/usr/lib/python2.7/dist-packages/dipy/core/tests/test_sphere.py is in python-dipy 0.10.1-1.
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import numpy as np
import numpy.testing as nt
import warnings
from ...utils.six.moves import xrange
from dipy.core.sphere import (Sphere, HemiSphere, unique_edges, unique_sets,
faces_from_sphere_vertices, HemiSphere,
disperse_charges, _get_forces,
unit_octahedron, unit_icosahedron,
hemi_icosahedron)
from dipy.core.subdivide_octahedron import create_unit_sphere
from dipy.core.geometry import cart2sphere, sphere2cart, vector_norm
from numpy.testing.decorators import skipif
try:
from scipy.spatial import Delaunay
except ImportError:
needs_delaunay = skipif(True, "Need scipy.spatial.Delaunay")
else:
needs_delaunay = skipif(False)
verts = unit_octahedron.vertices
edges = unit_octahedron.edges
oct_faces = unit_octahedron.faces
r, theta, phi = cart2sphere(*verts.T)
def test_sphere_construct_args():
nt.assert_raises(ValueError, Sphere)
nt.assert_raises(ValueError, Sphere, x=1, theta=1)
nt.assert_raises(ValueError, Sphere, xyz=1, theta=1)
nt.assert_raises(ValueError, Sphere, xyz=1, theta=1, phi=1)
def test_sphere_edges_faces():
nt.assert_raises(ValueError, Sphere, xyz=1, edges=1, faces=None)
Sphere(xyz=[0, 0, 1], faces=[0, 0, 0])
Sphere(xyz=[[0, 0, 1],
[1, 0, 0],
[0, 1, 0]],
edges=[[0, 1],
[1, 2],
[2, 0]],
faces=[0, 1, 2])
def test_sphere_not_unit():
with warnings.catch_warnings():
warnings.simplefilter('error')
nt.assert_raises(UserWarning, Sphere, xyz=[0, 0, 1.5])
def test_bad_edges_faces():
nt.assert_raises(ValueError, Sphere, xyz=[0, 0, 1.5], edges=[[1, 2]])
def test_sphere_construct():
s0 = Sphere(xyz=verts)
s1 = Sphere(theta=theta, phi=phi)
s2 = Sphere(*verts.T)
nt.assert_array_almost_equal(s0.theta, s1.theta)
nt.assert_array_almost_equal(s0.theta, s2.theta)
nt.assert_array_almost_equal(s0.theta, theta)
nt.assert_array_almost_equal(s0.phi, s1.phi)
nt.assert_array_almost_equal(s0.phi, s2.phi)
nt.assert_array_almost_equal(s0.phi, phi)
def array_to_set(a):
return set(frozenset(i) for i in a)
def test_unique_edges():
faces = np.array([[0, 1, 2],
[1, 2, 0]])
e = array_to_set([[1, 2],
[0, 1],
[0, 2]])
u = unique_edges(faces)
nt.assert_equal(e, array_to_set(u))
u, m = unique_edges(faces, return_mapping=True)
nt.assert_equal(e, array_to_set(u))
edges = [[[0, 1], [1, 2], [2, 0]],
[[1, 2], [2, 0], [0, 1]]]
nt.assert_equal(np.sort(u[m], -1), np.sort(edges, -1))
def test_unique_sets():
sets = np.array([[0, 1, 2],
[1, 2, 0],
[0, 2, 1],
[1, 2, 3]])
e = array_to_set([[0, 1, 2],
[1, 2, 3]])
# Run without inverse
u = unique_sets(sets)
nt.assert_equal(len(u), len(e))
nt.assert_equal(array_to_set(u), e)
# Run with inverse
u, m = unique_sets(sets, return_inverse=True)
nt.assert_equal(len(u), len(e))
nt.assert_equal(array_to_set(u), e)
nt.assert_equal(np.sort(u[m], -1), np.sort(sets, -1))
@needs_delaunay
def test_faces_from_sphere_vertices():
faces = faces_from_sphere_vertices(verts)
faces = array_to_set(faces)
expected = array_to_set(oct_faces)
nt.assert_equal(faces, expected)
def test_sphere_attrs():
s = Sphere(xyz=verts)
nt.assert_array_almost_equal(s.vertices, verts)
nt.assert_array_almost_equal(s.x, verts[:, 0])
nt.assert_array_almost_equal(s.y, verts[:, 1])
nt.assert_array_almost_equal(s.z, verts[:, 2])
@needs_delaunay
def test_edges_faces():
s = Sphere(xyz=verts)
faces = oct_faces
nt.assert_equal(array_to_set(s.faces), array_to_set(faces))
nt.assert_equal(array_to_set(s.edges), array_to_set(edges))
s = Sphere(xyz=verts, faces=[[0, 1, 2]])
nt.assert_equal(array_to_set(s.faces), array_to_set([[0, 1, 2]]))
nt.assert_equal(array_to_set(s.edges),
array_to_set([[0, 1], [1, 2], [0, 2]]))
s = Sphere(xyz=verts, faces=[[0, 1, 2]], edges=[[0, 1]])
nt.assert_equal(array_to_set(s.faces), array_to_set([[0, 1, 2]]))
nt.assert_equal(array_to_set(s.edges),
array_to_set([[0, 1]]))
@needs_delaunay
def test_sphere_subdivide():
sphere1 = unit_octahedron.subdivide(4)
sphere2 = Sphere(xyz=sphere1.vertices)
nt.assert_equal(sphere1.faces.shape, sphere2.faces.shape)
nt.assert_equal(array_to_set(sphere1.faces), array_to_set(sphere2.faces))
sphere1 = unit_icosahedron.subdivide(4)
sphere2 = Sphere(xyz=sphere1.vertices)
nt.assert_equal(sphere1.faces.shape, sphere2.faces.shape)
nt.assert_equal(array_to_set(sphere1.faces), array_to_set(sphere2.faces))
# It might be good to also test the vertices somehow if we can think of a
# good test for them.
def test_sphere_find_closest():
sphere1 = unit_octahedron.subdivide(4)
for ii in range(sphere1.vertices.shape[0]):
nt.assert_equal(sphere1.find_closest(sphere1.vertices[ii]), ii)
def test_hemisphere_find_closest():
hemisphere1 = hemi_icosahedron.subdivide(4)
for ii in range(hemisphere1.vertices.shape[0]):
nt.assert_equal(hemisphere1.find_closest(hemisphere1.vertices[ii]), ii)
nt.assert_equal(hemisphere1.find_closest(-hemisphere1.vertices[ii]), ii)
nt.assert_equal(hemisphere1.find_closest(hemisphere1.vertices[ii] * 2),
ii)
@needs_delaunay
def test_hemisphere_subdivide():
def flip(vertices):
x, y, z = vertices.T
f = (z < 0) | ((z == 0) & (y < 0)) | ((z == 0) & (y == 0) & (x < 0))
return 1 - 2*f[:, None]
decimals = 6
# Test HemiSphere.subdivide
# Create a hemisphere by dividing a hemi-icosahedron
hemi1 = HemiSphere.from_sphere(unit_icosahedron).subdivide(4)
vertices1 = np.round(hemi1.vertices, decimals)
vertices1 *= flip(vertices1)
order = np.lexsort(vertices1.T)
vertices1 = vertices1[order]
# Create a hemisphere from a subdivided sphere
sphere = unit_icosahedron.subdivide(4)
hemi2 = HemiSphere.from_sphere(sphere)
vertices2 = np.round(hemi2.vertices, decimals)
vertices2 *= flip(vertices2)
order = np.lexsort(vertices2.T)
vertices2 = vertices2[order]
# The two hemispheres should have the same vertices up to their order
nt.assert_array_equal(vertices1, vertices2)
# Create a hemisphere from vertices
hemi3 = HemiSphere(xyz=hemi1.vertices)
nt.assert_array_equal(hemi1.faces, hemi3.faces)
nt.assert_array_equal(hemi1.edges, hemi3.edges)
def test_hemisphere_constructor():
s0 = HemiSphere(xyz=verts)
s1 = HemiSphere(theta=theta, phi=phi)
s2 = HemiSphere(*verts.T)
uniq_verts = verts[::2].T
rU, thetaU, phiU = cart2sphere(*uniq_verts)
nt.assert_array_almost_equal(s0.theta, s1.theta)
nt.assert_array_almost_equal(s0.theta, s2.theta)
nt.assert_array_almost_equal(s0.theta, thetaU)
nt.assert_array_almost_equal(s0.phi, s1.phi)
nt.assert_array_almost_equal(s0.phi, s2.phi)
nt.assert_array_almost_equal(s0.phi, phiU)
@needs_delaunay
def test_mirror():
verts = [[0, 0, 1],
[0, 1, 0],
[1, 0, 0],
[-1, -1, -1]]
verts = np.array(verts, 'float')
verts = verts / np.sqrt((verts * verts).sum(-1)[:, None])
faces = [[0, 1, 3],
[0, 2, 3],
[1, 2, 3]]
h = HemiSphere(xyz=verts, faces=faces)
s = h.mirror()
nt.assert_equal(len(s.vertices), 8)
nt.assert_equal(len(s.faces), 6)
verts = s.vertices
def _angle(a, b):
return np.arccos(np.dot(a, b))
for triangle in s.faces:
a, b, c = triangle
nt.assert_(_angle(verts[a], verts[b]) <= np.pi/2)
nt.assert_(_angle(verts[a], verts[c]) <= np.pi/2)
nt.assert_(_angle(verts[b], verts[c]) <= np.pi/2)
@needs_delaunay
def test_hemisphere_faces():
t = (1 + np.sqrt(5)) / 2
vertices = np.array(
[[ -t, -1, 0],
[ -t, 1, 0],
[ 1, 0, t],
[ -1, 0, t],
[ 0, t, 1],
[ 0, -t, 1],
])
vertices /= vector_norm(vertices, keepdims=True)
faces = np.array(
[[0, 1, 2],
[0, 1, 3],
[0, 2, 4],
[1, 3, 4],
[2, 3, 4],
[1, 2, 5],
[0, 3, 5],
[2, 3, 5],
[0, 4, 5],
[1, 4, 5],
])
edges = np.array(
[(0, 1),
(0, 2),
(0, 3),
(0, 4),
(0, 5),
(1, 2),
(1, 3),
(1, 4),
(1, 5),
(2, 3),
(2, 4),
(2, 5),
(3, 4),
(3, 5),
(4, 5),
])
h = HemiSphere(xyz=vertices)
nt.assert_equal(len(h.edges), len(edges))
nt.assert_equal(array_to_set(h.edges), array_to_set(edges))
nt.assert_equal(len(h.faces), len(faces))
nt.assert_equal(array_to_set(h.faces), array_to_set(faces))
def test_get_force():
charges = np.array([[1., 0, 0],
[0, 1., 0],
[0, 0, 1.]])
force, pot = _get_forces(charges)
nt.assert_array_almost_equal(force, 0)
charges = np.array([[1, -.1, 0],
[1, 0, 0]])
force, pot = _get_forces(charges)
nt.assert_array_almost_equal(force[1, [0, 2]], 0)
nt.assert_(force[1, 1] > 0)
def test_disperse_charges():
charges = np.array([[1., 0, 0],
[0, 1., 0],
[0, 0, 1.]])
d_sphere, pot = disperse_charges(HemiSphere(xyz=charges), 10)
nt.assert_array_almost_equal(charges, d_sphere.vertices)
a = np.sqrt(3)/2
charges = np.array([[3./5, 4./5, 0],
[4./5, 3./5, 0]])
expected_charges = np.array([[0, 1., 0],
[1., 0, 0]])
d_sphere, pot = disperse_charges(HemiSphere(xyz=charges), 1000, .2)
nt.assert_array_almost_equal(expected_charges, d_sphere.vertices)
for ii in xrange(1, len(pot)):
#check that the potential of the system is going down
nt.assert_(pot[ii] - pot[ii-1] <= 0)
# Check that the disperse_charges does not blow up with a large constant
d_sphere, pot = disperse_charges(HemiSphere(xyz=charges), 1000, 20.)
nt.assert_array_almost_equal(expected_charges, d_sphere.vertices)
for ii in xrange(1, len(pot)):
#check that the potential of the system is going down
nt.assert_(pot[ii] - pot[ii-1] <= 0)
#check that the function seems to work with a larger number of charges
charges = np.arange(21).reshape(7,3)
norms = np.sqrt((charges*charges).sum(-1))
charges = charges / norms[:, None]
d_sphere, pot = disperse_charges(HemiSphere(xyz=charges), 1000, .05)
for ii in xrange(1, len(pot)):
#check that the potential of the system is going down
nt.assert_(pot[ii] - pot[ii-1] <= 0)
#check that the resulting charges all lie on the unit sphere
d_charges = d_sphere.vertices
norms = np.sqrt((d_charges*d_charges).sum(-1))
nt.assert_array_almost_equal(norms, 1)
def test_interp_rbf():
def data_func(s, a, b):
return a * np.cos(s.theta) + b * np.sin(s.phi)
from dipy.core.sphere import Sphere, interp_rbf
import numpy as np
s0 = create_unit_sphere(3)
s1 = create_unit_sphere(4)
for a, b in zip([1, 2, 0.5], [1, 0.5, 2]):
data = data_func(s0, a, b)
expected = data_func(s1, a, b)
interp_data_a = interp_rbf(data, s0, s1, norm="angle")
nt.assert_(np.mean(np.abs(interp_data_a - expected)) < 0.1)
# Test that using the euclidean norm raises a warning
# (following https://docs.python.org/2/library/warnings.html#testing-warnings)
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter("always")
interp_data_en = interp_rbf(data, s0, s1, norm ="euclidean_norm")
nt.assert_(len(w) == 1)
nt.assert_(issubclass(w[-1].category, DeprecationWarning))
nt.assert_("deprecated" in str(w[-1].message))
if __name__ == "__main__":
nt.run_module_suite()
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