from __future__ import print_function
import numpy as np
from scipy import spatial
from . import wcsutils, utils, enmap, coordinates, fft, curvedsky
# Python 2/3 compatibility
try: basestring
except NameError: basestring = str
[docs]def thumbnails(imap, coords, r=5*utils.arcmin, res=None, proj=None, apod=2*utils.arcmin,
order=3, oversample=4, pol=None, oshape=None, owcs=None, extensive=False, verbose=False,
filter=None,pixwin=False,pixwin_order=0):
"""Given an enmap [...,ny,nx] and a set of coordinates in a numpy array
coords with shape (n,2) and ordering [n,{dec,ra}], extract a set
of thumbnail images [n,...,thumby,thumbx] centered on each set of
coordinates, where n is the number of images.
When proj is 'tan', each of these thumbnail images is projected onto a local
tangent plane, removing the effect of size and shape distortions in the input
map.
If oshape, owcs are specified, then the thumbnails will have this geometry,
which should be centered on [0,0]. Otherwise, a geometry with the given
projection (defaults to "tan" = gnomonic projection) will be constructed,
going up to a maximum radius of r. FIXME: Defaults to "car" instead while
enmap.pixsizemap is buggy for non-cylindrical projections.
The reprojection involved in this operation implies interpolation. The default
is to use fft rescaling to oversample the input pixels by the given pixel, and
then use bicubic spline interpolation to read off the values at the output
pixel centers. The fft oversampling can be controlled with the oversample argument.
Values <= 1 turns this off. The other interpolation step is controlled using the
"order" argument. 0/1/3 corresponds to nearest neighbor, bilinear and bicubic spline
interpolation respectively.
If pol == True, then Q,U will be rotated to take into account the change in
the local northward direction impled in the reprojection. The default is to
do polarization rotation automatically if the input map has a compatible shape,
e.g. at least 3 axes and a length of 3 for the 3rd last one. TODO: I haven't
tested this yet.
If extensive == True (not the default), then the map is assumed to contain an
extensive field rather than an intensive one. An extensive field is one where
the values in the pixels depend on the size of the pixel. For example, if the
inverse variance in the map is given per pixel, then this ivar map will be
extensive, but if it's given in units of inverse variance per square arcmin
then it's intensive.
For reprojecting inverse variance maps, consider using the wrapper thumbnails_ivar,
which makes it easier to avoid common pitfalls.
If pixwin is True, the pixel window will be deconvolved."""
# FIXME: Specifying a geometry manually is broken - see usage of r in neighborhood_pixboxes below
# Handle arbitrary coords shape
if proj is None: proj = "car"
coords = np.asarray(coords)
ishape = coords.shape[:-1]
coords = coords.reshape(-1, coords.shape[-1])
# If the output geometry was not given explicitly, then build one
if oshape is None:
if res is None: res = min(np.abs(imap.wcs.wcs.cdelt))*utils.degree/2
oshape, owcs = enmap.thumbnail_geometry(r=r, res=res, proj=proj)
# Check if we should be doing polarization rotation
pol_compat = imap.ndim >= 3 and imap.shape[-3] == 3
if pol is None: pol = pol_compat
if pol and not pol_compat: raise ValueError("Polarization rotation requested, but can't interpret map shape %s as IQU map" % (str(imap.shape)))
nsrc = len(coords)
if verbose: print("Extracting %d %dx%d thumbnails from %s map" % (nsrc, oshape[-2], oshape[-1], str(imap.shape)))
opos = enmap.posmap(oshape, owcs)
# Get the pixel area around each of the coordinates
rtot = r + apod
apod_pix = utils.nint(apod/(np.min(np.abs(imap.wcs.wcs.cdelt))*utils.degree))
pixboxes = enmap.neighborhood_pixboxes(imap.shape, imap.wcs, coords, rtot)
# Define our output maps, which we will fill below
omaps = enmap.zeros((nsrc,)+imap.shape[:-2]+oshape, owcs, imap.dtype)
for si, pixbox in enumerate(pixboxes):
if oversample > 1:
# Make the pixbox fft-friendly
for i in range(2):
pixbox[1,i] = pixbox[0,i] + fft.fft_len(pixbox[1,i]-pixbox[0,i], direction="above", factors=[2,3,5])
ithumb = imap.extract_pixbox(pixbox)
if extensive: ithumb /= ithumb.pixsizemap()
ithumb = ithumb.apod(apod_pix, fill="median")
if pixwin: ithumb = enmap.unapply_window(ithumb, order=pixwin_order)
if filter is not None: ithumb = filter(ithumb)
if verbose:
print("%4d/%d %6.2f %6.2f %8.2f %dx%d" % (si+1, nsrc, coords[si,0]/utils.degree, coords[si,1]/utils.degree, np.max(ithumb), ithumb.shape[-2], ithumb.shape[-1]))
# Oversample using fourier if requested. We do this because fourier
# interpolation is better than spline interpolation overall
if oversample > 1:
fshape = utils.nint(np.array(oshape[-2:])*oversample)
ithumb = ithumb.resample(fshape, method="fft")
# I apologize for the syntax. There should be a better way of doing this
ipos = coordinates.transform("cel", ["cel",[[0,0,coords[si,1],coords[si,0]],False]], opos[::-1], pol=pol)
ipos, rest = ipos[1::-1], ipos[2:]
omaps[si] = ithumb.at(ipos, order=order)
# Apply the polarization rotation. The sign is flipped because we computed the
# rotation from the output to the input
if pol: omaps[si] = enmap.rotate_pol(omaps[si], -rest[0])
if extensive: omaps *= omaps.pixsizemap()
# Restore original dimension
omaps = omaps.reshape(ishape + omaps.shape[1:])
return omaps
[docs]def thumbnails_ivar(imap, coords, r=5*utils.arcmin, res=None, proj=None,
oshape=None, owcs=None, order=1, extensive=True, verbose=False):
"""Like thumbnails, but for hitcounts, ivars, masks, and other quantities that
should stay positive and local. Remember to set extensive to True if you have an
extensive quantity, i.e. if the values in each pixel would go up if multiple pixels
combined. An example of this is a hitcount map or ivar per pixel. Conversely, if
you have an intensive quantity like ivar per arcmin you should set extensive=False."""
return thumbnails(imap, coords, r=r, res=res, proj=proj, oshape=oshape, owcs=owcs,
order=order, oversample=1, pol=False, extensive=extensive, verbose=verbose,
pixwin=False)
[docs]def map2healpix(imap, nside=None, lmax=None, out=None, rot=None, spin=[0,2], method="harm", order=1, extensive=False, bsize=100000, nside_mode="pow2", boundary="constant", verbose=False, niter=0):
"""Reproject from an enmap to healpix, optionally including a rotation.
imap: The input enmap[...,ny,nx]. Stokes along the -3rd axis if
present.
nside: The nside of the healpix map to generate. Not used if
an output map is passed. Otherwise defaults to the same
resolution as the input map.
lmax: The highest multipole to use in any harmonic-space
operations. Defaults to the input maps' Nyquist limit.
out: An optional array [...,npix] to write the output map to.
The ... part must match the input map, as must the data
type.
rot: An optional coordinate rotation to apply. Either a string
"isys,osys", where isys is the system to transform from,
and osys is the system to transform to. Currently the values
"cel"/"equ" and "gal" are recognized. Alternatively, a tuple of
3 euler zyz euler angles can be passed, in the same convention
as healpy.rotate_alm.
spin: A description of the spin of the entries along the stokes
axis. Defaults to [0,2], which means that the first entry
is spin-0, followed by a spin-2 pair (any non-zero spin
covers a pair of entries). If the axis is longer than
what's covered in the description, then it is repeated as
necessary. Pass spin=[0] to disable any special treatment
of this axis.
method: How to interpolate between the input and output
pixelizations. Can be "harm" (default) or "spline".
"harm" maps between them using spherical harmonics
transforms. This preserves the power spectrum (so no window
function is introduced), and averages noise down when the
output pixels are larger than the input pixels. However, it
can suffer from ringing around very bright features, and an
all-positive input map may end up with small negative values.
"spline" instead uses spline interpolation to look up the
value in the intput map corresponding to each pixel center
in the output map. The spline order is controlled with the
"order" argument. Overall "harm" is best suited for normal
sky maps, while "spline" with order = 0 or 1 is best suited
for hitcount maps and masks.
order: The spline order to use when method="spline".
0 corresponds to nearest neighbor interpolation.
1 corresponds to bilinear interpolation (default)
3 corresponds to bicubic spline interpolation.
0 and 1 are local and do not introduce values outside
the input range, but introduce some aliasing and loss of
power. 3 has less power loss, but still non-zero, and
is vulnerable to ringing.
extensive: Whether the map represents an extensive (as opposed to
intensive) quantity. Extensive quantities have values
proportional to the pixel size, unlike intensive quantities.
Hitcount per pixel is an extensive quantity. Hitcount per
square degree is an intensive quantity, as is a temperature
map. Defaults to False.
bsize: The spline method operates on batches of pixels to save memory.
This controls the batch size, in pixels. Defaults to 100000.
nside_mode: Controls which restrictions apply to nside in the case where
it has to be inferred automatically. Can be "pow2", "mul32" and "any".
"pow2", the default, results in nside being a power of two, as
required by the healpix standard.
"mul32" relaxes this requirement, making a map where nside is a
multiple of 32. This is compatible with most healpix operations,
but not with ud_grade or the nest pixel ordering.
"any" allows for any integer nside.
boundary: The boundary conditions assumed for the input map when
method="spline". Defaults to "constant", which assumes that
anything outsize the map has a constant value of 0. Another
useful value is "wrap", which assumes that the right side
wraps over to the left, and the top to the bottom. See
scipy.ndimage.distance_transform's documentation for other,
less useful values. method="harm" always assumes "constant"
regardless of this setting.
verbose: Whether to print information about what it's doing.
Defaults to False, which doesn't print anything.
Typical usage:
* map_healpix = map2healpix(map, rot="cel,gal")
* ivar_healpix = map2healpix(ivar, rot="cel,gal", method="spline", spin=[0], extensive=True)
"""
# Get the map's typical resolution from cdelt
ires = np.mean(np.abs(imap.wcs.wcs.cdelt))*utils.degree
lnyq = np.pi/ires
if out is None:
if nside is None:
nside = restrict_nside(((4*np.pi/ires**2)/12)**0.5, nside_mode)
out = np.zeros(imap.shape[:-2]+(12*nside**2,), imap.dtype)
npix = out.shape[-1]
opixsize = 4*np.pi/npix
# Might not be safe to go all the way to the Nyquist l, but looks that way to my tests.
if lmax is None: lmax = lnyq
if extensive:
imap = imap * (opixsize / imap.pixsizemap(broadcastable=True)) # not /= to avoid changing original imap
if method in ["harm", "harmonic"]:
# Harmonic interpolation preserves the power spectrum, but can introduce ringing.
# Probably not a good choice for positive-only quantities like hitcounts.
# Coordinate rotation is slow.
alm = curvedsky.map2alm(imap, lmax=lmax, spin=spin, niter=niter)
if rot is not None:
curvedsky.rotate_alm(alm, *rot2euler(rot), inplace=True)
curvedsky.alm2map_healpix(alm, out, spin=spin)
del alm
elif method == "spline":
# Covers both cubic spline interpolation (order=3), linear interpolation (order=1)
# and nearest neighbor (order=0). Harmonic interpolation is preferable to cubic
# splines, but linear and nearest neighbor may be useful. Coordinate rotation may
# be slow.
import healpy
imap_pre = utils.interpol_prefilter(imap, npre=-2, order=order, mode=boundary)
# Figure out if we need to compute polarization rotations
pol = imap.ndim > 2 and any([s != 0 for s,c1,c2 in enmap.spin_helper(spin, imap.shape[-3])])
# Batch to save memory
for i1 in range(0, npix, bsize):
i2 = min(i1+bsize, npix)
opix = np.arange(i1,i2)
pos = healpy.pix2ang(nside, opix)[::-1]
pos[1][:] = np.pi/2-pos[1]
if rot is not None:
# Not sure why the [::-1] is necessary here. Maybe psi,theta,phi vs. phi,theta,psi?
pos = coordinates.transform_euler(inv_euler(rot2euler(rot))[::-1], pos, pol=pol)
# The actual interpolation happens here
vals = imap_pre.at(pos[1::-1], order=order, prefilter=False, mode=boundary)
if rot is not None and imap.ndim > 2:
# Update the polarization to account for the new coordinate system
for s, c1, c2 in enmap.spin_helper(spin, imap.shape[-3]):
if s != 0:
vals = enmap.rotate_pol(vals, -pos[2], spin=s, comps=[c1,c2-1], axis=-2)
out[...,i1:i2] = vals
else:
raise ValueError("Map reprojection method '%s' not recognized" % str(method))
return out
[docs]def healpix2map(iheal, shape=None, wcs=None, lmax=None, out=None, rot=None, spin=[0,2], method="harm", order=1, extensive=False, bsize=100000, verbose=False, niter=0):
"""Reproject from healpix to an enmap, optionally including a rotation.
iheal: The input healpix map [...,npix]. Stokes along the -2nd axis if
present.
shape: The (...,ny,nx) shape of the output map. Only the last two entries
are used, the rest of the dimensions are taken from iheal.
Mandatory unless an output map is passed.
wcs : The world woordinate system object the output map.
Mandatory unless an output map is passed.
lmax: The highest multipole to use in any harmonic-space
operations. Defaults to 3 times the nside of iheal.
out: An optional enmap [...,ny,nx] to write the output map to.
The ... part must match iheal, as must the data type.
rot: An optional coordinate rotation to apply. Either a string
"isys,osys", where isys is the system to transform from,
and osys is the system to transform to. Currently the values
"cel"/"equ" and "gal" are recognized. Alternatively, a tuple of
3 euler zyz euler angles can be passed, in the same convention
as healpy.rotate_alm.
spin: A description of the spin of the entries along the stokes
axis. Defaults to [0,2], which means that the first entry
is spin-0, followed by a spin-2 pair (any non-zero spin
covers a pair of entries). If the axis is longer than
what's covered in the description, then it is repeated as
necessary. Pass spin=[0] to disable any special treatment
of this axis.
method: How to interpolate between the input and output
pixelizations. Can be "harm" (default) or "spline".
"harm" maps between them using spherical harmonics
transforms. This preserves the power spectrum (so no window
function is introduced), and averages noise down when the
output pixels are larger than the input pixels. However, it
can suffer from ringing around very bright features, and an
all-positive input map may end up with small negative values.
"spline" instead uses spline interpolation to look up the
value in the intput map corresponding to each pixel center
in the output map. The spline order is controlled with the
"order" argument. Overall "harm" is best suited for normal
sky maps, while "spline" with order = 0 or 1 is best suited
for hitcount maps and masks.
order: The spline order to use when method="spline".
0 corresponds to nearest neighbor interpolation.
1 corresponds to bilinear interpolation (default)
Higher order interpolation is not supported - use
method="harm" for that.
extensive: Whether the map represents an extensive (as opposed to
intensive) quantity. Extensive quantities have values
proportional to the pixel size, unlike intensive quantities.
Hitcount per pixel is an extensive quantity. Hitcount per
square degree is an intensive quantity, as is a temperature
map. Defaults to False.
bsize: The spline method operates on batches of pixels to save memory.
This controls the batch size, in pixels. Defaults to 100000.
verbose: Whether to print information about what it's doing.
Defaults to False, which doesn't print anything.
Typical usage:
* map = healpix2map(map_healpix, shape, wcs, rot="gal,cel")
* ivar = healpix2map(ivar_healpix, shape, wcs, rot="gal,cel", method="spline", spin=[0], extensive=True)
"""
iheal = np.asarray(iheal)
npix = iheal.shape[-1]
nside = curvedsky.npix2nside(npix)
ipixsize = 4*np.pi/npix
if out is None:
out = enmap.zeros(iheal.shape[:-1]+shape[-2:], wcs, dtype=iheal.dtype)
else: shape, wcs = out.geometry
if lmax is None: lmax = 3*nside
if method in ["harm", "harmonic"]:
# Harmonic interpolation preserves the power spectrum, but can introduce ringing.
# Probably not a good choice for positive-only quantities like hitcounts.
# Coordinate rotation is slow.
alm = curvedsky.map2alm_healpix(iheal, lmax=lmax, spin=spin, niter=niter)
if rot is not None:
curvedsky.rotate_alm(alm, *rot2euler(rot), inplace=True)
curvedsky.alm2map(alm, out, spin=spin)
del alm
elif method == "spline":
# Covers linear interpolation (order=1) and nearest neighbor (order=0).
# Coordinate rotation may be slow.
import healpy
if order > 1:
raise ValueError("Only order 0 and order 1 spline interpolation supported from healpix maps")
# Figure out if we need to compute polarization rotations
pol = iheal.ndim > 1 and any([s != 0 for s,c1,c2 in enmap.spin_helper(spin, iheal.shape[-2])])
# Batch to save memory
brow = (bsize+out.shape[-1]-1)//out.shape[-1]
for i1 in range(0, out.shape[-2], brow):
i2 = min(i1+brow, out.shape[-2])
pos = out[...,i1:i2,:].posmap().reshape(2,-1)[::-1]
if rot is not None:
# Not sure why the [::-1] is necessary here. Maybe psi,theta,phi vs. phi,theta,psi?
pos = coordinates.transform_euler(inv_euler(rot2euler(rot))[::-1], pos, pol=pol)
pos[1] = np.pi/2 - pos[1]
if order == 0:
# Nearest neighbor. Just read off from the pixels
vals = iheal[...,healpy.ang2pix(nside, pos[1], pos[0])]
else:
# Bilinear interpolation. healpy only supports one component at a time, so loop
vals = np.zeros(iheal.shape[:-1]+pos.shape[-1:], iheal.dtype)
for I in utils.nditer(iheal.shape[:-1]):
vals[I] = healpy.get_interp_val(iheal[I], pos[1], pos[0])
if rot is not None and iheal.ndim > 1:
# Update the polarization to account for the new coordinate system
for s, c1, c2 in enmap.spin_helper(spin, iheal.shape[-2]):
vals = enmap.rotate_pol(vals, -pos[2], spin=s, comps=[c1,c2-1], axis=-2)
out[...,i1:i2,:] = vals.reshape(vals.shape[:-1]+(i2-i1,-1))
else:
raise ValueError("Map reprojection method '%s' not recognized" % str(method))
if extensive:
out *= out.pixsizemap(broadcastable=True)/ipixsize
return out
[docs]def rot2euler(rot):
"""Given a coordinate rotation description, return the [rotz,roty,rotz] euler
angles it corresponds to. The rotation desciption can either be those angles
directly, or a string of the form isys,osys"""
gal2cel = np.array([57.06793215, 62.87115487, -167.14056929])*utils.degree
if isinstance(rot, basestring):
try: isys, osys = rot.split(",")
except ValueError:
raise ValueError("Rotation string must be of form 'isys,osys', but got '%s'" % str(rot))
R = spatial.transform.Rotation.identity()
# Handle input system
if isys in ["cel","equ"]: pass
elif isys == "gal": R *= spatial.transform.Rotation.from_euler("zyz", gal2cel)
else: raise ValueError("Unrecognized system '%s'" % isys)
# Handle output system
if osys in ["cel","equ"]: pass
elif osys == "gal": R *= spatial.transform.Rotation.from_euler("zyz", gal2cel).inv()
else: raise ValueError("Unrecognized system '%s'" % osys)
return R.as_euler("zyz")
else:
rot = np.asfarray(rot)
return rot
[docs]def inv_euler(euler): return [-euler[2], -euler[1], -euler[0]]
[docs]def restrict_nside(nside, mode="mul32", round="ceil"):
"""Given an arbitrary Healpix nside, return one that's restricted in
various ways according to the "mode" argument:
"pow2": Restrict to a power of 2. This is required for compatibility
with the rarely used "nest" pixel ordering in Healpix, and is the standard
in the Healpix world.
"mul32": Restrict to multiple of 32, unless 12*nside**2<=1024.
This is enough to make the maps writable by healpy.
"any": No restriction
The "round" argument controls how any rounding is done. This can be one
of the strings "ceil" (default), "round" or "floor", or you can pass in
a custom function(nside) -> nside.
In all cases, the final nside is converted to an integer and capped to
1 below.
"""
if isinstance(round, basestring):
round = {"floor":np.floor, "round":np.round, "ceil":np.ceil}[round]
if mode == "any": nside = round(nside)
elif mode == "mul32":
if 12*nside**2 > 1024:
nside = round(nside/32)*32
elif mode == "pow2":
nside = 2**round(np.log2(nside))
else:
raise ValueError("Unrecognized nside mode '%s'" % str(mode))
nside = max(1,int(nside))
return nside
################################
####### Old stuff below ########
################################
[docs]def centered_map(imap, res, box=None, pixbox=None, proj='car', rpix=None,
width=None, height=None, width_multiplier=1.,
rotate_pol=True, **kwargs):
"""Reproject a map such that its central pixel is at the origin of a
given projection system (default: CAR).
imap -- (Ny,Nx) enmap array from which to extract stamps
TODO: support leading dimensions
res -- width of pixel in radians
box -- optional bounding box of submap in radians
pixbox -- optional bounding box of submap in pixel numbers
proj -- coordinate system for target map; default is 'car';
can also specify 'cea' or 'gnomonic'
rpix -- optional pre-calculated pixel positions from get_rotated_pixels()
"""
warnings.warn("reproject.centered_map is deprecated. Use reproject.thumbnails instead")
if imap.ndim==2: imap = imap[None,:]
ncomp = imap.shape[0]
proj = proj.strip().lower()
assert proj in ['car', 'cea']
# cut out a stamp assuming CAR ; TODO: generalize?
if box is not None:
pixbox = enmap.skybox2pixbox(imap.shape, imap.wcs, box)
if pixbox is not None:
omap = enmap.extract_pixbox(imap, pixbox)
else:
omap = imap
sshape, swcs = omap.shape, omap.wcs
# central pixel of source geometry
dec, ra = enmap.pix2sky(sshape, swcs, (sshape[0] / 2., sshape[1] / 2.))
dims = enmap.extent(sshape, swcs)
dheight, dwidth = dims
if height is None:
height = dheight
if width is None:
width = dwidth
width *= width_multiplier
tshape, twcs = rect_geometry(
width=width, res=res, proj=proj, height=height)
if rpix is None:
rpix = get_rotated_pixels(sshape, swcs, tshape, twcs, inverse=False,
pos_target=None, center_target=(0., 0.),
center_source=(dec, ra))
rot = enmap.enmap(rotate_map(omap, pix_target=rpix[:2], **kwargs), twcs)
if ncomp==3 and rotate_pol:
rot[1:3] = enmap.rotate_pol(rot[1:3], -rpix[2]) # for polarization rotation if enough components
return rot, rpix
[docs]def healpix_from_enmap_interp(imap, **kwargs):
return imap.to_healpix(**kwargs)
[docs]def healpix_from_enmap(imap, lmax, nside):
"""Convert an ndmap to a healpix map such that the healpix map is
band-limited up to lmax. Only supports single component (intensity)
currently. The resulting map will be band-limited. Bright sources and
sharp edges could cause ringing. Use healpix_from_enmap_interp if you
are worried about this (e.g. for a mask), but that routine will not ensure
power to be correct to some lmax.
Args:
imap: ndmap of shape (Ny,Nx)
lmax: integer specifying maximum multipole of map
nside: integer specifying nside of healpix map
Returns:
retmap: (Npix,) healpix map as array
"""
from pixell import curvedsky
import healpy as hp
alm = curvedsky.map2alm(imap, lmax=lmax, spin=0)
if alm.ndim > 1:
assert alm.shape[0] == 1
alm = alm[0]
retmap = hp.alm2map(alm.astype(np.complex128), nside, lmax=lmax)
return retmap
[docs]def enmap_from_healpix(hp_map, shape, wcs, ncomp=1, unit=1, lmax=0,
rot="gal,equ", first=0, is_alm=False, return_alm=False, f_ell=None):
"""Convert a healpix map to an ndmap using harmonic space reprojection.
The resulting map will be band-limited. Bright sources and sharp edges
could cause ringing. Use enmap_from_healpix_interp if you are worried
about this (e.g. for a mask), but that routine will not ensure power to
be correct to some lmax.
Args:
hp_map: an (Npix,) or (ncomp,Npix,) healpix map, or alms, or a string containing
the path to a healpix map on disk
shape: the shape of the ndmap geometry to project to
wcs: the wcs object of the ndmap geometry to project to
ncomp: the number of components in the healpix map (either 1 or 3)
unit: a unit conversion factor to divide the map by
lmax: the maximum multipole to include in the reprojection
rot: comma separated string that specify a coordinate rotation to
perform. Use None to perform no rotation. e.g. default "gal,equ"
to rotate a Planck map in galactic coordinates to the equatorial
coordinates used in ndmaps.
first: if a filename is provided for the healpix map, this specifies
the index of the first FITS field
is_alm: if True, interprets hp_map as alms
return_alm: if True, returns alms also
f_ell: optionally apply a transfer function f_ell(ell) -- this should be
a function of a single variable ell. e.g., lambda x: exp(-x**2/2/sigma**2)
Returns:
res: the reprojected ndmap or the a tuple (ndmap,alms) if return_alm
is True
"""
from pixell import curvedsky
import healpy as hp, warnings
warnings.warn("enmap_from_healpix is deprecated. Use healpix2map instead. enmap_from_healpix has not been tested after the port from libsharp to ducc0. It also uses a very inefficient approach for coordinate rotation.")
dtype = np.float64
if not(is_alm):
assert ncomp == 1 or ncomp == 3, "Only 1 or 3 components supported"
ctype = np.result_type(dtype, 0j)
# Read the input maps
if type(hp_map) == str:
m = np.atleast_2d(hp.read_map(hp_map, field=tuple(
range(first, first + ncomp)))).astype(dtype)
else:
m = np.atleast_2d(hp_map).astype(dtype)
if unit != 1:
m /= unit
# Perform the actual transform
print("map -> alm")
nside = hp.npix2nside(m.shape[1])
lmax = lmax or 3 * nside
alm = curvedsky.map2alm_healpix(m, lmax=lmax)
del m
else:
alm = hp_map
if f_ell is not None: alm = curvedsky.almxfl(alm,f_ell)
if rot is not None:
# Rotate by displacing coordinates and then fixing the polarization
print("Computing pixel positions")
pmap = enmap.posmap(shape, wcs)
if rot:
print("Computing rotated positions")
s1, s2 = rot.split(",")
opos = coordinates.transform(s2, s1, pmap[::-1], pol=ncomp == 3)
pmap[...] = opos[1::-1]
if len(opos) == 3:
psi = -opos[2].copy()
del opos
print("Projecting")
res = curvedsky.alm2map_pos(alm, pmap)
if rot and ncomp == 3:
print("Rotating polarization vectors")
res[1:3] = enmap.rotate_pol(res[1:3], psi)
else:
print("Projecting")
res = enmap.zeros((len(alm),) + shape[-2:], wcs, dtype)
res = curvedsky.alm2map(alm, res)
if return_alm: return res,alm
return res
[docs]def enmap_from_healpix_interp(hp_map, shape, wcs , rot="gal,equ",
interpolate=False):
"""Project a healpix map to an enmap of chosen shape and wcs. The wcs
is assumed to be in equatorial (ra/dec) coordinates. No coordinate systems
other than equatorial or galactic are currently supported. Only intensity
maps are supported.
Args:
hp_map: an (Npix,) healpix map
shape: the shape of the ndmap geometry to project to
wcs: the wcs object of the ndmap geometry to project to
rot: comma separated string that specify a coordinate rotation to
perform. Use None to perform no rotation. e.g. default "gal,equ"
to rotate a Planck map in galactic coordinates to the equatorial
coordinates used in ndmaps.
interpolate: if True, bilinear interpolation using 4 nearest neighbours
is done.
"""
warnings.warn("enmap_from_healpix_interp is deprecated. Use healpix2map instead.")
import healpy as hp
from astropy.coordinates import SkyCoord
import astropy.units as u
eq_coords = ['fk5', 'j2000', 'equatorial']
gal_coords = ['galactic']
imap = enmap.zeros(shape, wcs)
Ny, Nx = shape
pixmap = enmap.pixmap(shape, wcs)
y = pixmap[0, ...].T.ravel()
x = pixmap[1, ...].T.ravel()
del pixmap
posmap = enmap.posmap(shape, wcs)
if rot is not None:
s1, s2 = rot.split(",")
opos = coordinates.transform(s2,s1, posmap[::-1], pol=None)
posmap[...] = opos[1::-1]
th = np.rad2deg(posmap[1, ...].T.ravel())
ph = np.rad2deg(posmap[0, ...].T.ravel())
del posmap
if interpolate:
imap[y, x] = hp.get_interp_val(
hp_map, th, ph, lonlat=True)
else:
ind = hp.ang2pix(hp.get_nside(hp_map),
th, ph, lonlat=True)
del th
del ph
imap[:] = 0.
imap[(y, x)] = hp_map[ind]
del y
del x
return enmap.ndmap(imap, wcs)
[docs]def ivar_hp_to_cyl(hmap, shape, wcs, rot=False,do_mask=True,extensive=True):
from . import mpi, utils
import healpy as hp
warnings.warn("ivar_hp_to_cyl is deprecated. Use healpix2map instead. See the example at the bottom of its docstring for how to do this with ivar maps")
comm = mpi.COMM_WORLD
rstep = 100
dtype = np.float32
nside = hp.npix2nside(hmap.size)
dec, ra = enmap.posaxes(shape, wcs)
pix = np.zeros(shape, np.int32)
# Get the pixel area. We assume a rectangular pixelization, so this is just
# a function of y
ipixsize = 4 * np.pi / (12 * nside ** 2)
opixsize = get_pixsize_rect(shape, wcs)
nblock = (shape[-2] + rstep - 1) // rstep
for bi in range(comm.rank, nblock, comm.size):
if bi % comm.size != comm.rank:
continue
i = bi * rstep
rdec = dec[i : i + rstep]
opos = np.zeros((2, len(rdec), len(ra)))
opos[0] = rdec[:, None]
opos[1] = ra[None, :]
if rot:
# This is unreasonably slow
ipos = coordinates.transform("equ", "gal", opos[::-1], pol=True)
else:
ipos = opos[::-1]
pix[i : i + rstep, :] = hp.ang2pix(nside, np.pi / 2 - ipos[1], ipos[0])
del ipos, opos
for i in range(0, shape[-2], rstep):
pix[i : i + rstep] = utils.allreduce(pix[i : i + rstep], comm)
omap = enmap.zeros((1,) + shape, wcs, dtype)
imap = np.array(hmap).astype(dtype)
imap = imap[None]
if do_mask:
bad = hp.mask_bad(imap)
bad |= imap <= 0
imap[bad] = 0
del bad
# Read off the nearest neighbor values
omap[:] = imap[:, pix]
if extensive: omap *= opixsize[:, None] / ipixsize
# We ignore QU mixing during rotation for the noise level, so
# it makes no sense to maintain distinct levels for them
if do_mask:
mask = omap[1:] > 0
omap[1:] = np.mean(omap[1:], 0)
omap[1:] *= mask
del mask
return omap
# Helper functions
[docs]def gnomonic_pole_wcs(shape, res):
Ny, Nx = shape[-2:]
wcs = wcsutils.WCS(naxis=2)
wcs.wcs.ctype = ['RA---TAN', 'DEC--TAN']
wcs.wcs.crval = [0., 0.]
wcs.wcs.cdelt[:] = np.rad2deg(res)
wcs.wcs.crpix = [Ny / 2. + 0.5, Nx / 2. + 0.5]
return wcs
[docs]def gnomonic_pole_geometry(width, res, height=None):
if height is None:
height = width
Ny = int(height / res)
Nx = int(width / res)
return (Ny, Nx), gnomonic_pole_wcs((Ny, Nx), res)
[docs]def rotate_map(imap, shape_target=None, wcs_target=None, shape_source=None,
wcs_source=None, pix_target=None, **kwargs):
if pix_target is None:
pix_target = get_rotated_pixels(
shape_source, wcs_source, shape_target, wcs_target)
else:
assert (shape_target is None) and (
wcs_target is None), "Both pix_target and shape_target, \
wcs_target must not be specified."
rotmap = enmap.at(imap, pix_target[:2], unit="pix", **kwargs)
return rotmap
[docs]def get_rotated_pixels(shape_source, wcs_source, shape_target, wcs_target,
inverse=False, pos_target=None,
center_target=None, center_source=None):
""" Given a source geometry (shape_source,wcs_source)
return the pixel positions in the target geometry (shape_target,wcs_target)
if the source geometry were rotated such that its center lies on the center
of the target geometry.
WARNING: Only currently tested for a rotation along declination
from one CAR geometry to another CAR geometry.
"""
# what are the center coordinates of each geometries
if center_source is None:
center_source = enmap.pix2sky(
shape_source, wcs_source,
(shape_source[0] / 2., shape_source[1] / 2.))
if center_target is None:
center_target = enmap.pix2sky(
shape_target, wcs_target,
(shape_target[0] / 2., shape_target[1] / 2.))
decs, ras = center_source
dect, rat = center_target
# what are the angle coordinates of each pixel in the target geometry
if pos_target is None:
pos_target = enmap.posmap(shape_target, wcs_target)
#del pos_target
# recenter the angle coordinates of the target from the target center
# to the source center
if inverse:
transfun = lambda x: coordinates.decenter(x, (rat, dect, ras, decs))
else:
transfun = lambda x: coordinates.recenter(x, (rat, dect, ras, decs))
res = coordinates.transform_meta(transfun, pos_target[1::-1], fields=["ang"])
pix_new = enmap.sky2pix(shape_source, wcs_source, res.ocoord[1::-1])
pix_new = np.concatenate((pix_new,res.ang[None]))
return pix_new
[docs]def cutout(imap, width=None, ra=None, dec=None, pad=1, corner=False,
res=None, npix=None, return_slice=False,sindex=None):
if type(imap) == str:
shape, wcs = enmap.read_map_geometry(imap)
else:
shape, wcs = imap.shape, imap.wcs
Ny, Nx = shape[-2:]
def fround(x):
return int(np.round(x))
iy, ix = enmap.sky2pix(shape, wcs, coords=(dec, ra), corner=corner)
if res is None:
res = np.min(enmap.extent(shape, wcs) / shape[-2:])
if npix is None:
npix = int(width / res)
if fround(iy - npix / 2) < pad or fround(ix - npix / 2) < pad or \
fround(iy + npix / 2) > (Ny - pad) or \
fround(ix + npix / 2) > (Nx - pad):
return None
if sindex is None:
s = np.s_[...,fround(iy - npix / 2. + 0.5):fround(iy + npix / 2. + 0.5),
fround(ix - npix / 2. + 0.5):fround(ix + npix / 2. + 0.5)]
else:
s = np.s_[sindex,fround(iy - npix / 2. + 0.5):fround(iy + npix / 2. + 0.5),
fround(ix - npix / 2. + 0.5):fround(ix + npix / 2. + 0.5)]
if return_slice:
return s
cutout = imap[s]
return cutout
[docs]def rect_box(width, center=(0., 0.), height=None):
if height is None:
height = width
ycen, xcen = center
box = np.array([[-height / 2. + ycen, -width / 2. + xcen],
[height / 2. + ycen, width / 2. + xcen]])
return box
[docs]def get_pixsize_rect(shape, wcs):
"""Return the exact pixel size in steradians for the rectangular cylindrical
projection given by shape, wcs. Returns area[ny], where ny = shape[-2] is the
number of rows in the image. All pixels on the same row have the same area."""
ymin = enmap.sky2pix(shape, wcs, [-np.pi / 2, 0])[0]
ymax = enmap.sky2pix(shape, wcs, [np.pi / 2, 0])[0]
y = np.arange(shape[-2])
x = y * 0
dec1 = enmap.pix2sky(shape, wcs, [np.maximum(ymin, y - 0.5), x])[0]
dec2 = enmap.pix2sky(shape, wcs, [np.minimum(ymax, y + 0.5), x])[0]
area = np.abs((np.sin(dec2) - np.sin(dec1)) * wcs.wcs.cdelt[0] * np.pi / 180)
return area
[docs]def rect_geometry(width, res, height=None, center=(0., 0.), proj="car"):
shape, wcs = enmap.geometry(pos=rect_box(
width, center=center, height=height), res=res, proj=proj)
return shape, wcs
[docs]def distribute(N,nmax):
"""
Distribute N things into cells as equally as possible such that
no cell has more than nmax things.
"""
actual_max = int(2.*(nmax+1)/3.)
numcells = int(round(N*1./actual_max))
each_cell = [actual_max]*(numcells-1)
rem = N-sum(each_cell)
if rem>0: each_cell.append(rem)
assert sum(each_cell)==N
return each_cell
[docs]def populate(shape,wcs,ofunc,maxpixy = 400,maxpixx = 400):
"""
Loop through tiles in a new map of geometry (shape,wcs)
with tiles that have maximum allowed shape (maxpixy,maxpixx)
such that each tile is populated with the result of
ofunc(oshape,owcs) where oshape,owcs is the geometry of each
tile.
"""
omap = enmap.zeros(shape,wcs)
Ny,Nx = shape[-2:]
tNys = distribute(Ny,maxpixy)
tNxs = distribute(Nx,maxpixx)
numy = len(tNys)
numx = len(tNxs)
sny = 0
ntiles = numy*numx
print("Number of tiles = ",ntiles)
done = 0
for i in range(numy):
eny = sny+tNys[i]
snx = 0
for j in range(len(tNxs)):
enx = snx+tNxs[j]
sel = np.s_[...,sny:eny,snx:enx]
oshape,owcs = enmap.slice_geometry(shape,wcs,sel)
omap[sel] = ofunc(oshape,owcs)
snx += tNxs[j]
done += 1
sny += tNys[i]
print(done , " / ", ntiles, " tiles done...")
return omap
[docs]def postage_stamp(inmap, ra_deg, dec_deg, width_arcmin,
res_arcmin, proj='gnomonic', return_cutout=False,
npad=3, rotate_pol=True, **kwargs):
raise Exception("postage_stamp has been deprecated. Please use thumbnails instead.")