def to_pixel(self, Nside=None, Npix=None, dtype=None, out=None):
"""
::
>>> insh = harmonic_sphere_map(0, 0, 4)
>>> insh.to_pixel(8)
Pixel sphere map (ring-ordered, Nside=8, Npix=768)
Convert a uniform map::
>>> shmap = harmonic_sphere_map([[23], [0, 0], [0, 0, 0]])
>>> pixmap = shmap.to_pixel(8); pixmap
Pixel sphere map (ring-ordered, Nside=8, Npix=768)
>>> np.allclose(pixmap, 23.0 / np.sqrt(4*np.pi))
True
One can convert multiple maps at once::
>>> M = shmap
>>> M = np.hstack((M[:,None], M[:,None], M[:,None], M[:,None]))
>>> M = np.dstack((M, M))
>>> M = harmonic_sphere_map(M, 0, 2); M
(4, 2)-stack of brief complex harmonic sphere maps with l=0..2 (6 coefficients)
>>> x = M.to_pixel(4); x
(4, 2)-stack of pixel sphere maps (ring-ordered, Nside=4, Npix=192)
>>> np.allclose(x, 23.0 / np.sqrt(4*np.pi))
True
"""
self._check_not_pretending()
if self.format is not COMPLEX_BRIEF:
return self.to_complex().to_pixel(Nside, Npix, dtype, out)
if Nside is None:
if Npix is None: raise ValueError("Provide Nside or Npix")
Nside = npix2nside(Npix)
if Npix is None:
Npix = nside2npix(Nside)
if dtype is None:
dtype = self.dtype
dtype = to_real_dtype(dtype)
# for now, only double...
assert dtype == np.float64
size = self.shape[1:]
if out is None:
out = np.empty((Npix,) + size, dtype, order='F')
# Todo: Optimize -- have lmin in complexpacked2complexmatrix
if self.lmin == 0:
source = self
else:
source = np.empty((l_to_lm(self.lmax + 1),) + size, complex_dtype, order='F')
source[:l_to_lm(self.lmin)] = 0
source[l_to_lm(self.lmin):] = self
for mapidx in np.ndindex(*size):
idx = (slice(None),) + mapidx
alm_matrix = mapdatautils.alm_complexpacked2complexmatrix(source[idx])
mapdatautils.alm2map(Nside, alm_matrix, out=out[idx])
return _PixelSphereMap(out, pixel_order='ring')
def rotate(self, psi, theta, phi):
"""
Returns a rotated copy of self. O(lmax^3).
::
>>> M = harmonic_sphere_map([[1, 0], [1, 0, 0]], lmin=1)
>>> R = M.rotate(0, np.pi, 0); R
Brief complex harmonic sphere map with l=1..2 (5 coefficients)
>>> np.round(R.to_array(), 4)
array([-1.+0.j, -0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j])
One can convert multiple maps at once::
TODO write tests
"""
from healpix import rotate_alm_d
self._check_not_pretending()
if psi == 0 and theta == 0 and phi == 0:
return self.copy()
if self.format is not COMPLEX_BRIEF:
x = self.to_complex().rotate(psi, theta, phi)
if self.format is REAL_FULL:
return x.to_real()
else:
assert False
size = self.shape[1:]
# Todo: Optimize -- have lmin in complexpacked2complexmatrix
out = np.empty((l_to_lm(self.lmax + 1),) + size, complex_dtype, order='F')
out[:l_to_lm(self.lmin), ...] = 0
out[l_to_lm(self.lmin):, ...] = self
alm_matrix = np.empty((1, self.lmax + 1, self.lmax + 1), complex_dtype, order='F')
for mapidx in np.ndindex(*size):
idx = (slice(None),) + mapidx
mapdatautils.alm_complexpacked2complexmatrix(out[idx], alm_matrix[0,:,:])
rotate_alm_d(self.lmax, alm_matrix, psi, theta, phi)
mapdatautils.alm_complexmatrix2complexpacked(alm_matrix[0,:,:], out[idx])
out = out[l_to_lm(self.lmin):, ...]
return _HarmonicSphereMap(out, self.lmin, self.lmax, COMPLEX_BRIEF)
def simulate_harmonic_sphere_maps(lmin, lmax, size=None, state=np.random):
"""
Simulates standard normal maps in spherical harmonic space.
INPUT:
- ``n`` - The number of maps to simulate
EXAMPLES::
>>> simulate_harmonic_sphere_maps(0, 3)
Brief complex harmonic sphere map with l=0..3 (10 coefficients)
>>> simulate_harmonic_sphere_maps(2, 3, size=10)
(10,)-stack of brief complex harmonic sphere maps with l=2..3 (7 coefficients)
"""
if size is None:
size = ()
if not isinstance(size, tuple):
size = (size,)
real_coefs = (lmax+1)**2
complex_coefs = l_to_lm(lmax+1)
lmin_lm = l_to_lm(lmin)
Zreal = state.standard_normal((real_coefs,) + size).astype(real_dtype)
Zcomplex = np.empty((complex_coefs,) + size, complex_dtype)
Zcomplex
if len(size) > 1:
raise NotImplementedError()
# TODO: Have lmin in realpacked2complexpacked
# For now, just slice away output for 0:lmin
if size == ():
mapdatautils.alm_realpacked2complexpacked(Zreal, out=Zcomplex)
else:
for i in range(size[0]):
mapdatautils.alm_realpacked2complexpacked(Zreal[:,i], out=Zcomplex[:,i])
return _HarmonicSphereMap(Zcomplex[l_to_lm(lmin):, ...], lmin, lmax, COMPLEX_BRIEF)
def harmonic_sphere_map(data, lmin=0, lmax=None, is_complex=None, is_brief=None):
"""
Constructs a sphere map in harmonic space.
EXAMPLES::
>>> M = harmonic_sphere_map([[0], [1, 3+1j], [1, 1, 1], [1, 1, 1, 1]]); M
Brief complex harmonic sphere map with l=0..3 (10 coefficients)
>>> M2 = harmonic_sphere_map([[1, 1, 1, 1]], lmin=3); M2
Brief complex harmonic sphere map with l=3..3 (4 coefficients)
>>> harmonic_sphere_map([[0], [1 + 1j, 3+1j]])
Traceback (most recent call last):
...
ValueError: Entries on m=0-positions must be real
>>> harmonic_sphere_map(np.dstack((M[:,None,None], M[:,None,None])))
(1, 2)-stack of brief complex harmonic sphere maps with l=0..3 (10 coefficients)
>>> M = harmonic_sphere_map(2, 0, 100); M
Brief complex harmonic sphere map with l=0..100 (5151 coefficients)
>>> np.sin(M) + 34 * M
Brief complex harmonic sphere map with l=0..100 (5151 coefficients)
Real coefficients are also supported::
>>> M = harmonic_sphere_map([[0], [-1, 1, 3], [-1, -2, 3, 4, 5]]); M
Real harmonic sphere map with l=0..2 (9 coefficients)
Scalar initialization::
>>> harmonic_sphere_map(10, 2, 4)
Brief complex harmonic sphere map with l=2..4 (12 coefficients)
"""
if np.isscalar(data):
if is_complex is None:
is_complex = True
if lmax is None:
raise ValueError('Cannot infer lmax from data')
data = (np.ones(l_to_lm(lmax + 1, is_complex) - l_to_lm(lmin, is_complex),
dtype=complex_dtype if is_complex else real_dtype, order='F') *
float(data))
elif isinstance(data, list):
# Need at least two nesting levels of lists
if (not isinstance(data[0], list) or isinstance(data[0][0], list)):
raise ValueError("Please provide coefficients as [[a00], [a10, a11], ...]")
if lmax is None:
lmax = len(data) + lmin - 1
if is_complex is None:
# Auto-detect is_complex from data
if lmin == 0 and len(data) == 1:
is_complex = True # only a00 given; assume is_complex
elif lmin == 0:
is_complex = (len(data[1]) == 2)
else:
is_complex = len(data[0]) == lmin + 1
num_coefs = l_to_lm(lmax + 1, is_complex) - l_to_lm(lmin, is_complex)
buf = np.zeros(num_coefs, dtype=complex_dtype if is_complex else real_dtype, order='F')
i = 0
for l, coefs_for_l in zip(range(lmin, lmax+1), data):
n = l+1 if is_complex else 2*l + 1
if len(coefs_for_l) != n:
raise ValueError("Wrong number of coefficients for l=%d" % l)
if coefs_for_l[0].imag != 0:
raise ValueError("Entries on m=0-positions must be real")
buf[i:i+n] = coefs_for_l
i += n
data = buf
else:
if is_complex is None:
is_complex = True
data = np.asfortranarray(data, dtype=complex_dtype if is_complex else real_dtype)
lmax_wanted = num_alm_to_lmax(l_to_lm(lmin, is_complex) + data.shape[0], is_complex)
if lmax is not None and lmax != lmax_wanted:
raise ValueError('lmax given does not match data lmax')
if lmax is None:
lmax = lmax_wanted
if is_brief is None:
is_brief = is_complex
if is_complex:
format = COMPLEX_BRIEF if is_brief else COMPLEX_FULL
else:
if is_brief:
raise ValueError()
format = REAL_FULL
return _HarmonicSphereMap(data, lmin=lmin, lmax=lmax, format=format)
def to_harmonic(self, lmin, lmax, use_weights=True,
weights_transform=None):
"""
::
>>> inpix = pixel_sphere_map(0, 4)
>>> inpix.to_harmonic(0, 8)
Brief complex harmonic sphere map with l=0..8 (45 coefficients)
Convert a uniform map. First elements should be 12*sqrt(4 pi),
the remaining elements 0::
>>> N = pixel_sphere_map(Nside=8, data=12)
>>> x = N.to_harmonic(0, 16)
>>> np.allclose(x[0], 12 * np.sqrt(4*np.pi))
True
>>> np.allclose(x[1:], 0, atol=1e-1)
True
One can convert multiple maps at once:
>>> N = np.hstack((N[:,None], N[:,None], N[:,None], N[:,None]))
>>> N = np.dstack((N, N))
>>> N = pixel_sphere_map(data=N, Nside=8); N
(4, 2)-stack of pixel sphere maps (ring-ordered, Nside=8, Npix=768)
>>> x = N.to_harmonic(0, 16); x
(4, 2)-stack of brief complex harmonic sphere maps with l=0..16 (153 coefficients)
>>> np.allclose(x[0,:,:], 12 * np.sqrt(4*np.pi))
True
>>> np.allclose(x[1:,:,:], 0, atol=.1)
True
"""
if self.pixel_order == 'nested':
return self.to_ring().to_harmonic(lmin, lmax)
assert self.pixel_order == 'ring'
self._check_not_pretending()
dtype = to_complex_dtype(self.dtype)
# for now, only double...
assert dtype == np.complex128
size = self.shape[1:]
numalm = l_to_lm(lmax + 1)
alm_matrix_buf = np.empty((lmax + 1, lmax + 1), complex_dtype, order='F')
alm = np.empty((numalm,) + size, complex_dtype, order='F')
if use_weights:
weight_ring_temperature = healpix_res.weight_ring(Nside=self.Nside)[0,:]
if weights_transform is not None:
weight_ring_temperature = weights_transform(weight_ring_temperature)
else:
weight_ring_temperature = np.ones(2 * self.Nside)
for mapidx in np.ndindex(*size):
idx = (slice(None),) + mapidx
map = self[idx]
mapdatautils.map2alm(lmax, map, weight_ring_temperature, out=alm_matrix_buf)
mapdatautils.alm_complexmatrix2complexpacked(alm_matrix_buf, out=alm[idx])
# Trim away portion up to lmin
alm = alm[l_to_lm(lmin):,...]
return _HarmonicSphereMap(alm, lmin, lmax, COMPLEX_BRIEF)