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 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)
