def test_spherical_coordinate_projections():
normal = [0, 0, 1]
theta = get_sph_theta(coords, normal)
phi = get_sph_phi(coords, normal)
zero = np.tile(0, coords.shape[1])
# Purely radial field
vecs = np.array([
np.sin(theta) * np.cos(phi),
np.sin(theta) * np.sin(phi),
np.cos(theta)
])
assert_array_almost_equal(
zero, get_sph_theta_component(vecs, theta, phi, normal))
assert_array_almost_equal(zero, get_sph_phi_component(vecs, phi, normal))
# Purely toroidal field
vecs = np.array([-np.sin(phi), np.cos(phi), zero])
assert_array_almost_equal(
zero, get_sph_theta_component(vecs, theta, phi, normal))
assert_array_almost_equal(zero,
get_sph_r_component(vecs, theta, phi, normal))
# Purely poloidal field
vecs = np.array([
np.cos(theta) * np.cos(phi),
np.cos(theta) * np.sin(phi), -np.sin(theta)
])
assert_array_almost_equal(zero, get_sph_phi_component(vecs, phi, normal))
assert_array_almost_equal(zero,
get_sph_r_component(vecs, theta, phi, normal))
def test_spherical_coordinate_projections():
normal = [0, 0, 1]
theta = get_sph_theta(coords, normal)
phi = get_sph_phi(coords, normal)
zero = np.tile(0,coords.shape[1])
# Purely radial field
vecs = np.array([np.sin(theta)*np.cos(phi), np.sin(theta)*np.sin(phi), np.cos(theta)])
assert_array_almost_equal(zero, get_sph_theta_component(vecs, theta, phi, normal))
assert_array_almost_equal(zero, get_sph_phi_component(vecs, phi, normal))
# Purely toroidal field
vecs = np.array([-np.sin(phi), np.cos(phi), zero])
assert_array_almost_equal(zero, get_sph_theta_component(vecs, theta, phi, normal))
assert_array_almost_equal(zero, get_sph_r_component(vecs, theta, phi, normal))
# Purely poloidal field
vecs = np.array([np.cos(theta)*np.cos(phi), np.cos(theta)*np.sin(phi), -np.sin(theta)])
assert_array_almost_equal(zero, get_sph_phi_component(vecs, phi, normal))
assert_array_almost_equal(zero, get_sph_r_component(vecs, theta, phi, normal))
def _spherical_theta_component(field, data):
"""The spherical theta component of the vector field
Relative to the coordinate system defined by the *normal* vector,
*center*, and *bulk_* field parameters.
"""
normal = data.get_field_parameter("normal")
vectors = obtain_rv_vec(data, (xn, yn, zn), "bulk_%s" % basename)
theta = resize_vector(data["index", "spherical_theta"], vectors)
phi = resize_vector(data["index", "spherical_phi"], vectors)
return get_sph_theta_component(vectors, theta, phi, normal)
def _magnetic_field_poloidal(field, data):
normal = data.get_field_parameter("normal")
d = data[ftype, 'magnetic_field_x']
Bfields = data.ds.arr([
data[ftype, 'magnetic_field_x'], data[ftype, 'magnetic_field_y'],
data[ftype, 'magnetic_field_z']
], d.units)
theta = data["index", 'spherical_theta']
phi = data["index", 'spherical_phi']
return get_sph_theta_component(Bfields, theta, phi, normal)
def _spherical_theta_component(field, data):
"""The spherical theta component of the vector field
Relative to the coordinate system defined by the *normal* vector,
*center*, and *bulk_* field parameters.
"""
normal = data.get_field_parameter("normal")
vectors = obtain_rv_vec(data, (xn, yn, zn),
"bulk_%s" % basename)
theta = resize_vector(data["index", "spherical_theta"], vectors)
phi = resize_vector(data["index", "spherical_phi"], vectors)
return get_sph_theta_component(vectors, theta, phi, normal)
def _magnetic_field_poloidal(field, data):
normal = data.get_field_parameter("normal")
Bfields = ustack([
data[ftype, "relative_magnetic_field_x"],
data[ftype, "relative_magnetic_field_y"],
data[ftype, "relative_magnetic_field_z"],
])
theta = data["index", "spherical_theta"]
phi = data["index", "spherical_phi"]
return get_sph_theta_component(Bfields, theta, phi, normal)
def _magnetic_field_poloidal(field, data):
normal = data.get_field_parameter("normal")
Bfields = ustack([
data[ftype, 'relative_magnetic_field_x'],
data[ftype, 'relative_magnetic_field_y'],
data[ftype, 'relative_magnetic_field_z']
])
theta = data["index", 'spherical_theta']
phi = data["index", 'spherical_phi']
return get_sph_theta_component(Bfields, theta, phi, normal)
def _particle_velocity_spherical_theta(field, data):
"""The spherical theta component of the particle velocities in an
arbitrary coordinate system
Relative to the coordinate system defined by the *normal* vector,
*bulk_velocity* vector and *center* field parameters.
"""
normal = data.get_field_parameter("normal")
pos = data["relative_particle_position"].T
vel = data["relative_particle_velocity"].T
theta = get_sph_theta(pos, normal)
phi = get_sph_phi(pos, normal)
spht = get_sph_theta_component(vel, theta, phi, normal)
return spht
def _particle_spherical_position_theta(field, data):
"""
Theta component of the particles' position vectors in spherical coords
on the provided field parameters for 'normal', 'center', and
'bulk_velocity',
"""
normal = data.get_field_parameter('normal')
center = data.get_field_parameter('center')
bv = data.get_field_parameter("bulk_velocity")
pos = spos
pos = YTArray([data[ptype, pos % ax] for ax in "xyz"])
theta = get_sph_theta(pos, center)
phi = get_sph_phi(pos, center)
pos = pos - np.reshape(center, (3, 1))
spht = get_sph_theta_component(pos, theta, phi, normal)
return spht
def _particle_velocity_spherical_theta(field, data):
"""The spherical theta component of the particle velocities in an
arbitrary coordinate system
Relative to the coordinate system defined by the *normal* vector,
*bulk_velocity* vector and *center* field parameters.
"""
normal = data.get_field_parameter('normal')
center = data.get_field_parameter('center')
bv = data.get_field_parameter("bulk_velocity")
pos = data.ds.arr([data[ptype, spos % ax] for ax in "xyz"])
vel = data.ds.arr([data[ptype, svel % ax] for ax in "xyz"])
pos = pos - np.reshape(center, (3, 1))
vel = vel - np.reshape(bv, (3, 1))
theta = get_sph_theta(pos, normal)
phi = get_sph_phi(pos, normal)
spht = get_sph_theta_component(vel, theta, phi, normal)
return spht
def _particle_velocity_spherical_theta(field, data):
"""The spherical theta component of the particle velocities in an
arbitrary coordinate system
Relative to the coordinate system defined by the *normal* vector,
*bulk_velocity* vector and *center* field parameters.
"""
normal = data.get_field_parameter('normal')
center = data.get_field_parameter('center')
bv = data.get_field_parameter("bulk_velocity")
pos = data.ds.arr([data[ptype, spos % ax] for ax in "xyz"])
vel = data.ds.arr([data[ptype, svel % ax] for ax in "xyz"])
theta = get_sph_theta(pos, normal)
phi = get_sph_phi(pos, normal)
pos = pos - np.reshape(center, (3, 1))
vel = vel - np.reshape(bv, (3, 1))
spht = get_sph_theta_component(vel, theta, phi, normal)
return spht
