def func(d):
x_ = np.array(x if d.kind == 'c' else x.real, dtype=d)
actual = abs2(x_)
expected = np.abs(x_**2)
assert_same(actual, expected)
abs2(x_, actual)
assert_same(actual, expected)
def psd2(array, sampling_frequency=1, fftw_flag='FFTW_MEASURE'):
"""
Return two-dimensional PSD.
Parameters
----------
array : array-like
Two-dimensional array.
sampling_frequency : float
The sampling frequency.
fftw_flag : string
The FFTW planner flag.
Returns
-------
psd : ndarray
The Power Spectrum Density, such as
sum psd * bandwidth = mean(array**2)
with bandwidth = sampling_frequency ** 2 / array.size is the PSD bin
area.
"""
array = np.asarray(array)
if array.ndim != 2:
raise ValueError('The input array is not two-dimensional.')
s = abs2(FFTOperator(array.shape, fftw_flag=fftw_flag)(array))
s /= array.size**2
bandwidth = sampling_frequency**2 / array.size
s /= bandwidth
return Map(scipy.fftpack.fftshift(s))
def psd2(array, sampling_frequency=1, fftw_flag='FFTW_MEASURE'):
"""
Return two-dimensional PSD.
Parameters
----------
array : array-like
Two-dimensional array.
sampling_frequency : float
The sampling frequency.
fftw_flag : string
The FFTW planner flag.
Returns
-------
psd : ndarray
The Power Spectrum Density, such as
sum psd * bandwidth = mean(array**2)
with bandwidth = sampling_frequency ** 2 / array.size is the PSD bin
area.
"""
array = np.asarray(array)
if array.ndim != 2:
raise ValueError('The input array is not two-dimensional.')
s = abs2(FFTOperator(array.shape, fftw_flag=fftw_flag)(array))
s /= array.size**2
bandwidth = sampling_frequency**2 / array.size
s /= bandwidth
return Map(scipy.fftpack.fftshift(s))
def _get_synthbeam(scene,
position,
area,
nu,
bandwidth,
horn,
primary_beam,
secondary_beam,
synthbeam_dtype=np.float32,
theta_max=45):
"""
Return the monochromatic synthetic beam for a specified location
on the focal plane, multiplied by a given area and bandwidth.
Parameters
----------
scene : QubicScene
The scene.
position : array-like of shape (..., 3)
The 3D coordinates where the response is computed, in meters.
area : array-like
The integration area, in m^2.
nu : float
The frequency for which the response is computed [Hz].
bandwidth : float
The filter bandwidth [Hz].
horn : PackedArray
The horn layout.
primary_beam : Beam
The primary beam.
secondary_beam : Beam
The secondary beam.
synthbeam_dtype : dtype, optional
The data type for the synthetic beams (default: float32).
It is the dtype used to store the values of the pointing matrix.
theta_max : float, optional
The maximum zenithal angle above which the synthetic beam is
assumed to be zero, in degrees.
"""
MAX_MEMORY_B = 1e9
theta, phi = hp.pix2ang(scene.nside, scene.index)
index = np.where(theta <= np.radians(theta_max))[0]
nhorn = int(np.sum(horn.open))
npix = len(index)
nbytes_B = npix * nhorn * 24
ngroup = np.ceil(nbytes_B / MAX_MEMORY_B).astype(np.int)
out = np.zeros(position.shape[:-1] + (len(scene), ),
dtype=synthbeam_dtype)
for s in split(npix, ngroup):
index_ = index[s]
sb = QubicInstrument._get_response(theta[index_], phi[index_],
bandwidth, position, area, nu,
horn, primary_beam,
secondary_beam)
out[..., index_] = abs2(sb, dtype=synthbeam_dtype)
return out
def _get_synthbeam_(
scene, position, area, nu, bandwidth, horn, primary_beam,
secondary_beam, spectral_irradiance=1,
synthbeam_dtype=np.float32, theta_max=30):
"""
Return the monochromatic synthetic beam for a specified location
on the focal plane, multiplied by a given area and bandwidth.
Parameters
----------
scene : QubicScene
The scene.
x : array-like
The X-coordinate in the focal plane where the response is
computed, in meters. If not provided, the detector central
positions are assumed.
y : array-like
The Y-coordinate in the focal plane where the response is
computed, in meters. If not provided, the detector central
positions are assumed.
area : array-like
The integration area, in m^2.
nu : float
The frequency for which the response is computed [Hz].
bandwidth : float
The filter bandwidth [Hz].
horn : PackedArray
The horn layout.
primary_beam : Beam
The primary beam.
secondary_beam : Beam
The secondary beam.
synthbeam_dtype : dtype, optional
The data type for the synthetic beams (default: float32).
It is the dtype used to store the values of the pointing matrix.
theta_max : float, optional
The maximum zenithal angle above which the synthetic beam is
assumed to be zero, in degrees.
"""
MAX_MEMORY_B = 1e9
theta, phi = hp.pix2ang(scene.nside, scene.index)
index = np.where(theta <= np.radians(theta_max))[0]
nhorn = int(np.sum(horn.open))
npix = len(index)
nbytes_B = npix * nhorn * 24
ngroup = np.ceil(nbytes_B / MAX_MEMORY_B)
out = np.zeros(position.shape[:-1] + (len(scene),),
dtype=synthbeam_dtype)
for s in split(npix, ngroup):
index_ = index[s]
sb = MultiQubicInstrument._get_response(
theta[index_], phi[index_], spectral_irradiance, position,
area, nu, horn, primary_beam, secondary_beam)
out[..., index_] = abs2(sb, dtype=synthbeam_dtype)
return out * bandwidth * deriv_and_const(nu, scene.nside)
# out : complex array of shape (#positions, #horns)
# The phase and transmission from the horns to the focal plane.
#A = inst._get_response_A(position, area, nu, horn, secondary_beam)
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)
A = ne.evaluate('tr * exp(const * product)')
ih=122
clf()
subplot(1,3,1)
amp = np.reshape(abs2(A[:,ih])/np.max(abs2(A)),(100,100))
imshow(amp, extent= [np.min(xx), np.max(xx), np.min(xx), np.max(xx)])
colorbar()
subplot(1,3,2)
phase = np.reshape(angle(A[:,ih]),(100,100))
imshow(phase, extent= [np.min(xx), np.max(xx), np.min(xx), np.max(xx)])
colorbar()
draw()
subplot(1,3,3)
inst.horn.plot(facecolor_open='grey')
plot(inst.horn.center[ih,0],inst.horn.center[ih,1],'ro')
draw()
def _get_synthbeam(
scene,
position,
area,
nu,
bandwidth,
horn,
primary_beam,
secondary_beam,
synthbeam_dtype=np.float32,
theta_max=45,
external_A=None,
):
"""
Return the monochromatic synthetic beam for a specified location
on the focal plane, multiplied by a given area and bandwidth.
Parameters
----------
scene : QubicScene
The scene.
position : array-like of shape (..., 3)
The 3D coordinates where the response is computed, in meters.
area : array-like
The integration area, in m^2.
nu : float
The frequency for which the response is computed [Hz].
bandwidth : float
The filter bandwidth [Hz].
horn : PackedArray
The horn layout.
primary_beam : Beam
The primary beam.
secondary_beam : Beam
The secondary beam.
synthbeam_dtype : dtype, optional
The data type for the synthetic beams (default: float32).
It is the dtype used to store the values of the pointing matrix.
theta_max : float, optional
The maximum zenithal angle above which the synthetic beam is
assumed to be zero, in degrees.
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
"""
MAX_MEMORY_B = 1e9
theta, phi = hp.pix2ang(scene.nside, scene.index)
index = np.where(theta <= np.radians(theta_max))[0]
nhorn = int(np.sum(horn.open))
npix = len(index)
nbytes_B = npix * nhorn * 24
ngroup = np.ceil(nbytes_B / MAX_MEMORY_B)
out = np.zeros(position.shape[:-1] + (len(scene),), dtype=synthbeam_dtype)
for s in split(npix, ngroup):
index_ = index[s]
sb = QubicInstrument._get_response(
theta[index_],
phi[index_],
bandwidth,
position,
area,
nu,
horn,
primary_beam,
secondary_beam,
external_A=external_A,
)
out[..., index_] = abs2(sb, dtype=synthbeam_dtype)
return out