def test_pol2cart():
theta = np.pi/3.
phi = np.pi/3.
x = 1/2. * np.sqrt(3/4.)
y = 3/4.
z = 1/2.
res = pol2cart(np.array([theta, phi]))
assert_almost_equal(np.array((x,y,z)), res)
def random_pars(mu=None, kappa=None, verbose=False):
if mu == None:
theta = np.random.uniform(low = -np.pi/2., high = np.pi/2.)
phi = np.random.uniform(low = -np.pi, high = np.pi)
if verbose: print "theta = %.3f, phi = %.3f" % (theta, phi)
mu = pol2cart(np.array([theta, phi]))
if kappa == None:
kappa = np.random.uniform(low=0., high=5.)
return mu, kappa
def test_coordinate_conversions():
n_tests = int(1e3)
for i in xrange(n_tests):
theta = np.random.uniform(low = 0., high = np.pi)
phi = np.random.uniform(low = 0., high = 2 * np.pi)
cart = pol2cart(np.array([theta, phi]))
theta_prime, phi_prime = cart2pol(cart)
assert_almost_equal(np.array((theta, phi % (2 * np.pi))),
np.array((theta_prime, phi_prime % (2 * np.pi))))
def _map_data(data, task, pd, resolution=100):
'''
Parameters
----------
data : ndarray
shape (ntime, ntask)
task : ndarray
shape (ntask, 6)
pd : ndarray
shape (3,)
Returns
-------
mapped_data : ndarray
shape (ntime, resolution, resolution)
Notes
-----
need to incorporate PD so that it lies at center of plot
'''
if data.shape[-1] != task.shape[0]:
raise ValueError('last axis of data (len %d) must be same length as\n'
'first axis of task (len %d)' % \
(data.shape[-1], data.shape[0]))
# generate theta, phi grid
# or rather map x,y grid to nearest of 26 targets
thetas = np.linspace(0., np.pi, resolution)
phis = np.linspace(0., 2 * np.pi, resolution)
theta_grid = np.tile(thetas[:,None], (1, resolution))
phi_grid = np.tile(phis[None,:], (resolution, 1))
# convert polar to cartesian co-ordinates
tp_grid = np.concatenate((theta_grid[None], phi_grid[None]), axis=0)
xyz_grid = pol2cart(tp_grid, axis=0)
# calculate direction of each task
start = task[:,:3]
stop = task[:,3:]
direction_task = unitvec(stop - start, axis=-1)
# rotate task directions until pd points towards 0,0,1
rotated_toz = rotate_targets(direction_task, cart2pol(pd))
# now rotate again to point pd towards 0,1,0
rotated_toy = rotate_targets(rotated_toz, np.array([np.pi/2., 0]))
# calculate angle between each grid square and each direction
angles = np.arccos(np.tensordot(rotated_toy, xyz_grid, [1,0]))
# get index of closest direction for each grid square
# = get argmin along 0th axis
nearest = np.argmin(angles, axis=0)
mapped_data = data[..., nearest]
return mapped_data
