import numpy as np
[docs]def azimuthalAverage(image, center=None, stddev=False, returnradii=False, return_nr=False,
binsize=0.5, weights=None, steps=False, interpnan=False, left=None, right=None,
mask=None ):
"""
Calculate the azimuthally averaged radial profile.
image - The 2D image
center - The [x,y] pixel coordinates used as the center. The default is
None, which then uses the center of the image (including
fractional pixels).
stddev - if specified, return the azimuthal standard deviation instead of the average
returnradii - if specified, return (radii_array,radial_profile)
return_nr - if specified, return number of pixels per radius *and* radius
binsize - size of the averaging bin. Can lead to strange results if
non-binsize factors are used to specify the center and the binsize is
too large
weights - can do a weighted average instead of a simple average if this keyword parameter
is set. weights.shape must = image.shape. weighted stddev is undefined, so don't
set weights and stddev.
steps - if specified, will return a double-length bin array and radial
profile so you can plot a step-form radial profile (which more accurately
represents what's going on)
interpnan - Interpolate over NAN values, i.e. bins where there is no data?
left,right - passed to interpnan; they set the extrapolated values
mask - can supply a mask (boolean array same size as image with True for OK and False for not)
to average over only select data.
If a bin contains NO DATA, it will have a NAN value because of the
divide-by-sum-of-weights component. I think this is a useful way to denote
lack of data, but users let me know if an alternative is prefered...
"""
# Calculate the indices from the image
y, x = np.indices(image.shape)
if center is None:
center = np.array([(x.max()-x.min())/2.0, (y.max()-y.min())/2.0])
r = np.hypot(x - center[0], y - center[1])
if weights is None:
weights = np.ones(image.shape)
elif stddev:
raise ValueError("Weighted standard deviation is not defined.")
if mask is None:
mask = np.ones(image.shape,dtype='bool')
# obsolete elif len(mask.shape) > 1:
# obsolete mask = mask.ravel()
# the 'bins' as initially defined are lower/upper bounds for each bin
# so that values will be in [lower,upper)
nbins = int(np.round(r.max() / binsize)+1)
maxbin = nbins * binsize
bins = np.linspace(0,maxbin,nbins+1)
# but we're probably more interested in the bin centers than their left or right sides...
bin_centers = (bins[1:]+bins[:-1])/2.0
# how many per bin (i.e., histogram)?
# there are never any in bin 0, because the lowest index returned by digitize is 1
#nr = np.bincount(whichbin)[1:]
nr = np.histogram(r,bins)[0]
# recall that bins are from 1 to nbins (which is expressed in array terms by arange(nbins)+1 or xrange(1,nbins+1) )
# radial_prof.shape = bin_centers.shape
if stddev:
# Find out which radial bin each point in the map belongs to
whichbin = np.digitize(r.flat,bins)
# This method is still very slow; is there a trick to do this with histograms?
radial_prof = np.array([image.flat[mask.flat*(whichbin==b)].std() for b in xrange(1,nbins+1)])
else:
radial_prof = np.histogram(r, bins, weights=(image*weights*mask))[0] / np.histogram(r, bins, weights=(mask*weights))[0]
if interpnan:
radial_prof = np.interp(bin_centers,bin_centers[radial_prof==radial_prof],radial_prof[radial_prof==radial_prof],left=left,right=right)
if steps:
xarr = np.array(zip(bins[:-1],bins[1:])).ravel()
yarr = np.array(zip(radial_prof,radial_prof)).ravel()
return xarr,yarr
elif returnradii:
return bin_centers,radial_prof
elif return_nr:
return nr,bin_centers,radial_prof
else:
return radial_prof
[docs]def azimuthalAverageBins(image,azbins,symmetric=None, center=None, **kwargs):
""" Compute the azimuthal average over a limited range of angles
kwargs are passed to azimuthalAverage """
y, x = np.indices(image.shape)
if center is None:
center = np.array([(x.max()-x.min())/2.0, (y.max()-y.min())/2.0])
r = np.hypot(x - center[0], y - center[1])
theta = np.arctan2(x - center[0], y - center[1])
theta[theta < 0] += 2*np.pi
theta_deg = theta*180.0/np.pi
if isinstance(azbins,np.ndarray):
pass
elif isinstance(azbins,int):
if symmetric == 2:
azbins = np.linspace(0,90,azbins)
theta_deg = theta_deg % 90
elif symmetric == 1:
azbins = np.linspace(0,180,azbins)
theta_deg = theta_deg % 180
elif azbins == 1:
return azbins,azimuthalAverage(image,center=center,returnradii=True,**kwargs)
else:
azbins = np.linspace(0,359.9999999999999,azbins)
else:
raise ValueError("azbins must be an ndarray or an integer")
azavlist = []
for blow,bhigh in zip(azbins[:-1],azbins[1:]):
mask = (theta_deg > (blow % 360)) * (theta_deg < (bhigh % 360))
rr,zz = azimuthalAverage(image,center=center,mask=mask,returnradii=True,**kwargs)
azavlist.append(zz)
return azbins,rr,azavlist
[docs]def radialAverage(image, center=None, stddev=False, returnAz=False, return_naz=False,
binsize=1.0, weights=None, steps=False, interpnan=False, left=None, right=None,
mask=None, symmetric=None ):
"""
Calculate the radially averaged azimuthal profile.
(this code has not been optimized; it could be speed boosted by ~20x)
image - The 2D image
center - The [x,y] pixel coordinates used as the center. The default is
None, which then uses the center of the image (including
fractional pixels).
stddev - if specified, return the radial standard deviation instead of the average
returnAz - if specified, return (azimuthArray,azimuthal_profile)
return_naz - if specified, return number of pixels per azimuth *and* azimuth
binsize - size of the averaging bin. Can lead to strange results if
non-binsize factors are used to specify the center and the binsize is
too large
weights - can do a weighted average instead of a simple average if this keyword parameter
is set. weights.shape must = image.shape. weighted stddev is undefined, so don't
set weights and stddev.
steps - if specified, will return a double-length bin array and azimuthal
profile so you can plot a step-form azimuthal profile (which more accurately
represents what's going on)
interpnan - Interpolate over NAN values, i.e. bins where there is no data?
left,right - passed to interpnan; they set the extrapolated values
mask - can supply a mask (boolean array same size as image with True for OK and False for not)
to average over only select data.
If a bin contains NO DATA, it will have a NAN value because of the
divide-by-sum-of-weights component. I think this is a useful way to denote
lack of data, but users let me know if an alternative is prefered...
"""
# Calculate the indices from the image
y, x = np.indices(image.shape)
if center is None:
center = np.array([(x.max()-x.min())/2.0, (y.max()-y.min())/2.0])
r = np.hypot(x - center[0], y - center[1])
theta = np.arctan2(x - center[0], y - center[1])
theta[theta < 0] += 2*np.pi
theta_deg = theta*180.0/np.pi
maxangle = 360
if weights is None:
weights = np.ones(image.shape)
elif stddev:
raise ValueError("Weighted standard deviation is not defined.")
if mask is None:
# mask is only used in a flat context
mask = np.ones(image.shape,dtype='bool').ravel()
elif len(mask.shape) > 1:
mask = mask.ravel()
# allow for symmetries
if symmetric == 2:
theta_deg = theta_deg % 90
maxangle = 90
elif symmetric == 1:
theta_deg = theta_deg % 180
maxangle = 180
# the 'bins' as initially defined are lower/upper bounds for each bin
# so that values will be in [lower,upper)
nbins = int(np.round(maxangle / binsize))
maxbin = nbins * binsize
bins = np.linspace(0,maxbin,nbins+1)
# but we're probably more interested in the bin centers than their left or right sides...
bin_centers = (bins[1:]+bins[:-1])/2.0
# Find out which azimuthal bin each point in the map belongs to
whichbin = np.digitize(theta_deg.flat,bins)
# how many per bin (i.e., histogram)?
# there are never any in bin 0, because the lowest index returned by digitize is 1
nr = np.bincount(whichbin)[1:]
# recall that bins are from 1 to nbins (which is expressed in array terms by arange(nbins)+1 or xrange(1,nbins+1) )
# azimuthal_prof.shape = bin_centers.shape
if stddev:
azimuthal_prof = np.array([image.flat[mask*(whichbin==b)].std() for b in xrange(1,nbins+1)])
else:
azimuthal_prof = np.array([(image*weights).flat[mask*(whichbin==b)].sum() / weights.flat[mask*(whichbin==b)].sum() for b in xrange(1,nbins+1)])
#import pdb; pdb.set_trace()
if interpnan:
azimuthal_prof = np.interp(bin_centers,
bin_centers[azimuthal_prof==azimuthal_prof],
azimuthal_prof[azimuthal_prof==azimuthal_prof],
left=left,right=right)
if steps:
xarr = np.array(zip(bins[:-1],bins[1:])).ravel()
yarr = np.array(zip(azimuthal_prof,azimuthal_prof)).ravel()
return xarr,yarr
elif returnAz:
return bin_centers,azimuthal_prof
elif return_naz:
return nr,bin_centers,azimuthal_prof
else:
return azimuthal_prof
[docs]def radialAverageBins(image,radbins, corners=True, center=None, **kwargs):
""" Compute the radial average over a limited range of radii """
y, x = np.indices(image.shape)
if center is None:
center = np.array([(x.max()-x.min())/2.0, (y.max()-y.min())/2.0])
r = np.hypot(x - center[0], y - center[1])
if isinstance(radbins,np.ndarray):
pass
elif isinstance(radbins,int):
if radbins == 1:
return radbins,radialAverage(image,center=center,returnAz=True,**kwargs)
elif corners:
radbins = np.linspace(0,r.max(),radbins)
else:
radbins = np.linspace(0,np.max(np.abs(np.array([x-center[0],y-center[1]]))),radbins)
else:
raise ValueError("radbins must be an ndarray or an integer")
radavlist = []
for blow,bhigh in zip(radbins[:-1],radbins[1:]):
mask = (r<bhigh)*(r>blow)
az,zz = radialAverage(image,center=center,mask=mask,returnAz=True,**kwargs)
radavlist.append(zz)
return radbins,az,radavlist