def get_radial_profile(image, center=None, stddev=False, binsize=1, mask=None, weights=None):
""" Calculates radial profiles of an image at the center.
"""
# import external modules
import numpy as np
from scipy.optimize import curve_fit
from agpy import azimuthalAverage as radial_average
if stddev and weights is not None:
weights = None
result = radial_average(
image,
binsize=binsize,
center=center,
stddev=stddev,
mask=mask,
interpnan=False,
returnradii=True,
weights=weights,
)
return result
def get_radial_profile(image,
center=None,
stddev=False,
binsize=1,
mask=None,
weights=None):
''' Calculates radial profiles of an image at the center.
'''
# import external modules
import numpy as np
from scipy.optimize import curve_fit
from agpy import azimuthalAverage as radial_average
if stddev and weights is not None:
weights = None
result = radial_average(image,
binsize=binsize,
center=center,
stddev=stddev,
mask=mask,
interpnan=False,
returnradii=True,
weights=weights)
return result
def plot_power_spectrum(image, title=None, filename_prefix=None,
filename_suffix='.png', show=False, savedir='./'):
'''
Plots power spectrum derived from a fourier transform of the image.
'''
# import external modules
import numpy as np
from agpy import azimuthalAverage as radial_average
from scipy import fftpack
import matplotlib.pyplot as plt
import matplotlib
from mpl_toolkits.axes_grid1 import ImageGrid
from matplotlib import cm
if 0:
plt.close(); plt.clf()
plt.imshow(image)
plt.show()
image[np.isnan(image)] = 1e10
# Determine power spectrum
# -------------------------------------------------------------------------
# Take the fourier transform of the image.
#F1 = fftpack.fft2(np.ma.array(image, mask=np.isnan(image)))
F1 = fftpack.fft2(image)
# Now shift the quadrants around so that low spatial frequencies are in
# the center of the 2D fourier transformed image.
F2 = fftpack.fftshift(F1)
# Calculate a 2D power spectrum
psd2D = np.abs(F2)**2
if 0:
plt.close(); plt.clf()
plt.imshow(psd2D)
plt.show()
power_spectrum = radial_average(psd2D, interpnan=True)
# Write frequency in arcmin
freq = fftpack.fftfreq(len(power_spectrum))
freq *= 5.0
# Simulate power spectrum for white noise
noise_image = np.random.normal(scale=0.1, size=image.shape)
F1 = fftpack.fft2(noise_image)
# Now shift the quadrants around so that low spatial frequencies are in
# the center of the 2D fourier transformed image.
F2 = fftpack.fftshift(F1)
# Calculate a 2D power spectrum
psd2D_noise = np.abs(F2)**2
power_spectrum_noise = radial_average(psd2D_noise, interpnan=True)
# Plot power spectrum 1D
# -------------------------------------------------------------------------
# Set up plot aesthetics
plt.clf()
plt.rcdefaults()
colormap = plt.cm.gist_ncar
#color_cycle = [colormap(i) for i in np.linspace(0, 0.9, len(flux_list))]
font_scale = 12
params = {#'backend': .pdf',
'axes.labelsize': font_scale,
'axes.titlesize': font_scale,
'text.fontsize': font_scale,
'legend.fontsize': font_scale * 3 / 4.0,
'xtick.labelsize': font_scale,
'ytick.labelsize': font_scale,
'font.weight': 500,
'axes.labelweight': 500,
'text.usetex': False,
'figure.figsize': (5, 5),
#'axes.color_cycle': color_cycle # colors of different plots
}
plt.rcParams.update(params)
# Create figure instance
fig = plt.figure()
nrows = 1; ncols = 1; ngrids = 1;
imagegrid = ImageGrid(fig, (1,1,1),
nrows_ncols=(nrows, ncols),
ngrids=ngrids,
axes_pad=0.25,
aspect=False,
label_mode='L',
share_all=True,
#cbar_mode='single',
cbar_pad=0.1,
cbar_size=0.2,
)
ax = imagegrid[0]
ax.plot(freq, power_spectrum / np.nanmax(power_spectrum),
color='k',
linestyle='-',
linewidth=1.5,
drawstyle='steps-mid',
label='Data Residuals')
ax.plot(freq, power_spectrum_noise / np.nanmax(power_spectrum_noise),
color='r',
linestyle='-',
linewidth=0.4,
drawstyle='steps-mid',
label='White Noise Residuals')
#ax.set_xscale('log')
ax.legend(loc='best')
#ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('Spatial Frequency [1/arcmin]')
ax.set_ylabel('Normalized Power Spectrum')
ax.set_xlim(0, 0.4)
if title is not None:
fig.suptitle(title, fontsize=font_scale)
if filename_prefix is not None:
plt.savefig(savedir + filename_prefix + '_1D' + filename_suffix,
bbox_inches='tight')
if show:
plt.show()
# Plot power spectrum image
# -------------------------
# Create figure instance
fig = plt.figure()
nrows = 1; ncols = 1; ngrids = 1;
imagegrid = ImageGrid(fig, (1,1,1),
nrows_ncols=(nrows, ncols),
ngrids=ngrids,
axes_pad=0.25,
aspect=False,
label_mode='L',
share_all=True,
#cbar_mode='single',
cbar_pad=0.1,
cbar_size=0.2,
)
ax = imagegrid[0]
extent = [- image.shape[0] / 2.0, + image.shape[0] / 2.0,
- image.shape[1] / 2.0, + image.shape[1] / 2.0]
ax.imshow(psd2D,
origin='lower',
cmap=cm.gist_heat,
norm=matplotlib.colors.LogNorm(),
extent=extent
)
#ax.set_xscale('log')
#ax.legend(loc='center right')
#ax.set_yscale('log')
ax.set_xlabel('Spatial Frequency in Right Ascension')
ax.set_ylabel('Spatial Frequency in Declination')
ax.set_xlim(-20, 20)
ax.set_ylim(-20, 20)
if title is not None:
fig.suptitle(title, fontsize=font_scale)
if filename_prefix is not None:
plt.savefig(savedir + filename_prefix + '_2D' + filename_suffix,
bbox_inches='tight')
if show:
plt.show()
def plot_power_spectrum(image,
title=None,
filename_prefix=None,
filename_suffix='.png',
show=False,
savedir='./'):
'''
Plots power spectrum derived from a fourier transform of the image.
'''
# import external modules
import numpy as np
from agpy import azimuthalAverage as radial_average
from scipy import fftpack
import matplotlib.pyplot as plt
import matplotlib
from mpl_toolkits.axes_grid1 import ImageGrid
from matplotlib import cm
if 0:
plt.close()
plt.clf()
plt.imshow(image)
plt.show()
image[np.isnan(image)] = 1e10
# Determine power spectrum
# -------------------------------------------------------------------------
# Take the fourier transform of the image.
#F1 = fftpack.fft2(np.ma.array(image, mask=np.isnan(image)))
F1 = fftpack.fft2(image)
# Now shift the quadrants around so that low spatial frequencies are in
# the center of the 2D fourier transformed image.
F2 = fftpack.fftshift(F1)
# Calculate a 2D power spectrum
psd2D = np.abs(F2)**2
if 0:
plt.close()
plt.clf()
plt.imshow(psd2D)
plt.show()
power_spectrum = radial_average(psd2D, interpnan=True)
# Write frequency in arcmin
freq = fftpack.fftfreq(len(power_spectrum))
freq *= 5.0
# Simulate power spectrum for white noise
noise_image = np.random.normal(scale=0.1, size=image.shape)
F1 = fftpack.fft2(noise_image)
# Now shift the quadrants around so that low spatial frequencies are in
# the center of the 2D fourier transformed image.
F2 = fftpack.fftshift(F1)
# Calculate a 2D power spectrum
psd2D_noise = np.abs(F2)**2
power_spectrum_noise = radial_average(psd2D_noise, interpnan=True)
# Plot power spectrum 1D
# -------------------------------------------------------------------------
# Set up plot aesthetics
plt.clf()
plt.rcdefaults()
colormap = plt.cm.gist_ncar
#color_cycle = [colormap(i) for i in np.linspace(0, 0.9, len(flux_list))]
font_scale = 12
params = { #'backend': .pdf',
'axes.labelsize': font_scale,
'axes.titlesize': font_scale,
'text.fontsize': font_scale,
'legend.fontsize': font_scale * 3 / 4.0,
'xtick.labelsize': font_scale,
'ytick.labelsize': font_scale,
'font.weight': 500,
'axes.labelweight': 500,
'text.usetex': False,
'figure.figsize': (5, 5),
#'axes.color_cycle': color_cycle # colors of different plots
}
plt.rcParams.update(params)
# Create figure instance
fig = plt.figure()
nrows = 1
ncols = 1
ngrids = 1
imagegrid = ImageGrid(
fig,
(1, 1, 1),
nrows_ncols=(nrows, ncols),
ngrids=ngrids,
axes_pad=0.25,
aspect=False,
label_mode='L',
share_all=True,
#cbar_mode='single',
cbar_pad=0.1,
cbar_size=0.2,
)
ax = imagegrid[0]
ax.plot(freq,
power_spectrum / np.nanmax(power_spectrum),
color='k',
linestyle='-',
linewidth=1.5,
drawstyle='steps-mid',
label='Data Residuals')
ax.plot(freq,
power_spectrum_noise / np.nanmax(power_spectrum_noise),
color='r',
linestyle='-',
linewidth=0.4,
drawstyle='steps-mid',
label='White Noise Residuals')
#ax.set_xscale('log')
ax.legend(loc='best')
#ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('Spatial Frequency [1/arcmin]')
ax.set_ylabel('Normalized Power Spectrum')
ax.set_xlim(0, 0.4)
if title is not None:
fig.suptitle(title, fontsize=font_scale)
if filename_prefix is not None:
plt.savefig(savedir + filename_prefix + '_1D' + filename_suffix,
bbox_inches='tight')
if show:
plt.show()
# Plot power spectrum image
# -------------------------
# Create figure instance
fig = plt.figure()
nrows = 1
ncols = 1
ngrids = 1
imagegrid = ImageGrid(
fig,
(1, 1, 1),
nrows_ncols=(nrows, ncols),
ngrids=ngrids,
axes_pad=0.25,
aspect=False,
label_mode='L',
share_all=True,
#cbar_mode='single',
cbar_pad=0.1,
cbar_size=0.2,
)
ax = imagegrid[0]
extent = [
-image.shape[0] / 2.0, +image.shape[0] / 2.0, -image.shape[1] / 2.0,
+image.shape[1] / 2.0
]
ax.imshow(psd2D,
origin='lower',
cmap=cm.gist_heat,
norm=matplotlib.colors.LogNorm(),
extent=extent)
#ax.set_xscale('log')
#ax.legend(loc='center right')
#ax.set_yscale('log')
ax.set_xlabel('Spatial Frequency in Right Ascension')
ax.set_ylabel('Spatial Frequency in Declination')
ax.set_xlim(-20, 20)
ax.set_ylim(-20, 20)
if title is not None:
fig.suptitle(title, fontsize=font_scale)
if filename_prefix is not None:
plt.savefig(savedir + filename_prefix + '_2D' + filename_suffix,
bbox_inches='tight')
if show:
plt.show()
