def _get_response_A(position, area, nu, horn, secondary_beam):
"""
Phase and transmission from the switches to the focal plane.
Parameters
----------
position : array-like of shape (..., 3)
The 3D coordinates where the response is computed [m].
area : array-like
The integration area, in m^2.
nu : float
The frequency for which the response is computed [Hz].
horn : PackedArray
The horn layout.
secondary_beam : Beam
The secondary beam.
Returns
-------
out : complex array of shape (#positions, #horns)
The phase and transmission from the horns to the focal plane.
"""
uvec = position / np.sqrt(np.sum(position**2, axis=-1))[..., None]
thetaphi = Cartesian2SphericalOperator('zenith,azimuth')(uvec)
sr = -area / position[..., 2]**2 * np.cos(thetaphi[..., 0])**3
tr = np.sqrt(
secondary_beam(thetaphi[..., 0], thetaphi[..., 1]) * sr /
secondary_beam.solid_angle)[..., None]
const = 2j * np.pi * nu / c
product = np.dot(uvec, horn[horn.open].center.T)
return ne.evaluate('tr * exp(const * product)')
def func(c1, c2):
op1 = Cartesian2SphericalOperator(c1)
op2 = Spherical2CartesianOperator(c2)
op = op1(op2)
if c1 == c2:
assert_is_type(op, IdentityOperator)
else:
assert_is_type(op, CompositionOperator)
def create_random_pointings(center,
npointings,
dtheta,
date_obs=None,
period=None,
latitude=None,
longitude=None,
seed=None):
"""
Return pointings randomly and uniformly distributed in a spherical cap.
Parameters
----------
center : 2-tuple
The R.A. and declination of the center of the FOV, in degrees.
npointings : int
The number of requested pointings
dtheta : float
The maximum angular distance to the center.
date_obs : str or astropy.time.Time, optional
The starting date of the observation (UTC).
period : float, optional
The sampling period of the pointings, in seconds.
latitude : float, optional
The observer's latitude [degrees]. Default is DOMEC's.
longitude : float, optional
The observer's longitude [degrees]. Default is DOMEC's.
"""
r = np.random.RandomState(seed)
cosdtheta = np.cos(np.radians(dtheta))
theta = np.degrees(
np.arccos(cosdtheta + (1 - cosdtheta) * r.rand(npointings)))
phi = r.rand(npointings) * 360
pitch = r.rand(npointings) * 360
p = QubicSampling(npointings,
date_obs=date_obs,
period=period,
latitude=latitude,
longitude=longitude)
time = p.date_obs + TimeDelta(p.time, format='sec')
c2s = Cartesian2SphericalOperator('azimuth,elevation', degrees=True)
e2h = CartesianEquatorial2HorizontalOperator('NE', time, p.latitude,
p.longitude)
rot = Rotation3dOperator("ZY'", center[0], 90 - center[1], degrees=True)
s2c = Spherical2CartesianOperator('zenith,azimuth', degrees=True)
rotation = c2s(e2h(rot(s2c)))
coords = rotation(np.asarray([theta.T, phi.T]).T)
p.azimuth = coords[..., 0]
p.elevation = coords[..., 1]
p.pitch = pitch
p.angle_hwp = r.random_integers(0, 7, npointings) * 11.25
p.fix_az = False
return p
def _get_response_A(position,
area,
nu,
horn,
secondary_beam,
external_A=None):
"""
Phase and transmission from the switches to the focal plane.
Parameters
----------
position : array-like of shape (..., 3)
The 3D coordinates where the response is computed [m].
area : array-like
The integration area, in m^2.
nu : float
The frequency for which the response is computed [Hz].
horn : PackedArray
The horn layout.
secondary_beam : Beam
The secondary beam.
external_A : list of tables describing the phase and amplitude at each point of the focal
plane for each of the horns:
[0] : array of nn with x values in meters
[1] : array of nn with y values in meters
[2] : array of [nhorns, nn, nn] with amplitude
[3] : array of [nhorns, nn, nn] with phase in degrees
Returns
-------
out : complex array of shape (#positions, #horns)
The phase and transmission from the horns to the focal plane.
"""
if external_A is None:
uvec = position / np.sqrt(np.sum(position**2, axis=-1))[..., None]
thetaphi = Cartesian2SphericalOperator('zenith,azimuth')(uvec)
sr = -area / position[..., 2]**2 * np.cos(thetaphi[..., 0])**3
tr = np.sqrt(
secondary_beam(thetaphi[..., 0], thetaphi[..., 1]) * sr /
secondary_beam.solid_angle)[..., None]
const = 2j * np.pi * nu / c
product = np.dot(uvec, horn[horn.open].center.T)
return ne.evaluate('tr * exp(const * product)')
else:
xx = external_A[0]
yy = external_A[1]
amp = external_A[2]
phi = external_A[3]
ix = np.argmin(np.abs(xx - position[0, 0]))
jy = np.argmin(np.abs(yy - position[0, 1]))
return np.array([
amp[:, ix, jy] *
(np.cos(phi[:, ix, jy]) + 1j * np.sin(phi[:, ix, jy]))
])
def func(c, v, s, d, r):
orig = v
if not d:
v = np.radians(v)
s2c = Spherical2CartesianOperator(c, degrees=d)
c2s = Cartesian2SphericalOperator(c, degrees=d)
assert_allclose(s2c(v), r)
a = c2s(s2c(v))
if not d:
a = np.degrees(a)
assert_equal(a.shape, s + (2, ))
assert_allclose(a, orig, atol=1e-16)
def test_cartesian_spherical_error():
assert_raises(TypeError, Cartesian2SphericalOperator, 3)
assert_raises(ValueError, Cartesian2SphericalOperator, 'bla')
op = Cartesian2SphericalOperator('zenith,azimuth')
def func(i, o):
if i.shape == (3, ) and o.shape == (2, ):
op(i, o)
return
assert_raises(ValueError, op.__call__, i, o)
for i, o in itertools.product((np.array(1.), np.zeros(2), np.zeros(3)),
(np.array(1.), np.zeros(2), np.zeros(3))):
yield func, i, o
def test_cartesian_spherical_rules():
def func(c1, c2):
op1 = Cartesian2SphericalOperator(c1)
op2 = Spherical2CartesianOperator(c2)
op = op1(op2)
if c1 == c2:
assert_is_type(op, IdentityOperator)
else:
assert_is_type(op, CompositionOperator)
for c1 in 'zenith,azimuth', 'azimuth,elevation':
op = Cartesian2SphericalOperator(c1)
assert_is_type(op.I, Spherical2CartesianOperator)
assert_equal(op.convention, c1)
for c2 in 'zenith,azimuth', 'azimuth,elevation':
yield func, c1, c2
def func(cls_sph, cls_car, cin, cout, v, s, d):
if 'Horizontal' in str(cls_sph):
args = ('NE', Time('1980-04-22 14:36:51.67',
scale='ut1'), 100.1, -80)
else:
args = ()
op_sph = cls_sph(*args,
conventionin=cin,
conventionout=cout,
degrees=d)
actual = op_sph(v)
assert_equal(actual.shape, s + (2, ))
if d:
v = np.radians(v)
expected = Cartesian2SphericalOperator(cout)(cls_car(*args)(
Spherical2CartesianOperator(cin)(v)))
if d:
np.degrees(expected, expected)
assert_same(actual, expected)
def create_repeat_pointings(center,
npointings,
dtheta,
nhwp_angles=3,
date_obs=None,
period=None,
latitude=None,
longitude=None,
seed=None):
"""
Return pointings randomly and uniformly distributed in a spherical cap.
The same pointing is repeated nhwp_angles times with a different
hwp angle each time.
Parameters
----------
center : 2-tuple
The R.A. and declination of the center of the FOV, in degrees.
npointings : int
The number of requested pointings
dtheta : float
The maximum angular distance to the center.
nhwp_angles : int
The number of HWP angles used.
date_obs : str or astropy.time.Time, optional
The starting date of the observation (UTC).
period : float, optional
The sampling period of the pointings, in seconds.
latitude : float, optional
The observer's latitude [degrees]. Default is DOMEC's.
longitude : float, optional
The observer's longitude [degrees]. Default is DOMEC's.
seed : int
Random seed.
"""
r = np.random.RandomState(seed)
nrandom = np.int(npointings /
nhwp_angles) # number of real random pointings
# Creation of nrandom pointing
cosdtheta = np.cos(np.radians(dtheta))
theta = np.degrees(np.arccos(cosdtheta +
(1 - cosdtheta) * r.rand(nrandom)))
phi = r.rand(nrandom) * 360
pitch = r.rand(nrandom) * 360
p = QubicSampling(nrandom,
date_obs=date_obs,
period=period,
latitude=latitude,
longitude=longitude)
time = p.date_obs + TimeDelta(p.time, format='sec')
c2s = Cartesian2SphericalOperator('azimuth,elevation', degrees=True)
e2h = CartesianEquatorial2HorizontalOperator('NE', time, p.latitude,
p.longitude)
rot = Rotation3dOperator("ZY'", center[0], 90 - center[1], degrees=True)
s2c = Spherical2CartesianOperator('zenith,azimuth', degrees=True)
rotation = c2s(e2h(rot(s2c)))
coords = rotation(np.asarray([theta.T, phi.T]).T)
p.azimuth = coords[..., 0]
p.elevation = coords[..., 1]
p.pitch = pitch
p.fix_az = False
# Replication of the same pointing with others fix hwp angles
pp = QubicSampling(nrandom * nhwp_angles,
date_obs=date_obs,
period=period,
latitude=latitude,
longitude=longitude)
pp.azimuth = np.tile(p.azimuth, nhwp_angles)
pp.elevation = np.tile(p.elevation, nhwp_angles)
pp.pitch = np.tile(p.pitch, nhwp_angles)
pp.time = np.tile(p.time, nhwp_angles)
pp.angle_hwp = np.zeros(nrandom * nhwp_angles)
pp.fix_az = False
for hwp in range(nhwp_angles):
pp.angle_hwp[hwp * nrandom:(hwp + 1) * nrandom] = np.array(
np.rad2deg(hwp * np.pi / (nhwp_angles * 2)))
return pp
def create_hall_pointing(d,
az,
el,
hor_center,
angspeed_psi=0,
maxpsi=0,
period=0,
fillfield=False,
date_obs=None,
latitude=None,
longitude=None,
doplot=False,
fix_azimuth=None,
random_hwp=True,
verbose=False):
'''
Model of the pointing used in the hall. No back and forth.
Input coordinates are az, el. The function authomatically will convert (az, el) into (phi, theta)
defined as qubic.sampling.create_random_pointing to match with qubicsoft.
The coverage map center the region in hor_center coordinates. Take it into account for
plotting and projecting maps
Parameters:
d: QUBIC dictionary
az, el: azimuth and elevation data from housekeeping data or fits file. 1-d array
period: QubicSampling parameter. If equal to zero, it matches with transformation from az,el
to ra, dec using qubic.hor2equ(az, el time = 0). Otherwise is not equal. Default: zero.
hor_center: center of the FOV
Return:
QUBIC's pointing object
'''
if fillfield:
az = np.arange(az[0], az[-1],
hp.nside2resol(d['nside'], arcmin=True) / 60)
el = np.arange(el[0], el[-1],
hp.nside2resol(d['nside'], arcmin=True) / 60)
nsamples = len(az) * len(el)
mult_az, mult_el = generate_region(az, el)
theta = np.array(mult_el) #- np.mean(el)
phi = np.array(mult_az[0]) #- np.mean(az)
# By defalut it computes HorizontalSampling in with SphericalSamplig
pp = qubic.QubicSampling(
nsamples, #azimuth = mult_az[0], elevation = mult_el[0],
date_obs=d['date_obs'],
period=period,
latitude=latitude,
longitude=longitude)
time = pp.date_obs + TimeDelta(pp.time, format='sec')
print("time", np.shape(time))
c2s = Cartesian2SphericalOperator('azimuth,elevation', degrees=True)
h2e = CartesianHorizontal2EquatorialOperator('NE', time, pp.latitude,
pp.longitude)
s2c = Spherical2CartesianOperator('elevation,azimuth', degrees=True)
rotation = c2s(h2e(s2c))
coords = rotation(np.asarray([theta.T, phi.T]).T)
pp.elevation = mult_el
pp.azimuth = mult_az[0]
pp.equatorial[:, 0] = coords[:, 0]
pp.equatorial[:, 1] = coords[:, 1]
if doplot:
fig, ax = subplots(nrows=1, ncols=1, figsize=(14, 6))
pixsH = hp.ang2pix(d['nside'], np.radians(90 - theta), np.radians(phi))
mapaH = np.ones((12 * d['nside']**2))
mapaH[pixsH] = 100
axes(ax)
hp.gnomview(mapaH,
title="Horizontal coordinates Nside = {}".format(
d['nside']),
reso=12,
xsize=320,
ysize=190,
rot=[np.mean(phi), np.mean(theta)],
hold=True,
cbar=False)
hp.graticule(verbose=False, dmer=10, dpar=10)
#pixsEq = hp.ang2pix(d['nside'], np.radians(90 - pp.equatorial[:,1]), np.radians(pp.equatorial[:,0]))
#mapaEq = np.ones((12*d['nside']**2))
#mapaEq[pixsEq] = 100
#axes(ax[1])
#hp.mollview(mapaEq, title = "Equatorial coordinates", hold = True)
#hp.graticule(verbose = False)
azcen_fov, elcen_fov = hor_center[0], hor_center[1]
if period < 1e-4:
newcenter = qubic.hor2equ(azcen_fov, elcen_fov, 0)
else:
newcenter = qubic.hor2equ(azcen_fov, elcen_fov,
pp.time[int(len(pp.time) / 2)])
warn("Update RA, DEC in dictionary")
d['RA_center'], d['DEC_center'] = newcenter[0], newcenter[1]
# center = ra, dec
#center = (d['RA_center'], d['DEC_center'])
if verbose:
print("Time: len(time) = {} \n t0 {} \n time/2 {} \n tf {}".format(
time, time[0], time[int(len(time) / 2)], time[-1]))
### scan psi as well,
pitch = pp.time * angspeed_psi
pitch = pitch % (4 * maxpsi)
mask = pitch > (2 * maxpsi)
pitch[mask] = -pitch[mask] + 4 * maxpsi
pitch -= maxpsi
pp.pitch = pitch
if random_hwp:
pp.angle_hwp = np.random.randint(0, 7, nsamples) * 11.25
if d['fix_azimuth']['apply']:
pp.fix_az = True
if d['fix_azimuth']['fix_hwp']:
pp.angle_hwp = pp.pitch * 0 + 11.25
if d['fix_azimuth']['fix_pitch']:
pp.pitch = 0
else:
pp.fix_az = False
return pp
def create_random_pointings(center,
npointings,
dtheta,
hwp_stepsize,
date_obs=None,
period=None,
latitude=None,
longitude=None,
seed=None):
"""
Return pointings randomly and uniformly distributed in a spherical cap.
1) Creates random coordinates theta, phi. Range: 0 < theta < dtheta, 0 < phi < 360
(then are converted from spherical to cartesian coordinates),
2) It rotates the points to center them in direction (RA, DEC) using Rotation3dOperator
(equatorial reference system)
3) Convertion: Equatorial to Horizontal reference system
(using CartesianEquatorial2HorizontalOperator's operator)
4) Back to cartesian coordinates (using Cartesian2SphericalOperator)
Parameters
----------
center : 2-tuple
The R.A. and declination of the center of the FOV, in degrees.
npointings : int
The number of requested pointings
dtheta : float
The maximum angular distance to the center.
hwp_stepsize : float
Step angle size for the HWP.
date_obs : str or astropy.time.Time, optional
The starting date of the observation (UTC).
period : float, optional
The sampling period of the pointings, in seconds.
latitude : float, optional
The observer's latitude [degrees]. Default is DOMEC's.
longitude : float, optional
The observer's longitude [degrees]. Default is DOMEC's.
seed : int
Random seed.
"""
r = np.random.RandomState(seed)
cosdtheta = np.cos(np.radians(dtheta))
theta = np.degrees(
np.arccos(cosdtheta + (1 - cosdtheta) * r.rand(npointings)))
phi = r.rand(npointings) * 360
pitch = r.rand(npointings) * 360
p = QubicSampling(npointings,
date_obs=date_obs,
period=period,
latitude=latitude,
longitude=longitude)
time = p.date_obs + TimeDelta(p.time, format='sec')
c2s = Cartesian2SphericalOperator('azimuth,elevation', degrees=True)
e2h = CartesianEquatorial2HorizontalOperator('NE', time, p.latitude,
p.longitude)
rot = Rotation3dOperator("ZY'", center[0], 90 - center[1], degrees=True)
s2c = Spherical2CartesianOperator('zenith,azimuth', degrees=True)
rotation = c2s(e2h(rot(s2c)))
coords = rotation(np.asarray([theta.T, phi.T]).T)
p.azimuth = coords[..., 0]
p.elevation = coords[..., 1]
p.pitch = pitch
p.fix_az = False
p.angle_hwp = r.randint(0, int(90 / hwp_stepsize + 1),
npointings) * hwp_stepsize
return p
def func(c, v, s, d):
c2s = Cartesian2SphericalOperator(c, degrees=d)
s2c = Spherical2CartesianOperator(c, degrees=d)
a = s2c(c2s(v))
assert_equal(a.shape, s + (3, ))
assert_allclose(a, v, atol=1e-16)