Source code for pixell.reproject

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, method="mixed", 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 method == "nufft" or method == "mixed" and 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 method == "mixed" and 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 to do 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:] if method in ["spline", "mixed"]: ipol_mode = "spline" elif method in ["nufft"]: ipol_mode = "nufft" else: raise ValueError("Unrecognized method '%s'" % (str(method))) omaps[si] = ithumb.at(ipos, mode=ipol_mode, 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 ip = utils.interpolator(imap, npre=-2, order=order, mode="spline", border=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.at(pos[1::-1], order=order, border=boundary, ip=ip) 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 = utils.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): raise NotImplementedError("This function has been removed.")
[docs] def healpix_from_enmap_interp(imap, **kwargs): raise RuntimeError("This function has been removed. Use reproject.map2healpix(...method='spline').")
[docs] def healpix_from_enmap(imap, lmax, nside): raise RuntimeError("This function has been removed. Use reproject.map2healpix(...method='harm').")
[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): raise RuntimeError("This function has been removed. Use reproject.healpix2map(...method='harm').")
[docs] def enmap_from_healpix_interp(hp_map, shape, wcs , rot="gal,equ", interpolate=False): raise RuntimeError("This function has been removed. Use reproject.healpix2map(...method='spline').")
[docs] def ivar_hp_to_cyl(hmap, shape, wcs, rot=False,do_mask=True,extensive=True): raise NotImplementedError("This function has been removed.")
# Helper functions
[docs] def gnomonic_pole_wcs(shape, res): raise NotImplementedError("This function has been removed.")
[docs] def gnomonic_pole_geometry(width, res, height=None): raise NotImplementedError("This function has been removed.")
[docs] def rotate_map(imap, shape_target=None, wcs_target=None, shape_source=None, wcs_source=None, pix_target=None, **kwargs): raise NotImplementedError("This function has been removed.")
[docs] def get_rotated_pixels(shape_source, wcs_source, shape_target, wcs_target, inverse=False, pos_target=None, center_target=None, center_source=None): raise NotImplementedError("This function has been removed.")
[docs] def cutout(imap, width=None, ra=None, dec=None, pad=1, corner=False, res=None, npix=None, return_slice=False,sindex=None): raise NotImplementedError("This function has been removed.")
[docs] def rect_box(width, center=(0., 0.), height=None): raise NotImplementedError("This function has been removed.")
[docs] def get_pixsize_rect(shape, wcs): raise NotImplementedError("This function has been removed.")
[docs] def rect_geometry(width, res, height=None, center=(0., 0.), proj="car"): raise NotImplementedError("This function has been removed.")
[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 RuntimeError("postage_stamp has been removed. Please use thumbnails instead.")