def test_lorentzian():
"""
Test the lorentzian function
"""
freq = np.linspace(0,6,100)
freq0 = 3
area = 1
hwhm = 1
phase = np.pi
baseline0 = 1
baseline1 = 0
ut.lorentzian(freq, freq0, area, hwhm, phase, baseline0, baseline1)
def fit_lorentzian(spectra, f_ppm, lb=2.6, ub=3.6):
"""
Fit a lorentzian function to spectra
This is used in estimation of the water peak and for estimation of the NAA
peak.
Parameters
----------
spectra : array of shape (n_transients, n_points)
Typically the sum of the on/off spectra in each transient.
f_ppm : array
lb, ub: floats
In ppm, the range over which optimization is bounded
"""
# We are only going to look at the interval between lb and ub
idx = ut.make_idx(f_ppm, lb, ub)
n_points = np.abs(idx.stop - idx.start)
n_params = 6
# Set the bounds for the optimization
bounds = [
(lb, ub), #peak
(0, None), #area
(0, None), #hwhm
(-np.pi / 2, np.pi / 2), #phase
(None, None), #offset
(None, None)
] #drift
model = np.empty((spectra.shape[0], n_points))
signal = np.empty((spectra.shape[0], n_points))
params = np.empty((spectra.shape[0], n_params))
for ii, xx in enumerate(spectra):
# We fit to the real spectrum:
signal[ii] = np.real(xx[idx])
params[ii] = _do_lorentzian_fit(f_ppm[idx],
np.real(signal[ii]),
bounds=bounds)
model[ii] = ut.lorentzian(f_ppm[idx], *params[ii])
return model, signal, params
def fit_lorentzian(spectra, f_ppm, lb=2.6, ub=3.6):
"""
Fit a lorentzian function to spectra
This is used in estimation of the water peak and for estimation of the NAA
peak.
Parameters
----------
spectra : array of shape (n_transients, n_points)
Typically the sum of the on/off spectra in each transient.
f_ppm : array
lb, ub: floats
In ppm, the range over which optimization is bounded
"""
# We are only going to look at the interval between lb and ub
idx = ut.make_idx(f_ppm, lb, ub)
n_points = np.abs(idx.stop - idx.start)
n_params = 6
# Set the bounds for the optimization
bounds = [(lb,ub), #peak
(0,None), #area
(0,None), #hwhm
(-np.pi/2, np.pi/2), #phase
(None,None), #offset
(None, None)] #drift
model = np.empty((spectra.shape[0], n_points))
signal = np.empty((spectra.shape[0], n_points))
params = np.empty((spectra.shape[0], n_params))
for ii, xx in enumerate(spectra):
# We fit to the real spectrum:
signal[ii] = np.real(xx[idx])
params[ii] = _do_lorentzian_fit(f_ppm[idx], np.real(signal[ii]),
bounds=bounds)
model[ii] = ut.lorentzian(f_ppm[idx], *params[ii])
return model, signal, params
def fit_creatine(self, reject_outliers=3.0, fit_lb=2.7, fit_ub=3.5):
"""
Fit a model to the portion of the summed spectra containing the
creatine and choline signals.
Parameters
----------
reject_outliers : float or bool
If set to a float, this is the z score threshold for rejection (on
any of the parameters). If set to False, no outlier rejection
fit_lb, fit_ub : float
What part of the spectrum (in ppm) contains the creatine peak.
Default (2.7, 3.5)
Note
----
We use upper and lower bounds that are a variation on the bounds
mentioned on the GANNET ISMRM2013 poster [1]_.
[1] RAE Edden et al (2013). Gannet GABA analysis toolkit. ISMRM
conference poster.
"""
# We fit a two-lorentz function to this entire chunk of the spectrum,
# to catch both choline and creatine
model, signal, params = ana.fit_two_lorentzian(self.sum_spectra,
self.f_ppm,
lb=fit_lb,
ub=fit_ub)
# Use an array of ones to index everything but the outliers and nans:
ii = np.ones(signal.shape[0], dtype=bool)
# Reject outliers:
if reject_outliers:
model, signal, params, ii = self._outlier_rejection(
params, model, signal, ii)
# We'll keep around a private attribute to tell us which transients
# were good (this is for both creatine and choline):
self._cr_transients = np.where(ii)
# Now we separate choline and creatine params from each other (remember
# that they both share offset and drift!):
self.choline_params = params[:, (0, 2, 4, 6, 8, 9)]
self.creatine_params = params[:, (1, 3, 5, 7, 8, 9)]
self.cr_idx = ut.make_idx(self.f_ppm, fit_lb, fit_ub)
# We'll need to generate the model predictions from these parameters,
# because what we're holding in 'model' is for both together:
self.choline_model = np.zeros(
(self.creatine_params.shape[0],
np.abs(self.cr_idx.stop - self.cr_idx.start)))
self.creatine_model = np.zeros(
(self.choline_params.shape[0],
np.abs(self.cr_idx.stop - self.cr_idx.start)))
for idx in range(self.creatine_params.shape[0]):
self.creatine_model[idx] = ut.lorentzian(
self.f_ppm[self.cr_idx], *self.creatine_params[idx])
self.choline_model[idx] = ut.lorentzian(self.f_ppm[self.cr_idx],
*self.choline_params[idx])
self.creatine_signal = signal
self.creatine_auc = self._calc_auc(ut.lorentzian, self.creatine_params,
self.cr_idx)
self.choline_auc = self._calc_auc(ut.lorentzian, self.choline_params,
self.cr_idx)
def fit_creatine(self, reject_outliers=3.0, fit_lb=2.7, fit_ub=3.5):
"""
Fit a model to the portion of the summed spectra containing the
creatine and choline signals.
Parameters
----------
reject_outliers : float or bool
If set to a float, this is the z score threshold for rejection (on
any of the parameters). If set to False, no outlier rejection
fit_lb, fit_ub : float
What part of the spectrum (in ppm) contains the creatine peak.
Default (2.7, 3.5)
Note
----
We use upper and lower bounds that are a variation on the bounds
mentioned on the GANNET ISMRM2013 poster [1]_.
[1] RAE Edden et al (2013). Gannet GABA analysis toolkit. ISMRM
conference poster.
"""
# We fit a two-lorentz function to this entire chunk of the spectrum,
# to catch both choline and creatine
model, signal, params = ana.fit_two_lorentzian(self.sum_spectra,
self.f_ppm,
lb=fit_lb,
ub=fit_ub)
# Use an array of ones to index everything but the outliers and nans:
ii = np.ones(signal.shape[0], dtype=bool)
# Reject outliers:
if reject_outliers:
model, signal, params, ii = self._outlier_rejection(params,
model,
signal,
ii)
# We'll keep around a private attribute to tell us which transients
# were good (this is for both creatine and choline):
self._cr_transients = np.where(ii)
# Now we separate choline and creatine params from each other (remember
# that they both share offset and drift!):
self.choline_params = params[:, (0,2,4,6,8,9)]
self.creatine_params = params[:, (1,3,5,7,8,9)]
self.cr_idx = ut.make_idx(self.f_ppm, fit_lb, fit_ub)
# We'll need to generate the model predictions from these parameters,
# because what we're holding in 'model' is for both together:
self.choline_model = np.zeros((self.creatine_params.shape[0],
np.abs(self.cr_idx.stop-self.cr_idx.start)))
self.creatine_model = np.zeros((self.choline_params.shape[0],
np.abs(self.cr_idx.stop-self.cr_idx.start)))
for idx in range(self.creatine_params.shape[0]):
self.creatine_model[idx] = ut.lorentzian(self.f_ppm[self.cr_idx],
*self.creatine_params[idx])
self.choline_model[idx] = ut.lorentzian(self.f_ppm[self.cr_idx],
*self.choline_params[idx])
self.creatine_signal = signal
self.creatine_auc = self._calc_auc(ut.lorentzian,
self.creatine_params,
self.cr_idx)
self.choline_auc = self._calc_auc(ut.lorentzian,
self.choline_params,
self.cr_idx)
