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Diffstat (limited to 'python/calc_radial_psd.py')
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diff --git a/python/calc_radial_psd.py b/python/calc_radial_psd.py new file mode 100755 index 0000000..96bc081 --- /dev/null +++ b/python/calc_radial_psd.py @@ -0,0 +1,279 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +# +# Credit: +# [1] 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 +# +# Aaron LI <aaronly.me@gmail.com> +# Created: 2015-04-22 +# Updated: 2016-04-28 +# +# Changelog: +# 2016-04-28: +# * Set default value for 'args.png' +# * Rename from 'radialPSD2d.py' to 'calc_radial_psd.py' +# 2016-04-26: +# * Adjust plot function +# * Update normalize argument; Add pixel argument +# 2016-04-25: +# * Update plot function +# * Add command line scripting support +# * Encapsulate the functions within class 'PSD' +# * Update docs/comments +# + +""" +Compute the radially averaged power spectral density (i.e., power spectrum). +""" + +__version__ = "0.3.2" +__date__ = "2016-04-28" + + +import sys +import os +import argparse + +import numpy as np +from scipy import fftpack +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. + + Return: + 2D power spectral density, which is dimensionless if normalized, + otherwise has unit ${pixel_unit}^2. + """ + rows, cols = self.img.shape + ## Compute the power spectral density (i.e., power spectrum) + imgf = fftpack.fftshift(fftpack.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 + return self.psd2d + + def calc_radial_psd1d(self, k_geometric=True, k_step=1.2): + """ + Computes the radially averaged power spectral density from the + provided 2D power spectral density. + + XXX/TODO: + + Arguments: + * k_geometric: whether the k (i.e., frequency) varies as + geometric sequences (i.e., k, k*k_step, ...), + otherwise, k varies as (k, k+k_step, ...) + * k_step: the step ratio or step length for k + + Return: + (freqs, radial_psd, radial_psd_err) + freqs: spatial freqencies (unit: ${pixel_unit}^(-1)) + if k_geometric=True, frequencies are taken as the + geometric means. + radial_psd: radially averaged power spectral density for each + frequency + radial_psd_err: standard deviations of each radial_psd + """ + psd2d = self.psd2d.copy() + rows, cols = psd2d.shape + ## Adjust the PSD array size + dim_diff = np.abs(rows - cols) + dim_max = max(rows, cols) + # Pad the 2D PSD array to be sqaure + if rows > cols: + # pad columns + if np.mod(dim_diff, 2) == 0: + cols_left = np.zeros((rows, dim_diff/2)) + cols_left[:] = np.nan + cols_right = np.zeros((rows, dim_diff/2)) + cols_right[:] = np.nan + psd2d = np.hstack((cols_left, psd2d, cols_right)) + else: + cols_left = np.zeros((rows, np.floor(dim_diff/2))) + cols_left[:] = np.nan + cols_right = np.zeros((rows, np.floor(dim_diff/2)+1)) + cols_right[:] = np.nan + psd2d = np.hstack((cols_left, psd2d, cols_right)) + elif rows < cols: + # pad rows + if np.mod(dim_diff, 2) == 0: + rows_top = np.zeros((dim_diff/2, cols)) + rows_top[:] = np.nan + rows_bottom = np.zeros((dim_diff/2, cols)) + rows_bottom[:] = np.nan + psd2d = np.vstack((rows_top, psd2d, rows_bottom)) + else: + rows_top = np.zeros((np.floor(dim_diff/2), cols)) + rows_top[:] = np.nan + rows_bottom = np.zeros((np.floor(dim_diff/2)+1, cols)) + rows_bottom[:] = np.nan + psd2d = np.vstack((rows_top, psd2d, rows_bottom)) + ## Compute radially average power spectrum + px = np.arange(-dim_max/2, dim_max/2) + x, y = np.meshgrid(px, px) + rho, phi = self.cart2pol(x, y) + rho = np.around(rho).astype(np.int) + dim_half = int(np.floor(dim_max/2) + 1) + radial_psd = np.zeros(dim_half) + radial_psd_err = np.zeros(dim_half) # standard error + 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 = fftpack.fftfreq(dim_max, d=1) # sample spacing: set to 1 pixel + freqs = np.abs(f[:dim_half]) + # + self.freqs = freqs + self.psd1d = radial_psd + self.psd1d_err = radial_psd_err + 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) + + 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) + + +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("-i", "--infile", dest="infile", + required=True, help="input image") + parser.add_argument("-o", "--outfile", dest="outfile", + required=True, help="output file to store the PSD data") + parser.add_argument("-p", "--png", dest="png", + help="plot the PSD and save (default: same basename as outfile)") + parser.add_argument("-v", "--verbose", dest="verbose", + action="store_true", help="show verbose information") + parser.add_argument("-C", "--clobber", dest="clobber", + action="store_true", + help="overwrite the output files if already exist") + args = parser.parse_args() + + if args.png == "": + 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 + if args.verbose: + print("Loading input image ...", file=sys.stderr) + with fits.open(args.infile) as ffile: + img = ffile[0].data + psd = PSD(img, normalize=True) + + # Calculate the power spectral density + if args.verbose: + print("Calculate 2D power spectral density ...", file=sys.stderr) + psd.calc_psd2d() + if args.verbose: + print("Calculate radially averaged (1D) power spectral density ...", + file=sys.stderr) + 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)) + canvas = 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() + |