def _components(data, p=1, phi=0.0, axis=None, weights=None):
# Utility function for computing the generalized rectangular components
# of the circular data.
if weights is None:
weights = np.ones((1,))
try:
weights = broadcast_to(weights, data.shape)
except ValueError:
raise ValueError("Weights and data have inconsistent shape.")
C = np.sum(weights * np.cos(p * (data - phi)), axis) / np.sum(weights, axis)
S = np.sum(weights * np.sin(p * (data - phi)), axis) / np.sum(weights, axis)
return C, S
def _components(data, p=1, phi=0.0, axis=None, weights=None):
# Utility function for computing the generalized rectangular components
# of the circular data.
if weights is None:
weights = np.ones((1,))
try:
weights = broadcast_to(weights, data.shape)
except ValueError:
raise ValueError('Weights and data have inconsistent shape.')
C = np.sum(weights * np.cos(p * (data - phi)), axis)/np.sum(weights, axis)
S = np.sum(weights * np.sin(p * (data - phi)), axis)/np.sum(weights, axis)
return C, S
def vtest(data, mu=0.0, axis=None, weights=None):
""" Performs the Rayleigh test of uniformity where the alternative
hypothesis H1 is assumed to have a known mean angle ``mu``.
Parameters
----------
data : numpy.ndarray or Quantity
Array of circular (directional) data, which is assumed to be in
radians whenever ``data`` is ``numpy.ndarray``.
mu : float or Quantity, optional
Mean angle. Assumed to be known.
axis : int, optional
Axis along which the V test will be performed.
weights : numpy.ndarray, optional
In case of grouped data, the i-th element of ``weights`` represents a
weighting factor for each group such that ``sum(weights, axis)``
equals the number of observations. See [1], remark 1.4, page 22, for
detailed explanation.
Returns
-------
p-value : float or dimensionless Quantity
p-value.
Examples
--------
>>> import numpy as np
>>> from astropy.stats import vtest
>>> from astropy import units as u
>>> data = np.array([130, 90, 0, 145])*u.deg
>>> vtest(data) # doctest: +FLOAT_CMP
<Quantity 0.6223678199713766>
References
----------
.. [1] S. R. Jammalamadaka, A. SenGupta. "Topics in Circular Statistics".
Series on Multivariate Analysis, Vol. 5, 2001.
.. [2] C. Agostinelli, U. Lund. "Circular Statistics from 'Topics in
Circular Statistics (2001)'". 2015.
<https://cran.r-project.org/web/packages/CircStats/CircStats.pdf>
.. [3] M. Chirstman., C. Miller. "Testing a Sample of Directions for
Uniformity." Lecture Notes, STA 6934/5805. University of Florida, 2007.
"""
from scipy.stats import norm
if weights is None:
weights = np.ones((1, ))
try:
weights = broadcast_to(weights, data.shape)
except ValueError:
raise ValueError('Weights and data have inconsistent shape.')
n = np.size(data, axis=axis)
R0bar = np.sum(weights * np.cos(data - mu), axis) / np.sum(weights, axis)
z = np.sqrt(2.0 * n) * R0bar
pz = norm.cdf(z)
fz = norm.pdf(z)
# see reference [3]
p_value = 1 - pz + fz * ((3 * z - z**3) / (16.0 * n) +
(15 * z + 305 * z**3 - 125 * z**5 + 9 * z**7) /
(4608.0 * n * n))
return p_value
def vtest(data, mu=0.0, axis=None, weights=None):
""" Performs the Rayleigh test of uniformity where the alternative
hypothesis H1 is assumed to have a known mean angle ``mu``.
Parameters
----------
data : numpy.ndarray or Quantity
Array of circular (directional) data, which is assumed to be in
radians whenever ``data`` is ``numpy.ndarray``.
mu : float or Quantity, optional
Mean angle. Assumed to be known.
axis : int, optional
Axis along which the V test will be performed.
weights : numpy.ndarray, optional
In case of grouped data, the i-th element of ``weights`` represents a
weighting factor for each group such that ``sum(weights, axis)``
equals the number of observations. See [1], remark 1.4, page 22, for
detailed explanation.
Returns
-------
p-value : float or dimensionless Quantity
p-value.
Examples
--------
>>> import numpy as np
>>> from astropy.stats import vtest
>>> from astropy import units as u
>>> data = np.array([130, 90, 0, 145])*u.deg
>>> vtest(data) # doctest: +FLOAT_CMP
<Quantity 0.6223678199713766>
References
----------
.. [1] S. R. Jammalamadaka, A. SenGupta. "Topics in Circular Statistics".
Series on Multivariate Analysis, Vol. 5, 2001.
.. [2] C. Agostinelli, U. Lund. "Circular Statistics from 'Topics in
Circular Statistics (2001)'". 2015.
<https://cran.r-project.org/web/packages/CircStats/CircStats.pdf>
.. [3] M. Chirstman., C. Miller. "Testing a Sample of Directions for
Uniformity." Lecture Notes, STA 6934/5805. University of Florida, 2007.
"""
from scipy.stats import norm
if weights is None:
weights = np.ones((1,))
try:
weights = broadcast_to(weights, data.shape)
except ValueError:
raise ValueError("Weights and data have inconsistent shape.")
n = np.size(data, axis=axis)
R0bar = np.sum(weights * np.cos(data - mu), axis) / np.sum(weights, axis)
z = np.sqrt(2.0 * n) * R0bar
pz = norm.cdf(z)
fz = norm.pdf(z)
# see reference [3]
p_value = (
1
- pz
+ fz * ((3 * z - z ** 3) / (16.0 * n) + (15 * z + 305 * z ** 3 - 125 * z ** 5 + 9 * z ** 7) / (4608.0 * n * n))
)
return p_value
def __call__(self, observer, targets, times=None,
time_range=None, time_grid_resolution=0.5*u.hour,
grid_times_targets=False):
"""
Compute the constraint for this class
Parameters
----------
observer : `~astroplan.Observer`
the observation location from which to apply the constraints
targets : sequence of `~astroplan.Target`
The targets on which to apply the constraints.
times : `~astropy.time.Time`
The times to compute the constraint.
WHAT HAPPENS WHEN BOTH TIMES AND TIME_RANGE ARE SET?
time_range : `~astropy.time.Time` (length = 2)
Lower and upper bounds on time sequence.
time_grid_resolution : `~astropy.units.quantity`
Time-grid spacing
grid_times_targets : bool
if True, grids the constraint result with targets along the first
index and times along the second. Otherwise, we rely on broadcasting
the shapes together using standard numpy rules.
Returns
-------
constraint_result : 1D or 2D array of float or bool
The constraints. If 2D with targets along the first index and times along
the second.
"""
if times is None and time_range is not None:
times = time_grid_from_range(time_range,
time_resolution=time_grid_resolution)
if grid_times_targets:
targets = get_skycoord(targets)
# TODO: these broadcasting operations are relatively slow
# but there is potential for huge speedup if the end user
# disables gridding and re-shapes the coords themselves
# prior to evaluating multiple constraints.
if targets.isscalar:
# ensure we have a (1, 1) shape coord
targets = SkyCoord(np.tile(targets, 1))[:, np.newaxis]
else:
targets = targets[..., np.newaxis]
times, targets = observer._preprocess_inputs(times, targets, grid_times_targets=False)
result = self.compute_constraint(times, observer, targets)
# make sure the output has the same shape as would result from
# broadcasting times and targets against each other
if targets is not None:
# broadcasting times v targets is slow due to
# complex nature of these objects. We make
# to simple numpy arrays of the same shape and
# broadcast these to find the correct shape
shp1, shp2 = times.shape, targets.shape
x = np.array([1])
a = as_strided(x, shape=shp1, strides=[0] * len(shp1))
b = as_strided(x, shape=shp2, strides=[0] * len(shp2))
output_shape = np.broadcast(a, b).shape
if output_shape != result.shape:
result = broadcast_to(result, output_shape)
return result
def __call__(self,
observer,
targets,
times=None,
time_range=None,
time_grid_resolution=0.5 * u.hour,
grid_times_targets=False):
"""
Compute the constraint for this class
Parameters
----------
observer : `~astroplan.Observer`
the observation location from which to apply the constraints
targets : sequence of `~astroplan.Target`
The targets on which to apply the constraints.
times : `~astropy.time.Time`
The times to compute the constraint.
WHAT HAPPENS WHEN BOTH TIMES AND TIME_RANGE ARE SET?
time_range : `~astropy.time.Time` (length = 2)
Lower and upper bounds on time sequence.
time_grid_resolution : `~astropy.units.quantity`
Time-grid spacing
grid_times_targets : bool
if True, grids the constraint result with targets along the first
index and times along the second. Otherwise, we rely on broadcasting
the shapes together using standard numpy rules.
Returns
-------
constraint_result : 1D or 2D array of float or bool
The constraints. If 2D with targets along the first index and times along
the second.
"""
if times is None and time_range is not None:
times = time_grid_from_range(time_range,
time_resolution=time_grid_resolution)
if grid_times_targets:
targets = get_skycoord(targets)
# TODO: these broadcasting operations are relatively slow
# but there is potential for huge speedup if the end user
# disables gridding and re-shapes the coords themselves
# prior to evaluating multiple constraints.
if targets.isscalar:
# ensure we have a (1, 1) shape coord
targets = SkyCoord(np.tile(targets, 1))[:, np.newaxis]
else:
targets = targets[..., np.newaxis]
times, targets = observer._preprocess_inputs(times,
targets,
grid_times_targets=False)
result = self.compute_constraint(times, observer, targets)
# make sure the output has the same shape as would result from
# broadcasting times and targets against each other
if targets is not None:
# broadcasting times v targets is slow due to
# complex nature of these objects. We make
# to simple numpy arrays of the same shape and
# broadcast these to find the correct shape
shp1, shp2 = times.shape, targets.shape
x = np.array([1])
a = as_strided(x, shape=shp1, strides=[0] * len(shp1))
b = as_strided(x, shape=shp2, strides=[0] * len(shp2))
output_shape = np.broadcast(a, b).shape
if output_shape != np.array(result).shape:
result = broadcast_to(result, output_shape)
return result
