def test_extrapolate(self):
self.Beam = beam.GaussianBeam(self.width,
self.frequencies,
extrapolate=False)
self.assertRaises(Exception, self.Beam.beam_function, 1.0, 6)
self.Beam = beam.GaussianBeam(self.width,
self.frequencies,
extrapolate=True)
# Compare FWHM=1 to FWHM = 1/4. Just check normalization.
self.assertAlmostEqual(float(self.Beam.beam_function(0, 5.0)),
float(self.Beam.beam_function(0, -2.5)) / 4**2)
def test_left_apply_map_norm(self):
self.Beam = beam.GaussianBeam(0.2, None)
self.map[3, 6, 8] = 1.0
self.map[9, 13, 6] = 2.0
self.map[2, 13, 6] = 1.0
conv_map = self.Beam.apply(self.map)
self.assertAlmostEqual(sp.sum(self.map.flat_view()),
sp.sum(conv_map.flat_view()), 4)
def test_checks_axes(self):
self.op.axes = ('freq', 'ra', 'dec', 'mode1', 'mode2')
self.Beam = beam.GaussianBeam([0.2, 0.3], [600, 900])
self.assertRaises(ce.DataError,
self.Beam.apply,
self.op,
right_apply=True)
conv_op = self.Beam.apply(self.op)
self.assertEqual(conv_op.axes, ('freq', 'ra', 'dec', 'mode1', 'mode2'))
def setUp(self):
self.width = (5 + sp.arange(6, dtype=float)) / 5 # between, 1 and 2.
self.frequencies = sp.arange(6, dtype=float)
self.Beam = beam.GaussianBeam(self.width, self.frequencies)
# 1/r^3 correlation function.
n = 50
r = sp.arange(n)
r[0] = 0.1
self.corr = 1.0 / r[:, None]**2 / r
self.corr *= 1.0 / n**3
def test_radial_transform(self):
Beam = beam.GaussianBeam(self.width, self.frequencies)
width = 6.0
factor = width / 2.0
transform = Beam.radial_transform(width)
r = sp.arange(1.5, 6)
self.assertTrue(
sp.allclose(transform(r),
sp.sin(r * factor) / r / factor))
self.assertAlmostEqual(transform(0), 1.0)
def test_apply_right(self):
self.op[0, 9, 8, 6, 4] = 2.0
self.op[1, 11, 7, 11, 8] = 2.0
self.op[1, 11, 7, 8, 6] = 1.0
self.map[1, 11, 8] = 2.0
self.map[1, 8, 6] = 1.0
self.Beam = beam.GaussianBeam([0.2, 0.3], [600, 900])
conv_op = self.Beam.apply(self.op, right_apply=True)
conv_map = self.Beam.apply(self.map)
self.assertAlmostEqual(sp.sum(self.op), sp.sum(conv_op), 3)
self.assertTrue(sp.allclose(conv_op[:, 11, 7, :, :], conv_map))
def test_wrap(self):
self.Beam = beam.GaussianBeam(0.2, None)
self.map[5, 0, 0] = 1.0
conv_map = self.Beam.apply(self.map, wrap=True)
self.assertAlmostEqual(sp.sum(self.map.flat_view()),
sp.sum(conv_map.flat_view()), 4)
self.assertNotAlmostEqual(conv_map[5, 0, 0], 1.0, 3)
self.assertNotAlmostEqual(conv_map[5, -1, 0], 0, 3)
self.assertNotAlmostEqual(conv_map[5, -1, -1], 0, 3)
self.assertAlmostEqual(conv_map[5, -1, 0], conv_map[5, 0, -1])
self.assertAlmostEqual(conv_map[5, -1, -1], conv_map[5, 1, 1])
def test_left_apply_map_vals(self):
self.Beam = beam.GaussianBeam(0.2, None)
self.map[3, 2, 13] = 1.0
self.map[3, 19, 13] = 1.0
conv_map = self.Beam.apply(self.map)
self.assertNotAlmostEqual(conv_map[3, 1, 13], 0, 3)
# Check Isotropy
self.assertAlmostEqual(conv_map[3, 1, 13], conv_map[3, 3, 13])
self.assertAlmostEqual(conv_map[3, 1, 13], conv_map[3, 2, 12])
self.assertAlmostEqual(conv_map[3, 1, 13], conv_map[3, 2, 14])
# Check 0 lag amplitude.
sig = 0.2 / 2 / sp.sqrt(2 * sp.log(2))
self.assertAlmostEqual(conv_map[3, 2, 13],
0.075**2 / (2 * sp.pi * sig**2))
def test_windows(self):
Beam = beam.GaussianBeam(self.width, self.frequencies)
# Radial window.
window, limits = Beam.radial_real_space_window(4.0, 8.0, True)
self.assertTrue(sp.allclose(window(sp.array([-6.0, 6, -10.0])), 0))
self.assertTrue(
sp.allclose(window(sp.array([-2.0, -1.0, 2.0, 0])), 1 / 8.0))
df = 0.01
self.assertAlmostEqual(
sp.sum(window(sp.arange(limits[0], limits[1], df))) * df, 1.0)
# Angular window.
window, limits = Beam.angular_real_space_window(3.0, 5.0, True)
dr = 0.0001
r = sp.arange(limits[0], limits[1], dr)
self.assertAlmostEqual(
sp.sum(window(r) * r * 2.0 * sp.pi) * dr, 1.0, 4)
def test_beam_function(self):
self.Beam = beam.GaussianBeam(self.width, self.frequencies)
# Check a case calculated by hand (FWHM=1 here).
self.assertAlmostEqual(self.Beam.beam_function(1.0, 5.0), 0.0551589, 6)
# Check that the delta r dependance is right.
norm = self.Beam.beam_function(0, 3.0)
self.assertAlmostEqual(
sp.log(self.Beam.beam_function(0.6, 3.0) / norm),
sp.log(self.Beam.beam_function(1.2, 3.0) / norm) / 4)
# Check that it works if I give an array.
self.Beam.beam_function(sp.arange(5.0), 5.0)
# Or 2 arrays of the same length.
self.Beam.beam_function(sp.arange(5), sp.arange(5))
# But fails if they are different lengths.
self.assertRaises(ValueError, self.Beam.beam_function, sp.arange(5),
sp.arange(6))
def convolve_by_beam(self):
r"""this produces self.sim_map_withbeam"""
print "convolving simulation by beam"
beamobj = beam.GaussianBeam(self.beam_data, self.beam_freq)
self.sim_map_withbeam = beamobj.apply(self.sim_map)
def execute(self, nprocesses=1) :
"""Function that does all the work.
Parameters
----------
nprocesses : int
Number of threads to use. So far this program is not threaded.
this argument is only included for compatibility with other
modules.
"""
params = self.params
#### Front end. Read in the power spectrum, convert it to 2d correlation
# function, etc.
# corr_function = f(params['unit_system'], params['power_file_name'],
# params['power_format'])
# Temporary face correlation to make the rest of the code run.
corr_function = lambda rho, f : (1.0e6/(rho**2 + 0.001)
/(abs(f) + 1.0e3))
#### Units. Figure out the axes in the proper units etc.
# Start by getting the map from which we will be getting our axes.
map = algebra.open_memmap(params["map_file"], mode='r')
map = algebra.make_vect(map)
if map.axes != ('freq', 'ra', 'dec') :
raise ce.DataError("Expeceted map to be in freq-ra-dec space.")
# Next figure out all the axes.
nfreq = map.shape[0]
nra = map.shape[1]
ndec = map.shape[2]
freq = map.get_axis('freq')
ra = map.get_axis('ra')*sp.cos(sp.pi*map.info['dec_centre']/180.0)
dec = map.get_axis('dec')
# Coordinate dependant conversion factors.
system = params['unit_system']
if system == "deg-freq" :
z = freq
z_width = sp.ones(nfreq)*map.info['freq_delta']
Drho_Ddeg = sp.ones(nfreq)
elif system == "Mpc/h-Mpc/h" :
# Do a bunch of cosmology dependant stuff.
# Not written yet, so bail here.
return
else :
raise ValueError('Unit system must be one of "deg-freq", '
'"Mpc/h-Mpc/h", "deg-log_freq" or "Mpc/h-mu".')
# Get the beam object.
# The following is temporary. Eventually need to read beam data from
# file.
beam_freq = sp.arange(600.0e6, 1000.0e6, 50.0e6)
beam_width = 0.3*600.0e6/beam_freq
Beam = beam.GaussianBeam(beam_width, beam_freq)
# Figure out the range of angular lags we need to consider in our
# coordinate system.
# First the max lag.
# This is inefficient if the range of Drho_Ddeg is very wide.
max_lag = (max(ra) - min(ra))**2 + (max(dec) - min(dec))**2
max_lag = sp.sqrt(max_lag)*max(Drho_Ddeg)
# Figure out the minimum lag step.
lag_step = min([abs(map.info['ra_delta']) *
sp.cos(sp.pi*map.info['dec_centre']/180.0),
abs(map.info['dec_delta'])])
if max_lag/lag_step > 10*(ndec + nra) :
raise RunTimeError("Dynamic range is very large. There will be "
"too many integrals to do.")
# There is probably a more efficient lag binning than this... peicewise
# linear then log?
divisions = 10.0
lag = sp.arange(0.0, max_lag + lag_step/divisions, lag_step/divisions)
sq_lag = lag**2
nlag = len(lag)
#### Integral. Loop over all possible lags and do the integral.
# Allowcate memory for all f,f',lag combinations.
integrals = sp.empty((nfreq, nfreq, nlag), dtype=float)
if self.feedback >= 2 :
print "Starting integrals."
for find1 in xrange(nfreq) :
for find2 in xrange(nfreq) :
for lind in xrange(nlag) :
# Get separation in radial direction.
delta_z = abs(z[find1] - z[find2])
# Get the window functions.
W, rho_limits = Beam.angular_real_space_window(freq[find1],
freq[find2], return_limits=True)
Q, z_limits = Beam.radial_real_space_window(z_width[find1],
z_width[find2], return_limits=True)
# Construct the integrand.
int = integrand(corr_function, W, Q, lag[lind], delta_z)
# Integrate.
# Reiman sum is the most efficient integration algorithm
# known to mankind.
z_vals = sp.arange(z_limits[0], z_limits[1],
(z_limits[1] - z_limits[0])/20)
z_vals = z_vals[None, :]
rho_vals = sp.arange(rho_limits[0], rho_limits[1],
(rho_limits[1] - rho_limits[0])/20)
rho_vals = rho_vals[:, None]
result = (sp.sum(int(rho_vals, z_vals))
* (z_limits[1] - z_limits[0])/20
* (rho_limits[1] - rho_limits[0])/20)
# Store the result.
integrals[find1, find2, lind] = result
if self.feedback >= 2 :
print "Integrals done."
#### Assignment. Allocate memory, loop over elements and assign.
# Allowcate memory and build final coraviance matrix object.
covariance = algebra.open_memmap(params["out_file_name"],
mode='w+', dtype=float, shape=(nfreq, nra, ndec, nfreq,
nra, ndec))
covariance = algebra.make_mat(covariance, axis_names=("freq", "ra",
"dec","freq", "ra", "dec"),
row_axes=(0, 1, 2), col_axes=(3, 4, 5))
covariance.copy_axis_info(map)
# Make a matrix of angular pairwise lags.
sq_angles = (dec[None, :, None, None] - dec[None, None, None, :])**2
sq_angles = sq_angles + \
(ra[:, None, None, None] - ra[None, None, :, None])**2
if self.feedback >= 2 :
print "Filling covariance matrix by interpolation."
# Now fill in the elements by interpolating integrals.
for find1 in xrange(nfreq) :
for find2 in xrange(nfreq) :
# The pairwise angular lags in the unit system.
this_sq_lag = (sq_angles*(Drho_Ddeg[find1] +
Drho_Ddeg[find2])**2/4)
# The interpolation function. Perhaps there is a better
# algorithm than cubic?
interpolator = interpolate.interp1d(sq_lag,
integrals[find1,find2,:], bounds_error=True,
kind='cubic')
covariance[find1,:,:,find2,:,:] = interpolator(this_sq_lag)
del covariance, map
if self.feedback >= 2 :
print "Done"
def test_freq_independant(self):
self.Beam = beam.GaussianBeam(1.0)
self.assertAlmostEqual(self.Beam.beam_function(1.0, 2.0), 0.0551589, 6)
self.assertAlmostEqual(self.Beam.beam_function(1.0, None), 0.0551589,
6)
def test_checks_axes(self):
self.map.axes = ('freq', 'lat', 'long')
self.Beam = beam.GaussianBeam(0.2, None)
self.assertRaises(ce.DataError, self.Beam.apply, self.map)