertTrue(res.success)
self.assertAlmostEqual(self.E, res.energy, 4)
self.check_attributes(res)
def getPairLJ(natoms=38):
from pygmin.systems import LJCluster
system = LJCluster(natoms)
ret1 = system.get_random_minimized_configuration()
ret2 = system.get_random_minimized_configuration()
coords1, coords2 = ret1[0], ret2[0]
E1, E2 = ret1[1], ret2[1]
mindist = system.get_mindist()
mindist(coords1, coords2)
return coords1, coords2, system.get_potential(), mindist, E1, E2
def getPairLJ(natoms=38):
from pygmin.systems import LJCluster
system = LJCluster(natoms)
ret1 = system.get_random_minimized_configuration()
ret2 = system.get_random_minimized_configuration()
coords1, coords2 = ret1[0], ret2[0]
E1, E2 = ret1[1], ret2[1]
mindist = system.get_mindist()
mindist(coords1, coords2)
return coords1, coords2, system.get_potential(), mindist, E1, E2
def test(Connect=DoubleEndedConnect, natoms=16):
# from pygmin.landscape import Graph
# from pygmin.storage.database import Database
from pygmin.systems import LJCluster
#get min1
system = LJCluster(natoms)
pot, database = getSetOfMinLJ(system)
# from pygmin.potentials.lj import LJ
# pot = LJ()
# saveit = Database(db="test.db")
minima = database.minima()
min1 = minima[0]
min2 = minima[1]
print min1.energy, min2.energy
mindist = system.get_mindist()
if False:
#test to see if min1 and min2 are already connected
connected = graph.areConnected(min1, min2)
print "at start are minima connected?", connected
return
connect = Connect(min1, min2, pot, mindist, database)
connect.connect()
graph = connect.graph
if False:
print graph
for node in graph.graph.nodes():
print node._id, node.energy
for ts in graph.storage.transition_states():
print ts.minimum1._id,ts.minimum2._id, "E", ts.minimum1.energy, ts.minimum2.energy, ts.energy
ret = graph.getPath(min1, min2)
if ret is None:
print "no path found"
return
distances, path = ret
with open("path.out", "w") as fout:
for i in range(len(path)-1):
m1 = path[i]
m2 = path[i+1]
n1 = m1._id
m2 = m2._id
# ts = graph._getTS(n1, n2)
# print "path", n1, "->", n2, m1.E, "/->", ts.E, "\->", m2.E
fout.write("%f\n" % m1.energy)
fout.write("%f\n" % ts.energy)
m2 = path[-1]
n2 = m2._id
fout.write("%f\n" % m2.energy)
def test(Connect=DoubleEndedConnect, natoms=16):
# from pygmin.landscape import TSGraph
# from pygmin.storage.database import Database
from pygmin.systems import LJCluster
#get min1
system = LJCluster(natoms)
pot, database = getSetOfMinLJ(system)
# from pygmin.potentials.lj import LJ
# pot = LJ()
# saveit = Database(db="test.db")
minima = database.minima()
min1 = minima[0]
min2 = minima[1]
print min1.energy, min2.energy
mindist = system.get_mindist()
if False:
#test to see if min1 and min2 are already connected
connected = graph.areConnected(min1, min2)
print "at start are minima connected?", connected
return
connect = Connect(min1, min2, pot, mindist, database)
connect.connect()
graph = connect.graph
if False:
print graph
for node in graph.graph.nodes():
print node._id, node.energy
for ts in graph.storage.transition_states():
print ts.minimum1._id, ts.minimum2._id, "E", ts.minimum1.energy, ts.minimum2.energy, ts.energy
ret = graph.getPath(min1, min2)
if ret is None:
print "no path found"
return
distances, path = ret
with open("path.out", "w") as fout:
for i in range(len(path) - 1):
m1 = path[i]
m2 = path[i + 1]
n1 = m1._id
m2 = m2._id
# ts = graph._getTS(n1, n2)
# print "path", n1, "->", n2, m1.E, "/->", ts.E, "\->", m2.E
fout.write("%f\n" % m1.energy)
fout.write("%f\n" % ts.energy)
m2 = path[-1]
n2 = m2._id
fout.write("%f\n" % m2.energy)
def size_scaling_smallest_eig(natoms):
from pygmin.systems import LJCluster
import time, sys
system = LJCluster(natoms)
pot = system.get_potential()
quencher = system.get_minimizer(tol=10.)
time1 = 0.
time2 = 0.
time3 = 0.
time4 = 0.
for i in range(100):
coords = system.get_random_configuration()
# print "len(coords)", len(coords)
coords = quencher(coords)[0]
e, g, h = pot.getEnergyGradientHessian(coords)
t0 = time.time()
w1, v1 = get_smallest_eig(h)
t1 = time.time()
w, v = get_smallest_eig_arpack(h)
t2 = time.time()
w2, v2 = get_smallest_eig_sparse(h)
t3 = time.time()
w3, v3 = get_smallest_eig_nohess(coords, system, tol=1e-3)
t4 = time.time()
time1 += t1 - t0
time2 += t2 - t1
time3 += t3 - t2
time4 += t4 - t3
wdiff = np.abs(w - w1) / np.max(np.abs([w, w1]))
if wdiff > 5e-3:
sys.stderr.write(
"eigenvalues for dense are different %g %g normalized diff %g\n"
% (w1, w, wdiff))
wdiff = np.abs(w - w2) / np.max(np.abs([w, w2]))
if wdiff > 5e-2:
sys.stderr.write(
"eigenvalues for sparse are different %g %g normalized diff %g\n"
% (w2, w, wdiff))
wdiff = np.abs(w - w3) / np.max(np.abs([w, w3]))
if wdiff > 5e-2:
sys.stderr.write(
"eigenvalues for nohess are different %g %g normalized diff %g\n"
% (w3, w, wdiff))
# print "times", n, t1-t0, t2-t1, w1, w
print "times", n, time1, time2, time3, time4
sys.stdout.flush()
def setUp(self):
from pygmin.systems import LJCluster
natoms = 31
self.system = LJCluster(natoms)
self.pot = self.system.get_potential()
# get a partially minimized structure
x0 = self.system.get_random_configuration()
ret = lbfgs_py(x0, self.pot.getEnergyGradient, tol=1.e-1)
self.x0 = ret[0]
self.E0 = ret[1]
ret = lbfgs_py(self.x0, self.pot.getEnergyGradient, tol=1e-7)
self.x = ret[0]
self.E = ret[1]
def spawnlj(**kwargs):
from pygmin.systems import LJCluster
from pygmin.config import config
import os
natoms = 13
sys = LJCluster(natoms)
db = sys.create_database()
x1, E1 = sys.get_random_minimized_configuration()[:2]
x2, E2 = sys.get_random_minimized_configuration()[:2]
m1 = db.addMinimum(E1, x1)
m2 = db.addMinimum(E2, x2)
optim = "/home/js850/git/OPTIM/source/build/OPTIM"
optim = config.get("exec", "OPTIM")
optim = os.path.expandvars(os.path.expanduser(optim))
spawner = SpawnOPTIM_LJ(x1, x2, sys, OPTIM=optim, **kwargs)
spawner.run()
spawner.load_results(db)
def spawnlj(**kwargs):
from pygmin.systems import LJCluster
from pygmin.config import config
import os
natoms = 13
sys = LJCluster(natoms)
db = sys.create_database()
x1, E1 = sys.get_random_minimized_configuration()[:2]
x2, E2 = sys.get_random_minimized_configuration()[:2]
m1 = db.addMinimum(E1, x1)
m2 = db.addMinimum(E2, x2)
optim = "/home/js850/git/OPTIM/source/build/OPTIM"
optim = config.get("exec", "OPTIM")
optim = os.path.expandvars(os.path.expanduser(optim))
spawner = SpawnOPTIM_LJ(x1, x2, sys, OPTIM=optim, **kwargs)
spawner.run()
spawner.load_results(db)
def size_scaling_smallest_eig(natoms):
from pygmin.systems import LJCluster
import time, sys
system = LJCluster(natoms)
pot = system.get_potential()
quencher = system.get_minimizer(tol=10.)
time1 = 0.
time2 = 0.
time3 = 0.
time4 = 0.
for i in range(100):
coords = system.get_random_configuration()
# print "len(coords)", len(coords)
coords = quencher(coords)[0]
e, g, h = pot.getEnergyGradientHessian(coords)
t0 = time.time()
w1, v1 = get_smallest_eig(h)
t1 = time.time()
w, v = get_smallest_eig_arpack(h)
t2 = time.time()
w2, v2 = get_smallest_eig_sparse(h)
t3 = time.time()
w3, v3 = get_smallest_eig_nohess(coords, system, tol=1e-3)
t4 = time.time()
time1 += t1-t0
time2 += t2-t1
time3 += t3-t2
time4 += t4-t3
wdiff = np.abs(w-w1) / np.max(np.abs([w,w1]))
if wdiff > 5e-3:
sys.stderr.write("eigenvalues for dense are different %g %g normalized diff %g\n" % (w1, w, wdiff))
wdiff = np.abs(w-w2) / np.max(np.abs([w,w2]))
if wdiff > 5e-2:
sys.stderr.write("eigenvalues for sparse are different %g %g normalized diff %g\n" % (w2, w, wdiff))
wdiff = np.abs(w-w3) / np.max(np.abs([w,w3]))
if wdiff > 5e-2:
sys.stderr.write("eigenvalues for nohess are different %g %g normalized diff %g\n" % (w3, w, wdiff))
# print "times", n, t1-t0, t2-t1, w1, w
print "times", n, time1, time2, time3, time4
sys.stdout.flush()
def get_database(natoms=13, nconn=5):
"""create a database for a lennard jones system
fill it with minima from a basinhopping run, then connect
some of those minima using DoubleEndedConnect
"""
ljsys = LJCluster(natoms)
db = ljsys.create_database()
bh = ljsys.get_basinhopping(database=db, outstream=None)
while (len(db.minima()) < nconn + 1):
bh.run(100)
minima = list(db.minima())
m1 = minima[0]
for m2 in minima[1:nconn + 1]:
connect = ljsys.get_double_ended_connect(m1, m2, db)
connect.connect()
return db
def get_database(natoms=13, nconn=5):
"""create a database for a lennard jones system
fill it with minima from a basinhopping run, then connect
some of those minima using DoubleEndedConnect
"""
ljsys = LJCluster(natoms)
db = ljsys.create_database()
bh = ljsys.get_basinhopping(database=db, outstream=None)
while len(db.minima()) < nconn + 1:
bh.run(100)
minima = list(db.minima())
m1 = minima[0]
for m2 in minima[1 : nconn + 1]:
connect = ljsys.get_double_ended_connect(m1, m2, db)
connect.connect()
return db
class TestBasinhopping(unittest.TestCase):
def setUp(self):
natoms = 6
self.system = LJCluster(natoms)
self.e1 = -12.7120622568
self.e2 = -12.302927529580728
def assertEnergy(self, e):
self.assertTrue( abs(e-self.e1) < 1e-4 or abs(e-self.e2) < 1e-4)
def test_create_basinhopping(self):
bh = self.system.get_basinhopping(outstream=None)
bh.run(3)
self.assertEnergy(bh.result.energy)
self.assertEnergy(bh.markovE)
def test_takestep(self):
takestep = self.system.get_takestep(stepsize=1.)
bh = self.system.get_basinhopping(outstream=None, takestep=takestep)
bh.run(3)
self.assertEnergy(bh.result.energy)
self.assertEnergy(bh.markovE)
def setUp(self):
from pygmin.systems import LJCluster
natoms = 10
self.system = LJCluster(natoms)
system = self.system
self.pot = system.get_potential()
quencher = system.get_minimizer(tol=2.)
x = system.get_random_configuration()
ret = quencher(x)
self.x = ret[0]
self.xmin = system.get_random_minimized_configuration()[0]
e, g, self.h = self.pot.getEnergyGradientHessian(self.x)
e, g, self.hmin = self.pot.getEnergyGradientHessian(self.xmin)
def setUp(self):
from pygmin.systems import LJCluster
natoms = 31
self.system = LJCluster(natoms)
self.pot = self.system.get_potential()
# get a partially minimized structure
x0 = self.system.get_random_configuration()
ret = lbfgs_py(x0, self.pot.getEnergyGradient, tol=1.e-1)
self.x0 = ret[0]
self.E0 = ret[1]
ret = lbfgs_py(self.x0, self.pot.getEnergyGradient, tol=1e-7)
self.x = ret[0]
self.E = ret[1]
class TestMinimizers(unittest.TestCase):
def setUp(self):
from pygmin.systems import LJCluster
natoms = 31
self.system = LJCluster(natoms)
self.pot = self.system.get_potential()
# get a partially minimized structure
x0 = self.system.get_random_configuration()
ret = lbfgs_py(x0, self.pot.getEnergyGradient, tol=1.e-1)
self.x0 = ret[0]
self.E0 = ret[1]
ret = lbfgs_py(self.x0, self.pot.getEnergyGradient, tol=1e-7)
self.x = ret[0]
self.E = ret[1]
def test_lbfgs_py(self):
res = lbfgs_py(self.x0, self.pot.getEnergyGradient)
self.assertAlmostEqual(self.E, res[1], 4)
def test_mylbfgs(self):
res = mylbfgs(self.x0, self.pot.getEnergyGradient)
self.assertAlmostEqual(self.E, res[1], 4)
def test_fire(self):
res = fire(self.x0, self.pot.getEnergyGradient, tol=1e-7)
self.assertAlmostEqual(self.E, res[1], 4)
def test_lbfgs_scipy(self):
res = lbfgs_scipy(self.x0, self.pot.getEnergyGradient, tol=1e-7)
self.assertAlmostEqual(self.E, res[1], 4)
def test_bfgs_scipy(self):
res = bfgs(self.x0, self.pot.getEnergyGradient, tol=1e-7)
self.assertAlmostEqual(self.E, res[1], 4)
class TestMinimizers(unittest.TestCase):
def setUp(self):
from pygmin.systems import LJCluster
natoms = 31
self.system = LJCluster(natoms)
self.pot = self.system.get_potential()
# get a partially minimized structure
x0 = self.system.get_random_configuration()
ret = lbfgs_py(x0, self.pot.getEnergyGradient, tol=1.e-1)
self.x0 = ret[0]
self.E0 = ret[1]
ret = lbfgs_py(self.x0, self.pot.getEnergyGradient, tol=1e-7)
self.x = ret[0]
self.E = ret[1]
def test_lbfgs_py(self):
res = lbfgs_py(self.x0, self.pot.getEnergyGradient)
self.assertAlmostEqual(self.E, res[1], 4)
def test_mylbfgs(self):
res = mylbfgs(self.x0, self.pot.getEnergyGradient)
self.assertAlmostEqual(self.E, res[1], 4)
def test_fire(self):
res = fire(self.x0, self.pot.getEnergyGradient, tol=1e-7)
self.assertAlmostEqual(self.E, res[1], 4)
def test_lbfgs_scipy(self):
res = lbfgs_scipy(self.x0, self.pot.getEnergyGradient, tol=1e-7)
self.assertAlmostEqual(self.E, res[1], 4)
def test_bfgs_scipy(self):
res = bfgs(self.x0, self.pot.getEnergyGradient, tol=1e-7)
self.assertAlmostEqual(self.E, res[1], 4)
import scipy import numpy as np from pygmin.systems import LJCluster from pygmin.mindist import ExactMatchAtomicCluster from pygmin.mindist import PointGroupOrderCluster from pygmin.thermodynamics import normalmode_frequencies, logproduct_freq2 beta = 1. system = LJCluster(13) db = system.create_database() pot = system.get_potential() bh = system.get_basinhopping(database=db) bh.run(50) min1 = db.minima()[0] coords = min1.coords print print "Done with basinghopping, performing frequency analysis" print #min1 = db.transition_states()[0] # determine point group order of system determine_pgorder = PointGroupOrderCluster(system.get_compare_exact()) pgorder = determine_pgorder(min1.coords) # free energy from symmetry Fpg = np.log(pgorder) / beta # get the hession e, g, hess = pot.getEnergyGradientHessian(min1.coords)
from random import choice
from pygmin.systems import LJCluster
from pygmin.storage import Minimum
from pygmin.concurrent import RandomConnectServer
server_name = "ljconnect_example"
hostname="localhost"
port=11567
print "setting up LJ38 with database lj38.sqlite"
system = LJCluster(38)
db = system.create_database("lj38.sqlite")
if db.session.query(Minimum).count() < 10:
print "The database is empty, run basinhopping to get some minima"
bh = system.get_basinhopping(database=db)
bh.run(100)
print "Working on %d minima"%db.session.query(Minimum).count()
print "Running basinhopping to generate initial database"
print "Creating new connect manager"
connect_manager=RandomConnectServer(system, db, server_name=server_name,
host=hostname, port=port)
connect_manager.run()
This example will be based on a cluster of 38 Lennard-Jones atoms.
We will load two sets of coordinates from a file, minimize them, and try to find
a connected set of minima and transition states betweeen them.
For more information about how to change parameters, see the documentation
for the system class, the parameter tree and DoubleEndedConnect.
See the class LJCluster for what the default parameters are for this system
"""
import numpy as np
from pygmin.systems import LJCluster
natoms = 38
system = LJCluster(natoms)
# load the coordinates from disk
coords1 = np.genfromtxt("coords.A").flatten()
coords2 = np.genfromtxt("coords.B").flatten()
# minimize them
quencher = system.get_minimizer()
ret1 = quencher(coords1)
ret2 = quencher(coords2)
# make a database and add the minima
db = system.create_database()
coords, E = ret1[:2]
min1 = db.addMinimum(E, coords)
coords, E = ret2[:2]
from pygmin.systems import LJCluster
import numpy as np
import scipy.sparse
import scikits.sparse.cholmod as cholmod
import time
import pygmin.transition_states as ts
from pygmin.utils.hessian import get_sorted_eig
natoms = 1000
system = LJCluster(natoms)
#system.params.structural_quench_params.debug = True
#system.params.structural_quench_params.iprint = 100
db = system.create_database()
bh = system.get_basinhopping(db)
bh.run(1)
m = db.minima()[0]
coords = m.coords
potential = system.get_potential()
energy, gradient, hessian = potential.getEnergyGradientHessian(coords)
dummy_vec = ts.gramm_schmidt(ts.zeroEV_cluster(coords))
shifted_hess = hessian.copy()
for i in range(6):
shifted_hess += np.outer(dummy_vec[i], dummy_vec[i])
shifted_eval, shifted_evec = get_sorted_eig(shifted_hess)
def create_system():
natoms = 38
system = LJCluster(natoms)
return system
wdiff = np.abs(w-w3) / np.max(np.abs([w,w3]))
if wdiff > 5e-2:
sys.stderr.write("eigenvalues for nohess are different %g %g normalized diff %g\n" % (w3, w, wdiff))
# print "times", n, t1-t0, t2-t1, w1, w
print "times", n, time1, time2, time3, time4
sys.stdout.flush()
def plot_hist(hess):
import pylab as pl
pl.hist(np.log10(np.abs(hess.reshape(-1))))
pl.show()
if __name__ == "__main__":
from pygmin.systems import LJCluster
natoms = 30
system = LJCluster(natoms)
pot = system.get_potential()
coords = system.get_random_configuration()
xmin = system.get_random_minimized_configuration()[0]
e, g, h = pot.getEnergyGradientHessian(xmin)
evals = get_eigvals(h)
print evals
quencher = system.get_minimizer(tol=10.)
coords = quencher(coords)[0]
e, g, h = pot.getEnergyGradientHessian(coords)
w1, v1 = get_smallest_eig(h)
print w1
w, v = get_smallest_eig_arpack(h)
print w
""" examples of how to do various things using the system class. I will use the Lennard-Jones system as an example """ import logging from pygmin.systems import LJCluster from pygmin.utils.disconnectivity_graph import DisconnectivityGraph, database2graph # initialize the system class natoms = 13 system = LJCluster(natoms) # make a random configuration coords = system.get_random_configuration() # compute the energy of that configuration potential = system.get_potential() energy = potential.getEnergy(coords) print "the energy of the random configuration is", energy # minimize that configuration quencher = system.get_minimizer() ret = quencher(coords) newcoords = ret[0] newenergy = ret[1] print "after quenching, the energy is", newenergy # create a database to store the minimum in db = system.create_database()
self.ui.label.setText(label)
if with_path:
coordspath = np.array(self.quench_path)
self.ui.show3d.setCoordsPath(coordspath, frame=-1)
else:
self.ui.show3d.setCoords(self.coords, index=2)
self.ui.show3d.setCoords(self.quenched, index=1)
if __name__ == "__main__":
import sys
import pylab as pl
from OpenGL.GLUT import glutInit
glutInit()
app = QtGui.QApplication(sys.argv)
from pygmin.systems import LJCluster
pl.ion()
natoms = 13
system = LJCluster(natoms)
system.params.double_ended_connect.local_connect_params.NEBparams.iter_density = 5.
x1, e1 = system.get_random_minimized_configuration()[:2]
x2, e2 = system.get_random_minimized_configuration()[:2]
db = system.create_database(db=":memory:")
system.database = db
min1 = db.addMinimum(e1, x1)
min2 = db.addMinimum(e2, x2)
wnd = TakestepExplorer(app=app, system=system, database = db)
wnd.show()
from PyQt4.QtCore import QTimer
sys.exit(app.exec_())
# wnd.do_NEB(min1.coords, min2.coords)
wnd.attach_to_NEB(neb)
neb.optimize()
if __name__ == "__main__":
from pygmin.systems import LJCluster
from pygmin.storage import Database
import pylab as pl
app = QApplication(sys.argv)
def process_events():
app.processEvents()
#setup system
natoms = 13
system = LJCluster(natoms)
system.params.double_ended_connect.local_connect_params.NEBparams.iter_density = 5.
x1, e1 = system.get_random_minimized_configuration()[:2]
x2, e2 = system.get_random_minimized_configuration()[:2]
db = Database()
min1 = db.addMinimum(e1, x1)
min2 = db.addMinimum(e2, x2)
#setup neb dialog
pl.ion()
# pl.show()
dlg = NEBDialog()
wnd = dlg.nebwgt
dlg.show()
wnd.process_events.connect(process_events)
""" Example 4: modify the parameters of the adaptive stepsize note that the system class uses adaptive stepsize by default, so the previous examples also use adaptive stepsize """ from pygmin.systems import LJCluster from pygmin.takestep import RandomDisplacement, AdaptiveStepsizeTemperature natoms = 12 niter = 100 system = LJCluster(natoms) db = system.create_database() # create takestep routine manually step = RandomDisplacement(stepsize=0.3) # wrap it in the class which will adaptively improve the stepsize wrapped_step = AdaptiveStepsizeTemperature(step, interval=30) bh = system.get_basinhopping(database=db, takestep=wrapped_step) bh.run(niter) print "the lowest energy found after", niter, " basinhopping steps is", db.minima( )[0].energy print ""
This example will be based on a cluster of 38 Lennard-Jones atoms.
We will load two sets of coordinates from a file, minimize them, and try to find
a connected set of minima and transition states betweeen them.
For more information about how to change parameters, see the documentation
for the system class, the parameter tree and DoubleEndedConnect.
See the class LJCluster for what the default parameters are for this system
"""
import numpy as np
from pygmin.systems import LJCluster
natoms = 38
system = LJCluster(natoms)
# load the coordinates from disk
coords1 = np.genfromtxt("coords.A").flatten()
coords2 = np.genfromtxt("coords.B").flatten()
# minimize them
quencher = system.get_minimizer()
ret1 = quencher(coords1)
ret2 = quencher(coords2)
# make a database and add the minima
db = system.create_database()
coords, E = ret1[:2]
min1 = db.addMinimum(E, coords)
coords, E = ret2[:2]
"""
example for how to use double ended connect to connect the minima in an existing database
we will use as an example system the Lennard-Jones cluster with a small number of atoms.
Since we don't already have a database, for this example we'll build a small one using
basinhopping"
"""
import numpy as np
import logging
from pygmin.systems import LJCluster
from pygmin.utils.disconnectivity_graph import DisconnectivityGraph, database2graph
natoms = 13
system = LJCluster(natoms)
use_existing_database = False
if use_existing_database:
db = system.create_database("lj13.sqlite", createdb=False)
else:
# build a small database using basinhopping
print "building a small database using basinhopping" ""
db = system.create_database()
bh = system.get_basinhopping(database=db, outstream=None)
bh.run(20)
print "starting with a database of", len(db.minima()), "minima"
# turn of status printing for the connect run
# first use the logging module to turn off the status messages
wnd.set_nebrunner(runner)
if __name__ == "__main__":
from pygmin.systems import LJCluster
from nebdlg import getNEB
from OpenGL.GLUT import glutInit
app = QApplication(sys.argv)
def process_events():
app.processEvents()
#setup system
natoms = 13
system = LJCluster(natoms)
system.params.double_ended_connect.local_connect_params.NEBparams.iter_density = 10.
system.params.double_ended_connect.local_connect_params.NEBparams.image_density = 3.
# system.params.double_ended_connect.local_connect_params.NEBparams.adaptive_nimages = 5.
system.params.double_ended_connect.local_connect_params.NEBparams.reinterpolate = 400
system.params.double_ended_connect.local_connect_params.NEBparams.max_images = 40
x1, e1 = system.get_random_minimized_configuration()[:2]
x2, e2 = system.get_random_minimized_configuration()[:2]
db = Database()
min1 = db.addMinimum(e1, x1)
min2 = db.addMinimum(e2, x2)
#setup neb dialog
wnd = ConnectExplorerDialog(system, app)
wnd.show()
def start():
wnd.start()
print >> sys.stderr, "started decrunner"
if __name__ == "__main__":
from OpenGL.GLUT import glutInit
import sys
import pylab as pl
app = QtGui.QApplication(sys.argv)
from pygmin.systems import LJCluster
pl.ion()
natoms = 113
system = LJCluster(natoms)
system.params.double_ended_connect.local_connect_params.NEBparams.iter_density = 5.
x1, e1 = system.get_random_minimized_configuration()[:2]
x2, e2 = system.get_random_minimized_configuration()[:2]
db = system.create_database()
min1 = db.addMinimum(e1, x1)
min2 = db.addMinimum(e2, x2)
wnd = ConnectViewer(system, db, min1=min1, min2=min2, app=app)
# decrunner = DECRunner(system, db, min1, min2, outstream=wnd.textEdit_writer)
glutInit()
wnd.show()
from PyQt4.QtCore import QTimer
QTimer.singleShot(10, start)
sys.exit(app.exec_())
open a dialog box to change the parameters
"""
if checked is None:
return
if not hasattr(self, "_paramsdlg"):
self._paramsdlg = DlgParams(self._params, parent=self)
self._paramsdlg.show()
if __name__ == "__main__":
from OpenGL.GLUT import glutInit
import sys
glutInit()
app = QtGui.QApplication(sys.argv)
from pygmin.systems import LJCluster
natoms = 13
system = LJCluster(natoms)
system.params.double_ended_connect.local_connect_params.NEBparams.iter_density = 5.
x1, e1 = system.get_random_minimized_configuration()[:2]
db = system.create_database()
match = system.get_compare_exact()
min1 = db.addMinimum(e1, x1)
com = match.measure.get_com(x1)
match.transform.translate(x1, -com)
wnd = NormalmodeBrowser(app=app, system=system)
wnd.set_coords(x1)
wnd.show()
sys.exit(app.exec_())
from pygmin.systems import LJCluster
import numpy as np
import scipy.sparse
import scikits.sparse.cholmod as cholmod
import time
import pygmin.transition_states as ts
from pygmin.utils.hessian import get_sorted_eig
natoms = 1000
system = LJCluster(natoms)
#system.params.structural_quench_params.debug = True
#system.params.structural_quench_params.iprint = 100
db = system.create_database()
bh = system.get_basinhopping(db)
bh.run(1)
m = db.minima()[0]
coords = m.coords
potential = system.get_potential()
energy, gradient, hessian = potential.getEnergyGradientHessian(coords)
dummy_vec = ts.gramm_schmidt(ts.zeroEV_cluster(coords))
shifted_hess = hessian.copy()
for i in range(6):
shifted_hess += np.outer(dummy_vec[i], dummy_vec[i])
shifted_eval, shifted_evec = get_sorted_eig(shifted_hess)
def start():
wnd.start()
print >> sys.stderr, "started decrunner"
if __name__ == "__main__":
from OpenGL.GLUT import glutInit
import sys
import pylab as pl
app = QtGui.QApplication(sys.argv)
from pygmin.systems import LJCluster
pl.ion()
natoms = 113
system = LJCluster(natoms)
system.params.double_ended_connect.local_connect_params.NEBparams.iter_density = 5.
x1, e1 = system.get_random_minimized_configuration()[:2]
x2, e2 = system.get_random_minimized_configuration()[:2]
db = system.create_database()
min1 = db.addMinimum(e1, x1)
min2 = db.addMinimum(e2, x2)
wnd = ConnectViewer(system, db, min1=min1, min2=min2, app=app)
# decrunner = DECRunner(system, db, min1, min2, outstream=wnd.textEdit_writer)
glutInit()
wnd.show()
from PyQt4.QtCore import QTimer
QTimer.singleShot(10, start)
import scipy
import numpy as np
from pygmin.systems import LJCluster
from pygmin.mindist import ExactMatchAtomicCluster
from pygmin.mindist import PointGroupOrderCluster
from pygmin.thermodynamics import normalmode_frequencies, logproduct_freq2
beta = 1.
system = LJCluster(13)
db = system.create_database()
pot = system.get_potential()
bh = system.get_basinhopping(database=db)
bh.run(50)
min1 = db.minima()[0]
coords = min1.coords
print
print "Done with basinghopping, performing frequency analysis"
print
#min1 = db.transition_states()[0]
# determine point group order of system
determine_pgorder = PointGroupOrderCluster(system.get_compare_exact())
pgorder = determine_pgorder(min1.coords)
# free energy from symmetry
Fpg = np.log(pgorder)/beta
def takeStep(self, coords, **kwargs):
#make a new monte carlo class
mc = MonteCarlo(coords,
self.potential,
self.mcstep,
temperature=self.T,
outstream=None)
mc.run(self.nsteps)
coords[:] = mc.coords[:]
def updateStep(self, acc, **kwargs):
pass
natoms = 12
niter = 100
system = LJCluster(natoms)
db = system.create_database()
# create takestep routine manually
potential = system.get_potential()
step = TakeStepMonteCarlo(potential)
bh = system.get_basinhopping(database=db, takestep=step)
bh.run(niter)
print "the lowest energy found after", niter, " basinhopping steps is", db.minima(
)[0].energy
print ""
self.widget.show_graph()
def start():
wnd.start()
if __name__ == "__main__":
from OpenGL.GLUT import glutInit
import sys
import pylab as pl
app = QtGui.QApplication(sys.argv)
from pygmin.systems import LJCluster
pl.ion()
natoms = 13
system = LJCluster(natoms)
system.params.double_ended_connect.local_connect_params.NEBparams.iter_density = 5.
dbname = "lj%dtest.db" % (natoms,)
db = system.create_database(dbname)
#get some minima
if False:
bh = system.get_basinhopping(database=db)
bh.run(10)
minima = db.minima()
else:
x1, e1 = system.get_random_minimized_configuration()[:2]
x2, e2 = system.get_random_minimized_configuration()[:2]
min1 = db.addMinimum(e1, x1)
min2 = db.addMinimum(e2, x2)
minima = [min1, min2]
"""
Example 2: reading coords from file
"""
import numpy as np
from pygmin.systems import LJCluster
natoms = 12
niter = 100
system = LJCluster(natoms)
coords = np.loadtxt('coords')
coords = coords.reshape(-1)
db = system.create_database()
bh = system.get_basinhopping(database=db)
bh.run(niter)
print "the lowest energy found after", niter, " basinhopping steps is", db.minima()[0].energy
print ""
# print "times", n, t1-t0, t2-t1, w1, w
print "times", n, time1, time2, time3, time4
sys.stdout.flush()
def plot_hist(hess):
import pylab as pl
pl.hist(np.log10(np.abs(hess.reshape(-1))))
pl.show()
if __name__ == "__main__":
from pygmin.systems import LJCluster
natoms = 30
system = LJCluster(natoms)
pot = system.get_potential()
coords = system.get_random_configuration()
xmin = system.get_random_minimized_configuration()[0]
e, g, h = pot.getEnergyGradientHessian(xmin)
evals = get_eigvals(h)
print evals
quencher = system.get_minimizer(tol=10.)
coords = quencher(coords)[0]
e, g, h = pot.getEnergyGradientHessian(coords)
w1, v1 = get_smallest_eig(h)
print w1
w, v = get_smallest_eig_arpack(h)
print w
else:
faccept = float(ndiff_accept) / ndiff
if faccept > self.target_new_min_accept_prob:
driver.acceptTest.temperature *= self.Tfactor
else:
driver.acceptTest.temperature /= self.Tfactor
if self.verbose:
print " temperature is now %.4g ratio %.4g target %.4g" % (driver.acceptTest.temperature,
faccept, self.target_new_min_accept_prob)
if __name__ == "__main__":
import numpy as np
from pygmin.takestep import displace
from pygmin.systems import LJCluster
#from pygmin.takestep import adaptive
natoms = 38
sys = LJCluster(natoms=38)
# random initial coordinates
coords = sys.get_random_configuration()
takeStep = displace.RandomDisplacement( stepsize=0.4 )
tsAdaptive = AdaptiveStepsizeTemperature(takeStep, interval=300, verbose=True)
db = sys.create_database()
opt = sys.get_basinhopping(database=db, takestep=tsAdaptive, coords=coords)
opt.printfrq = 50
opt.run(5000)
""" examples of how to do various things using the system class. I will use the Lennard-Jones system as an example """ import logging from pygmin.systems import LJCluster from pygmin.utils.disconnectivity_graph import DisconnectivityGraph, database2graph # initialize the system class natoms = 13 system = LJCluster(natoms) # make a random configuration coords = system.get_random_configuration() # compute the energy of that configuration potential = system.get_potential() energy = potential.getEnergy(coords) print "the energy of the random configuration is", energy # minimize that configuration quencher = system.get_minimizer() ret = quencher(coords) newcoords = ret[0] newenergy = ret[1] print "after quenching, the energy is", newenergy # create a database to store the minimum in db = system.create_database() # note: this creates a database in memory, if you want to save the results
return [range(self.ntypeA), range(self.ntypeA, self.natoms)]
if __name__ == '__main__':
unittest.main()
if __name__ == "__main__":
from pygmin.systems import LJCluster
natoms = 20
rho = .5
boxl = (float(natoms) / rho)**(1./3)
boxlengths = np.ones(3) * boxl
permlist = [range(natoms)]
measure = MeasurePeriodic(boxlengths, permlist)
system = LJCluster(natoms)
x1 = system.get_random_configuration()
x2 = x1.copy()
x2 = randomly_permute(x2, permlist)
exact_match = ExactMatchPeriodic(measure)
em = exact_match.are_exact(x1, x2)
print em
unittest.main()
def start():
wnd.start()
if __name__ == "__main__":
from OpenGL.GLUT import glutInit
import sys
import pylab as pl
app = QtGui.QApplication(sys.argv)
from pygmin.systems import LJCluster
pl.ion()
natoms = 13
system = LJCluster(natoms)
system.params.double_ended_connect.local_connect_params.NEBparams.iter_density = 5.
dbname = "lj%dtest.db" % (natoms, )
db = system.create_database(dbname)
#get some minima
if False:
bh = system.get_basinhopping(database=db)
bh.run(10)
minima = db.minima()
else:
x1, e1 = system.get_random_minimized_configuration()[:2]
x2, e2 = system.get_random_minimized_configuration()[:2]
min1 = db.addMinimum(e1, x1)
min2 = db.addMinimum(e2, x2)
minima = [min1, min2]
#########################################################################
return self.acceptstep, self.trial_coords, self.trial_energy
def printStep(self):
if self.stepnum % self.printfrq == 0:
if self.outstream != None:
self.outstream.write("Qu " + str(self.stepnum) + " E= " +
str(self.trial_energy) +
" quench_steps= " + str(self.funcalls) +
" RMS= " + str(self.rms) + " Markov E= " +
str(self.markovE_old) + " accepted= " +
str(self.acceptstep) + "\n")
def __getstate__(self):
ddict = self.__dict__.copy()
del ddict["outstream"]
del ddict["potential"]
return ddict #.items()
def __setstate__(self, dct):
self.__dict__.update(dct)
self.outstream = sys.stdout
if __name__ == "__main__":
from pygmin.systems import LJCluster
natoms = 13
sys = LJCluster(natoms)
bh = sys.get_basinhopping()
bh.run(100)
def setUp(self):
natoms = 6
self.system = LJCluster(natoms)
self.e1 = -12.7120622568
self.e2 = -12.302927529580728
class TestExactMatchPeriodicBLJ(TestExactMatchPeriodicLJ):
def get_permlist(self):
self.ntypeA = int(self.natoms * .8)
return [range(self.ntypeA), range(self.ntypeA, self.natoms)]
if __name__ == '__main__':
unittest.main()
if __name__ == "__main__":
from pygmin.systems import LJCluster
natoms = 20
rho = .5
boxl = (float(natoms) / rho)**(1. / 3)
boxlengths = np.ones(3) * boxl
permlist = [range(natoms)]
measure = MeasurePeriodic(boxlengths, permlist)
system = LJCluster(natoms)
x1 = system.get_random_configuration()
x2 = x1.copy()
x2 = randomly_permute(x2, permlist)
exact_match = ExactMatchPeriodic(measure)
em = exact_match.are_exact(x1, x2)
print em
unittest.main()
else:
faccept = float(ndiff_accept) / ndiff
if faccept > self.target_new_min_accept_prob:
driver.acceptTest.temperature *= self.Tfactor
else:
driver.acceptTest.temperature /= self.Tfactor
if self.verbose:
print " temperature is now %.4g ratio %.4g target %.4g" % (driver.acceptTest.temperature,
faccept, self.target_new_min_accept_prob)
if __name__ == "__main__":
import numpy as np
from pygmin.takestep import displace
from pygmin.systems import LJCluster
#from pygmin.takestep import adaptive
natoms = 38
sys = LJCluster(natoms=38)
# random initial coordinates
coords = sys.get_random_configuration()
takeStep = displace.RandomDisplacement( stepsize=0.4 )
tsAdaptive = AdaptiveStepsizeTemperature(takeStep, interval=300, verbose=True)
db = sys.create_database()
opt = sys.get_basinhopping(database=db, takestep=tsAdaptive, coords=coords)
opt.printfrq = 50
opt.run(5000)
self.nsteps = nsteps
self.mcstep = RandomDisplacement(stepsize=stepsize)
def takeStep(self, coords, **kwargs):
#make a new monte carlo class
mc = MonteCarlo(coords, self.potential, self.mcstep,
temperature = self.T, outstream=None)
mc.run( self.nsteps )
coords[:] = mc.coords[:]
def updateStep(self, acc, **kwargs):
pass
natoms = 12
niter = 100
system = LJCluster(natoms)
db = system.create_database()
# create takestep routine manually
potential = system.get_potential()
step = TakeStepMonteCarlo(potential)
bh = system.get_basinhopping(database=db, takestep=step)
bh.run(niter)
print "the lowest energy found after", niter, " basinhopping steps is", db.minima()[0].energy
print ""
""" Example 4: modify the parameters of the adaptive stepsize note that the system class uses adaptive stepsize by default, so the previous examples also use adaptive stepsize """ from pygmin.systems import LJCluster from pygmin.takestep import RandomDisplacement, AdaptiveStepsizeTemperature natoms = 12 niter = 100 system = LJCluster(natoms) db = system.create_database() # create takestep routine manually step = RandomDisplacement(stepsize=0.3) # wrap it in the class which will adaptively improve the stepsize wrapped_step = AdaptiveStepsizeTemperature(step, interval=30) bh = system.get_basinhopping(database=db, takestep=wrapped_step) bh.run(niter) print "the lowest energy found after", niter, " basinhopping steps is", db.minima()[0].energy print ""