def test_cpp_align(self):
x1 = np.array([random_aa() for _ in range(2*self.nrigid)]).ravel()
x2 = np.array([random_aa() for _ in range(2*self.nrigid)]).ravel()
x1_cpp = x1.copy()
x2_cpp = x2.copy()
x1_python = x1.copy()
x2_python = x2.copy()
ret = self.measure._align_pythonic(x1_python, x2_python)
self.assertIsNone(ret)
ret = self.measure.align(x1_cpp, x2_cpp)
self.assertIsNone(ret)
assert_arrays_almost_equal(self, x1_python, x1)
assert_arrays_almost_equal(self, x1_cpp, x1)
# assert that the center of mass coordinates didn't change
assert_arrays_almost_equal(self, x2_python[:3*self.nrigid], x2[:3*self.nrigid])
assert_arrays_almost_equal(self, x2_cpp[:3*self.nrigid], x2[:3*self.nrigid])
# assert that x2 actually changed
max_change = np.max(np.abs(x2_cpp - x2))
self.assertGreater(max_change, 1e-3)
assert_arrays_almost_equal(self, x2_python, x2_cpp)
def test_cpp_align(self):
x1 = np.array([random_aa() for _ in range(2 * self.nrigid)]).ravel()
x2 = np.array([random_aa() for _ in range(2 * self.nrigid)]).ravel()
x1_cpp = x1.copy()
x2_cpp = x2.copy()
x1_python = x1.copy()
x2_python = x2.copy()
ret = self.measure._align_pythonic(x1_python, x2_python)
self.assertIsNone(ret)
ret = self.measure.align(x1_cpp, x2_cpp)
self.assertIsNone(ret)
assert_arrays_almost_equal(self, x1_python, x1)
assert_arrays_almost_equal(self, x1_cpp, x1)
# assert that the center of mass coordinates didn't change
assert_arrays_almost_equal(self, x2_python[:3 * self.nrigid],
x2[:3 * self.nrigid])
assert_arrays_almost_equal(self, x2_cpp[:3 * self.nrigid],
x2[:3 * self.nrigid])
# assert that x2 actually changed
max_change = np.max(np.abs(x2_cpp - x2))
self.assertGreater(max_change, 1e-3)
assert_arrays_almost_equal(self, x2_python, x2_cpp)
def test_distpot():
#define two structures
natoms = 12
X1 = np.random.uniform(-1,1,[natoms*3])*(float(natoms))**(1./3)
X2 = np.random.uniform(-1,1,[natoms*3])*(float(natoms))**(1./3)
#make X2 a rotation of X1
print "testing with", natoms, "atoms, with X2 a rotated and permuted isomer of X1"
aa = rot.random_aa()
rot_mx = rot.aa2mx( aa )
for j in range(natoms):
i = 3*j
X2[i:i+3] = np.dot( rot_mx, X1[i:i+3] )
#import random, mindistutils
#perm = range(natoms)
#random.shuffle( perm )
#print perm
#X2 = mindistutils.permuteArray( X2, perm)
pot = MinPermDistPotential(X1, X2, L = .2)
aa = rot.random_aa()
e = pot.getEnergy(aa)
print "energy", e
de, dg = pot.getEnergyGradient(aa)
print "energy from gradient", de, "diff", e-de
den, dgn = pot.getEnergyGradientNumerical(aa)
maxgrad= np.max( np.abs( dg ) )
maxdiff = np.max( np.abs( dg - dgn ) )
print "maximum gradient", maxgrad
print "max difference in analytical vs numerical gradient", maxdiff
def testBLJ_isomer(self):
"""
test with BLJ potential. We have two classes of permutable atoms
test case where X2 is an isomer of X1.
"""
import pele.utils.rotations as rot
X1i = np.copy(self.X1)
X1 = np.copy(self.X1)
X2 = np.copy(X1)
#rotate X2 randomly
aa = rot.random_aa()
rot_mx = rot.aa2mx( aa )
for j in range(self.natoms):
i = 3*j
X2[i:i+3] = np.dot( rot_mx, X1[i:i+3] )
#permute X2
import random, copy
from pele.mindist.permutational_alignment import permuteArray
for atomlist in self.permlist:
perm = copy.copy(atomlist)
random.shuffle( perm )
X2 = permuteArray( X2, perm)
X2i = np.copy(X2)
#distreturned, X1, X2 = self.runtest(X1, X2)
distreturned, X1, X2 = self.runtest(X1, X2, MinPermDistCluster(measure=MeasureAtomicCluster(permlist=self.permlist)))
#it's an isomer, so the distance should be zero
self.assertTrue( abs(distreturned) < 1e-14, "didn't find isomer: dist = %g" % distreturned)
def get_random_coordinates(self):
coords = np.zeros([self.nmol*2, 3])
coords[:self.nmol,:] = np.random.uniform(-1,1,[self.nmol,3]) * (self.nmol*3)**(-1./3) * 1.5
from pele.utils.rotations import random_aa
for i in range(self.nmol, self.nmol*2):
coords[i,:] = random_aa()
return coords.flatten()
def testBLJ_isomer(self):
"""
test with BLJ potential. We have two classes of permutable atoms
test case where X2 is an isomer of X1.
"""
import pele.utils.rotations as rot
X1i = np.copy(self.X1)
X1 = np.copy(self.X1)
X2 = np.copy(X1)
#rotate X2 randomly
aa = rot.random_aa()
rot_mx = rot.aa2mx( aa )
for j in range(self.natoms):
i = 3*j
X2[i:i+3] = np.dot( rot_mx, X1[i:i+3] )
#permute X2
import random, copy
from pele.mindist.permutational_alignment import permuteArray
for atomlist in self.permlist:
perm = copy.copy(atomlist)
random.shuffle( perm )
X2 = permuteArray( X2, perm)
X2i = np.copy(X2)
#distreturned, X1, X2 = self.runtest(X1, X2)
distreturned, X1, X2 = self.runtest(X1, X2, MinPermDistCluster(measure=MeasureAtomicCluster(permlist=self.permlist)))
#it's an isomer, so the distance should be zero
self.assertTrue( abs(distreturned) < 1e-14, "didn't find isomer: dist = %g" % distreturned)
def test_cpp_rotate(self):
x0 = np.array([random_aa() for _ in range(2 * self.nrigid)]).ravel()
aa = random_aa()
mx = aa2mx(aa)
x0_rotated = x0.copy()
self.transform.rotate(x0_rotated, mx)
x0_rotated_python = x0.copy()
self.transform._rotate_python(x0_rotated_python, mx)
assert_arrays_almost_equal(self, x0_rotated, x0_rotated_python)
mx_reverse = aa2mx(-aa)
self.transform.rotate(x0_rotated, mx_reverse)
assert_arrays_almost_equal(self, x0, x0_rotated)
def randomCoords(nmol):
coords = np.zeros(2 * 3 * nmol, np.float64)
coords[0 : 3 * nmol] = np.random.uniform(-1, 1, [nmol * 3]) * 1.3 * (3 * nmol) ** (1.0 / 3)
for i in range(nmol):
k = 3 * nmol + 3 * i
coords[k : k + 3] = rot.random_aa()
return coords
def test_cpp_rotate(self):
x0 = np.array([random_aa() for _ in range(2*self.nrigid)]).ravel()
aa = random_aa()
mx = aa2mx(aa)
x0_rotated = x0.copy()
self.transform.rotate(x0_rotated, mx)
x0_rotated_python = x0.copy()
self.transform._rotate_python(x0_rotated_python, mx)
assert_arrays_almost_equal(self, x0_rotated, x0_rotated_python)
mx_reverse = aa2mx(-aa)
self.transform.rotate(x0_rotated, mx_reverse)
assert_arrays_almost_equal(self, x0, x0_rotated)
def get_random_configuration(self):
coords = 5. * np.random.uniform(-1, 1,
6 * self.aatopology.get_nrigid())
ca = self.aasystem.coords_adapter(coords)
for p in ca.rotRigid:
p[:] = rotations.random_aa()
return coords
def test(): # pragma: no cover
from math import sin, cos, pi
from copy import deepcopy
water = RigidFragment()
rho = 0.9572
theta = 104.52/180.0*pi
water.add_atom("O", np.array([0., -1., 0.]), 1.)
water.add_atom("O", np.array([0., 1., 0.]), 1.)
#water.add_atom("H", rho*np.array([0.0, sin(0.5*theta), cos(0.5*theta)]), 1.)
#water.add_atom("H", rho*np.array([0.0, -sin(0.5*theta), cos(0.5*theta)]), 1.)
water.finalize_setup()
# define the whole water system
system = RBTopology()
nrigid = 1
system.add_sites([deepcopy(water) for i in xrange(nrigid)])
from pele.utils import rotations
rbcoords=np.zeros(6)
rbcoords[3:]= rotations.random_aa()
coords = system.to_atomistic(rbcoords)
print "rb coords\n", rbcoords
print "coords\n", coords
grad = (np.random.random(coords.shape) -0.5)
v = coords[1] - coords[0]
v/=np.linalg.norm(v)
grad[0] -= np.dot(grad[0], v)*v
grad[1] -= np.dot(grad[1], v)*v
grad -= np.average(grad, axis=0)
grad /= np.linalg.norm(grad)
print "torque", np.linalg.norm(np.cross(grad, v))
rbgrad = system.transform_gradient(rbcoords, grad)
p = rbcoords[3:]
x = rbcoords[0:3]
gp = rbgrad[3:]
gx = rbgrad[:3]
R, R1, R2, R3 = rotations.rot_mat_derivatives(p)
print "test1", np.linalg.norm(R1*gp[0])
print "test2", np.linalg.norm(R2*gp[1])
print "test3", np.linalg.norm(R3*gp[2])
print "test4", np.linalg.norm(R1*gp[0]) + np.linalg.norm(R2*gp[1]) + np.linalg.norm(R3*gp[2])
dR = R1*gp[0] + R2*gp[1] + R3*gp[2]
print "test", np.linalg.norm(R1*gp[0] + R2*gp[1] + R3*gp[2])
print np.trace(np.dot(dR, dR.transpose()))
G = water.metric_tensor_aa(p)
print np.dot(p, np.dot(G, p))
exit()
gnew = system.redistribute_forces(rbcoords, rbgrad)
print gnew
print system.transform_grad(rbcoords, gnew)
def __call__(self, coords1, coords2):
'''
Parameters
----------
coords1, coords2 : np.array
the structures to align. X2 will be aligned with X1, both
the center of masses will be shifted to the origin
Returns
-------
a tripple of (dist, coords1, coords2). coords1 are the unchanged coords1
and coords2 are brought in best alignment with coords2
'''
# we don't want to change the given coordinates
check_inversion = False
coords1 = coords1.copy()
coords2 = coords2.copy()
x1 = np.copy(coords1)
x2 = np.copy(coords2)
com1 = self.measure.get_com(x1)
self.transform.translate(x1, -com1)
com2 = self.measure.get_com(x2)
self.transform.translate(x2, -com2)
self.com_shift = com1
self.mxbest = np.identity(3)
self.distbest = self.measure.get_dist(x1, x2)
self.x2_best = x2.copy()
if self.distbest < self.tol:
dist, x2 = self.finalize_best_match(coords1)
return self.distbest, coords1, x2
for rot, invert in self._standard_alignments(x1, x2):
self.check_match(x1, x2, rot, invert)
if self.distbest < self.tol:
dist, x2 = self.finalize_best_match(coords1)
return dist, coords1, x2
# if we didn't find a perfect match here, try random rotations to optimize the match
for i in range(self.niter):
rot = rotations.aa2mx(rotations.random_aa())
self.check_match(x1, x2, rot, False)
if(self.transform.can_invert()):
self.check_match(x1, x2, rot, True)
# self.transform.rotate(X2, mxbest)
# dist, perm = self.measure.find_permutation(X1, X2)
# X2 = self.transform.permute(X2, perm)
# tmp, mx = self.measure.find_rotation(X1.copy(), X2.copy())
# self.transform.rotate(X2, mx)
# TODO: should we do an additional sanity check for permutation / rotation?
dist, x2 = self.finalize_best_match(coords1)
return dist, coords1, x2
def get_random_configuration(self):
# js850> this is a bit sketchy because nrigid might not be defined here.
# probably we can get the number of molecules some other way.
coords = 10.*np.random.random(6*self.nrigid)
ca = self.aasystem.coords_adapter(coords)
for p in ca.rotRigid:
p[:] = rotations.random_aa()
return coords
def get_random_configuration(self):
# js850> this is a bit sketchy because nrigid might not be defined here.
# probably we can get the number of molecules some other way.
coords = 10.*np.random.random(6*self.nrigid)
ca = self.aasystem.coords_adapter(coords)
for p in ca.rotRigid:
p[:] = rotations.random_aa()
return coords
def random_coords(nmol, nsites = None):
if nsites == None: nsites = nmol
coords = np.zeros(2*3*nmol)
coords[0:nmol*3] = np.random.uniform(-1,1,[nmol*3]) * 1.3*(nsites)**(1./3)
for i in range(nmol):
k = nmol*3 + 3*i
coords[k : k + 3] = rot.random_aa()
return coords
def takeStep(self, coords, **kwargs):
# easy access to coordinates
ca = CoordsAdapter(nrigid=coords.size / 6, coords=coords)
# random displacement for positions
ca.posRigid[:] = 2. * self.radius * (np.random.random(ca.posRigid.shape) - 0.5)
# random rotation for angle-axis vectors
for rot in ca.rotRigid:
rot[:] = rotations.random_aa()
def test_align_exact(self):
x1 = np.array([random_aa() for _ in range(2*self.nrigid)]).ravel()
x2 = x1.copy()
tet = create_tetrahedron()
mx = tet.symmetries[2].copy()
p = x2[-3:].copy()
x2[-3:] = rotations.rotate_aa(rotations.mx2aa(mx), p)
self.measure._align_pythonic(x1, x2)
assert_arrays_almost_equal(self, x1, x2)
def test_align_exact(self):
x1 = np.array([random_aa() for _ in range(2 * self.nrigid)]).ravel()
x2 = x1.copy()
tet = create_tetrahedron()
mx = tet.symmetries[2].copy()
p = x2[-3:].copy()
x2[-3:] = rotations.rotate_aa(rotations.mx2aa(mx), p)
self.measure._align_pythonic(x1, x2)
assert_arrays_almost_equal(self, x1, x2)
def takeStep(self, coords, **kwargs):
# easy access to coordinates
ca = CoordsAdapter(nrigid=old_div(coords.size, 6), coords=coords)
# random displacement for positions
#ca.posRigid[:] = 2.*self.radius*(np.random.random(ca.posRigid.shape)-0.5)
# random rotation for angle-axis vectors
for rot in ca.rotRigid:
rot[:] = rotations.random_aa()
def align_structures(self, coords1, coords2):
"""
Parameters
----------
coords1, coords2 : np.array
the structures to align. X2 will be aligned with X1, both
the center of masses will be shifted to the origin
Returns
-------
a triple of (dist, coords1, coords2). coords1 are the unchanged coords1
and coords2 are brought in best alignment with coords2
"""
# we don't want to change the given coordinates
coords1 = coords1.copy()
coords2 = coords2.copy()
x1 = np.copy(coords1)
x2 = np.copy(coords2)
com1 = self.measure.get_com(x1)
self.transform.translate(x1, -com1)
com2 = self.measure.get_com(x2)
self.transform.translate(x2, -com2)
self.com_shift = com1
self.mxbest = np.identity(3)
self.distbest = self.measure.get_dist(x1, x2)
self.x2_best = x2.copy()
# sn402: The unlikely event that the structures are already nearly perfectly aligned.
if self.distbest < self.tol:
dist, x2 = self.finalize_best_match(coords1)
return self.distbest, coords1, x2
for rot, invert in self._standard_alignments(x1, x2):
self.check_match(x1, x2, rot, invert)
if self.distbest < self.tol:
dist, x2 = self.finalize_best_match(coords1)
return dist, coords1, x2
# if we didn't find a perfect match here, try random rotations to optimize the match
for i in range(self.niter):
rot = rotations.aa2mx(rotations.random_aa())
self.check_match(x1, x2, rot, False)
if self.transform.can_invert():
self.check_match(x1, x2, rot, True)
# TODO: should we do an additional sanity check for permutation / rotation?
dist, x2 = self.finalize_best_match(coords1)
return dist, coords1, x2
def align_structures(self, coords1, coords2):
"""
Parameters
----------
coords1, coords2 : np.array
the structures to align. X2 will be aligned with X1, both
the center of masses will be shifted to the origin
Returns
-------
a triple of (dist, coords1, coords2). coords1 are the unchanged coords1
and coords2 are brought in best alignment with coords2
"""
# we don't want to change the given coordinates
coords1 = coords1.copy()
coords2 = coords2.copy()
x1 = np.copy(coords1)
x2 = np.copy(coords2)
com1 = self.measure.get_com(x1)
self.transform.translate(x1, -com1)
com2 = self.measure.get_com(x2)
self.transform.translate(x2, -com2)
self.com_shift = com1
self.mxbest = np.identity(3)
self.distbest = self.measure.get_dist(x1, x2)
self.x2_best = x2.copy()
# sn402: The unlikely event that the structures are already nearly perfectly aligned.
if self.distbest < self.tol:
dist, x2 = self.finalize_best_match(coords1)
return self.distbest, coords1, x2
for rot, invert in self._standard_alignments(x1, x2):
self.check_match(x1, x2, rot, invert)
if self.distbest < self.tol:
dist, x2 = self.finalize_best_match(coords1)
return dist, coords1, x2
# if we didn't find a perfect match here, try random rotations to optimize the match
for i in range(self.niter):
rot = rotations.aa2mx(rotations.random_aa())
self.check_match(x1, x2, rot, False)
if self.transform.can_invert():
self.check_match(x1, x2, rot, True)
# TODO: should we do an additional sanity check for permutation / rotation?
dist, x2 = self.finalize_best_match(coords1)
return dist, coords1, x2
def test(): # pragma: no cover
from math import pi
from copy import deepcopy
water = RigidFragment()
rho = 0.9572
theta = 104.52 / 180.0 * pi
water.add_atom("O", np.array([0., -1., 0.]), 1.)
water.add_atom("O", np.array([0., 1., 0.]), 1.)
# water.add_atom("H", rho*np.array([0.0, sin(0.5*theta), cos(0.5*theta)]), 1.)
#water.add_atom("H", rho*np.array([0.0, -sin(0.5*theta), cos(0.5*theta)]), 1.)
water.finalize_setup()
# define the whole water system
system = RBTopology()
nrigid = 1
system.add_sites([deepcopy(water) for i in xrange(nrigid)])
from pele.utils import rotations
rbcoords = np.zeros(6)
rbcoords[3:] = rotations.random_aa()
coords = system.to_atomistic(rbcoords)
print "rb coords\n", rbcoords
print "coords\n", coords
grad = (np.random.random(coords.shape) - 0.5)
v = coords[1] - coords[0]
v /= np.linalg.norm(v)
grad[0] -= np.dot(grad[0], v) * v
grad[1] -= np.dot(grad[1], v) * v
grad -= np.average(grad, axis=0)
grad /= np.linalg.norm(grad)
print "torque", np.linalg.norm(np.cross(grad, v))
rbgrad = system.transform_gradient(rbcoords, grad)
p = rbcoords[3:]
x = rbcoords[0:3]
gp = rbgrad[3:]
gx = rbgrad[:3]
R, R1, R2, R3 = rotations.rot_mat_derivatives(p)
print "test1", np.linalg.norm(R1 * gp[0])
print "test2", np.linalg.norm(R2 * gp[1])
print "test3", np.linalg.norm(R3 * gp[2])
print "test4", np.linalg.norm(R1 * gp[0]) + np.linalg.norm(
R2 * gp[1]) + np.linalg.norm(R3 * gp[2])
dR = R1 * gp[0] + R2 * gp[1] + R3 * gp[2]
print "test", np.linalg.norm(R1 * gp[0] + R2 * gp[1] + R3 * gp[2])
print np.trace(np.dot(dR, dR.transpose()))
def test_LJ(natoms = 12, **kwargs):
from pele.potentials.lj import LJ
from pele.optimize import mylbfgs
import pele.utils.rotations as rot
from pele.mindist.permutational_alignment import permuteArray
import random
quench = mylbfgs
lj = LJ()
X1 = np.random.uniform(-1,1,[natoms*3])*(float(natoms))**(1./3)
#quench X1
ret = quench( X1, lj)
X1 = ret.coords
X2 = np.random.uniform(-1,1,[natoms*3])*(float(natoms))**(1./3)
#make X2 a rotation of X1
print "testing with", natoms, "atoms, with X2 a rotated and permuted isomer of X1"
aa = rot.random_aa()
rot_mx = rot.aa2mx( aa )
for j in range(natoms):
i = 3*j
X2[i:i+3] = np.dot( rot_mx, X1[i:i+3] )
perm = range(natoms)
random.shuffle( perm )
print perm
X2 = permuteArray( X2, perm)
#X1 = np.array( [ 0., 0., 0., 1., 0., 0., 0., 0., 1.,] )
#X2 = np.array( [ 0., 0., 0., 1., 0., 0., 0., 1., 0.,] )
import copy
X1i = copy.copy(X1)
X2i = copy.copy(X2)
print "******************************"
print "testing normal LJ ISOMER"
print "******************************"
test(X1, X2, lj, **kwargs)
print "******************************"
print "testing normal LJ non isomer"
print "******************************"
X2 = np.random.uniform(-1,1,[natoms*3])*(float(natoms))**(1./3)
ret = quench( X2, lj)
X2 = ret.coords
Y = X1.reshape([-1,3])
Y+=np.random.random(3)
X1[:] = Y.flatten()
test(X1, X2, lj, **kwargs)
distinit = np.linalg.norm(X1-X2)
print "distinit", distinit
def test_LJ(natoms=12, **kwargs): # pragma: no cover
from pele.potentials.lj import LJ
from pele.optimize import mylbfgs
import pele.utils.rotations as rot
from pele.mindist.permutational_alignment import permuteArray
import random
quench = mylbfgs
lj = LJ()
X1 = np.random.uniform(-1, 1, [natoms * 3]) * (float(natoms))**(1. / 3)
# quench X1
ret = quench(X1, lj)
X1 = ret.coords
X2 = np.random.uniform(-1, 1, [natoms * 3]) * (float(natoms))**(1. / 3)
# make X2 a rotation of X1
print("testing with", natoms,
"atoms, with X2 a rotated and permuted isomer of X1")
aa = rot.random_aa()
rot_mx = rot.aa2mx(aa)
for j in range(natoms):
i = 3 * j
X2[i:i + 3] = np.dot(rot_mx, X1[i:i + 3])
perm = list(range(natoms))
random.shuffle(perm)
print(perm)
X2 = permuteArray(X2, perm)
import copy
X1i = copy.copy(X1)
X2i = copy.copy(X2)
print("******************************")
print("testing normal LJ ISOMER")
print("******************************")
test(X1, X2, lj, **kwargs)
print("******************************")
print("testing normal LJ non isomer")
print("******************************")
X2 = np.random.uniform(-1, 1, [natoms * 3]) * (float(natoms))**(1. / 3)
ret = quench(X2, lj)
X2 = ret.coords
Y = X1.reshape([-1, 3])
Y += np.random.random(3)
X1[:] = Y.flatten()
test(X1, X2, lj, **kwargs)
distinit = np.linalg.norm(X1 - X2)
print("distinit", distinit)
def test_LJ(natoms = 12, **kwargs):
from pele.potentials.lj import LJ
import pele.defaults
import pele.utils.rotations as rot
from pele.mindist.permutational_alignment import permuteArray
import random
quench = pele.defaults.quenchRoutine
lj = LJ()
X1 = np.random.uniform(-1,1,[natoms*3])*(float(natoms))**(1./3)
#quench X1
ret = quench( X1, lj.getEnergyGradient)
X1 = ret[0]
X2 = np.random.uniform(-1,1,[natoms*3])*(float(natoms))**(1./3)
#make X2 a rotation of X1
print "testing with", natoms, "atoms, with X2 a rotated and permuted isomer of X1"
aa = rot.random_aa()
rot_mx = rot.aa2mx( aa )
for j in range(natoms):
i = 3*j
X2[i:i+3] = np.dot( rot_mx, X1[i:i+3] )
perm = range(natoms)
random.shuffle( perm )
print perm
X2 = permuteArray( X2, perm)
#X1 = np.array( [ 0., 0., 0., 1., 0., 0., 0., 0., 1.,] )
#X2 = np.array( [ 0., 0., 0., 1., 0., 0., 0., 1., 0.,] )
import copy
X1i = copy.copy(X1)
X2i = copy.copy(X2)
print "******************************"
print "testing normal LJ ISOMER"
print "******************************"
test(X1, X2, lj, **kwargs)
print "******************************"
print "testing normal LJ non isomer"
print "******************************"
X2 = np.random.uniform(-1,1,[natoms*3])*(float(natoms))**(1./3)
ret = quench( X2, lj.getEnergyGradient)
X2 = ret[0]
test(X1, X2, lj, **kwargs)
distinit = np.linalg.norm(X1-X2)
print "distinit", distinit
def takeStep(self, coords, **kwargs):
# easy access to coordinates
ca = CoordsAdapter(nrigid=coords.size / 6, coords=coords)
backbone = np.zeros(3)
# random rotation for angle-axis vectors
for pos, rot in zip(ca.posRigid, ca.rotRigid):
backbone += rotations.vec_random() * 0.7525
# choose a random rotation
rot[:] = rotations.random_aa()
# calcualte center of base from backgone
a1 = np.dot(rotations.aa2mx(rot), np.array([1., 0., 0.]))
pos[:] = backbone + 0.4 * a1
def takeStep(self, coords, **kwargs):
# easy access to coordinates
ca = CoordsAdapter(nrigid=old_div(coords.size, 6), coords=coords)
backbone = np.zeros(3)
# random rotation for angle-axis vectors
for pos, rot in zip(ca.posRigid, ca.rotRigid):
backbone += rotations.vec_random() * 0.7525
# choose a random rotation
rot[:] = rotations.random_aa()
# calcualte center of base from backgone
a1 = np.dot(rotations.aa2mx(rot), np.array([1., 0., 0.]))
pos[:] = backbone + 0.4 * a1
def translation_step(self, coords):
"""
take a random translational step.
note: this step is rotationally invariant, which is different than the normal take_step routine
note: this method also favors shorter steps than the normal take_step routine
"""
nmol = len(coords) / 2 / 3
stepsize = self.getTStep()
for j in range(nmol):
#get a random unit vector
#this is a dumb way to do it
v = rot.random_aa()
#make the step length random and uniform in [0,stepsize]
v *= self.RNG() * stepsize / np.linalg.norm(v)
#print "rand ", rand
coords[3*j : 3*j + 3] += v
def do(self, indices=None, stepsize=.8):
natoms = 4
x = np.array([rotations.random_aa() for _ in range(natoms)])
x0 = x.copy()
x = x.reshape(-1)
rotate(stepsize, x, indices=indices)
x = x.reshape(-1, 3)
rlist = [relative_angle(x[i], x0[i]) for i in range(natoms)]
for r in rlist:
self.assertLessEqual(r, stepsize)
if indices is not None:
for i, r in enumerate(rlist):
if i in indices:
self.assertGreater(r, 0)
else:
self.assertAlmostEqual(r, 0, places=16)
def do(self, indices=None, stepsize=.8):
natoms = 4
x = np.array([rotations.random_aa() for _ in xrange(natoms)])
x0 = x.copy()
x = x.reshape(-1)
rotate(stepsize, x, indices=indices)
x = x.reshape(-1,3)
rlist = [relative_angle(x[i], x0[i]) for i in xrange(natoms)]
for r in rlist:
self.assertLessEqual(r, stepsize)
if indices is not None:
for i, r in enumerate(rlist):
if i in indices:
self.assertGreater(r, 0)
else:
self.assertAlmostEqual(r, 0, places=16)
def test_rotation(self):
"""assert that the HSA energy is *not* invariant under rotation"""
pot = self.system.get_potential()
aa = rotations.random_aa()
rmat = rotations.aa2mx(aa)
from pele.mindist import TransformAtomicCluster
tform = TransformAtomicCluster(can_invert=True)
for m in self.database.minima():
x = m.coords.copy()
# randomly move the atoms by a small amount
x += np.random.uniform(-1e-3, 1e-3, x.shape)
ehsa1 = self.sampler.compute_energy(x, m, x0=m.coords)
ecalc = pot.getEnergy(x)
# now rotate by a random matrix
xnew = x.copy()
tform.rotate(xnew, rmat)
ehsa2 = self.sampler.compute_energy(xnew, m, x0=m.coords)
ecalc2 = pot.getEnergy(xnew)
self.assertAlmostEqual(ecalc, ecalc2, 5)
self.assertNotAlmostEqual(ehsa1, ehsa2, 1)
def test_rotation(self):
"""assert that the HSA energy is *not* invariant under rotation"""
pot = self.system.get_potential()
aa = rotations.random_aa()
rmat = rotations.aa2mx(aa)
from pele.mindist import TransformAtomicCluster
tform = TransformAtomicCluster(can_invert=True)
for m in self.database.minima():
x = m.coords.copy()
# randomly move the atoms by a small amount
x += np.random.uniform(-1e-3, 1e-3, x.shape)
ehsa1 = self.sampler.compute_energy(x, m, x0=m.coords)
ecalc = pot.getEnergy(x)
# now rotate by a random matrix
xnew = x.copy()
tform.rotate(xnew, rmat)
ehsa2 = self.sampler.compute_energy(xnew, m, x0=m.coords)
ecalc2 = pot.getEnergy(xnew)
self.assertAlmostEqual(ecalc, ecalc2, 5)
self.assertNotAlmostEqual(ehsa1, ehsa2, 1)
def _optimizePermRot(X1, X2, niter, permlist, verbose=False, use_quench=True):
if use_quench:
pot = MinPermDistPotential(X1, X2.copy(), permlist=permlist)
distbest = getDistxyz(X1, X2)
mxbest = np.identity(3)
X20 = X2.copy()
for i in range(niter):
#get and apply a random rotation
aa = random_aa()
if not use_quench:
mx = aa2mx(aa)
mxtot = mx
#print "X2.shape", X2.shape
else:
#optimize the rotation using a permutationally invariand distance metric
ret = defaults.quenchRoutine(aa, pot.getEnergyGradient, tol=0.01)
aa1 = ret[0]
mx1 = aa2mx(aa1)
mxtot = mx1
X2 = applyRotation(mxtot, X20)
#optimize the permutations
dist, X1, X2 = findBestPermutation(X1, X2, permlist)
if verbose:
print "dist", dist, "distbest", distbest
#print "X2.shape", X2.shape
#optimize the rotation
dist, Q2 = getAlignRotation(X1, X2)
# print "dist", dist, "Q2", Q2
mx2 = q2mx(Q2)
mxtot = np.dot(mx2, mxtot)
if dist < distbest:
distbest = dist
mxbest = mxtot
return distbest, mxbest
def test_takestep(nmol = 4):
#get an initial set of coordinates
import copy
nsites = nmol*3
comcoords = np.random.uniform(-1,1,[nmol*3]) * 1.3*(nsites)**(1./3)
aacoords = np.array( [copy.copy(rot.random_aa()) for i in range(nmol)] )
aacoords = aacoords.reshape(3*nmol)
coords = np.zeros(2*3*nmol, np.float64)
coords[0:3*nmol] = comcoords[:]
coords[3*nmol:2*3*nmol] = aacoords[:]
print "lencoords, len aacoords", len (coords), len(aacoords), len(comcoords)
takestep = RBTakeStep()
print coords
oldcoords = coords.copy()
takestep.translation_step(coords)
print coords
print coords - oldcoords
print ""
print "taking orientational step"
print ""
oldcoords = coords.copy()
takestep.orientational_step(coords)
print coords
print coords - oldcoords
print ""
print "taking one of each step"
print ""
oldcoords = coords.copy()
takestep.takeStep(coords)
takestep.takeStep(coords)
print coords
print coords - oldcoords
def test_aa2mx(self):
aa = random_aa()
mx1 = aa2mx(aa)
mx2 = rotations.aa2mx(aa)
self.arrays_equal(mx1, mx2)
def test_rotate_aa(self):
p1 = random_aa()
p2 = random_aa()
p3 = rotate_aa(p1, p2)
p4 = rotations.rotate_aa(p1, p2)
self.arrays_equal(p3, p4)
def test_aa2q(self):
aa = random_aa()
q1 = aa2q(aa)
q2 = rotations.aa2q(aa)
self.arrays_equal(q1, q2)
def test_aa2mx(self):
aa = random_aa()
mx1 = aa2mx(aa)
mx2 = rotations.aa2mx(aa)
self.arrays_equal(mx1, mx2)
def test_rotate_aa(self):
p1 = random_aa()
p2 = random_aa()
p3 = rotate_aa(p1, p2)
p4 = rotations.rotate_aa(p1, p2)
self.arrays_equal(p3, p4)
def test_aa2q(self):
aa = random_aa()
q1 = aa2q(aa)
q2 = rotations.aa2q(aa)
self.arrays_equal(q1, q2)
def get_random_configuration(self):
coords = 5.*np.random.random(6*self.nrigid)
ca = self.aasystem.coords_adapter(coords)
for p in ca.rotRigid:
p = rotations.random_aa()
return coords
def test_align_bad_input(self):
x1 = np.array([random_aa() for _ in range(2*self.nrigid)]).ravel()
x2 = list(x1)
with self.assertRaises(TypeError):
self.measure.align(x1, x2)
def test(): # pragma: no cover
natoms = 3
x = np.random.random([natoms, 3]) * 5
masses = [1., 1., 16.] # np.random.random(natoms)
print masses
x -= np.average(x, axis=0, weights=masses)
cog = np.average(x, axis=0)
S = np.zeros([3, 3])
for i in xrange(3):
for j in xrange(3):
S[i][j] = np.sum(x[:, i] * x[:, j])
site = AASiteType(M=natoms, S=S, W=natoms, cog=cog)
X1 = 10.1 * np.random.random(3)
X2 = 10.1 * np.random.random(3)
p1 = rotations.random_aa()
p2 = rotations.random_aa()
R1 = rotations.aa2mx(p1)
R2 = rotations.aa2mx(p2)
x1 = np.dot(R1, x.transpose()).transpose() + X1
x2 = np.dot(R2, x.transpose()).transpose() + X2
import _aadist
print "site representation:", np.sum((x1 - x2) ** 2)
print "distance function: ", site.distance_squared(X1, p1, X2, p2)
print "fortran function: ", _aadist.sitedist(X2 - X1, p1, p2, site.S, site.W, cog)
import time
t0 = time.time()
for i in xrange(1000):
site.distance_squared(X1, p1, X2, p2)
t1 = time.time()
print "time python", t1 - t0
for i in xrange(1000):
sitedist(X2 - X1, p1, p2, site.S, site.W, cog)
# _aadist.aadist(coords1, coords2, site.S, site.W, cog)
t2 = time.time()
print "time fortran", t2 - t1
# for i in xrange(1000/20):
# #_aadist.sitedist(X1, p1, X2, p2, site.S, site.W, cog)
# _aadist.aadist(coords1, coords2, site.S, site.W, cog)
t2 = time.time()
print "time fortran acc", t2 - t1
print site.distance_squared_grad(X1, p1, X2, p2)
g_M = np.zeros(3)
g_P = np.zeros(3)
for i in xrange(3):
eps = 1e-6
delta = np.zeros(3)
delta[i] = eps
g_M[i] = (site.distance_squared(X1 + delta, p1, X2, p2)
- site.distance_squared(X1, p1, X2, p2)) / eps
g_P[i] = (site.distance_squared(X1, p1 + delta, X2, p2)
- site.distance_squared(X1, p1, X2, p2)) / eps
print g_M, g_P
xx = site.distance_squared_grad(X1, p1, X2, p2)
print g_M / xx[0], g_P / xx[1]
print _aadist.sitedist_grad(X2 - X1, p1, p2, site.S, site.W, cog)
def rrot(self, x):
aa = rotations.random_aa()
mx = rotations.aa2mx(aa)
self.match.transform.rotate(x, mx)
def rrot(self, x):
aa = rotations.random_aa()
mx = rotations.aa2mx(aa)
self.match.transform.rotate(x, mx)
def test(): # pragma: no cover
natoms = 3
x = np.random.random([natoms, 3]) * 5
masses = [1., 1., 16.] # np.random.random(natoms)
print(masses)
x -= np.average(x, axis=0, weights=masses)
cog = np.average(x, axis=0)
S = np.zeros([3, 3])
for i in range(3):
for j in range(3):
S[i][j] = np.sum(x[:, i] * x[:, j])
site = AASiteType(M=natoms, S=S, W=natoms, cog=cog)
X1 = 10.1 * np.random.random(3)
X2 = 10.1 * np.random.random(3)
p1 = rotations.random_aa()
p2 = rotations.random_aa()
R1 = rotations.aa2mx(p1)
R2 = rotations.aa2mx(p2)
x1 = np.dot(R1, x.transpose()).transpose() + X1
x2 = np.dot(R2, x.transpose()).transpose() + X2
from . import _aadist
print("site representation:", np.sum((x1 - x2) ** 2))
print("distance function: ", site.distance_squared(X1, p1, X2, p2))
print("fortran function: ", _aadist.sitedist(X2 - X1, p1, p2, site.S, site.W, cog))
import time
t0 = time.time()
for i in range(1000):
site.distance_squared(X1, p1, X2, p2)
t1 = time.time()
print("time python", t1 - t0)
for i in range(1000):
sitedist(X2 - X1, p1, p2, site.S, site.W, cog)
# _aadist.aadist(coords1, coords2, site.S, site.W, cog)
t2 = time.time()
print("time fortran", t2 - t1)
# for i in xrange(1000/20):
# #_aadist.sitedist(X1, p1, X2, p2, site.S, site.W, cog)
# _aadist.aadist(coords1, coords2, site.S, site.W, cog)
t2 = time.time()
print("time fortran acc", t2 - t1)
print(site.distance_squared_grad(X1, p1, X2, p2))
g_M = np.zeros(3)
g_P = np.zeros(3)
for i in range(3):
eps = 1e-6
delta = np.zeros(3)
delta[i] = eps
g_M[i] = old_div((site.distance_squared(X1 + delta, p1, X2, p2)
- site.distance_squared(X1, p1, X2, p2)), eps)
g_P[i] = old_div((site.distance_squared(X1, p1 + delta, X2, p2)
- site.distance_squared(X1, p1, X2, p2)), eps)
print(g_M, g_P)
xx = site.distance_squared_grad(X1, p1, X2, p2)
print(old_div(g_M, xx[0]), old_div(g_P, xx[1]))
print(_aadist.sitedist_grad(X2 - X1, p1, p2, site.S, site.W, cog))
def random_rotation( aa):
aanew = rot.random_aa()
#print "aanew ", aanew
aa[:] = aanew[:]
def test_align_bad_input(self):
x1 = np.array([random_aa() for _ in range(2 * self.nrigid)]).ravel()
x2 = list(x1)
with self.assertRaises(TypeError):
self.measure.align(x1, x2)
from copy import deepcopy
water = RigidFragment()
rho = 0.9572
theta = 104.52/180.0*pi
water.add_atom("O", np.array([0., -1., 0.]), 1.)
water.add_atom("O", np.array([0., 1., 0.]), 1.)
#water.add_atom("H", rho*np.array([0.0, sin(0.5*theta), cos(0.5*theta)]), 1.)
#water.add_atom("H", rho*np.array([0.0, -sin(0.5*theta), cos(0.5*theta)]), 1.)
water.finalize_setup()
# define the whole water system
system = RBTopology()
nrigid = 1
system.add_sites([deepcopy(water) for i in xrange(nrigid)])
from pele.utils import rotations
rbcoords=np.zeros(6)
rbcoords[3:]= rotations.random_aa()
coords = system.to_atomistic(rbcoords)
print "rb coords\n", rbcoords
print "coords\n", coords
grad = (np.random.random(coords.shape) -0.5)
v = coords[1] - coords[0]
v/=np.linalg.norm(v)
grad[0] -= np.dot(grad[0], v)*v
grad[1] -= np.dot(grad[1], v)*v
grad -= np.average(grad, axis=0)
grad /= np.linalg.norm(grad)