def array_count_critical(rawdata,upsample=3,cut=True,cutoff=0.4):
'''
Count critical points in the phase gradient map
'''
# can only handle dim 3 for now
assert len(shape(rawdata))==3
if cut:
data = dct_upsample(dct_cut_antialias(rawdata,cutoff,ELECTRODE_SPACING),factor=upsample)
else:
data = dct_upsample(data,factor=upsample)
dz = array_phase_gradient(data).transpose((2,0,1))
# extract curl via a kernal
# take real component, centres have curl +- pi
curl = np.complex64([[-1-1j,-1+1j],[1-1j,1+1j]])
curl = np.convolve2d(curl,np.ones((2,2))/4,'full')
winding = arr([np.convolve2d(z,curl,'same','symm').real for z in dz])
# extract inflection points ( extrema, saddles )
# by looking for sign changes in derivatives
# avoid points that are close to singular
ok = ~(np.abs(winding)<1e-1)[...,:-1,:-1]
ddx = np.diff(np.sign(dz.real),1,1)[...,:,:-1]/2
ddy = np.diff(np.sign(dz.imag),1,2)[...,:-1,:]/2
saddles = (ddx*ddy==-1)*ok
maxima = (ddx*ddy== 1)*(ddx==-1)*ok
minima = (ddx*ddy== 1)*(ddx== 1)*ok
sum2 = lambda x: np.sum(np.int32(x),axis=(1,2))
nclockwise = sum2(winding>3)
nwidersyns = sum2(winding<-3)
nsaddles = sum2(saddles )
nmaxima = sum2(maxima )
nminima = sum2(minima )
return nclockwise, nwidersyns, nsaddles, nmaxima, nminima
def array_count_centers(rawdata,upsample=3,cut=True,cutoff=0.4):
'''
Counting centers -- looks for channels around which phase skips +-pi
will miss rotating centers closer than half the electrode spacing
'''
# can only handle dim 3 for now
assert len(rawdata.shape)==3
if cut:
data = dct_upsample(dct_cut_antialias(
rawdata,cutoff,ELECTRODE_SPACING),factor=upsample)
else:
data = dct_upsample(data,factor=upsample)
dz = array_phase_gradient(data)
curl = np.complex64([[-1-1j,-1+1j],[1-1j,1+1j]])
curl = np.convolve2d(curl,np.ones((2,2))/4,'full')
winding = arr([real(np.convolve2d(z,curl,'valid','symm')) for z in dz.transpose((2,0,1))])
nclockwise = np.sum(np.int32(winding> 3),axis=(1,2))
nwidersyns = np.sum(np.int32(winding<-3),axis=(1,2))
return nclockwise, nwidersyns