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pixelfunc.py
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1738 lines (1494 loc) · 49.8 KB
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#
# This file is part of Healpy.
#
# Healpy is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# Healpy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with Healpy; if not, write to the Free Software
# Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
#
# For more information about Healpy, see http://code.google.com/p/healpy
#
"""
=====================================================
pixelfunc.py : Healpix pixelization related functions
=====================================================
This module provides functions related to Healpix pixelization scheme.
conversion from/to sky coordinates
----------------------------------
- :func:`pix2ang` converts pixel number to angular coordinates
- :func:`pix2vec` converts pixel number to unit 3-vector direction
- :func:`ang2pix` converts angular coordinates to pixel number
- :func:`vec2pix` converts 3-vector to pixel number
- :func:`vec2ang` converts 3-vector to angular coordinates
- :func:`ang2vec` converts angular coordinates to unit 3-vector
- :func:`pix2xyf` converts pixel number to coordinates within face
- :func:`xyf2pix` converts coordinates within face to pixel number
- :func:`get_interp_weights` returns the 4 nearest pixels for given
angular coordinates and the relative weights for interpolation
- :func:`get_all_neighbours` return the 8 nearest pixels for given
angular coordinates
conversion between NESTED and RING schemes
------------------------------------------
- :func:`nest2ring` converts NESTED scheme pixel numbers to RING
scheme pixel number
- :func:`ring2nest` converts RING scheme pixel number to NESTED
scheme pixel number
- :func:`reorder` reorders a healpix map pixels from one scheme to another
nside/npix/resolution
---------------------
- :func:`nside2npix` converts healpix nside parameter to number of pixel
- :func:`npix2nside` converts number of pixel to healpix nside parameter
- :func:`nside2order` converts nside to order
- :func:`order2nside` converts order to nside
- :func:`nside2resol` converts nside to mean angular resolution
- :func:`nside2pixarea` converts nside to pixel area
- :func:`isnsideok` checks the validity of nside
- :func:`isnpixok` checks the validity of npix
- :func:`get_map_size` gives the number of pixel of a map
- :func:`get_min_valid_nside` gives the minimum nside possible for a given
number of pixel
- :func:`get_nside` returns the nside of a map
- :func:`maptype` checks the type of a map (one map or sequence of maps)
- :func:`ud_grade` upgrades or degrades the resolution (nside) of a map
Masking pixels
--------------
- :const:`UNSEEN` is a constant value interpreted as a masked pixel
- :func:`mask_bad` returns a map with ``True`` where map is :const:`UNSEEN`
- :func:`mask_good` returns a map with ``False`` where map is :const:`UNSEEN`
- :func:`ma` returns a masked array as map, with mask given by :func:`mask_bad`
Map data manipulation
---------------------
- :func:`fit_dipole` fits a monopole+dipole on the map
- :func:`fit_monopole` fits a monopole on the map
- :func:`remove_dipole` fits and removes a monopole+dipole from the map
- :func:`remove_monopole` fits and remove a monopole from the map
- :func:`get_interp_val` computes a bilinear interpolation of the map
at given angular coordinates, using 4 nearest neighbours
"""
try:
from exceptions import NameError
except:
pass
import numpy as np
from functools import wraps
UNSEEN = None
try:
from . import _healpy_pixel_lib as pixlib
#: Special value used for masked pixels
UNSEEN = pixlib.UNSEEN
except:
import warnings
warnings.warn('Warning: cannot import _healpy_pixel_lib module')
# We are using 64-bit integer types.
# nside > 2**29 requires extended integer types.
max_nside = 1 << 29
__all__ = ['pix2ang', 'pix2vec', 'ang2pix', 'vec2pix',
'ang2vec', 'vec2ang',
'get_interp_weights', 'get_neighbours', 'get_interp_val', 'get_all_neighbours',
'max_pixrad',
'nest2ring', 'ring2nest', 'reorder', 'ud_grade',
'UNSEEN', 'mask_good', 'mask_bad', 'ma',
'fit_dipole', 'remove_dipole', 'fit_monopole', 'remove_monopole',
'nside2npix', 'npix2nside', 'nside2order', 'order2nside',
'nside2resol', 'nside2pixarea',
'isnsideok', 'isnpixok',
'get_map_size', 'get_min_valid_nside',
'get_nside', 'maptype', 'ma_to_array']
def check_theta_valid(theta):
"""Raises exception if theta is not within 0 and pi"""
theta = np.asarray(theta)
if not((theta >= 0).all() and (theta <= np.pi + 1e-5).all()):
raise ValueError('THETA is out of range [0,pi]')
def maptype(m):
"""Describe the type of the map (valid, single, sequence of maps).
Checks : the number of maps, that all maps have same length and that this
length is a valid map size (using :func:`isnpixok`).
Parameters
----------
m : sequence
the map to get info from
Returns
-------
info : int
-1 if the given object is not a valid map, 0 if it is a single map,
*info* > 0 if it is a sequence of maps (*info* is then the number of
maps)
Examples
--------
>>> import healpy as hp
>>> hp.pixelfunc.maptype(np.arange(12))
0
>>> hp.pixelfunc.maptype([np.arange(12), np.arange(12)])
2
"""
if not hasattr(m, '__len__'):
raise TypeError('input map is a scalar')
if len(m) == 0:
raise TypeError('input map has length zero')
if hasattr(m[0], '__len__'):
npix=len(m[0])
for mm in m[1:]:
if len(mm) != npix:
raise TypeError('input maps have different npix')
if isnpixok(len(m[0])):
return len(m)
else:
raise TypeError('bad number of pixels')
else:
if isnpixok(len(m)):
return 0
else:
raise TypeError('bad number of pixels')
def ma_to_array(m):
"""Converts a masked array or a list of masked arrays to filled numpy arrays
Parameters
----------
m : a map (may be a sequence of maps)
Returns
-------
m : filled map or tuple of filled maps
Examples
--------
>>> import healpy as hp
>>> m = hp.ma(np.array([2., 2., 3, 4, 5, 0, 0, 0, 0, 0, 0, 0]))
>>> m.mask = np.array([0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], dtype=np.bool)
>>> print(m.data[1]) # data is not affected by mask
2.0
>>> print(m[1]) # shows that the value is masked
--
>>> print(ma_to_array(m)[1]) # filled array, masked values replace by UNSEEN
-1.6375e+30
"""
try:
return m.filled()
except AttributeError:
try:
return tuple([mm.filled() for mm in m])
except AttributeError:
pass
return m
def is_ma(m):
"""Converts a masked array or a list of masked arrays to filled numpy arrays
Parameters
----------
m : a map (may be a sequence of maps)
Returns
-------
is_ma : bool
whether the input map was a ma or not
"""
return hasattr(m, 'filled') or hasattr(m[0], 'filled')
def accept_ma(f):
"""Wraps a function in order to convert the input map from
a masked to a regular numpy array, and convert back the
output from a regular array to a masked array"""
@wraps(f)
def wrapper(map_in, *args, **kwds):
return_ma = is_ma(map_in)
m = ma_to_array(map_in)
out = f(m, *args, **kwds)
return ma(out) if return_ma else out
return wrapper
def mask_bad(m, badval = UNSEEN, rtol = 1.e-5, atol = 1.e-8):
"""Returns a bool array with ``True`` where m is close to badval.
Parameters
----------
m : a map (may be a sequence of maps)
badval : float, optional
The value of the pixel considered as bad (:const:`UNSEEN` by default)
rtol : float, optional
The relative tolerance
atol : float, optional
The absolute tolerance
Returns
-------
mask
a bool array with the same shape as the input map, ``True`` where input map is
close to badval, and ``False`` elsewhere.
See Also
--------
mask_good, ma
Examples
--------
>>> import healpy as hp
>>> import numpy as np
>>> m = np.arange(12.)
>>> m[3] = hp.UNSEEN
>>> hp.mask_bad(m)
array([False, False, False, True, False, False, False, False, False,
False, False, False], dtype=bool)
"""
m = np.asarray(m)
atol = np.absolute(atol)
rtol = np.absolute(rtol)
return np.absolute(m - badval) <= atol + rtol * np.absolute(badval)
def mask_good(m, badval = UNSEEN, rtol = 1.e-5, atol = 1.e-8):
"""Returns a bool array with ``False`` where m is close to badval.
Parameters
----------
m : a map (may be a sequence of maps)
badval : float, optional
The value of the pixel considered as bad (:const:`UNSEEN` by default)
rtol : float, optional
The relative tolerance
atol : float, optional
The absolute tolerance
Returns
-------
a bool array with the same shape as the input map, ``False`` where input map is
close to badval, and ``True`` elsewhere.
See Also
--------
mask_bad, ma
Examples
--------
>>> import healpy as hp
>>> m = np.arange(12.)
>>> m[3] = hp.UNSEEN
>>> hp.mask_good(m)
array([ True, True, True, False, True, True, True, True, True,
True, True, True], dtype=bool)
"""
m = np.asarray(m)
atol = np.absolute(atol)
rtol = np.absolute(rtol)
return np.absolute(m - badval) > atol + rtol * np.absolute(badval)
def ma(m, badval = UNSEEN, rtol = 1e-5, atol = 1e-8, copy = True):
"""Return map as a masked array, with ``badval`` pixels masked.
Parameters
----------
m : a map (may be a sequence of maps)
badval : float, optional
The value of the pixel considered as bad (:const:`UNSEEN` by default)
rtol : float, optional
The relative tolerance
atol : float, optional
The absolute tolerance
copy : bool, optional
If ``True``, a copy of the input map is made.
Returns
-------
a masked array with the same shape as the input map,
masked where input map is close to badval.
See Also
--------
mask_good, mask_bad, numpy.ma.masked_values
Examples
--------
>>> import healpy as hp
>>> m = np.arange(12.)
>>> m[3] = hp.UNSEEN
>>> hp.ma(m)
masked_array(data = [0.0 1.0 2.0 -- 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0],
mask = [False False False True False False False False False False False False],
fill_value = -1.6375e+30)
<BLANKLINE>
"""
if maptype(m) == 0:
return np.ma.masked_values(m, badval, rtol = rtol, atol = atol, copy = copy)
else:
return tuple([ma(mm) for mm in m])
def ang2pix(nside,theta,phi,nest=False):
"""ang2pix : nside,theta[rad],phi[rad],nest=False -> ipix (default:RING)
Parameters
----------
nside : int, scalar or array-like
The healpix nside parameter, must be a power of 2, less than 2**30
theta, phi : float, scalars or array-like
Angular coordinates of a point on the sphere
nest : bool, optional
if True, assume NESTED pixel ordering, otherwise, RING pixel ordering
Returns
-------
pix : int or array of int
The healpix pixel numbers. Scalar if all input are scalar, array otherwise.
Usual numpy broadcasting rules apply.
See Also
--------
pix2ang, pix2vec, vec2pix
Examples
--------
>>> import healpy as hp
>>> hp.ang2pix(16, np.pi/2, 0)
1440
>>> hp.ang2pix(16, [np.pi/2, np.pi/4, np.pi/2, 0, np.pi], [0., np.pi/4, np.pi/2, 0, 0])
array([1440, 427, 1520, 0, 3068])
>>> hp.ang2pix(16, np.pi/2, [0, np.pi/2])
array([1440, 1520])
>>> hp.ang2pix([1, 2, 4, 8, 16], np.pi/2, 0)
array([ 4, 12, 72, 336, 1440])
"""
check_theta_valid(theta)
check_nside(nside)
if nest:
return pixlib._ang2pix_nest(nside,theta,phi)
else:
return pixlib._ang2pix_ring(nside,theta,phi)
def pix2ang(nside,ipix,nest=False):
"""pix2ang : nside,ipix,nest=False -> theta[rad],phi[rad] (default RING)
Parameters
----------
nside : int or array-like
The healpix nside parameter, must be a power of 2, less than 2**30
ipix : int or array-like
Pixel indices
nest : bool, optional
if True, assume NESTED pixel ordering, otherwise, RING pixel ordering
Returns
-------
theta, phi : float, scalar or array-like
The angular coordinates corresponding to ipix. Scalar if all input
are scalar, array otherwise. Usual numpy broadcasting rules apply.
See Also
--------
ang2pix, vec2pix, pix2vec
Examples
--------
>>> import healpy as hp
>>> hp.pix2ang(16, 1440)
(1.5291175943723188, 0.0)
>>> hp.pix2ang(16, [1440, 427, 1520, 0, 3068])
(array([ 1.52911759, 0.78550497, 1.57079633, 0.05103658, 3.09055608]), array([ 0. , 0.78539816, 1.61988371, 0.78539816, 0.78539816]))
>>> hp.pix2ang([1, 2, 4, 8], 11)
(array([ 2.30052398, 0.84106867, 0.41113786, 0.2044802 ]), array([ 5.49778714, 5.89048623, 5.89048623, 5.89048623]))
"""
check_nside(nside)
if nest:
return pixlib._pix2ang_nest(nside, ipix)
else:
return pixlib._pix2ang_ring(nside,ipix)
def xyf2pix(nside,x,y,face,nest=False):
"""xyf2pix : nside,x,y,face,nest=False -> ipix (default:RING)
Parameters
----------
nside : int, scalar or array-like
The healpix nside parameter, must be a power of 2
x, y : int, scalars or array-like
Pixel indices within face
face : int, scalars or array-like
Face number
nest : bool, optional
if True, assume NESTED pixel ordering, otherwise, RING pixel ordering
Returns
-------
pix : int or array of int
The healpix pixel numbers. Scalar if all input are scalar, array otherwise.
Usual numpy broadcasting rules apply.
See Also
--------
pix2xyf
Examples
--------
>>> import healpy as hp
>>> hp.xyf2pix(16, 8, 8, 4)
1440
>>> hp.xyf2pix(16, [8, 8, 8, 15, 0], [8, 8, 7, 15, 0], [4, 0, 5, 0, 8])
array([1440, 427, 1520, 0, 3068])
"""
check_nside(nside)
if nest:
return pixlib._xyf2pix_nest(nside,x,y,face)
else:
return pixlib._xyf2pix_ring(nside,x,y,face)
def pix2xyf(nside,ipix,nest=False):
"""pix2xyf : nside,ipix,nest=False -> x,y,face (default RING)
Parameters
----------
nside : int or array-like
The healpix nside parameter, must be a power of 2
ipix : int or array-like
Pixel indices
nest : bool, optional
if True, assume NESTED pixel ordering, otherwise, RING pixel ordering
Returns
-------
x, y : int, scalars or array-like
Pixel indices within face
face : int, scalars or array-like
Face number
See Also
--------
xyf2pix
Examples
--------
>>> import healpy as hp
>>> hp.pix2xyf(16, 1440)
(8, 8, 4)
>>> hp.pix2xyf(16, [1440, 427, 1520, 0, 3068])
(array([ 8, 8, 8, 15, 0]), array([ 8, 8, 7, 15, 0]), array([4, 0, 5, 0, 8]))
>>> hp.pix2xyf([1, 2, 4, 8], 11)
(array([0, 1, 3, 7]), array([0, 0, 2, 6]), array([11, 3, 3, 3]))
"""
check_nside(nside)
if nest:
return pixlib._pix2xyf_nest(nside, ipix)
else:
return pixlib._pix2xyf_ring(nside,ipix)
def vec2pix(nside,x,y,z,nest=False):
"""vec2pix : nside,x,y,z,nest=False -> ipix (default:RING)
Parameters
----------
nside : int or array-like
The healpix nside parameter, must be a power of 2, less than 2**30
x,y,z : floats or array-like
vector coordinates defining point on the sphere
nest : bool, optional
if True, assume NESTED pixel ordering, otherwise, RING pixel ordering
Returns
-------
ipix : int, scalar or array-like
The healpix pixel number corresponding to input vector. Scalar if all input
are scalar, array otherwise. Usual numpy broadcasting rules apply.
See Also
--------
ang2pix, pix2ang, pix2vec
Examples
--------
>>> import healpy as hp
>>> hp.vec2pix(16, 1, 0, 0)
1504
>>> hp.vec2pix(16, [1, 0], [0, 1], [0, 0])
array([1504, 1520])
>>> hp.vec2pix([1, 2, 4, 8], 1, 0, 0)
array([ 4, 20, 88, 368])
"""
if nest:
return pixlib._vec2pix_nest(nside,x,y,z)
else:
return pixlib._vec2pix_ring(nside,x,y,z)
def pix2vec(nside,ipix,nest=False):
"""pix2vec : nside,ipix,nest=False -> x,y,z (default RING)
Parameters
----------
nside : int, scalar or array-like
The healpix nside parameter, must be a power of 2, less than 2**30
ipix : int, scalar or array-like
Healpix pixel number
nest : bool, optional
if True, assume NESTED pixel ordering, otherwise, RING pixel ordering
Returns
-------
x, y, z : floats, scalar or array-like
The coordinates of vector corresponding to input pixels. Scalar if all input
are scalar, array otherwise. Usual numpy broadcasting rules apply.
See Also
--------
ang2pix, pix2ang, vec2pix
Examples
--------
>>> import healpy as hp
>>> hp.pix2vec(16, 1504)
(0.99879545620517241, 0.049067674327418015, 0.0)
>>> hp.pix2vec(16, [1440, 427])
(array([ 0.99913157, 0.5000534 ]), array([ 0. , 0.5000534]), array([ 0.04166667, 0.70703125]))
>>> hp.pix2vec([1, 2], 11)
(array([ 0.52704628, 0.68861915]), array([-0.52704628, -0.28523539]), array([-0.66666667, 0.66666667]))
"""
check_nside(nside)
if nest:
return pixlib._pix2vec_nest(nside,ipix)
else:
return pixlib._pix2vec_ring(nside,ipix)
def ang2vec(theta, phi):
"""ang2vec : convert angles to 3D position vector
Parameters
----------
theta : float, scalar or arry-like
colatitude in radians measured southward from north pole (in [0,pi]).
phi : float, scalar or array-like
longitude in radians measured eastward (in [0, 2*pi]).
Returns
-------
vec : float, array
if theta and phi are vectors, the result is a 2D array with a vector per row
otherwise, it is a 1D array of shape (3,)
See Also
--------
vec2ang, rotator.dir2vec, rotator.vec2dir
"""
check_theta_valid(theta)
sintheta = np.sin(theta)
return np.array([sintheta*np.cos(phi),
sintheta*np.sin(phi),
np.cos(theta)]).T
def vec2ang(vectors):
"""vec2ang: vectors [x, y, z] -> theta[rad], phi[rad]
Parameters
----------
vectors : float, array-like
the vector(s) to convert, shape is (3,) or (N, 3)
Returns
-------
theta, phi : float, tuple of two arrays
the colatitude and longitude in radians
See Also
--------
ang2vec, rotator.vec2dir, rotator.dir2vec
"""
vectors = vectors.reshape(-1,3)
dnorm = np.sqrt(np.sum(np.square(vectors),axis=1))
theta = np.arccos(vectors[:,2]/dnorm)
phi = np.arctan2(vectors[:,1],vectors[:,0])
phi[phi < 0] += 2*np.pi
return theta, phi
def ring2nest(nside, ipix):
"""Convert pixel number from RING ordering to NESTED ordering.
Parameters
----------
nside : int, scalar or array-like
the healpix nside parameter
ipix : int, scalar or array-like
the pixel number in RING scheme
Returns
-------
ipix : int, scalar or array-like
the pixel number in NESTED scheme
See Also
--------
nest2ring, reorder
Examples
--------
>>> import healpy as hp
>>> hp.ring2nest(16, 1504)
1130
>>> hp.ring2nest(2, np.arange(10))
array([ 3, 7, 11, 15, 2, 1, 6, 5, 10, 9])
>>> hp.ring2nest([1, 2, 4, 8], 11)
array([ 11, 13, 61, 253])
"""
check_nside(nside)
return pixlib._ring2nest(nside, ipix)
def nest2ring(nside, ipix):
"""Convert pixel number from NESTED ordering to RING ordering.
Parameters
----------
nside : int, scalar or array-like
the healpix nside parameter
ipix : int, scalar or array-like
the pixel number in NESTED scheme
Returns
-------
ipix : int, scalar or array-like
the pixel number in RING scheme
See Also
--------
ring2nest, reorder
Examples
--------
>>> import healpy as hp
>>> hp.nest2ring(16, 1130)
1504
>>> hp.nest2ring(2, np.arange(10))
array([13, 5, 4, 0, 15, 7, 6, 1, 17, 9])
>>> hp.nest2ring([1, 2, 4, 8], 11)
array([ 11, 2, 12, 211])
"""
check_nside(nside)
return pixlib._nest2ring(nside, ipix)
@accept_ma
def reorder(map_in, inp=None, out=None, r2n=None, n2r=None):
"""Reorder an healpix map from RING/NESTED ordering to NESTED/RING
Parameters
----------
map_in : array-like
the input map to reorder, accepts masked arrays
inp, out : ``'RING'`` or ``'NESTED'``
define the input and output ordering
r2n : bool
if True, reorder from RING to NESTED
n2r : bool
if True, reorder from NESTED to RING
Returns
-------
map_out : array-like
the reordered map, as masked array if the input was a
masked array
Notes
-----
if ``r2n`` or ``n2r`` is defined, override ``inp`` and ``out``.
See Also
--------
nest2ring, ring2nest
Examples
--------
>>> import healpy as hp
>>> hp.reorder(np.arange(48), r2n = True)
array([13, 5, 4, 0, 15, 7, 6, 1, 17, 9, 8, 2, 19, 11, 10, 3, 28,
20, 27, 12, 30, 22, 21, 14, 32, 24, 23, 16, 34, 26, 25, 18, 44, 37,
36, 29, 45, 39, 38, 31, 46, 41, 40, 33, 47, 43, 42, 35])
>>> hp.reorder(np.arange(12), n2r = True)
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])
>>> hp.reorder(hp.ma(np.arange(12.)), n2r = True)
masked_array(data = [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.],
mask = False,
fill_value = -1.6375e+30)
<BLANKLINE>
>>> m = [np.arange(12.), np.arange(12.), np.arange(12.)]
>>> m[0][2] = hp.UNSEEN
>>> m[1][2] = hp.UNSEEN
>>> m[2][2] = hp.UNSEEN
>>> m = hp.ma(m)
>>> hp.reorder(m, n2r = True)
(masked_array(data = [0.0 1.0 -- 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0],
mask = [False False True False False False False False False False False False],
fill_value = -1.6375e+30)
, masked_array(data = [0.0 1.0 -- 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0],
mask = [False False True False False False False False False False False False],
fill_value = -1.6375e+30)
, masked_array(data = [0.0 1.0 -- 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0],
mask = [False False True False False False False False False False False False],
fill_value = -1.6375e+30)
)
"""
typ = maptype(map_in)
if typ == 0:
npix = len(map_in)
else:
npix = len(map_in[0])
nside = npix2nside(npix)
if nside>128:
bunchsize = npix//24
else:
bunchsize = npix
if r2n:
inp='RING'
out='NEST'
if n2r:
inp='NEST'
out='RING'
inp = str(inp).upper()[0:4]
out = str(out).upper()[0:4]
if inp not in ['RING','NEST'] or out not in ['RING','NEST']:
raise ValueError('inp and out must be either RING or NEST')
if typ == 0:
mapin = [map_in]
else:
mapin = map_in
mapout = []
for m_in in mapin:
if inp == out:
mapout.append(m_in)
elif inp == 'RING':
m_out = np.zeros(npix,dtype=type(m_in[0]))
for ibunch in range(npix//bunchsize):
ipix_n = np.arange(ibunch*bunchsize,
(ibunch+1)*bunchsize)
ipix_r = nest2ring(nside, ipix_n)
m_out[ipix_n] = np.asarray(m_in)[ipix_r]
mapout.append(m_out)
elif inp == 'NEST':
m_out = np.zeros(npix,dtype=type(m_in[0]))
for ibunch in range(npix//bunchsize):
ipix_r = np.arange(ibunch*bunchsize,
(ibunch+1)*bunchsize)
ipix_n = ring2nest(nside, ipix_r)
m_out[ipix_r] = np.asarray(m_in)[ipix_n]
mapout.append(m_out)
if typ == 0:
return mapout[0]
else:
return mapout
def nside2npix(nside):
"""Give the number of pixels for the given nside.
Parameters
----------
nside : int
healpix nside parameter; an exception is raised if nside is not valid
(nside must be a power of 2, less than 2**30)
Returns
-------
npix : int
corresponding number of pixels
Notes
-----
Raise a ValueError exception if nside is not valid.
Examples
--------
>>> import healpy as hp
>>> import numpy as np
>>> hp.nside2npix(8)
768
>>> np.all([hp.nside2npix(nside) == 12 * nside**2 for nside in [2**n for n in range(12)]])
True
>>> hp.nside2npix(7)
Traceback (most recent call last):
...
ValueError: 7 is not a valid nside parameter (must be a power of 2, less than 2**30)
"""
check_nside(nside)
return 12*nside**2
def nside2order(nside):
"""Give the resolution order for a given nside.
Parameters
----------
nside : int
healpix nside parameter; an exception is raised if nside is not valid
(nside must be a power of 2, less than 2**30)
Returns
-------
order : int
corresponding order where nside = 2**(order)
Notes
-----
Raise a ValueError exception if nside is not valid.
Examples
--------
>>> import healpy as hp
>>> import numpy as np
>>> hp.nside2order(128)
7
>>> np.all([hp.nside2order(2**o) == o for o in range(30)])
True
>>> hp.nside2order(7)
Traceback (most recent call last):
...
ValueError: 7 is not a valid nside parameter (must be a power of 2, less than 2**30)
"""
check_nside(nside)
return len('{0:b}'.format(nside)) - 1
def nside2resol(nside, arcmin=False):
"""Give approximate resolution (pixel size in radian or arcmin) for nside.
Resolution is just the square root of the pixel area, which is a gross
approximation given the different pixel shapes
Parameters
----------
nside : int
healpix nside parameter, must be a power of 2, less than 2**30
arcmin : bool
if True, return resolution in arcmin, otherwise in radian
Returns
-------
resol : float
approximate pixel size in radians or arcmin
Notes
-----
Raise a ValueError exception if nside is not valid.
Examples
--------
>>> import healpy as hp
>>> hp.nside2resol(128, arcmin = True)
27.483891294539248
>>> hp.nside2resol(256)
0.0039973699529159707
>>> hp.nside2resol(7)
Traceback (most recent call last):
...
ValueError: 7 is not a valid nside parameter (must be a power of 2, less than 2**30)
"""
check_nside(nside)
resol = np.sqrt(nside2pixarea(nside))
if arcmin:
resol = np.rad2deg(resol) * 60
return resol
def nside2pixarea(nside, degrees=False):
"""Give pixel area given nside in square radians or square degrees.
Parameters
----------
nside : int
healpix nside parameter, must be a power of 2, less than 2**30
degrees : bool
if True, returns pixel area in square degrees, in square radians otherwise
Returns
-------
pixarea : float
pixel area in square radian or square degree
Notes
-----
Raise a ValueError exception if nside is not valid.
Examples
--------
>>> import healpy as hp
>>> hp.nside2pixarea(128, degrees = True)
0.2098234113027917
>>> hp.nside2pixarea(256)
1.5978966540475428e-05
>>> hp.nside2pixarea(7)
Traceback (most recent call last):
...
ValueError: 7 is not a valid nside parameter (must be a power of 2, less than 2**30)
"""
check_nside(nside)
pixarea = 4*np.pi/nside2npix(nside)
if degrees:
pixarea = np.rad2deg(np.rad2deg(pixarea))
return pixarea
def npix2nside(npix):
"""Give the nside parameter for the given number of pixels.
Parameters
----------
npix : int
the number of pixels
Returns
-------
nside : int
the nside parameter corresponding to npix
Notes
-----
Raise a ValueError exception if number of pixel does not correspond to
the number of pixel of an healpix map.
Examples
--------
>>> import healpy as hp
>>> hp.npix2nside(768)
8