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Diffstat (limited to 'astro')
| -rwxr-xr-x | astro/calc_psd.py | 438 |
1 files changed, 438 insertions, 0 deletions
diff --git a/astro/calc_psd.py b/astro/calc_psd.py new file mode 100755 index 0000000..fe02b02 --- /dev/null +++ b/astro/calc_psd.py @@ -0,0 +1,438 @@ +#!/usr/bin/env python3 +# +# Copyright (c) 2015-2017 Aaron LI +# MIT License +# + +""" +Compute the radially averaged power spectral density (i.e., power spectrum) +of a 2D image. + +XXX: If the input image is NOT SQUARE; then are the horizontal frequencies + the same as the vertical frequencies ?? + +Credit +------ +* Radially averaged power spectrum of 2D real-valued matrix + Evan Ruzanski + 'raPsd2d.m' + https://www.mathworks.com/matlabcentral/fileexchange/23636-radially-averaged-power-spectrum-of-2d-real-valued-matrix +""" + +__version__ = "0.5.0" +__date__ = "2016-04-28" + + +import sys +import os +import argparse + +import numpy as np +from astropy.io import fits + +import matplotlib.pyplot as plt +from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas +from matplotlib.figure import Figure + +plt.style.use("ggplot") + + +class PSD: + """ + Computes the 2D power spectral density and the radially averaged power + spectral density (i.e., 1D power spectrum). + """ + # 2D image data + img = None + # value and unit of 1 pixel for the input image + pixel = (None, None) + # whether to normalize the power spectral density by image size + normalize = True + # 2D power spectral density + psd2d = None + # 1D (radially averaged) power spectral density + freqs = None + psd1d = None + psd1d_err = None + + def __init__(self, img, pixel=(1.0, "pixel"), normalize=True): + self.img = img.astype(np.float) + self.pixel = pixel + self.normalize = normalize + + def calc_psd2d(self): + """ + Computes the 2D power spectral density of the given image. + Note that the low frequency components are shifted to the center + of the FFT'ed image. + + NOTE: + The zero-frequency component is shifted to position of index (0-based) + (ceil((n-1) / 2), ceil((m-1) / 2)), + where (n, m) are the number of rows and columns of the image/psd2d. + + Return: + 2D power spectral density, which is dimensionless if normalized, + otherwise has unit ${pixel_unit}^2. + """ + print("Calculating 2D power spectral density ... ", end="", flush=True) + rows, cols = self.img.shape + # Compute the power spectral density (i.e., power spectrum) + imgf = np.fft.fftshift(np.fft.fft2(self.img)) + if self.normalize: + norm = rows * cols * self.pixel[0]**2 + else: + norm = 1.0 # Do not normalize + self.psd2d = (np.abs(imgf) / norm) ** 2 + print("DONE", flush=True) + return self.psd2d + + def calc_radial_psd1d(self): + """ + Computes the radially averaged power spectral density from the + provided 2D power spectral density. + + Return: + (freqs, radial_psd, radial_psd_err) + freqs: spatial freqencies (unit: ${pixel_unit}^(-1)) + radial_psd: radially averaged power spectral density for each + frequency + radial_psd_err: standard deviations of each radial_psd + """ + print("Calculating radial (1D) power spectral density ... ", + end="", flush=True) + print("padding ... ", end="", flush=True) + psd2d = self.pad_square(self.psd2d, value=np.nan) + dim = psd2d.shape[0] + dim_half = (dim+1) // 2 + # NOTE: + # The zero-frequency component is shifted to position of index + # (0-based): (ceil((n-1) / 2), ceil((m-1) / 2)) + px = np.arange(dim_half-dim, dim_half) + x, y = np.meshgrid(px, px) + rho, phi = self.cart2pol(x, y) + rho = np.around(rho).astype(np.int) + radial_psd = np.zeros(dim_half) + radial_psd_err = np.zeros(dim_half) + print("radially averaging ... ", end="", flush=True) + for r in range(dim_half): + # Get the indices of the elements satisfying rho[i,j]==r + ii, jj = (rho == r).nonzero() + # Calculate the mean value at a given radii + data = psd2d[ii, jj] + radial_psd[r] = np.nanmean(data) + radial_psd_err[r] = np.nanstd(data) + # Calculate frequencies + f = np.fft.fftfreq(dim, d=self.pixel[0]) + freqs = np.abs(f[:dim_half]) + # + self.freqs = freqs + self.psd1d = radial_psd + self.psd1d_err = radial_psd_err + print("DONE", flush=True) + return (freqs, radial_psd, radial_psd_err) + + @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) + + @staticmethod + def pol2cart(rho, phi): + """ + Convert polar coordinates to Cartesian coordinates. + """ + x = rho * np.cos(phi) + y = rho * np.sin(phi) + return (x, y) + + @staticmethod + def pad_square(data, value=np.nan): + """ + Symmetrically pad the supplied data matrix to make it square. + The padding rows are equally added to the top and bottom, + as well as the columns to the left and right sides. + The padded rows/columns are filled with the specified value. + """ + mat = data.copy() + rows, cols = mat.shape + dim_diff = abs(rows - cols) + dim_max = max(rows, cols) + if rows > cols: + # pad columns + if dim_diff // 2 == 0: + cols_left = np.zeros((rows, dim_diff/2)) + cols_left[:] = value + cols_right = np.zeros((rows, dim_diff/2)) + cols_right[:] = value + mat = np.hstack((cols_left, mat, cols_right)) + else: + cols_left = np.zeros((rows, np.floor(dim_diff/2))) + cols_left[:] = value + cols_right = np.zeros((rows, np.floor(dim_diff/2)+1)) + cols_right[:] = value + mat = np.hstack((cols_left, mat, cols_right)) + elif rows < cols: + # pad rows + if dim_diff // 2 == 0: + rows_top = np.zeros((dim_diff/2, cols)) + rows_top[:] = value + rows_bottom = np.zeros((dim_diff/2, cols)) + rows_bottom[:] = value + mat = np.vstack((rows_top, mat, rows_bottom)) + else: + rows_top = np.zeros((np.floor(dim_diff/2), cols)) + rows_top[:] = value + rows_bottom = np.zeros((np.floor(dim_diff/2)+1, cols)) + rows_bottom[:] = value + mat = np.vstack((rows_top, mat, rows_bottom)) + return mat + + def plot(self, ax=None, fig=None): + """ + Make a plot of the radial (1D) PSD with matplotlib. + """ + if ax is None: + fig, ax = plt.subplots(1, 1) + # + xmin = self.freqs[1] / 1.2 # ignore the first 0 + xmax = self.freqs[-1] + ymin = np.nanmin(self.psd1d) / 10.0 + ymax = np.nanmax(self.psd1d + self.psd1d_err) + # + eb = ax.errorbar(self.freqs, self.psd1d, yerr=self.psd1d_err, + fmt="none") + ax.plot(self.freqs, self.psd1d, "ko") + ax.set_xscale("log") + ax.set_yscale("log") + ax.set_xlim(xmin, xmax) + ax.set_ylim(ymin, ymax) + ax.set_title("Radially Averaged Power Spectral Density") + ax.set_xlabel(r"k (%s$^{-1}$)" % self.pixel[1]) + if self.normalize: + ax.set_ylabel("Power") + else: + ax.set_ylabel(r"Power (%s$^2$)" % self.pixel[1]) + fig.tight_layout() + return (fig, ax) + + +class AstroImage: + """ + Manipulate the astronimcal counts image, as well as the corresponding + exposure map and background map. + """ + # input counts image + image = None + # exposure map with respect to the input counts image + expmap = None + # background map (e.g., stowed background) + bkgmap = None + # exposure time of the input image + exposure = None + # exposure time of the background map + exposure_bkg = None + + def __init__(self, image, expmap=None, bkgmap=None): + self.load_image(image) + self.load_expmap(expmap) + self.load_bkgmap(bkgmap) + + @staticmethod + def open_image(infile): + """ + Open the slice image and return its header and 2D image data. + + NOTE + ---- + The input slice image may have following dimensions: + * NAXIS=2: [Y, X] + * NAXIS=3: [FREQ=1, Y, X] + * NAXIS=4: [STOKES=1, FREQ=1, Y, X] + + NOTE + ---- + Only open slice image that has only ONE frequency and ONE Stokes + parameter. + + Returns + ------- + header : `~astropy.io.fits.Header` + image : 2D `~numpy.ndarray` + The 2D [Y, X] image part of the slice image. + """ + with fits.open(infile) as f: + header = f[0].header + data = f[0].data + if data.ndim == 2: + # NAXIS=2: [Y, X] + image = data + elif data.ndim == 3 and data.shape[0] == 1: + # NAXIS=3: [FREQ=1, Y, X] + image = data[0, :, :] + elif data.ndim == 4 and data.shape[0] == 1 and data.shape[1] == 1: + # NAXIS=4: [STOKES=1, FREQ=1, Y, X] + image = data[0, 0, :, :] + else: + raise ValueError("Slice '{0}' has invalid dimensions: {1}".format( + infile, data.shape)) + return (header, image) + + def load_image(self, image): + print("Loading image ... ", end="", flush=True) + self.header, self.image = self.open_image(image) + self.exposure = self.header.get("EXPOSURE") + print("DONE", flush=True) + + def load_expmap(self, expmap): + if expmap: + print("Loading exposure map ... ", end="", flush=True) + __, self.expmap = self.open_image(expmap) + print("DONE", flush=True) + + def load_bkgmap(self, bkgmap): + if bkgmap: + print("Loading background map ... ", end="", flush=True) + header, self.bkgmap = self.open_image(bkgmap) + self.exposure_bkg = header.get("EXPOSURE") + print("DONE", flush=True) + + def fix_shapes(self, tolerance=2): + """ + Fix the shapes of self.expmap and self.bkgmap to make them have + the same shape as the self.image. + + NOTE: + * if the image is bigger than the reference image, then its + columns on the right and rows on the botton are clipped; + * if the image is smaller than the reference image, then padding + columns on the right and rows on the botton are added. + * Original images are REPLACED! + + Arguments: + * tolerance: allow absolute difference between images + """ + def _fix_shape(img, ref, tol=tolerance): + if img.shape == ref.shape: + print("SKIPPED", flush=True) + return img + elif np.allclose(img.shape, ref.shape, atol=tol): + print(img.shape, "->", ref.shape, flush=True) + rows, cols = img.shape + rows_ref, cols_ref = ref.shape + # rows + if rows > rows_ref: + img_fixed = img[:rows_ref, :] + else: + img_fixed = np.row_stack((img, + np.zeros((rows_ref-rows, cols), dtype=img.dtype))) + # columns + if cols > cols_ref: + img_fixed = img_fixed[:, :cols_ref] + else: + img_fixed = np.column_stack((img_fixed, + np.zeros((rows_ref, cols_ref-cols), dtype=img.dtype))) + return img_fixed + else: + raise ValueError("shape difference exceeds tolerance: " + \ + "(%d, %d) vs. (%d, %d)" % (img.shape + ref.shape)) + # + if self.bkgmap is not None: + print("Fixing shape for bkgmap ... ", end="", flush=True) + self.bkgmap = _fix_shape(self.bkgmap, self.image) + if self.expmap is not None: + print("Fixing shape for expmap ... ", end="", flush=True) + self.expmap = _fix_shape(self.expmap, self.image) + + def subtract_bkg(self): + print("Subtracting background ... ", end="", flush=True) + self.image -= (self.bkgmap / self.exposure_bkg * self.exposure) + print("DONE", flush=True) + + def correct_exposure(self, cut=0.015): + """ + Correct the image for exposure by dividing by the expmap to + create the exposure-corrected image. + + Arguments: + * cut: the threshold percentage with respect to the maximum + exposure map value; and those pixels with lower values + than this threshold will be excluded/clipped (set to ZERO) + if set to None, then skip clipping image + """ + print("Correcting image for exposure ... ", end="", flush=True) + with np.errstate(divide="ignore", invalid="ignore"): + self.image /= self.expmap + # set invalid values to ZERO + self.image[ ~ np.isfinite(self.image) ] = 0.0 + print("DONE", flush=True) + if cut is not None: + # clip image according the exposure threshold + print("Clipping image (%s) ... " % cut, end="", flush=True) + threshold = cut * np.max(self.expmap) + self.image[ self.expmap < threshold ] = 0.0 + print("DONE", flush=True) + + +def main(): + parser = argparse.ArgumentParser( + description="Compute the radially averaged power spectral density", + epilog="Version: %s (%s)" % (__version__, __date__)) + parser.add_argument("-V", "--version", action="version", + version="%(prog)s " + "%s (%s)" % (__version__, __date__)) + parser.add_argument("-C", "--clobber", dest="clobber", + action="store_true", + help="overwrite the output files if already exist") + parser.add_argument("-i", "--infile", dest="infile", + required=True, help="input image") + parser.add_argument("-b", "--bkgmap", dest="bkgmap", default=None, + help="background map (for background subtraction)") + parser.add_argument("-e", "--expmap", dest="expmap", default=None, + help="exposure map (for exposure correction)") + parser.add_argument("-o", "--outfile", dest="outfile", + required=True, help="output file to store the PSD data") + parser.add_argument("-p", "--png", dest="png", default=None, + help="plot the PSD and save (default: same basename as outfile)") + args = parser.parse_args() + + if args.png is None: + args.png = os.path.splitext(args.outfile)[0] + ".png" + + # Check output files whether already exists + if (not args.clobber) and os.path.exists(args.outfile): + raise ValueError("outfile '%s' already exists" % args.outfile) + if (not args.clobber) and os.path.exists(args.png): + raise ValueError("output png '%s' already exists" % args.png) + + # Load image data + image = AstroImage(image=args.infile, expmap=args.expmap, + bkgmap=args.bkgmap) + image.fix_shapes() + if args.bkgmap: + image.subtract_bkg() + if args.expmap: + image.correct_exposure() + + # Calculate the power spectral density + psd = PSD(img=image.image, normalize=True) + psd.calc_psd2d() + freqs, psd1d, psd1d_err = psd.calc_radial_psd1d() + + # Write out PSD results + psd_data = np.column_stack((freqs, psd1d, psd1d_err)) + np.savetxt(args.outfile, psd_data, header="freqs psd1d psd1d_err") + + # Make and save a plot + fig = Figure(figsize=(10, 8)) + FigureCanvas(fig) + ax = fig.add_subplot(111) + psd.plot(ax=ax, fig=fig) + fig.savefig(args.png, format="png", dpi=150) + + +if __name__ == "__main__": + main() |