def test_check_anagrad_diag_prec(self):
x_init = np.zeros(2, float)
prec_fun = DiagonalPreconditioner(fun, 20, 1e-2)
prec_fun.scales = np.random.uniform(1, 2, 2)
check_anagrad(prec_fun, x_init, 1e-5, 1e-4)
dxs = random_unit((100, len(x_init))) * 1e-4
check_delta(prec_fun, x_init, dxs)
def test_superpose(self):
# create a few test sets with random data points, including degenerate
# situations. (e.g. one point, two points, linear points)
references = [ # a list of 2-tuples: (points, degenerate)
(numpy.random.normal(0, 5, (n, 3)), False) for n in xrange(4, 40)
] + [
#(numpy.array([[0,0,1]], float), True),
#(numpy.array([[0,0,0],[0,0,1]], float), True),
#(numpy.array([[0,0,0],[0,0,1],[0,0,2]], float), True),
#(numpy.array([[0,0,0],[0,0,1],[0,0,2],[0,0,4]], float), True),
#(numpy.random.normal(0, 5, (3, 3)), True)
]
# Do a random transformation on the points
randomized = []
for points, degenerate in references:
#points[:] -= points.mean(axis=0)
axis = random_unit(3)
angle = numpy.random.uniform(0, numpy.pi * 2)
transformation = Complete()
transformation.set_rotation_properties(angle, axis, False)
transformation.t[:] = numpy.random.normal(0, 5, 3)
randomized.append(
(numpy.array([transformation.vector_apply(p)
for p in points]), transformation))
for (ref_points, degenerate), (tr_points,
transf) in zip(references, randomized):
check_transf = superpose(ref_points, tr_points)
# check whether the rotation matrix is orthogonal
self.assertArraysAlmostEqual(
numpy.dot(check_transf.r, check_transf.r.transpose()),
numpy.identity(3, float), 1e-5)
# first check whether check_transf brings the tr_points back to the ref_points
check_points = numpy.dot(
tr_points, check_transf.r.transpose()) + check_transf.t
self.assertArraysAlmostEqual(ref_points,
check_points,
1e-5,
doabs=True)
if not degenerate:
# if the set of points is not degenerate, check whether transf and check_transf
# are each other inverses
tmp = Complete()
tmp.apply_before(transf)
tmp.apply_before(check_transf)
self.assertArraysAlmostEqual(
numpy.dot(transf.r, check_transf.r),
numpy.identity(3, float), 1e-5)
self.assertArrayAlmostZero(tmp.t, 1e-5)
# Add some distortion to the transformed points
randomized = []
for tr_points, transf in randomized:
tr_points[:] += numpy.random.normal(0, 1.0, len(tr_points))
# Do a blind test
for (ref_points, degenerate), (tr_points,
transf) in zip(references, randomized):
superpose(ref_points, tr_points)
def test_radius_ranges(self):
for i in xrange(20):
uc = self.get_random_uc()
radius = numpy.random.uniform(1,5)
ranges = uc.get_radius_ranges(radius)
for j in xrange(100):
c0 = uc.to_cartesian(numpy.random.uniform(-0.5, 0.5, 3))
c1 = c0 + radius*random_unit()
f1 = uc.to_fractional(c1)
self.assert_((abs(f1) <= ranges+0.5).all(), "f1=%s ranges=%s" % (f1, ranges))
def test_check_anagrad_full_prec(self):
raise SkipTest
x_init = np.zeros(2, float)
prec_fun = FullPreconditioner(fun, 20, 1e-2)
A = np.random.normal(0, 1, (2, 2))
A = 0.5 * (A + A.transpose())
evals, evecs = np.linalg.eigh(A)
prec_fun.scales = abs(evals) + 1.0
prec_fun.rotation = evecs
check_anagrad(prec_fun, x_init, 1e-5, 1e-4)
dxs = random_unit((100, len(x_init))) * 1e-4
check_delta(prec_fun, x_init, dxs)
def test_superpose(self):
# create a few test sets with random data points, including degenerate
# situations. (e.g. one point, two points, linear points)
references = [ # a list of 2-tuples: (points, degenerate)
(numpy.random.normal(0, 5, (n, 3)), False) for n in xrange(4, 40)
] + [
#(numpy.array([[0,0,1]], float), True),
#(numpy.array([[0,0,0],[0,0,1]], float), True),
#(numpy.array([[0,0,0],[0,0,1],[0,0,2]], float), True),
#(numpy.array([[0,0,0],[0,0,1],[0,0,2],[0,0,4]], float), True),
#(numpy.random.normal(0, 5, (3, 3)), True)
]
# Do a random transformation on the points
randomized = []
for points, degenerate in references:
#points[:] -= points.mean(axis=0)
axis = random_unit(3)
angle = numpy.random.uniform(0, numpy.pi*2)
transformation = Complete()
transformation.set_rotation_properties(angle, axis, False)
transformation.t[:] = numpy.random.normal(0, 5, 3)
randomized.append((
numpy.array([transformation.vector_apply(p) for p in points]),
transformation
))
for (ref_points, degenerate), (tr_points, transf) in zip(references, randomized):
check_transf = superpose(ref_points, tr_points)
# check whether the rotation matrix is orthogonal
self.assertArraysAlmostEqual(numpy.dot(check_transf.r, check_transf.r.transpose()), numpy.identity(3, float), 1e-5)
# first check whether check_transf brings the tr_points back to the ref_points
check_points = numpy.dot(tr_points, check_transf.r.transpose()) + check_transf.t
self.assertArraysAlmostEqual(ref_points, check_points, 1e-5, doabs=True)
if not degenerate:
# if the set of points is not degenerate, check whether transf and check_transf
# are each other inverses
tmp = Complete()
tmp.apply_before(transf)
tmp.apply_before(check_transf)
self.assertArraysAlmostEqual(numpy.dot(transf.r, check_transf.r), numpy.identity(3, float), 1e-5)
self.assertArrayAlmostZero(tmp.t, 1e-5)
# Add some distortion to the transformed points
randomized = []
for tr_points, transf in randomized:
tr_points[:] += numpy.random.normal(0, 1.0, len(tr_points))
# Do a blind test
for (ref_points, degenerate), (tr_points, transf) in zip(references, randomized):
superpose(ref_points, tr_points)
def random_rotation():
from molmod.vectors import random_unit, trivial_orthonormal
result = Rotation()
# first generate a random unit vector, the new x-axis
result.r[:,0] = random_unit(3)
x = result.r[:,0]
# generate a not so random y-axis and z-axis
y = trivial_orthonormal(x)
z = numpy.cross(x, y)
# rotate y,z with about the x-axis by a random angle
angle = numpy.random.uniform(0, 2*numpy.pi)
result.r[:,1] = numpy.cos(angle)*y - numpy.sin(angle)*z
result.r[:,2] = numpy.sin(angle)*y + numpy.cos(angle)*z
return result
def random(cls):
"""Return a random rotation"""
axis = random_unit()
angle = numpy.random.uniform(0, 2 * numpy.pi)
invert = bool(numpy.random.randint(0, 2))
return Rotation.from_properties(angle, axis, invert)
def random_dimer(molecule0, molecule1, thresholds, shoot_max):
"""Create a random dimer.
molecule0 and molecule1 are placed in one reference frame at random
relative positions. Interatomic distances are above the thresholds.
Initially a dimer is created where one interatomic distance approximates
the threshold value. Then the molecules are given an additional
separation in the range [0, shoot_max].
thresholds has the following format:
{frozenset([atom_number1, atom_number2]): distance}
"""
# apply a random rotation to molecule1
center = np.zeros(3, float)
angle = np.random.uniform(0, 2 * np.pi)
axis = random_unit()
rotation = Complete.about_axis(center, angle, axis)
cor1 = np.dot(molecule1.coordinates, rotation.r)
# select a random atom in each molecule
atom0 = np.random.randint(len(molecule0.numbers))
atom1 = np.random.randint(len(molecule1.numbers))
# define a translation of molecule1 that brings both atoms in overlap
delta = molecule0.coordinates[atom0] - cor1[atom1]
cor1 += delta
# define a random direction
direction = random_unit()
cor1 += 1 * direction
# move molecule1 along this direction until all intermolecular atomic
# distances are above the threshold values
threshold_mat = np.zeros((len(molecule0.numbers), len(molecule1.numbers)),
float)
distance_mat = np.zeros((len(molecule0.numbers), len(molecule1.numbers)),
float)
for i1, n1 in enumerate(molecule0.numbers):
for i2, n2 in enumerate(molecule1.numbers):
threshold = thresholds.get(frozenset([n1, n2]))
threshold_mat[i1, i2] = threshold**2
while True:
cor1 += 0.1 * direction
distance_mat[:] = 0
for i in 0, 1, 2:
distance_mat += np.subtract.outer(molecule0.coordinates[:, i],
cor1[:, i])**2
if (distance_mat > threshold_mat).all():
break
# translate over a random distance [0, shoot] along the same direction
# (if necessary repeat until no overlap is found)
while True:
cor1 += direction * np.random.uniform(0, shoot_max)
distance_mat[:] = 0
for i in 0, 1, 2:
distance_mat += np.subtract.outer(molecule0.coordinates[:, i],
cor1[:, i])**2
if (distance_mat > threshold_mat).all():
break
# done
dimer = Molecule(np.concatenate([molecule0.numbers, molecule1.numbers]),
np.concatenate([molecule0.coordinates, cor1]))
dimer.direction = direction
dimer.atom0 = atom0
dimer.atom1 = atom1
return dimer
def random_dimer(molecule0, molecule1, thresholds, shoot_max, max_tries=1000):
"""Create a random dimer.
molecule0 and molecule1 are placed in one reference frame at random relative
positions. Interatomic distances are above the thresholds. Initially a dimer
is created where one interatomic distance approximates the threshold value.
Then the molecules are given an additional separation in the range
[0,shoot_max].
thresholds has the following format:
{frozenset([atom_number1, atom_number2]): distance}
"""
# apply a random rotation to molecule1
center = numpy.zeros(3, float)
angle = numpy.random.uniform(0, 2*numpy.pi)
axis = random_unit(3)
rotation = rotation_around_center(center, angle, axis)
cor1 = numpy.dot(molecule1.coordinates, rotation.r)
# select a random atom in each molecule
atom0 = numpy.random.randint(len(molecule0.numbers))
atom1 = numpy.random.randint(len(molecule1.numbers))
# define a translation of molecule1 that brings both atoms in overlap
delta = molecule0.coordinates[atom0] - cor1[atom1]
cor1 += delta
# define a random direction
direction = random_unit(3)
cor1 += 1*direction
# move molecule1 along this direction until all intermolecular atomic
# distances are above the threshold values
threshold_mat = numpy.zeros((len(molecule0.numbers), len(molecule1.numbers)), float)
distance_mat = numpy.zeros((len(molecule0.numbers), len(molecule1.numbers)), float)
for i1, n1 in enumerate(molecule0.numbers):
for i2, n2 in enumerate(molecule1.numbers):
threshold = thresholds.get(frozenset([n1,n2]))
threshold_mat[i1,i2] = threshold**2
while True:
cor1 += 0.1*direction
distance_mat[:] = 0
for i in 0,1,2:
distance_mat += numpy.subtract.outer(molecule0.coordinates[:,i], cor1[:,i])**2
if (distance_mat > threshold_mat).all():
break
# translate over a random distance [0,shoot] along the same direction
# (if necessary repeat until no overlap is found)
while True:
cor1 += direction*numpy.random.uniform(0,shoot_max)
distance_mat[:] = 0
for i in 0,1,2:
distance_mat += numpy.subtract.outer(molecule0.coordinates[:,i], cor1[:,i])**2
if (distance_mat > threshold_mat).all():
break
# done
dimer = Molecule(
numpy.concatenate([molecule0.numbers, molecule1.numbers]),
numpy.concatenate([molecule0.coordinates, cor1])
)
dimer.direction = direction
dimer.atom0 = atom0
dimer.atom1 = atom1
return dimer
def random(cls):
"""Return a random rotation"""
axis = random_unit()
angle = numpy.random.uniform(0, 2 * numpy.pi)
invert = bool(numpy.random.randint(0, 2))
return Rotation.from_properties(angle, axis, invert)