Making the figures for the kidney-speckle-methods manuscript

Load modules

In [1]: 
import os
import pickle
from scipy import ndimage
from imfun import fseq, lib, ui, filt, bwmorph
import speckle_process as sp

save_path = './figures/'
data_path = './'

if not os.path.exists(save_path):
    os.mkdir(save_path)
    
fnames = ['video_%03d.h5'%k for k in range(6)]

/usr/lib/python2.7/dist-packages/sklearn/pls.py:7: DeprecationWarning: This module has been moved to cross_decomposition and will be removed in 0.16
  "removed in 0.16", DeprecationWarning)

Create frequency- and phase-mapped movies

In [2]: 
## NB: may take a very long time to compute
for name in fnames:
    if not os.path.exists(name + '-freq-tgf-ver2-resized.npy'):
        print "Calculating frequency maps for file ", name
        sp.make_mapping_movie(name, type='freq')

Define pre-processing functions

In [3]: 
from scipy.interpolate import splev, splrep
def load_fft_cif(name):
    fft_ci = pickle.load(open(name))
    return {0.4: lambda x:splev(x, fft_ci[0.4]),
            1: lambda x:splev(x, fft_ci[1])}

def preprocess_file(fname, sign_lev=None,verbose=False):
    """
    Return:
        - resized frame sequence
        - mask, which is true, where oscillations were significant // lg(P)/10 > sign_lev
        - (peak, fm), where peak is a map of Fourier power lg(P)/10  and fm is a map of the frequency of the peak
    """
    # resized
    seqr = sp.try_load_resized(fname)
    print "Loaded downsampled data of shape ", seqr.data.shape
    print "sampling rate: ", seqr.dt
    maskr = sp.make_mask(seqr,100)
    bmaskr = lib.mask4overlay(maskr<1,2, 0.5)
    sys.stdout.flush()
    # fft
    freqs = np.fft.fftfreq(seqr.length(), seqr.dt)
    _frange = np.array(sp.frange_tgf) * np.array((0.75, 1.25))
    freqs_clip = freqs[sp.in_range(freqs, _frange)]
    frange = np.array(sp.frange_tgf) * np.array((0.75, 1.25)) # 25% margins round frange_tgf
    fn = lambda v: np.abs(np.fft.fft(lib.DFoSD(v))[sp.in_range(freqs,_frange)])**2
    seqt = seqr.pw_transform(fn, verbose=verbose) ## clipped power spectra
    
    # mask where oscillations were significant
    peak = log10(seqt.max_project())/10
    fm = seqt.time_project(fn=lambda aa: freqs_clip[np.argmax(aa)])
    
    fft_cif = load_fft_cif('fft_ci.pickle')
    
    if sign_lev is None:
        if seqr.dt in fft_cif:
            sign_lev = fft_cif[seqr.dt](seqr.length())
        else:
            sign_lev = fft_cif[1](seqr.length())
    
        print "Significance level is set to %2.2f" % sign_lev
    
    sig_osc = (peak > sign_lev)  # True where oscillations are significant
    sig_osc = maskr*sig_osc*filt.opening_of_closing(sig_osc) # filter out small dots
    
    maskF = bwmorph.filter_mask(sig_osc, lambda r: bwmorph.filter_size_regions(r, 25))
    maskF = ndimage.binary_fill_holes(maskF)
    
    # Return: resized frame sequence, mask1, (peak, fm)
    return seqr, maskF, (peak, fm)

Figure 1 (FFT)

In [4]: 
fname = data_path+'video_002.h5'
seq = fseq.FSeq_hdf5(fname,dt=1.0)
mf = seq.mean_frame(stop=250)
bmask = sp.make_mask(seq)
In [5]: 
seqr, maskr, (peak, fm) = preprocess_file(fname)

Loaded downsampled data of shape  (2694, 284, 380)
sampling rate:  1.0
Significance level is set to 0.43

Make FFT transform

In [6]: 
newfr, newyr,_ = sp.make_avg_fft('testing', seqr, rand=False,make_plots=False,verbose=False)
newf, newy,_ = sp.make_avg_fft(fname, seq,rand=False,sq_size=200,make_plots=False,verbose=False)

testing 2694 (284, 380)
91732 pixels in the mask


0.0 28026.6878224
./video_002.h5 2694 (568, 760)
366925 pixels in the mask


0.0 12581.1722101
In [7]: 
peak = ma.masked_where(-maskr, peak)
fm = ma.masked_where(-maskr, fm)
figure(figsize=(13,8))
subplot(221);

hold(True)

imshow(mf, aspect='equal', cmap='gray'); colorbar();
imshow(ma.masked_where(bmask,bmask), aspect='equal')
title('Time-averaged LSF image')

subplot(222);
imshow(peak, aspect='equal', cmap='hot');
colorbar();
title('Fourier power lg(P)/10')
#imshow(bmaskr, aspect='equal')

	
subplot(223);
imshow(fm, aspect='equal', cmap='spectral', vmin=0.015, vmax=0.027);
colorbar();
title('Map of peak Fourier  frequency')
#imshow(bmaskr, aspect='equal')
	
for ax in gcf().axes: setp(ax, frame_on=False, xticks=[], yticks=[])

subplot(224)
semilogy(newf[10:250], newy[10:250], 'gray', lw=3, label='original')
semilogy(newfr[10:250], newyr[10:250], 'k-', lw=0.75, label="downsampled");
legend()
xlabel('frequency, Hz',size=12)
ylabel('Fourier power $\\times$ $\sigma^2$',size=12)
title('Average power spectra')
#savefig(save_path+'Figure-1-draft-v2.svg')

/usr/lib/pymodules/python2.7/matplotlib/colorbar.py:211: UserWarning: Use the colorbar set_ticks() method instead.
  warnings.warn("Use the colorbar set_ticks() method instead.")
Out[7]:
<matplotlib.text.Text at 0x7fccdeacbe90>

Figure 2 (Rhythm tracking explanation)

In [8]: 
frmap,name = sp.get_frmap(fname)

./video_002.h5-freq-tgf-ver2-resized.npy
In [9]: 
_frange = np.array(sp.frange_tgf) * np.array((0.75, 1.25))
frmap, phasemap = frmap.real, frmap.imag
mask1w = reduce(sp.op.__and__, [f>0 for f in frmap]) * maskr # where oscillations are significant

extent = (0, seqr.length(), _frange[0], _frange[-1])
wfreqs = linspace(_frange[0], _frange[1], 256)
mwfreq = np.ma.masked_where(mask1w<1,frmap.mean(axis=0))
In [10]: 
from swan import pycwt
from swan import utils as su

freqs = sp.getfreqs(sp.frange_tgf)
extent=[0, seqr.dt*seqr.length(), freqs[0],freqs[-1]]

#locations = [(60,153), (98,64), (135,108), (73,108), (63,91), (50,41)]
loc = (103, 317)
v = seqr.data[:,loc[0], loc[1]]
vn = lib.DFoSD(v)

cwt = pycwt.cwt_f(vn, freqs, 1/seqr.dt, ppd='cpd')
eds = pycwt.eds(cwt)
phase = pycwt.cwt_phase(cwt)
tv, fv = sp.locmax_pos(eds)
In [11]: 
figure(figsize=(5,5))
hold(True)
imshow(seqr.mean_frame(), aspect='equal', cmap='gray')
axsize = axis()
plot(loc[1], loc[0], 's', color='yellow', ms=8,mec='yellow',alpha=0.5)
plot(loc[1], loc[0], '+', color='yellow', ms=14,lw=2)
axis(axsize)
setp(gca(), frame_on=False, xticks=[], yticks=[])
savefig(save_path+"Figure-3A-draft-v2.svg")

Figure 2B

In [12]: 
s = ndimage.generate_binary_structure(2,2)
min_pts_ridge = 100
fsd =pycwt.Morlet().sigma_f_f(np.mean(freqs))
rhsd = 3*fsd
dfr = np.diff(freqs).mean()
rhsd_i = int(round(fsd/dfr))

D = np.zeros(eds.shape)
weights = sp.eds2weights(eds)
D[fv,tv] = 1
D = 1.0*sp.ndimage.binary_dilation(D)
labels, nlab = sp.ndimage.label(D, s)
objs = sp.ndimage.find_objects(labels)
for mark,obj in enumerate(objs):
    m = labels == mark+1
    if m.sum() < min_pts_ridge:
	D[m] = 0
	continue
    tsl = obj[1]
    t_ext = tsl.stop - tsl.start
    D[m] = t_ext * eds[m].mean()

xf, xt = np.where(D)
z = D[xf,xt]
mw = lib.mask4overlay2(1-weights, (0,0,0), alpha= 1 -0.5*weights)

fh,eds = su.plot_spectrogram_with_ts(vn,1.0,freqs,figsize=(8,4.5))
savefig(save_path+"Figure-3B-draft-v2.svg")

/usr/local/lib/python2.7/dist-packages/swan/utils.py:259: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  tvec = np.arange(0, (Ns+2)/f_s, 1./f_s)[:Ns]

Figure 2D

In [13]: 
xfm, xtm = np.where(D>=D.max())
zm = D[xfm,xtm]
In [14]: 
fh, axs = subplots(2,1,figsize=(12,7))
mappable = axs[0].imshow(eds, extent=extent,cmap='gray_r',vmax=120);
axlim = axs[0].axis()
colorbar(mappable,ax=axs[0])
axs[0].scatter(xt, freqs[xf], c=z, s=1,edgecolors='none')
axs[0].axis(axlim)
setp(axs[0], title='Wavelet ridges')
mappable = axs[1].imshow(phase/pi, extent=extent, cmap='rainbow');
colorbar(mappable,ax=axs[1], ticks = [-1, -0.5, 0, 0.5, 1])
#axs[1].imshow(mw, extent=extent)
axs[1].scatter(xtm, freqs[xfm], c='red', s=1,edgecolors='none')
axs[1].axis(axlim)
setp(axs[1], xlabel='time, s',
ylabel='frequency, Hz', title='Wavelet phase $ \\times \pi$')

savefig(save_path+"Figure-3D-draft-v2.svg")

Figure 2C

In [15]: 
vdf = sp.dominant_freq(freqs, 1/seqr.dt)(vn)

vdf, vdph = vdf.real, vdf.imag

fh,axs = subplots(2,1,sharey=False, sharex=True)
axs[0].plot(vdf, 'k-')
setp(axs[0], ylim = (0.015, 0.027))
axs[0].set_title('Dominant wavelet ridge frequency')
axs[1].plot(vdph/pi, 'k-')
setp(axs[1], ylim = (-1.1, 1.1))
axs[1].set_title('Wavelet phase $\\times \pi$')
setp(axs[1], xlim=(0, len(vn)))

savefig(save_path+"Figure-3C-draft-v2.svg")

Figure 3 (Wavelet maps simple)

In [16]: 
out = sp.make_avg_spectrogram("testing", seq=seqr, rand=False)


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testing 2694 (284, 380)





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In [17]: 
figure(figsize=(13,8))
subplot(211)
imshow(out, extent=extent, cmap=sp.swanrgb); colorbar()
ax = axis()
xt, xf = sp.locmax_pos(out)
wfreqs = sp.getfreqs(sp.frange_tgf, 256)
mwfreq = ma.masked_where(-maskr, frmap.mean(axis=0))
plot(xt, wfreqs[xf], 'k,')
axis(ax)
title('Spatially averaged wavelet spectrogram')

subplot(223)
imshow(mwfreq, aspect='equal', cmap='spectral',vmin=0.015,vmax=0.027);
colorbar()
setp(gca(), xticks=[], yticks=[], frame_on=False)
title('Map of time-averaged wavelet ridge frequencies')

subplot(224)
hist(frmap[frmap>0.01],100, normed=True, histtype='step', color='black')
ylabel('Intensity',size=12)
xlabel('Frequency, Hz', size=12)
title('Distribution of wavelet ridge frequencies')

savefig(save_path+'Figure-2-draft-v2.svg')

Figure - Fourier power maps

In [18]: 
acc = []
for name in fnames:
    seqr,maskF, (peak,_) = preprocess_file(name)
    acc.append([name, seqr.mean_frame(stop=500), maskF, peak])

fh, axs = subplots(2,3, figsize=(12,5))
k = 0
axsfl = axs.ravel()
for de in acc: 
    h =de[1].shape[0]
    ax = axsfl[k]
    ax.imshow(de[1], cmap='gray')
    m = ax.imshow(ma.masked_where(-de[2],de[3]), cmap='hot', vmax=0.6, vmin=0.34, aspect='equal')
    colorbar(m, ax=ax)
    setp(ax, xticks=[], yticks=[], frame_on=False)
    rw  = Rectangle((10,h-40), 30,35,color='black')
    ax.add_patch(rw)
    ax.text(15, h-35, k+1, color='white', fontsize=16)
    k += 1
savefig(save_path+'Figure-peak-Fourier-power.svg')

Loaded downsampled data of shape  (2299, 284, 380)
sampling rate:  1.0
Significance level is set to 0.42
Loaded downsampled data of shape  (2202, 284, 380)
sampling rate:  1.0
Significance level is set to 0.42
Loaded downsampled data of shape  (2694, 284, 380)
sampling rate:  1.0
Significance level is set to 0.43
Loaded downsampled data of shape  (2520, 284, 380)
sampling rate:  1.0
Significance level is set to 0.43
Loaded downsampled data of shape  (1972, 284, 380)
sampling rate:  1.0
Significance level is set to 0.42
Loaded downsampled data of shape  (2672, 284, 380)
sampling rate:  1.0
Significance level is set to 0.43

Frequency locking with an example 1Hz file

In [19]: 
fname = data_path+'video_004.h5'

seqr, maskr, (peak, fm) = preprocess_file(fname)
frmap,name = sp.get_frmap(fname)
frmap, phasemap = frmap.real, frmap.imag

Loaded downsampled data of shape  (1972, 284, 380)
sampling rate:  1.0
Significance level is set to 0.42
./video_004.h5-freq-tgf-ver2-resized.npy
In [20]: 
mask1w1 = reduce(sp.op.__and__, [f>0 for f in frmap])
mask1w = mask1w1 * maskr
#frmap2 = array([ma.masked_where(-mask1w, f) for f in frmap])
In [21]: 
f = figure(figsize=(6,4))
imshow(seqr.mean_frame(100), aspect='equal', cmap='gray')
imshow(ma.masked_where(-mask1w, frmap.mean(axis=0)), aspect='equal', cmap='spectral'); 
colorbar()
Out[21]:
<matplotlib.colorbar.Colorbar instance at 0x7fccdd660560>

Below is a set of functions to help with frequency plots

In [22]: 
def sort_tracks_svd(tarr):
    X = tarr - tarr.mean(axis=0)
    u,s,vh = svd(tarr, full_matrices=False)
    ind = sorted(arange(len(tarr)), key = lambda i: u[i,0],reverse=True)
    return tarr[ind]
    
def rect2slice(r,step=2):
    x0,y0 = r.get_xy()
    w,h = r.get_width(), r.get_height()
    return [slice(None), slice(y0,y0+h,step), slice(x0,x0+w,step)]

def slice2size(s):
    return reduce(lambda a,b:a*b, [ceil(float(se.stop-se.start)/se.step) for se in s[1:]])
In [23]: 
def make_freqs_figure(frmap, mask1,rectlist,
                      saveto = None,
                      step=2,
                      vmin=0.015, vmax=0.03):
    fh = figure(figsize=(15,4))
    frmap_mean = frmap.mean(axis=0)
    colors = ['red','blue']
    rectangles = [Rectangle(rs[:2], *rs[2:], alpha=0.5, color=c,ec='black')
                  for rs,c in zip(rectlist, colors)]
    slices = [rect2slice(r,step) for r in rectangles]

    print map(slice2size, slices)
    print [frmap[s].shape for s in slices]
    
    tracks = amap(sort_tracks_svd, (frmap[s].reshape(frmap.shape[0], slice2size(s)).T for s in slices))
    if vmin is None:
        vmin = percentile(np.concatenate(tracks), 0.5)
    if vmax is None:
        vmax = percentile(np.concatenate(tracks), 99.5)
    
    subplot(121)
    imshow(ma.masked_where(-mask1, frmap_mean), aspect='equal', cmap='spectral',vmin=vmin,vmax=vmax)
    for k,r in enumerate(rectangles):
        gca().add_patch(r)
        x,y = r.get_xy()
        text(x + r.get_width()/2, y + r.get_height()/2, k+1, size='large',
             horizontalalignment='center', verticalalignment='center')
    setp(gca(), frame_on=False, xticks=[],yticks=[])
    

    L = len(tracks)
    subplot(222)
    for k, t in enumerate(tracks):
        subplot(L,2,2*(k+1))
        m = imshow(t,cmap='spectral',vmin=vmin, vmax=vmax);
        colorbar(m, ax = gca())
        ylabel(k+1,rotation='horizontal',size='large')
        if k == L-1:
            xlabel('Time, s')
    #suptitle("Frequency locking")
    tight_layout()
    if saveto:
        savefig(save_path + saveto)
    close(fh)
    return fh
In [24]: 
make_freqs_figure(frmap, mask1w,[(170,100, 64,32), (300, 160, 44,44)], saveto='Figure-freqs-new.svg')

-c:15: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
-c:15: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future


[512.0, 484.0]
[(1972, 16, 32), (1972, 22, 22)]
Out[24]:

Phase analysis

In [25]: 
phase_cmap = 'hsv'
In [26]: 
start, l, step = 925,160,4
T = 1/mean([f[maskr] for f in frmap[start:start+l]])
T, T/8, T/10,  step*T
Out[26]:
(41.248134367106566,
 5.1560167958883207,
 4.1248134367106566,
 164.99253746842626)
In [27]: 
maskw = reduce(sp.op.__and__, (f>0 for f in frmap))
maskwr = maskw*maskr
titles = map(int, arange(start,start+T*4, step))
mfn = lambda f: ma.masked_where(-maskwr, f)
lib.group_maps(map(mfn, phasemap[start:start+T*4-step:step]), 10, titles, 
               samerange=0, cbkw={'ticks':[-pi,-pi/2,0,pi/2,pi]},
               single_colorbar=True,
               imkw=dict(cmap=phase_cmap,vmin=-pi,vmax=pi),figsize=(17,6))
savefig(save_path+'Figure-phase-maps-sweep.svg')

0


-c:5: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future

SVD of phases

In [28]: 
def pairs_pcvecs(u,s,vh,mask1, n=4, saveto=None):
    fn_m = lambda f: np.ma.masked_where(-mask1,f)
    fh, axs = subplots(n,n,sharex=False,sharey=False,figsize=(9,8))
    maps = sp.reshape_to_masked_video(u[:,:n],mask1)
    print phase_cmap
    for i,j in sp.cluster.locations((n,n)):
		if i==j:
		    axs[i,j].imshow(fn_m(maps[i]), aspect='equal', cmap=phase_cmap)
		    setp(axs[i,j], frame_on=0, xticks=[],yticks=[])
		    axs[i,j].set_title('U%d'%(i+1))
		else:
		    if i>j:
			axs[i,j].plot(vh[i]*s[i], vh[j]*s[j], 'k-')
			setp(axs[i,j], xticks=[],yticks=[])#,aspect='equal')
			
		    else:
			setp(axs[i,j],visible=False)
    draw()
    subplot(222)
    plot(cumsum(s[:20]**2)/np.sum(s**2), 'ko')
    axis((-0.1, 20.1, 0,1))
    xlabel('singular value number')
    title('Cumulative fraction of variance explained')
    if saveto:
        savefig(save_path + saveto)        
    #close(fh)
    return fh
In [29]: 
u,s,vh = svd(sp.reshape_from_masked_video(phasemap[900:1100], maskwr),full_matrices=False)
_ = pairs_pcvecs(u,s,vh, maskwr, saveto='Figure-phase-svd-short.svg')

hsv
In [30]: 
def plot_pcvecs3d(_u,_s,_vh,mask1, saveto=None):
    from mpl_toolkits.mplot3d import Axes3D
    from mpl_toolkits.axes_grid1 import AxesGrid
    fn_m = lambda f: np.ma.masked_where(-mask1,f)
    fh = figure(figsize=(10,4.5))
    grid = AxesGrid(fh, 131,
                    nrows_ncols=(3,1),axes_pad=0.33,share_all=False)
    maps = map(fn_m, sp.reshape_to_masked_video(_u[:,:3],mask1))
    for i in range(3):
		grid[i].imshow(maps[i], aspect='equal', cmap=phase_cmap)
		setp(grid[i], frame_on=0, xticks=[],yticks=[])
		grid[i].set_title('U%d'%(i+1))
	    #grid[-1].plot(cumsum(_s[:20]**2)/np.sum(_s**2), 'ko')
	    #setp(grid[-1],visible=False)
    subplot(132)
    plot(cumsum(_s[:20]**2)/np.sum(_s**2), 'ko')
    ylim(0,1)
    xlabel('singular value number')
    title('Cumulative fraction of $\sigma^2$ explained')
    ax = subplot(133,projection='3d');
    ax.plot(*_vh[:3],alpha=0.5,color='k'),
    ax.scatter(*_vh[:3],c=arange(len(_vh[0])), edgecolor=(1,1,1,1));
	#ax.colorbar()
    title('SVD right singular vectors')
    if saveto:
        savefig(save_path + saveto)
    close(fh)
    return fh
In [31]: 
u,s,vh = svd(sp.reshape_from_masked_video(phasemap[500:1500], maskwr),full_matrices=False)
plot_pcvecs3d(u,s,vh,maskwr,saveto="Figure-phase-svd-long.svg")
Out[31]:
In [32]: 
def make_vec_explained(x, nmodes=4, nt=125,dt=1):
    tvec = arange(nt,x.shape[1]-nt,25)
    y = np.zeros(len(tvec))
    for k,t in enumerate(tvec):
        u,s,vh = svd(x[:,t-nt:t+nt], full_matrices=False)
        y[k] = (np.sum(s[:nmodes]**2)/np.sum(s**2))
        sys.stderr.write('\r %03d'%t)
    return tvec*dt, y
In [33]: 
def coll_svd_explained(flist1_c,nexplained=4):
    acc = []
    for name in flist1_c:
        print name
        seqr, maskr, (peak, fm) = preprocess_file(data_path + name)
        frmap,name = sp.get_frmap(data_path+name)
        frmap, phasemap = frmap.real, frmap.imag
        mask1w = reduce(sp.op.__and__, (f>0 for f in frmap))
        del frmap
        acc.append(make_vec_explained(sp.reshape_from_masked_video(phasemap, maskr*mask1w),nexplained))
    return acc
In [34]: 
if os.path.exists(save_path+'variance-explained-4.pickle'):
    fnames,out = pickle.load(open(save_path+'variance-explained-4.pickle', 'r'))
else:
    out = coll_svd_explained(fnames,4)
    pickle.dump([fnames, out], open(save_path+'variance-explained-4.pickle', 'w'))
In [35]: 
f = figure(figsize=(6,6))
subplot(211)
colors = ['r', 'g', 'b', 'y', 'm', 'k', 'cyan', 'khaki', 'royalblue', 'pink']
for n,(t,v) in enumerate(out): 
    plot(t,v, color=colors[n], label=n+1) 
    ylim(0,1)
    #xlim(0,3700)
    legend(loc=(0.9,0.05), fontsize='x-small')

subplot(212); 
h = boxplot([x[1] for x in out])
ylim(0,1)

for c,b in zip(colors, h['boxes']):
    setp(b, color=c,lw=2)

tight_layout()
savefig(save_path + 'Figure-variance-explained-1Hz.svg')

print " --- Simple stats ---"
pool = np.concatenate([x[1] for x in out])
print "Mean:", np.mean(pool)
print 'Percentiles: (0.5%, 50%, 99.5%)', np.percentile(pool, (0.5, 50, 99.5))

 --- Simple stats ---
Mean: 0.656107513404
Percentiles: (0.5%, 50%, 99.5%) [0.45176810122865196, 0.66624403835815815, 0.89520486752373452]

Local phase differences

Phase un-wrapping

In [36]: 
def my_unwrap(v):
    idx = arange(len(v))
    keep = diff(v) > 0
    if any(keep):
        uv = np.unwrap(v[keep])
        return np.interp(idx, idx[keep], uv)
    else:
        return unwrap(v)

def unwrap_phasemap(phm,mask1):
    sh = mask1.shape
    out = np.zeros(phm.shape)
    for row in xrange(sh[0]):
        for col in xrange(sh[1]):
            if mask1[row,col]:
                out[:,row,col] = my_unwrap(phm[:,row,col])
    return out
In [37]: 
v = phasemap[:, 100, 200]
fh, (u,l) = subplots(2,1,sharex=True,figsize=(12,4))
u.plot(v, 'k.-', lw=0.5)
u.axhline(pi, color='red')
u.axhline(-pi, color='blue')

l.plot(unwrap(v) , 'g.-', lw=0.5)
l.plot(my_unwrap(v), 'm-', lw=0.5)

close(fh); fh
Out[37]:
In [38]: 
loc = [180, 120]
f = figure(figsize=(12,5))
subplot(121)
imshow(ma.masked_where(-maskwr, frmap.mean(axis=0)), aspect='equal', cmap='spectral'); 
plot(loc[1], loc[0], 'ro')
plot(loc[1], loc[0]-4, 'go',alpha=0.5)
subplot(122);
subplot(122);
ph1 = my_unwrap(phasemap[:,loc[0], loc[1]])
ph2 = my_unwrap(phasemap[:,loc[0], loc[1]-4])
plot(ph1, 'b-', lw=0.5); 
plot(ph2, 'r-', lw=0.5);
In [39]: 
def rewrap0(v):
    if abs(v) > pi:
        return rewrap0(v - 2*sign(v)*pi)
    return v

def rewrap(v):
   return (pi + v)%(2*pi) - pi
In [40]: 
sync = exp(1j*(ph1-ph2))
print abs(mean(sync))

figure(figsize=(12,7))
subplot(211)
plot(sync.real, 'r-', sync.imag, 'b-')
legend(('real', 'imaginary'), loc=0)
title("$\exp[i (\phi_1 - \phi_2)]$")

subplot(212)
plot(movavg(sync, 50), 'k.-')
title("$|<exp[i (\phi_1 - \phi_2)] > |$")
ylim(0,1)

0.829817424593


/usr/lib/python2.7/dist-packages/numpy/core/numeric.py:460: ComplexWarning: Casting complex values to real discards the imaginary part
  return array(a, dtype, copy=False, order=order)
Out[40]:
(0, 1)
In [41]: 
reload(sp)

def pc_index(ph1,ph2):
    "calculate phase coherence index"
    return np.abs(np.mean(exp(1j*(ph1-ph2)),axis=0))

def point_sync(phm, (r0,c0),mask1, nhood=32,is_unwrapped=False):
    "with un-wrapped phase"
    sh = phm.shape[1:]
    out = np.zeros(sh)
    
    rbounds = max(0, r0-nhood), min(sh[0],r0+nhood+1)
    cbounds = max(0, c0-nhood), min(sh[1],c0+nhood+1)
    
    if is_unwrapped:
        v = phm[:,r0,c0]
        sl = (slice(None), slice(*rbounds),slice(*cbounds))
        out[sl[1:]] = pc_index(phm[sl],v.reshape(-1,1,1))
        mask2 = np.ones(sh,'bool')
        mask2[sl[1:]]=0
        return ma.masked_where(-mask1, out) 
    v = my_unwrap(phm[:,r0, c0])
    for i in xrange(*rbounds):
        for j in xrange(*cbounds):
            if mask1[i,j]:
                v2 = my_unwrap(phm[:,i,j])
                out[i,j] = pc_index(v,v2)
    return ma.masked_where(-mask1, out)
    
def point_sync_wrapped(phm, (r0,c0), mask1, nhood=32):
    sh = phm.shape[1:]
    out = np.zeros(sh)
    v = phm[:,r0, c0]
    rbounds = max(0, r0-nhood), min(sh[0],r0+nhood+1)
    cbounds = max(0, c0-nhood), min(sh[1],c0+nhood+1)
    for i in xrange(*rbounds):
        for j in xrange(*cbounds):
            if mask1[i,j]:
                out[i,j] = sp.mxsynctime_phase(v, phm[:,i,j])
    out[r0, c0] = np.median(out[r0-1:r0+2,c0-1:c0+2])
    return ma.masked_where(-mask1, out)
In [42]: 
if os.path.exists(save_path+'local_coh_maps.pickle'):
    local_coh_maps = pickle.load(open(save_path+'local_coh_maps.pickle'))
else:
    local_coh_maps = map(sp.local_coh_map, fnames)
    pickle.dump(local_coh_maps, open(save_path+'local_coh_maps.pickle','w'))
In [43]: 
lib.group_maps([a[1] for a in acc], 3, figsize=(12,5), samerange=0, imkw=dict(cmap='gray'))
nhood=8
fh = gcf()
axs = fh.axes
k = 0

for name,dx in zip(fnames, local_coh_maps):
    sh = dx.shape
    mask = -acc[k][2]
    m = axs[k].imshow(ma.masked_where(mask, dx), cmap=cm.gnuplot2,vmin=0,vmax=1, aspect='equal'); 
    r = Rectangle((10,10), nhood*2+1,nhood*2+1,edgecolor='red', facecolor='none')
    rw  = Rectangle((10,sh[0]-40), 30,35,color='black')
    axs[k].add_patch(r)
    axs[k].add_patch(rw)
    axs[k].text(15, sh[0]-35, k+1, color='white', fontsize=16)
    plt.colorbar(m, ax=axs[k])
    k +=1
    
savefig(save_path+"Figure-local-coherence-maps-nhood8.svg")

0
In [44]: 
if os.path.exists(save_path+'coh_clusters.pickle'):
    coh_clust = pickle.load(open(save_path+'coh_clusters.pickle'))
else:
    coh_clust = [sp.phase_coherence_clusterize(name, lc) for name,lc in zip(fnames, local_coh_maps)]
    pickle.dump(coh_clust, open(save_path+'coh_clusters.pickle','w'))

coh_clust = [ma.masked_where(-a[2], o) for o,a in zip(coh_clust, acc)]
maxclust = np.max(coh_clust)
lib.group_maps([a[1] for a in acc], 3, figsize=(12,5), samerange=0, imkw=dict(cmap='gray'))

fh = gcf()
axs = fh.axes
for k,dx in enumerate(coh_clust):
    m = axs[k].imshow(dx, cmap=cm.Set1_r,aspect='equal')
    sh = dx.shape
    rw  = Rectangle((10,sh[0]-40), 30,35,color='black')
    axs[k].add_patch(rw)
    axs[k].text(15, sh[0]-35, k+1, color='white', fontsize=16)
savefig(save_path + "Figure-coherence-clusters.svg")

0