def fit_gaussian(spectra, f_ppm, lb=2.6, ub=3.6):
"""
Fit a gaussian function to the difference spectra to be used for estimation
of the GABA peak.
Parameters
----------
spectra : array of shape (n_transients, n_points)
Typically the difference of the on/off spectra in each transient.
f_ppm : array
lb, ub : floats
In ppm, the range over which optimization is bounded
"""
idx = ut.make_idx(f_ppm, lb, ub)
# We are only going to look at the interval between lb and ub
n_points = idx.stop - idx.start
n_params = 5
fit_func = ut.gaussian
# Set the bounds for the optimization
bounds = [
(lb, ub), # peak location
(0, None), # sigma
(0, None), # amp
(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])
# Use the signal for a rough estimate of the parameters for
# initialization :
max_idx = np.argmax(signal[ii])
max_sig = np.max(signal[ii])
initial_f0 = f_ppm[idx][max_idx]
half_max_idx = np.argmin(np.abs(signal[ii] - max_sig / 2))
# We estimate sigma as the hwhm:
initial_sigma = np.abs(initial_f0 - f_ppm[idx][half_max_idx])
initial_off = np.min(signal[ii])
initial_drift = 0
initial_amp = max_sig
initial = (initial_f0, initial_sigma, initial_amp, initial_off,
initial_drift)
params[ii], _ = lsq.leastsqbound(mopt.err_func,
initial,
args=(f_ppm[idx], np.real(signal[ii]),
fit_func),
bounds=bounds)
model[ii] = fit_func(f_ppm[idx], *params[ii])
return model, signal, params
def _do_two_gaussian_fit(freqs, signal, bounds=None):
"""
Helper function for the two gaussian fit
"""
initial = _two_func_initializer(freqs, signal)
# Edit out the ones we want in the order we want them:
initial = (initial[0], initial[1], initial[6], initial[7], initial[2],
initial[3], initial[10], initial[11])
# We want to preferntially weight the error on estimating the height of the
# individual peaks, so we formulate an error-weighting function based on
# these peaks, which is simply a two-gaussian bumpety-bump:
w = (ut.gaussian(freqs, initial[0], 0.075, 1, 0, 0) +
ut.gaussian(freqs, initial[1], 0.075, 1, 0, 0))
# Further, we want to also optimize on the individual gaussians error, to
# restrict the fit space a bit more. For this purpose, we will pass a list
# of gaussians with indices into the parameter list, so that we can do
# that (see mopt.err_func for the mechanics).
func_list = [[
ut.gaussian, [0, 2, 4, 6, 7],
ut.gaussian(freqs, initial[0], 0.075, 1, 0, 0)
],
[
ut.gaussian, [1, 3, 5, 6, 7],
ut.gaussian(freqs, initial[1], 0.075, 1, 0, 0)
]]
params, _ = lsq.leastsqbound(mopt.err_func,
initial,
args=(freqs, np.real(signal), ut.two_gaussian,
w, func_list),
bounds=bounds)
return params
def _do_lorentzian_fit(freqs, signal, bounds=None):
"""
Helper function, so that Lorentzian fit can be generalized to different
frequency scales (Hz and ppm).
"""
# Use the signal for a rough estimate of the parameters for initialization:
max_idx = np.argmax(np.real(signal))
max_sig = np.max(np.real(signal))
initial_f0 = freqs[max_idx]
half_max_idx = np.argmin(np.abs(np.real(signal) - max_sig / 2))
initial_hwhm = np.abs(initial_f0 - freqs[half_max_idx])
# Everything should be treated as real, except for the phase!
initial_ph = np.angle(signal[signal.shape[-1] / 2.])
initial_off = np.min(np.real(signal))
initial_drift = 0
initial_a = (np.sum(
np.real(signal)[max_idx:max_idx + np.abs(half_max_idx) * 2])) * 2
initial = (initial_f0, initial_a, initial_hwhm, initial_ph, initial_off,
initial_drift)
params, _ = lsq.leastsqbound(mopt.err_func,
initial,
args=(freqs, np.real(signal), ut.lorentzian),
bounds=bounds)
return params
def _do_two_gaussian_fit(freqs, signal, bounds=None):
"""
Helper function for the two gaussian fit
"""
initial = _two_func_initializer(freqs, signal)
# Edit out the ones we want in the order we want them:
initial = (initial[0], initial[1],
initial[6], initial[7],
initial[2], initial[3],
initial[10], initial[11])
# We want to preferntially weight the error on estimating the height of the
# individual peaks, so we formulate an error-weighting function based on
# these peaks, which is simply a two-gaussian bumpety-bump:
w = (ut.gaussian(freqs, initial[0], 0.075, 1, 0, 0) +
ut.gaussian(freqs, initial[1], 0.075, 1, 0, 0))
# Further, we want to also optimize on the individual gaussians error, to
# restrict the fit space a bit more. For this purpose, we will pass a list
# of gaussians with indices into the parameter list, so that we can do
# that (see mopt.err_func for the mechanics).
func_list = [[ut.gaussian, [0,2,4,6,7],
ut.gaussian(freqs, initial[0], 0.075, 1, 0, 0)],
[ut.gaussian, [1,3,5,6,7],
ut.gaussian(freqs, initial[1], 0.075, 1, 0, 0)]]
params, _ = lsq.leastsqbound(mopt.err_func, initial,
args=(freqs, np.real(signal),
ut.two_gaussian, w, func_list),
bounds=bounds)
return params
def _do_lorentzian_fit(freqs, signal, bounds=None):
"""
Helper function, so that Lorentzian fit can be generalized to different
frequency scales (Hz and ppm).
"""
# Use the signal for a rough estimate of the parameters for initialization:
max_idx = np.argmax(np.real(signal))
max_sig = np.max(np.real(signal))
initial_f0 = freqs[max_idx]
half_max_idx = np.argmin(np.abs(np.real(signal) - max_sig/2))
initial_hwhm = np.abs(initial_f0 - freqs[half_max_idx])
# Everything should be treated as real, except for the phase!
initial_ph = np.angle(signal[signal.shape[-1]/2.])
initial_off = np.min(np.real(signal))
initial_drift = 0
initial_a = (np.sum(np.real(signal)[max_idx:max_idx +
np.abs(half_max_idx)*2]) ) * 2
initial = (initial_f0,
initial_a,
initial_hwhm,
initial_ph,
initial_off,
initial_drift)
params, _ = lsq.leastsqbound(mopt.err_func, initial,
args=(freqs, np.real(signal), ut.lorentzian),
bounds=bounds)
return params
def fit_gaussian(spectra, f_ppm, lb=2.6, ub=3.6):
"""
Fit a gaussian function to the difference spectra to be used for estimation
of the GABA peak.
Parameters
----------
spectra : array of shape (n_transients, n_points)
Typically the difference of the on/off spectra in each transient.
f_ppm : array
lb, ub: floats
In ppm, the range over which optimization is bounded
"""
idx = ut.make_idx(f_ppm, lb, ub)
# We are only going to look at the interval between lb and ub
n_points = idx.stop - idx.start
n_params = 5
fit_func = ut.gaussian
# Set the bounds for the optimization
bounds = [(lb,ub), # peak location
(0,None), # sigma
(0,None), # amp
(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])
# Use the signal for a rough estimate of the parameters for
# initialization :
max_idx = np.argmax(signal[ii])
max_sig = np.max(signal[ii])
initial_f0 = f_ppm[idx][max_idx]
half_max_idx = np.argmin(np.abs(signal[ii] - max_sig/2))
# We estimate sigma as the hwhm:
initial_sigma = np.abs(initial_f0 - f_ppm[idx][half_max_idx])
initial_off = np.min(signal[ii])
initial_drift = 0
initial_amp = max_sig
initial = (initial_f0,
initial_sigma,
initial_amp,
initial_off,
initial_drift)
params[ii], _ = lsq.leastsqbound(mopt.err_func,
initial,
args=(f_ppm[idx],
np.real(signal[ii]),
fit_func), bounds=bounds)
model[ii] = fit_func(f_ppm[idx], *params[ii])
return model, signal, params