def test_sph_to_cart():
"""Test conversion between sphere and cartesian."""
# Simple test, expected value (11, 0, 0)
r, theta, phi = 11., 0., np.pi / 2.
z = r * np.cos(phi)
rsin_phi = r * np.sin(phi)
x = rsin_phi * np.cos(theta)
y = rsin_phi * np.sin(theta)
coord = _sph_to_cart(np.array([[r, theta, phi]]))[0]
assert_allclose(coord, (x, y, z), atol=1e-7)
assert_allclose(coord, (r, 0, 0), atol=1e-7)
rng = np.random.RandomState(0)
# round-trip test
coords = rng.randn(10, 3)
assert_allclose(_sph_to_cart(_cart_to_sph(coords)), coords, atol=1e-5)
# equivalence tests to old versions
for coord in coords:
sph = _cart_to_sph(coord[np.newaxis])
cart = _sph_to_cart(sph)
sph_old = np.array(_cartesian_to_sphere(*coord))
cart_old = _sphere_to_cartesian(*sph_old)
sph_old[1] = np.pi / 2. - sph_old[1] # new convention
assert_allclose(sph[0], sph_old[[2, 0, 1]], atol=1e-7)
assert_allclose(cart[0], cart_old, atol=1e-7)
assert_allclose(cart[0], coord, atol=1e-7)
def test_sph_to_cart():
"""Test conversion between sphere and cartesian."""
# Simple test, expected value (11, 0, 0)
r, theta, phi = 11., 0., np.pi / 2.
z = r * np.cos(phi)
rsin_phi = r * np.sin(phi)
x = rsin_phi * np.cos(theta)
y = rsin_phi * np.sin(theta)
coord = _sph_to_cart(np.array([[r, theta, phi]]))[0]
assert_allclose(coord, (x, y, z), atol=1e-7)
assert_allclose(coord, (r, 0, 0), atol=1e-7)
rng = np.random.RandomState(0)
# round-trip test
coords = rng.randn(10, 3)
assert_allclose(_sph_to_cart(_cart_to_sph(coords)), coords, atol=1e-5)
# equivalence tests to old versions
for coord in coords:
sph = _cart_to_sph(coord[np.newaxis])
cart = _sph_to_cart(sph)
sph_old = np.array(_cartesian_to_sphere(*coord))
cart_old = _sphere_to_cartesian(*sph_old)
sph_old[1] = np.pi / 2. - sph_old[1] # new convention
assert_allclose(sph[0], sph_old[[2, 0, 1]], atol=1e-7)
assert_allclose(cart[0], cart_old, atol=1e-7)
assert_allclose(cart[0], coord, atol=1e-7)
def test_topo_to_sph():
"""Test topo to sphere conversion."""
rng = np.random.RandomState(0)
angles = rng.rand(10) * 360
radii = rng.rand(10)
angles[0] = 30
radii[0] = 0.25
# new way
sph = _topo_to_sph(np.array([angles, radii]).T)
new = _sph_to_cart(sph)
new[:, [0, 1]] = new[:, [1, 0]] * [-1, 1]
# old way
for ii, (angle, radius) in enumerate(zip(angles, radii)):
sph_phi, sph_theta = _topo_to_phi_theta(angle, radius)
if ii == 0:
assert_allclose(_topo_to_phi_theta(angle, radius), [45, -30])
azimuth = sph_theta / 180.0 * np.pi
elevation = sph_phi / 180.0 * np.pi
assert_allclose(sph[ii], [1., azimuth, np.pi / 2. - elevation],
atol=1e-7)
r = np.ones_like(radius)
x, y, z = _sphere_to_cartesian(azimuth, elevation, r)
pos = [-y, x, z]
if ii == 0:
expected = np.array([1. / 2., np.sqrt(3) / 2., 1.])
expected /= np.sqrt(2)
assert_allclose(pos, expected, atol=1e-7)
assert_allclose(pos, new[ii], atol=1e-7)
def test_topo_to_sph():
"""Test topo to sphere conversion."""
rng = np.random.RandomState(0)
angles = rng.rand(10) * 360
radii = rng.rand(10)
angles[0] = 30
radii[0] = 0.25
# new way
sph = _topo_to_sph(np.array([angles, radii]).T)
new = _sph_to_cart(sph)
new[:, [0, 1]] = new[:, [1, 0]] * [-1, 1]
# old way
for ii, (angle, radius) in enumerate(zip(angles, radii)):
sph_phi, sph_theta = _topo_to_sphere(angle, radius)
if ii == 0:
assert_allclose(_topo_to_sphere(angle, radius), [45, -30])
azimuth = sph_theta / 180.0 * np.pi
elevation = sph_phi / 180.0 * np.pi
assert_allclose(sph[ii], [1., azimuth, np.pi / 2. - elevation],
atol=1e-7)
r = np.ones_like(radius)
x, y, z = _sphere_to_cartesian(azimuth, elevation, r)
pos = [-y, x, z]
if ii == 0:
expected = np.array([1. / 2., np.sqrt(3) / 2., 1.])
expected /= np.sqrt(2)
assert_allclose(pos, expected, atol=1e-7)
assert_allclose(pos, new[ii], atol=1e-7)
def _read_eeglab_montage(fname):
"""Read an EEGLAB digitization file.
Parameters
----------
fname : str
The filepath of Polhemus ISOTrak formatted file.
File extension is expected to be '.loc', '.locs' or '.eloc'.
Returns
-------
montage : instance of DigMontage
The montage.
See Also
--------
make_dig_montage
"""
ch_names = np.genfromtxt(fname, dtype=str, usecols=3).tolist()
topo = np.loadtxt(fname, dtype=float, usecols=[1, 2])
sph = _topo_to_sph(topo)
pos = _sph_to_cart(sph)
pos[:, [0, 1]] = pos[:, [1, 0]] * [-1, 1]
return make_dig_montage(
ch_pos=dict(zip(ch_names, pos)),
coord_frame='head',
)
def test_tps():
"""Test TPS warping."""
az = np.linspace(0., 2 * np.pi, 20, endpoint=False)
pol = np.linspace(0, np.pi, 12)[1:-1]
sph = np.array(np.meshgrid(1, az, pol, indexing='ij'))
sph.shape = (3, -1)
assert_equal(sph.shape[1], 200)
source = _sph_to_cart(sph.T)
destination = source.copy()
destination *= 2
destination[:, 0] += 1
# fit with 100 points
warp = SphericalSurfaceWarp().fit(source[::2], destination[::2])
destination_est = warp.transform(source)
assert_allclose(destination_est, destination, atol=1e-2)
def test_tps():
"""Test TPS warping."""
az = np.linspace(0., 2 * np.pi, 20, endpoint=False)
pol = np.linspace(0, np.pi, 12)[1:-1]
sph = np.array(np.meshgrid(1, az, pol, indexing='ij'))
sph.shape = (3, -1)
assert_equal(sph.shape[1], 200)
source = _sph_to_cart(sph.T)
destination = source.copy()
destination *= 2
destination[:, 0] += 1
# fit with 100 points
warp = SphericalSurfaceWarp().fit(source[::2], destination[::2])
destination_est = warp.transform(source)
assert_allclose(destination_est, destination, atol=1e-2)
