def test_kcsd1d_estimate(self, cv_params={}):
self.test_params.update(cv_params)
result = KCSD1D(self.ele_pos, self.pots, **self.test_params)
result.cross_validate()
vals = result.values()
true_csd = self.csd_profile(result.estm_x, 42)
rms = np.linalg.norm(np.array(vals[:, 0]) - true_csd)
rms /= np.linalg.norm(true_csd)
self.assertLess(rms, 0.5, msg='RMS between trueCSD and estimate > 0.5')
def test_lcurve(self):
result = KCSD1D(self.ele_pos, self.pots, **self.test_params)
result.L_curve()
vals = result.values()
pvals = result.values('POT')
true_csd = self.csd_profile(result.estm_x, 42)
rms = np.linalg.norm(np.array(vals[:, 0]) - true_csd)
rms /= np.linalg.norm(true_csd)
self.assertLess(rms, 0.5, msg='RMS between trueCSD and estimate > 0.5')
def stability_M(n_src, total_ele, ele_pos, pots, R_init=0.23):
"""
Investigates stability of reconstruction for different number of basis
sources
Parameters
----------
n_src: int
Number of basis sources.
total_ele: int
Number of electrodes.
ele_pos: numpy array
Electrodes positions.
pots: numpy array
Values of potentials at ele_pos.
R_init: float
Initial value of R parameter - width of basis source
Default: 0.23.
Returns
-------
obj_all: class object
eigenvalues: numpy array
Eigenvalues of k_pot matrix.
eigenvectors: numpy array
Eigen vectors of k_pot matrix.
"""
obj_all = []
eigenvectors = np.zeros((len(n_src), total_ele, total_ele))
eigenvalues = np.zeros((len(n_src), total_ele))
for i, value in enumerate(n_src):
pots = pots.reshape((len(ele_pos), 1))
obj = KCSD1D(ele_pos,
pots,
src_type='gauss',
sigma=0.3,
h=0.25,
gdx=0.01,
n_src_init=n_src[i],
ext_x=0,
xmin=0,
xmax=1,
R_init=R_init)
try:
eigenvalue, eigenvector = np.linalg.eigh(
obj.k_pot + obj.lambd * np.identity(obj.k_pot.shape[0]))
except LinAlgError:
raise LinAlgError('EVD is failing - try moving the electrodes'
'slightly')
idx = eigenvalue.argsort()[::-1]
eigenvalues[i] = eigenvalue[idx]
eigenvectors[i] = eigenvector[:, idx]
obj_all.append(obj)
return obj_all, eigenvalues, eigenvectors
def modified_bases(k, pots, ele_pos, n_src, title, h=0.25, sigma=0.3,
gdx=0.035, ext_x=0, xmin=0, xmax=1):
'''
Parameters
----------
k: object of the class ValidateKCSD1D
pots: numpy array
Potentials measured (calculated) on electrodes.
ele_pos: numpy array
Locations of electrodes.
n_src: int
Number of basis sources.
title: string
Title of the plot.
h: float
Thickness of analyzed cylindrical slice.
Default: 0.25.
sigma: float
Space conductance of the medium.
Default: 0.3.
gdx: float
Space increments in the estimation space.
Default: 0.035.
ext_x: float
Length of space extension: xmin-ext_x ... xmax+ext_x.
Default: 0.
xmin: float
Boundaries for CSD estimation space.
xmax: float
boundaries for CSD estimation space.
Returns
-------
None
'''
pots = pots.reshape((len(ele_pos), 1))
obj_m = KCSD1D(ele_pos, pots, src_type='gauss', sigma=sigma, h=h, gdx=gdx,
n_src_init=n_src, ext_x=ext_x, xmin=xmin, xmax=xmax)
obj_m.cross_validate(Rs=np.arange(0.2, 0.5, 0.1))
est_csd = obj_m.values('CSD')
test_csd = csd_profile(obj_m.estm_x, [R, MU])
rms = val.calculate_rms(test_csd, est_csd)
titl = "Lambda: %0.2E; R: %0.2f; RMS_Error: %0.2E;" % (obj_m.lambd,
obj_m.R, rms)
fig = k.make_plot(csd_at, true_csd, obj_m, est_csd, ele_pos, pots, titl)
save_as = (SAVE_PATH)
fig.savefig(os.path.join(SAVE_PATH, save_as + '/' + title + '.png'))
plt.close()
ss = SpectralStructure(obj_m)
eigenvectors, eigenvalues = ss.evd()
plot_eigenvalues(eigenvalues, SAVE_PATH, title)
plot_eigenvectors(eigenvectors, SAVE_PATH, title)
plot_k_interp_cross_v(obj_m.k_interp_cross, eigenvectors, SAVE_PATH, title)
def pots_scan(n_src,
ele_lims,
true_csd_xlims,
total_ele,
ele_pos,
R_init=0.23):
"""
Investigates kCSD reconstructions for unitary potential on different
electrodes
Parameters
----------
n_src: int
Number of basis sources.
ele_lims: list
Boundaries for electrodes placement.
true_csd_xlims: list
Boundaries for ground truth space.
total_ele: int
Number of electrodes.
ele_pos: numpy array
Electrodes positions.
Returns
-------
obj_all: class object
eigenvalues: numpy array
Eigenvalues of k_pot matrix.
eigenvectors: numpy array
Eigen vectors of k_pot matrix.
"""
obj_all = []
est_csd = []
for i, value in enumerate(ele_pos):
pots = np.zeros(len(ele_pos))
pots[i] = 1
pots = pots.reshape((len(ele_pos), 1))
obj = KCSD1D(ele_pos,
pots,
src_type='gauss',
sigma=0.3,
h=0.25,
gdx=0.01,
n_src_init=n_src,
ext_x=0,
xmin=0,
xmax=1,
R_init=R_init)
est_csd.append(obj.values('CSD'))
obj_all.append(obj)
return obj_all, est_csd
def do_kcsd(ele_pos, pots, **params):
"""
Function that calls the KCSD1D module
"""
num_ele = len(ele_pos)
pots = pots.reshape(num_ele, 1)
ele_pos = ele_pos.reshape(num_ele, 1)
Lamb = [-9, -3]
lambdas = np.logspace(Lamb[0], Lamb[1], 50, base=10)
k = KCSD1D(ele_pos, pots, **params)
if name == 'lc':
k.L_curve(lambdas=lambdas, Rs=ery)
else:
k.cross_validate(Rs=ery, lambdas=lambdas)
est_csd = k.values('CSD')
est_pot = k.values('POT')
return k, est_csd, est_pot
def do_kcsd(i, ele_pos, pots, **params):
"""
Function that calls the KCSD1D module
"""
num_ele = len(ele_pos)
pots = pots.reshape(num_ele, 1)
ele_pos = ele_pos.reshape(num_ele, 1)
k = KCSD1D(ele_pos, pots, **params)
noreg_csd = k.values('CSD')
k.cross_validate(Rs=Rs, lambdas=lambdas)
errsy = k.errs
LandR[1,0,i] = k.lambd
LandR[1,1,i] = k.R
est_csd_cv = k.values('CSD')
k.L_curve(lambdas=lambdas, Rs=Rs)
LandR[0,0,i] = k.lambd
LandR[0,1,i] = k.R
est_csd = k.values('CSD')
est_pot = k.values('POT')
return k, est_csd, est_pot, noreg_csd, errsy, est_csd_cv
def modified_bases(val,
pots,
ele_pos,
n_src,
title=None,
h=0.25,
sigma=0.3,
gdx=0.01,
ext_x=0,
xmin=0,
xmax=1,
R=0.2,
MU=0.25,
method='cross-validation',
Rs=None,
lambdas=None):
'''
Parameters
----------
val: object of the class ValidateKCSD1D
pots: numpy array
Potentials measured (calculated) on electrodes.
ele_pos: numpy array
Locations of electrodes.
n_src: int
Number of basis sources.
title: string
Title of the plot.
h: float
Thickness of analyzed cylindrical slice.
Default: 0.25.
sigma: float
Space conductance of the medium.
Default: 0.3.
gdx: float
Space increments in the estimation space.
Default: 0.035.
ext_x: float
Length of space extension: xmin-ext_x ... xmax+ext_x.
Default: 0.
xmin: float
Boundaries for CSD estimation space.
xmax: float
boundaries for CSD estimation space.
R: float
Thickness of the groundtruth source.
Default: 0.2.
MU: float
Central position of Gaussian source
Default: 0.25.
method: string
Determines the method of regularization.
Default: cross-validation.
Rs: numpy 1D array
Basis source parameter for crossvalidation.
Default: None.
lambdas: numpy 1D array
Regularization parameter for crossvalidation.
Default: None.
Returns
-------
obj_m: object of the class KCSD1D
'''
pots = pots.reshape((len(ele_pos), 1))
obj_m = KCSD1D(ele_pos,
pots,
src_type='gauss',
sigma=sigma,
h=h,
gdx=gdx,
n_src_init=n_src,
ext_x=ext_x,
xmin=xmin,
xmax=xmax)
if method == 'cross-validation':
obj_m.cross_validate(Rs=Rs, lambdas=lambdas)
elif method == 'L-curve':
obj_m.L_curve(Rs=Rs, lambdas=lambdas)
est_csd = obj_m.values('CSD')
test_csd = csd_profile(obj_m.estm_x, [R, MU])
rms = val.calculate_rms(test_csd, est_csd)
# titl = "Lambda: %0.2E; R: %0.2f; RMS_Error: %0.2E;" % (obj_m.lambd,
# obj_m.R, rms)
# fig = k.make_plot(csd_at, true_csd, obj_m, est_csd, ele_pos, pots, titl)
# save_as = (SAVE_PATH)
# fig.savefig(os.path.join(SAVE_PATH, save_as + '/' + title + '.png'))
# plt.close()
# ss = SpectralStructure(obj_m)
# eigenvectors, eigenvalues = ss.evd()
return obj_m
def make_reconstruction(self,
csd_profile,
csd_seed,
noise=0,
nr_broken_ele=None,
Rs=None,
lambdas=None,
method='cross-validation'):
"""
Makes the whole kCSD reconstruction.
Parameters
----------
csd_profile: function
function to produce csd profile
csd_seed: int
Seed for random generator to choose random CSD profile.
noise: float
Determines the level of noise in the data.
Default: 0.
nr_broken_ele: int
How many electrodes are broken (excluded from analysis)
Default: None.
Rs: numpy 1D array
Basis source parameter for crossvalidation.
Default: None.
lambdas: numpy 1D array
Regularization parameter for crossvalidation.
Default: None.
method: string
Determines the method of regularization.
Default: cross-validation.
Returns
-------
rms: float
Error of reconstruction.
point_error: numpy array
Error of reconstruction calculated at every point of reconstruction
space.
"""
ele_pos, pots = self.electrode_config(csd_profile, csd_seed,
self.total_ele, self.ele_lims,
self.h, self.sigma, noise,
nr_broken_ele)
k = KCSD1D(ele_pos,
pots,
h=self.h,
gdx=self.est_xres,
xmax=np.max(self.kcsd_xlims),
xmin=np.min(self.kcsd_xlims),
sigma=self.sigma,
n_src_init=self.n_src_init)
if method == 'cross-validation':
k.cross_validate(Rs=Rs, lambdas=lambdas)
elif method == 'L-curve':
k.L_curve(Rs=Rs, lambdas=lambdas)
else:
raise ValueError('Invalid value of reconstruction method,'
'pass either cross-validation or L-curve')
est_csd = k.values('CSD')
test_csd = csd_profile(k.estm_x, csd_seed)
rms = self.calculate_rms(test_csd, est_csd[:, 0])
point_error = self.calculate_point_error(test_csd, est_csd[:, 0])
return rms, point_error
Kt = gpcsd_model.temporal_cov_list[0].compute_Kt(
) + gpcsd_model.temporal_cov_list[1].compute_Kt()
Ks = gpcsd_model.spatial_cov.compKphi_1d(
gpcsd_model.R['value']) + 1e-8 * np.eye(nx)
Qs, Qt, Dvec = comp_eig_D(Ks, Kt, gpcsd_model.sig2n['value'])
cov_probe['Qs'] = Qs
cov_probe['Qt'] = Qt
cov_probe['Dvec'] = Dvec
# Compute empirical mean of CSD estimated by GPCSD as evoked response
gpcsd_model.predict(z, trial_pred_t)
evoked_probe['gpcsd'] = np.mean(gpcsd_model.csd_pred, 2)
# kCSD estimation of evoked response for comparison
kcsd_evoked_model = KCSD1D(x,
lfp_trial_pred_evoked,
gdx=1.,
h=gpcsd_model.R['value'])
kcsd_evoked_model.cross_validate(Rs=np.linspace(100, 800, 15),
lambdas=np.logspace(1,
-15,
25,
base=10.))
evoked_probe['kcsd'] = kcsd_evoked_model.values()
with open('%s/results/gpcsd_evoked_%s.pkl' % (root_path, probe_name),
'wb') as f:
pickle.dump(evoked_probe, f)
evoked[probe_name] = evoked_probe
with open('%s/results/gpcsd_cov_%s.pkl' % (root_path, probe_name),
'wb') as f:
gpcsd_model = GPCSD1D(lfp[:, :, 50:], x, t)
gpcsd_model.R['value'] = R_true
gpcsd_model.sig2n['value'] = sig2n_true
gpcsd_model.spatial_cov.params['ell']['value'] = ellSE_true
gpcsd_model.temporal_cov_list[0].params['ell']['value'] = elltSE_true
gpcsd_model.temporal_cov_list[0].params['sigma2']['value'] = sig2tSE_true
gpcsd_model.temporal_cov_list[1].params['ell']['value'] = elltM_true
gpcsd_model.temporal_cov_list[1].params['sigma2']['value'] = sig2tM_true
print(gpcsd_model)
gpcsd_model.predict(xshort, t)
# %% kCSD estimation
# use first five trials concatenated for estimating parameters (for computational reasons)
kcsd_model = KCSD1D(x,
lfp[:, :, :5].reshape((nx, -1)),
gdx=deltax / 20,
h=R_true)
kcsd_model.cross_validate(Rs=np.linspace(100, 1000, 15))
kcsd_R = kcsd_model.R
kcsd_lambda = kcsd_model.lambd
kcsd_values = []
# Predict on test set
for i in range(ntrials):
kcsd_model_tmp = KCSD1D(x,
lfp[:, :, 50 + i].squeeze(),
gdx=deltax / 20,
h=R_true,
R_init=kcsd_R,
lambd=kcsd_lambda)
kcsd_values_tmp = kcsd_model_tmp.values()
# %% GPCSD fitting and predictions
for k in lfp.keys():
print('\nStarting %s' % k)
gpcsd[k].fit(n_restarts=10)
gpcsd[k].predict(z, t)
# %% Print GPCSD fitting results
for k in lfp.keys():
print(gpcsd[k])
# %% kCSD estimation
from kcsd import KCSD1D # https://github.com/Neuroinflab/kCSD-python/releases/tag/v2.0
start_t = time.process_time()
est_kcsd = {}
for k in lfp.keys():
kcsd_tmp = KCSD1D(x, lfp[k], gdx=deltaz, h=R_true)
kcsd_tmp.cross_validate(Rs=np.linspace(100, 800, 15),
lambdas=np.logspace(1, -15, 25, base=10.))
est_kcsd[k] = kcsd_tmp.values()
end_t = time.process_time()
print('kCSD took %0.2f s (per dataset, with cross-validation)' %
((end_t - start_t) / len(est_kcsd)))
# %% Visualize results
vmlfp = np.amax(np.abs(lfp['noiseless']))
vmcsd = np.amax(np.abs(normalize(csd_true)))
plt.rcParams.update({'font.size': 12})
f = plt.figure(figsize=(16, 8))
ax = plt.subplot(251)