#!/usr/bin/env python3 # # Copyright (c) 2017 Weitian LI # MIT license # """ Calculate the 2D cylindrical-averaged power spectrum from the 3D image spectral cube. """ import os import sys import argparse import logging import numpy as np from scipy import fftpack from scipy.signal import windows from astropy.io import fits from astropy.wcs import WCS from astropy.cosmology import FlatLambdaCDM import astropy.constants as ac logging.basicConfig(level=logging.INFO, format="%(asctime)s [%(levelname)s] %(message)s", datefmt="%Y-%m-%dT%H:%M:%S") logger = logging.getLogger(os.path.basename(sys.argv[0])) # present Hubble parameter H0 = 71.0 # [km/s/Mpc] # present density parameter of matter OmegaM0 = 0.27 # HI line frequency freq21cm = 1420.405751 # [MHz] def freq2z(freq): z = freq21cm / freq - 1.0 return z def get_frequencies(wcs, nfreq): pix = np.zeros(shape=(nfreq, 3), dtype=np.int) pix[:, -1] = np.arange(nfreq) world = wcs.wcs_pix2world(pix, 0) freqMHz = world[:, -1] / 1e6 return freqMHz class PS2D: """ 2D cylindrical-averaged power spectrum cube dimensions: [nfreq, height, width] / [Z, Y, X] """ def __init__(self, cube, pixelsize, frequencies, window="nuttall", width="extended"): logger.info("Initializing PS2D instance ...") self.cube = cube self.pixelsize = pixelsize # [arcmin] logger.info("Image pixel size: %.2f [arcmin]" % pixelsize) self.frequencies = np.array(frequencies) # [MHz] self.nfreq = len(self.frequencies) # Central frequency and redshift self.freqc = self.frequencies.mean() self.zc = freq2z(self.freqc) logger.info("Central frequency %.2f [MHz] <-> redshift %.4f" % (self.freqc, self.zc)) self.cosmo = FlatLambdaCDM(H0=H0, Om0=OmegaM0) # Transverse comoving distance at zc; unit: [Mpc] self.DMz = self.cosmo.comoving_transverse_distance(self.zc).value self.window = self.gen_window(name=window, width=width) def gen_window(self, name=None, width="extended"): if name is None: window = np.ones(self.nfreq) return window window_func = getattr(windows, name) if width == "extended": w = window_func(self.nfreq, sym=False) ex = 1.0 / (w.sum() / self.nfreq) width_pix = int(ex * self.nfreq) else: width_pix = self.nfreq window = window_func(width_pix, sym=False) if len(window) > self.nfreq: # cut the filter midx = int(len(window) / 2) # index of the peak element nleft = int(self.nfreq / 2) # number of element on the left nright = int((self.nfreq-1) / 2) # number of element on the right window = window[(midx-nleft):(midx+nright+1)] logger.info("Generated window: %s (%s/%d)" % (name, width, width_pix)) return window def pad_cube(self): # Pad the image cube to be square in spatial dimensions. # TODO __, ny, nz = self.cube.shape if ny != nz: logger.info("Padding image to be square ...") raise NotImplementedError def calc_ps3d(self): """ Calculate the 3D power spectrum of the image cube. """ logger.info("Applying window to frequency axis ...") cube2 = self.cube * self.window[:, np.newaxis, np.newaxis] logger.info("Calculating 3D FFT and PS ...") cubefft = fftpack.fftshift(fftpack.fftn(cube2)) self.ps3d = np.abs(cubefft) ** 2 return self.ps3d def calc_ps2d(self): """ Calculate the 2D power spectrum by cylindrically binning the above 3D power spectrum. """ nz, ny, nx = self.cube.shape k_x, k_y = self.k_xy k_z = self.k_z dkx = np.abs(k_x[0] - k_x[1]) dkz = np.abs(k_z[0] - k_z[1]) vcell = dkx**2 * dkz # volume of each cell [Mpc^-3] eps = 1e-8 ic_x = (np.abs(k_x) < eps).nonzero()[0][0] ic_z = (np.abs(k_z) < eps).nonzero()[0][0] p_x = np.arange(nx) - ic_x p_z = np.abs(np.arange(nz) - ic_z) mx, my = np.meshgrid(p_x, p_x) rho, phi = self.cart2pol(mx, my) rho = np.around(rho).astype(np.int) n_k_perp = (nx+1) // 2 n_k_los = (nz+1) // 2 ps2d = np.zeros(shape=(n_k_los, n_k_perp)) # (k_los, k_perp) logger.info("Calculating 2D PS by binning 3D PS ...") for r in range(n_k_perp): ix, iy = (rho == r).nonzero() for s in range(n_k_los): iz = (p_z == s).nonzero()[0] cells = np.concatenate([self.ps3d[z, iy, ix] for z in iz]) volume = cells.size * vcell ps2d[s, r] = cells.sum() / volume self.ps2d = ps2d return ps2d def save(self, outfile, clobber=False): """ Save the calculated 2D power spectrum as a FITS image. """ hdu = fits.PrimaryHDU(data=self.ps2d, header=self.header) try: hdu.writeto(outfile, overwrite=clobber) except TypeError: hdu.writeto(outfile, clobber=clobber) logger.info("PS2D results saved to file: %s" % outfile) @property def k_xy(self): __, ny, nx = self.cube.shape dxy = self.DMz * np.deg2rad(self.pixelsize / 60.0) # [Mpc] kx = 2*np.pi * fftpack.fftshift(fftpack.fftfreq(nx, dxy)) ky = 2*np.pi * fftpack.fftshift(fftpack.fftfreq(ny, dxy)) return (kx, ky) # [Mpc^-1] @property def k_z(self): freq_step = 1e6 * (self.frequencies[1] - self.frequencies[0]) # [Hz] eta = fftpack.fftshift(fftpack.fftfreq(self.nfreq, freq_step)) # [s] c = ac.c.si.value # [m/s] h = H0 * 1000.0 # [m/s/Mpc] f21cm = freq21cm * 1e6 # [Hz] denom = c * (1+self.zc)**2 / h / f21cm / self.cosmo.efunc(self.zc) kz = 2*np.pi * eta / denom return kz # [Mpc^-1] @property def k_perp(self): """ Comoving wavenumbers perpendicular to the LoS NOTE: The Nyquist frequency just located at the first element after fftshift when the length is even, and it is negative. """ k_x, k_y = self.k_xy return k_x[k_x >= 0] @property def k_los(self): """ Comoving wavenumbers along the LoS """ k_z = self.k_z return k_z[k_z >= 0] @staticmethod def cart2pol(x, y): """ Convert Cartesian coordinates to polar coordinates. """ rho = np.sqrt(x**2 + y**2) phi = np.arctan2(y, x) return (rho, phi) @property def header(self): kx, __ = self.k_xy kz = self.k_z dkx = np.abs(kx[0] - kx[1]) dkz = np.abs(kz[0] - kz[1]) hdr = fits.Header() hdr["HDUNAME"] = ("PS2D", "block name") hdr["CONTENT"] = ("2D cylindrical-averaged power spectrum", "data product") hdr["BUNIT"] = ("K^2 Mpc^3", "data unit") # Physical coordinates: IRAF LTM/LTV # Li{Image} = LTMi_i * Pi{Physical} + LTVi # Reference: ftp://iraf.noao.edu/iraf/web/projects/fitswcs/specwcs.html hdr["LTV1"] = 0.0 hdr["LTM1_1"] = 1.0 / dkx hdr["LTV2"] = 0.0 hdr["LTM2_2"] = 1.0 / dkz # WCS physical coordinates hdr["WCSTY1P"] = "PHYSICAL" hdr["CTYPE1P"] = ("k_perp", "wavenumbers perpendicular to LoS") hdr["CRPIX1P"] = (0.5, "reference pixel") hdr["CRVAL1P"] = (0.0, "coordinate of the reference pixel") hdr["CDELT1P"] = (dkx, "coordinate delta/step") hdr["CUNIT1P"] = ("Mpc^-1", "coordinate unit") hdr["WCSTY2P"] = "PHYSICAL" hdr["CTYPE2P"] = ("k_los", "wavenumbers along LoS") hdr["CRPIX2P"] = (0.5, "reference pixel") hdr["CRVAL2P"] = (0.0, "coordinate of the reference pixel") hdr["CDELT2P"] = (dkz, "coordinate delta/step") hdr["CUNIT2P"] = ("Mpc^-1", "coordinate unit") # Command history hdr.add_history(" ".join(sys.argv)) return hdr def main(): parser = argparse.ArgumentParser( description="Calculate 2D PS from 3D image cube") parser.add_argument("-C", "--clobber", dest="clobber", action="store_true", help="overwrite existing file") parser.add_argument("-p", "--pixelsize", dest="pixelsize", type=float, required=True, help="image cube pixel size; unit: [arcmin]") parser.add_argument("--no-window", dest="no_window", action="store_true", help="do not apply window along frequency axis") parser.add_argument("-i", "--infile", dest="infile", required=True, help="input FITS image cube") parser.add_argument("-o", "--outfile", dest="outfile", required=True, help="output 2D power spectrum FITS file") args = parser.parse_args() with fits.open(args.infile) as f: cube = f[0].data wcs = WCS(f[0].header) nfreq = cube.shape[0] frequencies = get_frequencies(wcs, nfreq) logger.info("%d frequencies [MHz]:" % nfreq) for f in frequencies: logger.info("* %.2f" % f) window = None if args.no_window else "nuttall" ps2d = PS2D(cube=cube, pixelsize=args.pixelsize, frequencies=frequencies, window=window) ps2d.calc_ps3d() ps2d.calc_ps2d() ps2d.save(outfile=args.outfile, clobber=args.clobber) if __name__ == "__main__": main()