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(data,
upsample=3,
cut=True,
cutoff=0.4,
electrode_spacing=0.4):
'''
Counting centers -- looks for channels around which phase skips +-np.pi
Parameters
----------
data : np.array
Data should be sent in a 3-dimensional np.array of complex analytic
signals, where the first two dimensions are the (x,y) spatial
dimensions of the multi-electrode array.
Other Parameters
----------------
upsample : int, default is 3
Upsampling factor for interpolating between electrodes
cut : bool, default is True
Whether to apply a spatial frequency cutoff.
cutoff : float, default is 0.4
Spatial scale cutoff for analysis, in mm
electrode_spacing : float, default 0.4
Spacing between electrodes in array in mm. Default is 0.4mm for
the Utah arrays
Returns
-------
nclockwise : np.array
number of clockwise centers found at each time point
nanticlockwise : np.array
number of anticlockwise centers found at each time point
'''
if not len(shape(data)) == 3:
raise ValueError('Data should be formatted with shape (x,y,t)')
if cut:
data = dct_upsample(dct_cut_antialias(data, 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))
nanticlockwise = np.sum(np.int32(winding < -3), axis=(1, 2))
return nclockwise, nanticlockwise
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
def array_count_critical(data,
upsample=3,
cut=True,
cutoff=0.4,
electrode_spacing=0.4):
'''
Count critical points in the phase gradient map
Parameters
----------
data : np.array
Data should be sent in a 3-dimensional np.array of complex analytic
signals, where the first two dimensions are the (x,y) spatial
dimensions of the multi-electrode array.
Other Parameters
----------------
upsample : int, default is 3
Upsampling factor for interpolating between electrodes
cut : bool, default is True
Whether to apply a spatial frequency cutoff.
cutoff : float, default is 0.4
Spatial scale cutoff for analysis.
electrode_spacing : float, default 0.4
Spacing between electrodes in array in mm. Default is 0.4mm for
the Utah arrays
Returns
-------
nclockwise : np.array
number of clockwise centers found at each time point
nanticlockwise : np.array
number of anticlockwise centers found at each time point
nsaddles : np.array
number of saddle points
nmaxima : np.array
number of local maxima
nminima : np.array
number of local minima
'''
if not len(shape(data)) == 3:
raise ValueError('Data should be formatted with shape (x,y,t)')
if cut:
data = dct_upsample(dct_cut_antialias(data, 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 +- np.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)
nanticlockwise = sum2(winding < -3)
nsaddles = sum2(saddles)
nmaxima = sum2(maxima)
nminima = sum2(minima)
return nclockwise, nanticlockwise, nsaddles, nmaxima, nminima
