# Copyright (c) 2016 Weitian LI # MIT license # # References: # [1] K. M. Gorski, et al. 2005, ApJ, 622, 759 # "HEALPix: A Framework for High-resolution Discretization and Fast # Analysis of Data Distributed on the Sphere" # http://healpix.sourceforge.net/ # [2] M. R. Calabretta & B. F. Roukema 2007, MNRAS, 381, 865 # "Mapping on the HEALPix Grid" # [3] M. R. Calabretta: WCSLIB: HPXcvt # http://www.atnf.csiro.au/people/mcalabre/WCS/ """ HEALPix utilities ----------------- healpix2hpx: reorganize the HEALPix data (1D array as FITS table) into 2D FITS image in HPX coordinate system hpx2healpix: revert the above reorganization and turn the 2D image in HPX format back into HEALPix data as 1D array. """ from datetime import datetime, timezone import logging import numpy as np import healpy as hp from astropy.io import fits from . import read_fits_healpix logger = logging.getLogger(__name__) def healpix2hpx(data, append_history=None, append_comment=None): """Reorganize the HEALPix data (1D array as FITS table) into 2D FITS image in HPX coordinate system. Parameters ---------- data : str or `~astropy.io.fits.BinTableHDU` The input HEALPix map to be converted to the HPX image, which can be either the filename of the HEALPix FITS file, or be a `~astropy.io.fits.BinTableHDU` instance containing the HEALPix data as well as its header. header : `~astropy.io.fits.Header`, optional Header of the HEALPix FITS file append_history : list[str] Append the provided history to the output FITS header append_comment : list[str] Append the provided comment to the output FITS header Returns ------- hpx_data : 2D `~numpy.ndarray` The reorganized HPX image hpx_header : `~astropy.io.fits.Header` FITS header for the HPX image """ hp_data, hp_header = read_fits_healpix(data) dtype = hp_data.dtype npix = len(hp_data) nside = hp.npix2nside(npix) logger.info("Loaded HEALPix data: dtype={0}, Npixel={1}, Nside={2}".format( dtype, npix, nside)) hp_data = np.append(hp_data, np.nan).astype(dtype) hpx_idx = _calc_hpx_indices(nside) # Fix indices of "-1" to set empty pixels with above appended NaN hpx_idx[hpx_idx == -1] = len(hp_data) - 1 hpx_data = hp_data[hpx_idx] hpx_header = _make_hpx_header(hp_header, append_history=append_history, append_comment=append_comment) return (hpx_data.astype(hp_data.dtype), hpx_header) def hpx2healpix(data, append_history=None, append_comment=None): """Revert the reorganization and turn the 2D image in HPX format back into HEALPix data as 1D array. Parameters ---------- data : str or `~astropy.io.fits.PrimaryHDU` The input HPX image to be converted to the HEALPix data, which can be either the filename of the HPX FITS image, or be a `~astropy.io.fits.PrimaryHDU` instance containing the HPX image as well as its header. append_history : list[str] Append the provided history to the output FITS header append_comment : list[str] Append the provided comment to the output FITS header Returns ------- hp_data : 1D `~numpy.ndarray` HEALPix data reorganized from the input HPX image hp_header : `~astropy.io.fits.Header` FITS header for the HEALPix data """ if isinstance(data, str): hpx_hdu = fits.open(data)[0] hpx_data, hpx_header = hpx_hdu.data, hpx_hdu.header logger.info("Read HPX image from FITS file: %s" % data) else: hpx_data, hpx_header = data.data, data.header logger.info("Read HPX image from PrimaryHDU") logger.info("HPX image dtype: {0}".format(hpx_data.dtype)) logger.info("HPX coordinate system: ({0}, {1})".format( hpx_header["CTYPE1"], hpx_header["CTYPE2"])) if ((hpx_header["CTYPE1"], hpx_header["CTYPE2"]) != ("GLON-HPX", "GLAT-HPX")): raise ValueError("only Galactic 'HPX' projection currently supported") # Calculate Nside nside = round(hpx_header["NAXIS1"] / 5) nside2 = round(90 / np.sqrt(2) / hpx_header["CDELT2"]) if nside != nside2: raise ValueError("Cannot determine the Nside value") logger.info("Determined HEALPix Nside=%d" % nside) # npix = hp.nside2npix(nside) hpx_idx = _calc_hpx_indices(nside).flatten() hpx_idx_uniq, idxx = np.unique(hpx_idx, return_index=True) if np.sum(hpx_idx_uniq >= 0) != npix: raise ValueError("Number of pixels does not match indices") hpx_data = hpx_data.flatten() hp_data = hpx_data[idxx[hpx_idx_uniq >= 0]] hp_header = _make_healpix_header(hpx_header, nside=nside, append_history=append_history, append_comment=append_comment) return (hp_data.astype(hpx_data.dtype), hp_header) def _calc_hpx_indices(nside): """Calculate HEALPix element indices for the HPX projection scheme. Parameters ---------- nside : int Nside of the input/output HEALPix data Returns ------- indices : 2D integer `~numpy.ndarray` 2D integer array of same size as the input/output HPX FITS image, with elements tracking the indices of the HPX pixels in the HEALPix 1D array, while elements with value "-1" indicating null/empty HPX pixels. NOTE ---- * The indices are 0-based; * Currently only HEALPix RING ordering supported; * The null/empty elements in the HPX projection are filled with "-1". """ # number of horizontal/vertical facet nfacet = 5 # Facets layout of the HPX projection scheme. # Note that this appears to be upside-down, and the blank facets # are marked with "-1". # Ref: ref.[2], Fig.4 FACETS_LAYOUT = [[ 6, 9, -1, -1, -1], [ 1, 5, 8, -1, -1], [-1, 0, 4, 11, -1], [-1, -1, 3, 7, 10], [-1, -1, -1, 2, 6]] # shape = (nfacet*nside, nfacet*nside) indices = -np.ones(shape).astype(np.int) logger.info("HPX indices matrix shape: {0}".format(shape)) logger.info("Calculating the HPX indices ... (may take a while ...)") # # Loop vertically facet-by-facet for jfacet in range(nfacet): # Loop row-by-row for j in range(nside): row = jfacet * nside + j # Loop horizontally facet-by-facet for ifacet in range(nfacet): facet = FACETS_LAYOUT[jfacet][ifacet] if facet < 0: # blank facet pass else: idx = _calc_hpx_row_idx(nside, facet, j) col = ifacet * nside indices[row, col:(col+nside)] = idx # return indices def _calc_hpx_row_idx(nside, facet, jmap): """Calculate the HEALPix indices for one row of a facet. NOTE ---- * Only RING ordering is currently supported. * This function calculates the double-pixelization index then converts it to the regular RING index. References: ref.[2], Sec.3.1 """ I0 = [1, 3, -3, -1, 0, 2, 4, -2, 1, 3, -3, -1] J0 = [1, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1] # n2side = 2 * nside n8side = 8 * nside nside1 = nside - 1 # double-pixelization index of the last pixel in the north polar cap npole = (n2side - 1) ** 2 - 1 # double-pixelization pixel coordinates of the center of the facet i0 = nside * I0[facet] j0 = nside * J0[facet] # row_idx = [] for imap in range(nside): # (i, j) are 0-based, double-pixelization pixel coordinates. # The origin is at the intersection of the equator and prime # meridian, `i` increases to the east (N.B.) and `j` to the north. i = i0 + nside1 - (jmap + imap) j = j0 + jmap - imap # convert `i` for counting pixels if i < 0: i += n8side i += 1 # if j > nside: # north polar regime if j == n2side: idx2 = 0 else: # number of pixels in a polar facet with this value of `j` npj = 2 * (n2side - j) # index of the last pixel in the row above this idx2 = (npj - 1) ** 2 - 1 # number of pixels in this row in the polar facets before this idx2 += npj * (i // n2side) # pixel number in this polar facet idx2 += i % n2side - (j - nside) - 1 elif j >= -nside: # equatorial regime idx2 = npole + n8side * (nside - j) + i else: # south polar regime idx2 = 24 * nside**2 + 1 if j > -n2side: # number of pixels in a polar facet with this value of `j` npj = 2 * (n2side + j) # total number of pixels in this row or below it idx2 -= (npj + 1) ** 2 # number of pixels in this row in the polar facets before this idx2 += npj * (i // n2side) # pixel number in this polar facet idx2 += i % n2side + (j + nside) - 1 # convert double-pixelization index to regular RING index idx = (idx2 - 1) // 2 row_idx.append(idx) return row_idx def _make_hpx_header(header, append_history=None, append_comment=None): """Make the FITS header for the HPX image.""" header = header.copy(strip=True) nside = header["NSIDE"] # set pixel transformation parameters crpix1 = (5 * nside + 1) / 2.0 crpix2 = crpix1 header["CRPIX1"] = (crpix1, "Coordinate reference pixel") header["CRPIX2"] = (crpix2, "Coordinate reference pixel") cos45 = np.cos(np.deg2rad(45)) header["PC1_1"] = (cos45, "Transformation matrix element") header["PC1_2"] = (cos45, "Transformation matrix element") header["PC2_1"] = (-cos45, "Transformation matrix element") header["PC2_2"] = (cos45, "Transformation matrix element") cdelt1 = -90.0 / nside / np.sqrt(2) cdelt2 = -cdelt1 header["CDELT1"] = (cdelt1, "[deg] Coordinate increment") header["CDELT2"] = (cdelt2, "[deg] Coordinate increment") # set celestial transformation parameters header["CTYPE1"] = ("GLON-HPX", "Galactic longitude in an HPX projection") header["CTYPE2"] = ("GLAT-HPX", "Galactic latitude in an HPX projection") header["CRVAL1"] = (0.0, "[deg] Galactic longitude at the reference point") header["CRVAL2"] = (0.0, "[deg] Galactic latitude at the reference point") header["PV2_1"] = (4, "HPX H parameter (longitude)") header["PV2_2"] = (3, "HPX K parameter (latitude)") logger.info("Made HPX FITS header") # header["DATE"] = (datetime.now(timezone.utc).astimezone().isoformat(), "File creation date") comments = [ 'The HPX coordinate system is an reorganization of the HEALPix', 'data without regridding or interpolation, which is described in', '"Mapping on the HEALPix Grid" by M. Calabretta and B. Roukema', '(2007, MNRAS, 381, 865-872)', 'See also http://www.atnf.csiro.au/people/Mark.Calabretta/' ] for comment in comments: header.add_comment(comment) # if append_history is not None: logger.info("HPX FITS header: append history") for history in append_history: header.add_history(history) if append_comment is not None: logger.info("HPX FITS header: append comments") for comment in append_comment: header.add_comment(comment) return header def _make_healpix_header(header, nside, append_history=None, append_comment=None): """Make the FITS header for the HEALPix data.""" header = header.copy(strip=True) # set HEALPix parameters header["PIXTYPE"] = ("HEALPIX", "HEALPix pixelization") header["ORDERING"] = ("RING", "Pixel ordering scheme, either RING or NESTED") header["NSIDE"] = (nside, "HEALPix resolution parameter") npix = hp.nside2npix(nside) header["NPIX"] = (npix, "Total number of pixels") header["FIRSTPIX"] = (0, "First pixel # (0 based)") header["LASTPIX"] = (npix-1, "Last pixel # (0 based)") logger.info("Made HEALPix FITS header") # header["DATE"] = (datetime.now(timezone.utc).astimezone().isoformat(), "File creation date") # if append_history is not None: logger.info("HEALPix FITS header: append history") for history in append_history: header.add_history(history) if append_comment is not None: logger.info("HEALPix FITS header: append comments") for comment in append_comment: header.add_comment(comment) return header