def plot_screen(self):
import stf
tsl = []
try:
l = stf.get_selected_indices()
for idx in l:
tsl.append(
stfio_plot.Timeseries(stf.get_trace(idx),
stf.get_sampling_interval(),
yunits=stf.get_yunits(),
color='0.2'))
fit = stf.get_fit(idx)
if fit is not None:
self.axes.plot(fit[0],
fit[1],
color='0.4',
alpha=0.5,
lw=5.0)
except:
pass
tsl.append(
stfio_plot.Timeseries(stf.get_trace(),
stf.get_sampling_interval(),
yunits=stf.get_yunits()))
if stf.get_size_recording() > 1:
tsl2 = [
stfio_plot.Timeseries(
stf.get_trace(trace=-1,
channel=stf.get_channel_index(False)),
stf.get_sampling_interval(),
yunits=stf.get_yunits(
trace=-1, channel=stf.get_channel_index(False)),
color='r',
linestyle='-r')
]
stfio_plot.plot_traces(tsl,
traces2=tsl2,
ax=self.axes,
textcolor2='r',
xmin=stf.plot_xmin(),
xmax=stf.plot_xmax(),
ymin=stf.plot_ymin(),
ymax=stf.plot_ymax(),
y2min=stf.plot_y2min(),
y2max=stf.plot_y2max())
else:
stfio_plot.plot_traces(tsl,
ax=self.axes,
xmin=stf.plot_xmin(),
xmax=stf.plot_xmax(),
ymin=stf.plot_ymin(),
ymax=stf.plot_ymax())
fit = stf.get_fit()
if fit is not None:
self.axes.plot(fit[0], fit[1], color='0.2', alpha=0.5, lw=5.0)
def detect(template, mode, th, min_int):
"""
Detect events using the given template and the algorithm specified in
'mode' with a threshold 'th' and a minimal interval of 'min_int' between
events. Returns amplitudes and interevent intervals.
"""
import stf
# Compute criterium
crit = stf.detect_events(template,
mode=mode,
norm=False,
lowpass=0.1,
highpass=0.001)
dt = stf.get_sampling_interval()
# Find event onset times (corresponding to peaks in criteria)
onsets_i = stf.peak_detection(crit, th, int(min_int / dt))
trace = stf.get_trace()
# Use event onset times to find event amplitudes (negative for epscs)
peak_window_i = min_int / dt
amps_i = np.array([
int(np.argmin(trace[onset_i:onset_i + peak_window_i]) + onset_i)
for onset_i in onsets_i
],
dtype=np.int)
amps = trace[amps_i]
onsets = onsets_i * dt
return amps, onsets, crit
def hpfilter(n):
"""
Perform median smoothing filter on the active trace.
Computationally this is achieved by a central simple moving
median over a sliding window of n points. The function then
subtracts the smoothed trace from the original trace.
The function uses reflect (or bounce) end corrections
"""
# Check that the number of points in the sliding window is odd
n = int(n)
if n % 2 != 1:
raise ValueError('The filter rank must be an odd integer')
elif n <= 1:
raise ValueError('The filter rank must > 1')
# Apply smoothing filter
filtered_trace = []
l = stf.get_size_trace()
padded_trace = np.pad(stf.get_trace(), (n - 1) / 2, 'reflect')
filtered_trace.append([np.median(padded_trace[j:n + j]) for j in range(l)])
print "Window width was %g ms" % (stf.get_sampling_interval() * (n - 1))
# Apply subtraction
subtracted_trace = stf.get_trace() - np.array(filtered_trace)
return stf.new_window_list(subtracted_trace)
def get_dv_dt(slice_indicies=(0, 0)):
"""Main function to take 1st derivative of V_trace and return an array with V_values
and dv_dt value for plotting
--input tuple to use slice of trace"""
#determine if using whole trace or slice
if slice_indicies != 0:
sample_start = slice_indicies[0]
sample_end = slice_indicies[1]
else:
sample_start = 0
sample_end = len(stf.get_trace())
#get sampling interval to create dt part of dv/dt
#dt is just sampling interval
si = stf.get_sampling_interval()
#read V values from trace,
V_values = stf.get_trace()[sample_start:sample_end]
#compute dv and by iterating over voltage vectors
dv = [V_values[i + 1] - V_values[i] for i in range(len(V_values) - 1)]
#compute dv/dt
dv_dt = [(dv[i] / si) for i in range(len(dv))]
#V values for a dv/dt / V graph is just truncated trace with final sample point removed
V_plot = V_values[:-1]
#combine for a plotting function/further manipulation
V_dv_dt = np.vstack([V_plot, dv_dt])
stf.new_window(dv_dt)
return (V_dv_dt)
def count_aps():
"""
Shows a result table with the number of action potentials (i.e
events whose potential is above 0 mV) in selected traces. If
no trace is selected, then the current trace is analyzed.
Returns:
False if document is not open.
"""
if not stf.check_doc():
print("Open file first")
return False
if len( stf.get_selected_indices() )==0:
sel_trace = [ stf.get_trace_index()]
else:
sel_trace = stf.get_selected_indices()
mytable = dict()
for trace in sel_trace:
tstart = 0
tend = stf.get_size_trace(trace)*stf.get_sampling_interval()
threshold = 0
spikes = count_events(tstart, tend, threshold, True, trace, True)
mytable["Trace %.3d" %trace] = spikes
stf.show_table(mytable)
return True
def count_aps():
"""
Shows a result table with the number of action potentials (i.e
events whose potential is above 0 mV) in selected traces. If
no trace is selected, then the current trace is analyzed.
Returns:
False if document is not open.
"""
if not stf.check_doc():
print("Open file first")
return False
if len(stf.get_selected_indices()) == 0:
sel_trace = [stf.get_trace_index()]
else:
sel_trace = stf.get_selected_indices()
mytable = dict()
for trace in sel_trace:
tstart = 0
tend = stf.get_size_trace(trace) * stf.get_sampling_interval()
threshold = 0
spikes = count_events(tstart, tend, threshold, True, trace, True)
mytable["Trace %.3d" % trace] = spikes
stf.show_table(mytable)
return True
def median_filter(n):
"""
Perform median smoothing filter on the selected traces.
Computationally this is achieved by a central simple moving
median over a sliding window of n points.
The function uses reflect (or bounce) end corrections
"""
# Check that at least one trace was selected
if not stf.get_selected_indices():
raise IndexError('No traces were selected')
# Check that the number of points in the sliding window is odd
n = int(n)
if n % 2 != 1:
raise ValueError('The filter rank must be an odd integer')
elif n <= 1:
raise ValueError('The filter rank must > 1')
# Apply smoothing filter
filtered_traces = []
for i in stf.get_selected_indices():
l = stf.get_size_trace(i)
padded_trace = np.pad(stf.get_trace(i), (n - 1) / 2, 'reflect')
filtered_traces.append(
[np.median(padded_trace[j:n + j]) for j in range(l)])
print "Window width was %g ms" % (stf.get_sampling_interval() * (n - 1))
return stf.new_window_list(filtered_traces)
def scan_through_train_expt(params_expt_input, train_increment, num_stims):
len_peak_region_in_samples = round(
(params_expt_input[3] - params_expt_input[2]) /
stf.get_sampling_interval())
expt_peaks = np.zeros((stf.get_size_channel(), num_stims))
expt_peak_arrays = np.zeros(
(stf.get_size_channel(), num_stims, len_peak_region_in_samples))
trace = 0
while trace < stf.get_size_channel():
params_expt = params_expt_input
[expt_peaks[trace], expt_peak_arrays[trace]
] = scan_through_train(params_expt, train_increment, num_stims, trace)
params_expt[2] = params_expt_input[2] - (train_increment * (num_stims))
params_expt[3] = params_expt_input[3] - (train_increment * (num_stims))
trace += 1
loaded_file = stf.get_filename()[:-3]
np.savetxt(loaded_file + '_peaks.csv',
expt_peaks,
delimiter=',',
newline='\n')
return (expt_peaks, expt_peak_arrays)
def plot_traces(plotwindow=None, ichannel=0, vchannel=1):
"""
Show traces in a figure
Parameters
----------
plotwindow : (float, float), optional
Plot window (in ms from beginning of trace)
None for whole trace. Default: None
ichannel : int, optional
current channel number. Default: 0
vchannel : int, optional
voltage channel number. Default: 1
"""
import stf
if not stf.check_doc():
return None
nchannels = stf.get_size_recording()
if nchannels < 2:
sys.stderr.write(
"Function requires 2 channels (0: current; 1: voltage)\n")
return
dt = stf.get_sampling_interval()
fig = stf.mpl_panel(figsize=(12, 8)).fig
fig.clear()
gs = gridspec.GridSpec(4, 1)
ax_currents = stfio_plot.StandardAxis(
fig, gs[:3, 0], hasx=False, hasy=False)
ax_voltages = stfio_plot.StandardAxis(
fig, gs[3:, 0], hasx=False, hasy=False, sharex=ax_currents)
if plotwindow is not None:
istart = int(plotwindow[0]/dt)
istop = int(plotwindow[1]/dt)
else:
istart = 0
istop = None
for ntrace in range(stf.get_size_channel()):
stf.set_trace(ntrace)
stf.set_channel(ichannel)
trace = stf.get_trace()[istart:istop]
ax_currents.plot(np.arange(len(trace))*dt, trace)
# Measure pulse amplitude
stf.set_channel(vchannel)
trace = stf.get_trace()[istart:istop]
ax_voltages.plot(np.arange(len(trace))*dt, trace)
# Reset active channel
stf.set_channel(ichannel)
stfio_plot.plot_scalebars(
ax_currents, xunits=stf.get_xunits(), yunits=stf.get_yunits(channel=0))
stfio_plot.plot_scalebars(
ax_voltages, xunits=stf.get_xunits(), yunits=stf.get_yunits(channel=1))
def find_sample_points_of_detected_events(whole_trace_file,
extracted_events_file, sweep_num):
"""takes the window of detected events from stimfit and, for each events, runs through the full trace to pull out time (in samples) of event
"""
#open and load trace from whole file
stf.file_open(whole_trace_file)
stf.set_trace(sweep_num)
whole_trace = stf.get_trace()
sampling_interval = stf.get_sampling_interval()
#open extracted events file
stf.file_open(extracted_events_file)
time_points = []
for trace in range(stf.get_size_channel()):
stf.set_trace(trace)
trace_to_search = stf.get_trace(trace)
# run find trace with updated search index
# start at sample = 0 for first run through
if len(time_points) == 0:
sample_start = 0
else:
sample_start = int(time_points[len(time_points) - 1] /
sampling_interval)
output_index = sub_func_find_trace(trace_to_search, whole_trace,
sample_start)
time_point = output_index * sampling_interval
time_points.append(time_point)
return (time_points)
def plot_spectrum(self):
import stf
Pow, freq = mlab.psd(stf.get_trace(),
Fs=(1.0/stf.get_sampling_interval())*1e3,
detrend=mlab.detrend_linear)
self.axes.plot(freq, 10*np.log10(Pow))
self.axes.set_xlabel("Frequency (Hz)")
self.axes.set_ylabel("Power spectral density (dB/Hz)")
def stf_fit( p0, lsfunc ):
data = stf.get_trace()[ stf.get_fit_start() : stf.get_fit_end() ]
dt = stf.get_sampling_interval()
x = np.arange(0, len(data)*dt, dt)
plsq = leastsq(leastsq_stf, p0, args=(data, lsfunc, x))
return plsq[0]
def stf_fit(p0, lsfunc):
data = stf.get_trace()[stf.get_fit_start():stf.get_fit_end()]
dt = stf.get_sampling_interval()
x = np.arange(0, len(data) * dt, dt)
plsq = leastsq(leastsq_stf, p0, args=(data, lsfunc, x))
return plsq[0]
def crop():
si = stf.get_sampling_interval()
start = stf.get_fit_start() * si
end = stf.get_fit_end() * si
spells.cut_sweeps(start, end - start)
return
def plot_spectrum(self):
import stf
Pow, freq = mlab.psd(stf.get_trace(),
Fs=(1.0 / stf.get_sampling_interval()) * 1e3,
detrend=mlab.detrend_linear)
self.axes.plot(freq, 10 * np.log10(Pow))
self.axes.set_xlabel("Frequency (Hz)")
self.axes.set_ylabel("Power spectral density (dB/Hz)")
def monoexpfit(optimization=True, Tn=20):
"""
Fits monoexponential function with offset to data between the fit cursors
in the current trace of the active channel using a Chebyshev-Levenberg-
Marquardt hybrid algorithm. Optimization requires Scipy. Setting optimization
to False forces this function to use just the Chebyshev algorithm. The maximum
order of the Chebyshev polynomials can be set using Tn.
"""
# Get data
fit_start = stf.get_fit_start()
fit_end = stf.get_fit_end()
y = np.double(stf.get_trace()[fit_start:fit_end])
si = stf.get_sampling_interval()
l = len(y)
t = si * np.arange(0, l, 1, np.double)
# Define monoexponential function
def f(t, *p):
return p[0] + p[1] * np.exp(-t / p[2])
# Get initial values from Chebyshev transform fit
init = chebexp(1, Tn)
p0 = (init.get('Offset'), )
p0 += (init.get('Amp_0'), )
p0 += (init.get('Tau_0'), )
# Optimize (if applicable)
if optimization == True:
# Optimize fit using Levenberg-Marquardt algorithm
options = {"ftol": 2.22e-16, "xtol": 2.22e-16, "gtol": 2.22e-16}
[p, pcov] = optimize.curve_fit(f, t, y, p0, **options)
elif optimization == False:
p = list(p0)
fit = f(t, *p)
# Calculate SSE
SSE = np.sum((y - fit)**2)
# Plot fit in a new window
matrix = np.zeros((2, stf.get_size_trace())) * np.nan
matrix[0, :] = stf.get_trace()
matrix[1, fit_start:fit_end] = fit
stf.new_window_matrix(matrix)
# Create table of results
retval = [("p0_Offset", p[0])]
retval += [("p1_Amp_0", p[1])]
retval += [("p2_Tau_0", p[2])]
retval += [("SSE", SSE)]
retval += [("dSSE", 1.0 - np.sum((y - f(t, *p0))**2) / SSE)]
retval += [("Time fit begins", fit_start * si)]
retval += [("Time fit ends", fit_end * si)]
retval = dict(retval)
stf.show_table(
retval, "monoexpfit, Section #%i" % float(stf.get_trace_index() + 1))
return
def automated_search_triexponential(trace_region_to_search, search_period,
threshold, min_btw_events, tau_rise,
tau_1_decay, tau_2_decay):
"""searches section of trace based on a user input triexponential function (tau_rise, tau_1_decay, tau_2_decay)"""
#converts some inputs to sample points
min_samples_btw_events = min_btw_events / stf.get_sampling_interval()
#pull out region to search
region_to_search = stf.get_trace(
)[trace_region_to_search[0]:trace_region_to_search[1]]
#list to store detected events
event_times = []
#creates vector of time points
t = np.linspace(0, 50, (50 / stf.get_sampling_interval()))
#creates triexponential pattern function
p_t = [(1 - math.exp(-(t_point - 0) / tau_rise)) *
(math.exp(-(t_point - 0) / tau_1_decay)) *
(math.exp(-(t_point - 0) / tau_2_decay)) for t_point in t]
#slides window along
pt = 0
while pt < range(len(region_to_search) - int(min_samples_btw_events)):
EPSC_test = stf.get_trace()[pt:(
pt + (search_period / stf.get_sampling_interval()))]
corr_coeff = stats.pearsonr(p_t, EPSC_test)[0]
if corr_coeff > threshold:
stf.set_marker(pt,
region_to_search[trace_region_to_search[0] + pt])
event_times.append(pt * stf.get_sampling_interval())
pt += min_samples_btw_events
else:
pt += 1
return (event_times)
def upsample_flex():
"""
Upsample to sampling interval of 1 ms using cubic spline interpolation
"""
old_time = [
i * stf.get_sampling_interval() for i in range(stf.get_size_trace())
]
new_time = range(
int(np.fix((stf.get_size_trace() - 1) * stf.get_sampling_interval())))
new_traces = []
for i in range(stf.get_size_channel()):
f = interpolate.interp1d(old_time, stf.get_trace(i), 'cubic')
new_traces.append(f(new_time))
stf.new_window_list(new_traces)
stf.set_sampling_interval(1)
return
def jjm_count(start, delta, threshold=0, up=True, trace=None, mark=True): """ Counts the number of events (e.g action potentials (AP)) in the current trace. Arguments: start -- starting time (in ms) to look for events. delta -- time interval (in ms) to look for events. threshold -- (optional) detection threshold (default = 0). up -- (optional) True (default) will look for upward events, False downwards. trace -- (optional) zero-based index of the trace in the current channel, if None, the current trace is selected. mark -- (optional) if True (default), set a mark at the point of threshold crossing Returns: An integer with the number of events. Examples: count_events(500,1000) returns the number of events found between t=500 ms and t=1500 ms above 0 in the current trace and shows a stf marker. count_events(500,1000,0,False,-10,i) returns the number of events found below -10 in the trace i and shows the corresponding stf markers. """ # sets the current trace or the one given in trace. if trace is None: sweep = stf.get_trace_index() else: if type(trace) !=int: print "trace argument admits only integers" return False sweep = trace # set the trace described in sweep stf.set_trace(sweep) # transform time into sampling points dt = stf.get_sampling_interval() pstart = int( round(start/dt) ) pdelta = int( round(delta/dt) ) # select the section of interest within the trace selection = stf.get_trace()[pstart:(pstart+pdelta)] # algorithm to detect events EventCounter,i = 0,0 # set counter and index to zero # list of sample points sample_points = [] # choose comparator according to direction: if up: comp = lambda a, b: a > b else: comp = lambda a, b: a < b # run the loop while i<len(selection): if comp(selection[i],threshold): EventCounter +=1 if mark: sample_point = pstart+i; sample_points.append(sample_point); stf.set_marker(pstart+i, selection[i]) while i<len(selection) and comp(selection[i],threshold): i+=1 # skip values if index in bounds AND until the value is below/above threshold again else: i+=1 time_points = [sample_point*dt for sample_point in sample_points]; return (EventCounter, sample_points, time_points)
def slice_peak_region(params, trace):
"""use time for params, function converts to samples for cutting/displaying"""
stf.select_trace(trace)
sampling_interval = stf.get_sampling_interval()
peak_2_start_samples = (params[2] / sampling_interval)
peak_2_end_samples = (params[3] / sampling_interval)
peak_region = stf.get_trace()[peak_2_start_samples:peak_2_end_samples]
return (peak_region)
def remove_artifacts(first_artifact_start, length_time_to_remove,
time_between_artifacts, number_of_artifacts):
#get sampling interval of current tract
sampling_interval = stf.get_sampling_interval()
#convert input paramenters (units of time) to samples
first_artifact_start_samples = float(first_artifact_start) / float(
sampling_interval)
length_time_to_remove_samples = float(length_time_to_remove) / float(
sampling_interval)
time_between_artifacts_samples = float(time_between_artifacts) / float(
sampling_interval)
#create variable for artifact end
first_artifact_end_samples = first_artifact_start_samples + length_time_to_remove_samples
#get trace, convert trace to normal list
original_trace = list(stf.get_trace())
#create list for section of trace up until 1st artifact
trace_artifacts_removed = original_trace[0:int(first_artifact_start_samples
)]
#add remaining sections of trace with artifacts removed
for artifact_number in range(0, number_of_artifacts):
start_sample = int(first_artifact_end_samples +
(time_between_artifacts_samples * artifact_number))
end_sample = int(first_artifact_start_samples +
(time_between_artifacts_samples *
(artifact_number + 1)))
print(start_sample)
print(end_sample)
trace_artifacts_removed.extend(original_trace[start_sample:end_sample])
#plots trace in new window
stf.new_window(trace_artifacts_removed)
return (trace_artifacts_removed)
def update(self):
""" update current trace sampling rate,
cursors position and measurements (peak, baseline & AP kinetics)
according to the threshold value set at construction or when
the object is called with a threshold argument.
"""
# set slope
stf.set_slope(self._thr) # on stf v0.93 or above
# update sampling rate
self._dt = stf.get_sampling_interval()
# update cursors and AP kinetics (peak and half-width)
stf.measure()
def get_time_points(self):
#need to get specified sweep of the whole trace to an array
stf.file_open(self.whole_trace_file)
stf.set_trace(self.sweep_number)
trace_array = stf.get_trace()
#runs program to find sample indicies of selected EPSCs and converts to times
stf.file_open(self.event_file)
event_samples_list = find_sample_points_of_detected_events(trace_array)
sampling_interval = stf.get_sampling_interval()
event_times_list = [(sample * sampling_interval)
for sample in event_samples_list]
return (event_times_list)
def update(self):
""" update current trace sampling rate,
cursors position and measurements (peak, baseline & AP kinetics)
according to the threshold value set at construction or when
the object is called with a threshold argument.
"""
# set slope
stf.set_slope(self._thr) # on stf v0.93 or above
# update sampling rate
self._dt = stf.get_sampling_interval()
# update cursors and AP kinetics (peak and half-width)
stf.measure()
def fit_experiment(params, pulse_length, function_to_fit):
num_sweeps = stf.get_size_channel()
stf.set_channel(0)
stf.set_trace(0)
#jjm_analysis.set_params(params);
#stf.measure();
#this is in samples
#peak_index = stf.peak_index();
#stf.set_fit_start(peak_index, is_time=False);
#fit_start_time = peak_index*stf.get_sampling_interval();
#stf.set_fit_end(fit_start_time+pulse_length-(10*stf.get_sampling_interval()), is_time=True);
#fit_func = stf.leastsq(function_to_fit);
#fit_func['Baseline(pA)']=stf.get_base();
#fit_df = pd.DataFrame(fit_func, index=[0]);
fits = []
traces = []
for x in range(0, num_sweeps):
stf.set_trace(x)
jjm_analysis.set_params(params)
stf.measure()
#this is in samples
peak_index = stf.peak_index()
stf.set_fit_start(peak_index, is_time=False)
fit_start_time = peak_index * stf.get_sampling_interval()
stf.set_fit_end(fit_start_time + pulse_length -
(10 * stf.get_sampling_interval()),
is_time=True)
sweep_fit = stf.leastsq(function_to_fit)
sweep_fit['Baseline(pA)'] = stf.get_base()
fits.append(sweep_fit)
traces.append(x)
fit_df = pd.DataFrame(fits)
return (fit_df)
def plot_screen(self):
import stf
tsl = []
try:
l = stf.get_selected_indices()
for idx in l:
tsl.append(stfio_plot.Timeseries(stf.get_trace(idx),
stf.get_sampling_interval(),
yunits = stf.get_yunits(),
color='0.2'))
fit = stf.get_fit(idx)
if fit is not None:
self.axes.plot(fit[0], fit[1], color='0.4', alpha=0.5, lw=5.0)
except:
pass
tsl.append(stfio_plot.Timeseries(stf.get_trace(),
stf.get_sampling_interval(),
yunits = stf.get_yunits()))
if stf.get_size_recording()>1:
tsl2 = [stfio_plot.Timeseries(stf.get_trace(trace=-1, channel=stf.get_channel_index(False)),
stf.get_sampling_interval(),
yunits = stf.get_yunits(trace=-1, channel=stf.get_channel_index(False)),
color='r', linestyle='-r')]
stfio_plot.plot_traces(tsl, traces2=tsl2, ax=self.axes, textcolor2 = 'r',
xmin=stf.plot_xmin(), xmax=stf.plot_xmax(),
ymin=stf.plot_ymin(), ymax=stf.plot_ymax(),
y2min=stf.plot_y2min(), y2max=stf.plot_y2max())
else:
stfio_plot.plot_traces(tsl, ax=self.axes,
xmin=stf.plot_xmin(), xmax=stf.plot_xmax(),
ymin=stf.plot_ymin(), ymax=stf.plot_ymax())
fit = stf.get_fit()
if fit is not None:
self.axes.plot(fit[0], fit[1], color='0.2', alpha=0.5, lw=5.0)
def trainpeaks():
"""
Measure a 20 Hz train of peaks starting at 260 ms into the trace
"""
pk = []
for i in range(5):
stf.set_base_start(
int(255 / stf.get_sampling_interval()) +
(50 / stf.get_sampling_interval()) * i)
stf.set_base_end(
int(259 / stf.get_sampling_interval()) +
(50 / stf.get_sampling_interval()) * i)
stf.set_peak_start(
int(260.5 / stf.get_sampling_interval()) +
(50 / stf.get_sampling_interval()) * i)
stf.set_peak_end(
int(270.5 / stf.get_sampling_interval()) +
(50 / stf.get_sampling_interval()) * i)
stf.measure()
pk.append(stf.get_peak() - stf.get_base())
# Create table of results
dictlist = [("Peak 1", pk[0])]
dictlist += [("Peak 2", pk[1])]
dictlist += [("Peak 3", pk[2])]
dictlist += [("Peak 4", pk[3])]
dictlist += [("Peak 5", pk[4])]
retval = dict(dictlist)
stf.show_table(retval,
"peaks, Section #%i" % float(stf.get_trace_index() + 1))
# Create table of results
dictlist = [("Peak 1", pk[0] / pk[0] * 100)]
dictlist += [("Peak 2", pk[1] / pk[0] * 100)]
dictlist += [("Peak 3", pk[2] / pk[0] * 100)]
dictlist += [("Peak 4", pk[3] / pk[0] * 100)]
dictlist += [("Peak 5", pk[4] / pk[0] * 100)]
retval = dict(dictlist)
stf.show_table(
retval, "norm peaks, Section #%i" % float(stf.get_trace_index() + 1))
return
def batch_integration():
"""
Perform batch integration between the decay/fit cursors of all traces
in the active window
"""
n = int(stf.get_fit_end() + 1 - stf.get_fit_start())
x = [i * stf.get_sampling_interval() for i in range(n)]
dictlist = []
for i in range(stf.get_size_channel()):
stf.set_trace(i)
y = stf.get_trace()[int(stf.get_fit_start()):int(stf.get_fit_end() +
1)]
auc = np.trapz(y - stf.get_base(), x)
dictlist += [("%i" % (i + 1), auc)]
retval = dict(dictlist)
stf.show_table(retval, "Area Under Curve")
stf.set_trace(0)
return
def interpstim():
"""
Interpolate values between fit cursors in all traces in the active channel.
Typically used to remove stimulus artifacts.
"""
x = np.array(
[i * stf.get_sampling_interval() for i in range(stf.get_size_trace())])
fit_start = int(stf.get_fit_start())
fit_end = int(stf.get_fit_end())
interp_traces = []
for i in range(stf.get_size_channel()):
tmp = stf.get_trace(i)
tmp[fit_start:fit_end] = np.interp(x[fit_start:fit_end],
[x[fit_start], x[fit_end]],
[tmp[fit_start], tmp[fit_end]])
interp_traces.append(tmp)
stf.new_window_list(interp_traces)
return
def remove_artifacts_from_sweeps(artifact_start_time, artifact_end_time):
sampling_interval = stf.get_sampling_interval()
artifact_start = int(artifact_start_time / sampling_interval)
artifact_end = int(artifact_end_time / sampling_interval)
continuous_trace = []
output_artifacts_removed = []
for sweep in range(stf.get_size_channel()):
sweep_trace_before_artifact = stf.get_trace(sweep)[0:artifact_start]
sweep_trace_after_artifact = stf.get_trace(sweep)[artifact_end:]
sweep_trace = np.append(sweep_trace_before_artifact,
sweep_trace_after_artifact)
output_artifacts_removed.append(sweep_trace)
continuous_trace.extend(sweep_trace)
stf.new_window_list(output_artifacts_removed)
return (continuous_trace)
def find_baseline_amplitude(sigma):
# gaussian filter with sigma 10
trace_ = stf.get_trace()
trace_filtered = ndimage.filters.gaussian_filter(trace_, sigma)
# take derivative
si = stf.get_sampling_interval()
#read V values from trace,
V_values = stf.get_trace()
#compute dv and by iterating over voltage vectors
dv = [V_values[i + 1] - V_values[i] for i in range(len(V_values) - 1)]
#compute dv/dt
dv_dt = [(dv[i] / si) for i in range(len(dv))]
# find index of derivative peak
deriv_max = np.argmin(dv_dt)
# use derivative peak index to get baseline from original trace
# use a mean of 10 sample points
baseline = np.mean(trace_[deriv_max - 10:deriv_max])
peak_amplitude = np.min(stf.get_trace())
peak_from_baseline = peak_amplitude - baseline
return (baseline, peak_amplitude, peak_from_baseline)
def cut_sweeps(start, delta, sequence=None):
"""
Cuts a sequence of traces and present
them in a new window.
Arguments:
start -- starting point (in ms) to cut.
delta -- time interval (in ms) to cut
sequence -- list of indices to be cut. If None, every trace in the
channel will be cut.
Returns:
A new window with the traced cut.
Examples:
cut_sweeps(200,300) cut the traces between t=200 ms and t=500 ms
within the whole channel.
cut_sweeps(200,300,range(30,60)) the same as above, but only between
traces 30 and 60.
cut_sweeps(200,300,stf.get_selected_indices()) cut between 200 ms and 500 ms only in the selected traces.
"""
# select every trace in the channel if not selection is given in sequence
if sequence is None:
sequence = range(stf.get_size_channel())
# transform time into sampling points
dt = stf.get_sampling_interval()
pstart = int( round(start/dt) )
pdelta = int( round(delta/dt) )
# creates a destination python list
dlist = [ stf.get_trace(i)[pstart:(pstart+pdelta)] for i in sequence ]
return stf.new_window_list(dlist)
def cut_sweeps(start, delta, sequence=None):
"""
Cuts a sequence of traces and present
them in a new window.
Arguments:
start -- starting point (in ms) to cut.
delta -- time interval (in ms) to cut
sequence -- list of indices to be cut. If None, every trace in the
channel will be cut.
Returns:
A new window with the traced cut.
Examples:
cut_sweeps(200,300) cut the traces between t=200 ms and t=500 ms
within the whole channel.
cut_sweeps(200,300,range(30,60)) the same as above, but only between
traces 30 and 60.
cut_sweeps(200,300,stf.get_selected_indices()) cut between 200 ms and 500 ms only in the selected traces.
"""
# select every trace in the channel if not selection is given in sequence
if sequence is None:
sequence = range(stf.get_size_channel())
# transform time into sampling points
dt = stf.get_sampling_interval()
pstart = int(round(start / dt))
pdelta = int(round(delta / dt))
# creates a destination python list
dlist = [stf.get_trace(i)[pstart:(pstart + pdelta)] for i in sequence]
return stf.new_window_list(dlist)
def scan_through_train(start_params, train_increment, num_stims, train_trace):
"""scans through a tran of length "num_stims" in time increments of "train_increment", saves peak
amplitudes to an array peak_values (1st output) and sweep segments of peak regions for viewing are in peak_arrays"""
stf.set_trace(train_trace)
baseline_s = start_params[0]
baseline_e = start_params[1]
params_ = start_params
len_trace_in_samples = len(stf.get_trace(train_trace))
peak_values = np.zeros(num_stims)
len_peak_region_in_samples = round(
(start_params[3] - start_params[2]) / stf.get_sampling_interval())
peak_arrays = np.zeros((num_stims, (len_peak_region_in_samples)))
stim_count = 1
while stim_count <= num_stims:
peak_start = params_[2]
peak_end = params_[3]
print(peak_start, peak_end)
peak = jjm_peak(baseline_s, baseline_e, peak_start, peak_end)
print(peak)
peak_values[stim_count - 1] = peak
peak_region_slice = slice_peak_region(params_, train_trace)
peak_arrays[stim_count - 1] = peak_region_slice
params_ = increment_peak(params_, True, train_increment)
stim_count += 1
return (peak_values, peak_arrays)
def timeconstants(fitwindow, pulsewindow, ichannel=0, vchannel=1):
"""
Compute and plot decay time constants
Parameters
----------
fitwindow : (float, float), optional
Window for fitting time constant (time in ms from beginning of sweep)
None for current cursor settings. Default: None
pulsewindow : (float, float), optional
Window for voltage pulse measurement (time in ms from beginning of sweep)
None for current cursor settings. Default: None
ichannel : int, optional
current channel number. Default: 0
vchannel : int, optional
voltage channel number. Default: 1
Returns
-------
v_commands : numpy.ndarray
Command voltages
taus : numpy.ndarray
Time constants
"""
import stf
if not stf.check_doc():
return None
nchannels = stf.get_size_recording()
if nchannels < 2:
sys.stderr.write(
"Function requires 2 channels (0: current; 1: voltage)\n")
return
dt = stf.get_sampling_interval()
v_commands = []
taus = []
fig = stf.mpl_panel(figsize=(12, 8)).fig
fig.clear()
gs = gridspec.GridSpec(4, 8)
ax_currents = stfio_plot.StandardAxis(
fig, gs[:3, :4], hasx=False, hasy=False)
ax_voltages = stfio_plot.StandardAxis(
fig, gs[3:, :4], hasx=False, hasy=False, sharex=ax_currents)
for ntrace in range(stf.get_size_channel()):
stf.set_trace(ntrace)
stf.set_channel(ichannel)
trace = stf.get_trace()
ax_currents.plot(np.arange(len(trace))*dt, trace)
if fitwindow is not None:
stf.fit.cursor_time = fitwindow
res = stf.leastsq(0, False)
taus.append(res['Tau_0'])
# Measure pulse amplitude
stf.set_channel(vchannel)
trace = stf.get_trace()
ax_voltages.plot(np.arange(len(trace))*dt, trace)
stf.set_peak_direction("up")
stf.set_peak_mean(-1)
if pulsewindow is not None:
stf.peak.cursor_time = pulsewindow
stf.measure()
v_commands.append(stf.peak.value)
stfio_plot.plot_scalebars(
ax_currents, xunits=stf.get_xunits(),
yunits=stf.get_yunits(channel=ichannel))
stfio_plot.plot_scalebars(
ax_voltages, xunits=stf.get_xunits(),
yunits=stf.get_yunits(channel=vchannel))
v_commands = np.array(v_commands)
taus = np.array(taus)
ax_taus = plot_iv(
taus, v_commands, "ms",
stf.get_yunits(channel=vchannel), fig, 122)
# Reset peak computation to single sampling point
stf.set_peak_mean(1)
# Reset active channel
stf.set_channel(ichannel)
# Compute conductances:
stf.show_table_dictlist({
"Voltage ({0})".format(
stf.get_yunits(channel=vchannel)): v_commands.tolist(),
"Taus (ms)": taus.tolist(),
})
return v_commands, taus
def find_AP_peak_ADP_trace(*argv):
""" count number of APs, find ADPs and thesholds in indicated trace with current injection/gradually increasing steps
inputs: (time (msec) to start search, length of search region, starting current value,
current delta between traces, threshold value, deflection direction ('up'/'down'), mark traces (True/False))"""
##if times are input, use those, otherwise use peak cursor settings
#TO DO: optional change to threshold_values and deflection_direction
if len(argv) > 0:
trace_selection = argv[0]
threshold_value = float(argv[1])
deflection_direction = argv[2]
mark_option = argv[3]
start_msec = float(argv[4])
delta_msec = float(argv[5])
else:
trace_selection = stf.get_trace_index()
threshold_value = 0
deflection_direction = 'up'
mark_option = True
start_msec = float(stf.get_peak_start(True))
delta_msec = float(stf.get_peak_end(True) - start_msec)
stf.set_trace(trace_selection)
##gets AP counts and sample points in current trace
if deflection_direction == 'up':
direction_input = True
else:
direction_input = False
##count function will return number of APs in trace and sample points for subsequent functions
trace_count, trace_sample_points_absolute = jjm_count(
start_msec,
delta_msec,
threshold=threshold_value,
up=direction_input,
trace=trace_selection,
mark=mark_option)
##finds afterdepolarizations--minimums between peaks
trace_ADP_values, trace_ADP_indicies = find_ADPs(
trace_sample_points_absolute)
trace_si = stf.get_sampling_interval()
trace_ADP_times = [sample * trace_si for sample in trace_ADP_indicies]
trace_AP_values, trace_AP_indicies = find_ADPs(
trace_sample_points_absolute)
trace_si = stf.get_sampling_interval()
trace_ADP_times = [sample * trace_si for sample in trace_AP_indicies]
trace_thresholds_indicies = find_thresholds(stf.get_trace(trace_selection),
trace_si, trace_ADP_indicies)
trace_threshold_values = [
stf.get_trace(trace_selection)[index]
for index in trace_thresholds_indicies
]
trace_threshold_times = [
sample * trace_si for sample in trace_thresholds_indicies
]
for sample, mv in zip(trace_thresholds_indicies, trace_threshold_values):
stf.set_marker(sample, mv)
for x in range(len(trace_threshold_values)):
if trace_threshold_values[
x] > threshold_value or trace_threshold_values[
x] < trace_ADP_values[x]:
trace_threshold_values[x] = 'NaN'
#arrays for output
ADP_out_array = np.transpose(np.array([trace_ADP_times, trace_ADP_values]))
threshold_out_array = np.transpose(
np.array([trace_threshold_times, trace_threshold_values]))
out_array = np.hstack([ADP_out_array, threshold_out_array])
df_out = pd.DataFrame(
out_array,
columns=['ADP time', 'ADP (mV)', 'threshold time', 'threshold (mV)'])
return (trace_count, df_out)
def iv(peakwindow=None, basewindow=None, pulsewindow=None,
erev=None, peakmode="both", ichannel=0, vchannel=1,
exclude=None):
"""
Compute and plot an IV curve for currents
Parameters
----------
peakwindow : (float, float), optional
Window for peak measurement (time in ms from beginning of sweep)
None for current cursor settings. Default: None
basewindow : (float, float), optional
Window for baseline measurement (time in ms from beginning of sweep)
None for current cursor settings. Default: None
pulsewindow : (float, float), optional
Window for voltage pulse measurement (time in ms from beginning of sweep)
None for current cursor settings. Default: None
erev : float, optional
End of v clamp pulse in ms or None to determine automatically.
Default: None
peakmode : string, optional
Peak direction - one of "up", "down", "both" or "mean". Default: "up"
ichannel : int, optional
current channel number. Default: 0
vchannel : int, optional
voltage channel number. Default: 1
exclude : list of ints, optional
List of trace indices to be excluded from the analysis. Default: None
Returns
-------
v_commands : numpy.ndarray
Command voltages
ipeaks : numpy.ndarray
Peak currents
gpeaks : numpy.ndarray
Peak normalized conductances
g_fit : numpy.ndarray
Half-maximal voltage and slope of best-fit Boltzmann function
"""
import stf
if not stf.check_doc():
return None
nchannels = stf.get_size_recording()
if nchannels < 2:
sys.stderr.write(
"Function requires 2 channels (0: current; 1: voltage)\n")
return
dt = stf.get_sampling_interval()
olddirection = stf.get_peak_direction()
v_commands = []
ipeaks = []
if basewindow is not None:
stf.base.cursor_time = basewindow
fig = stf.mpl_panel(figsize=(12, 8)).fig
fig.clear()
gs = gridspec.GridSpec(4, 8)
ax_currents = stfio_plot.StandardAxis(
fig, gs[:3, :4], hasx=False, hasy=False)
ax_voltages = stfio_plot.StandardAxis(
fig, gs[3:, :4], hasx=False, hasy=False, sharex=ax_currents)
for ntrace in range(stf.get_size_channel()):
if exclude is not None:
if ntrace in exclude:
continue
stf.set_trace(ntrace)
stf.set_channel(ichannel)
trace = stf.get_trace()
ax_currents.plot(np.arange(len(trace))*dt, trace)
# Measure only downward peaks (inward currents)
if peakmode is "mean":
stf.set_peak_direction("up")
stf.set_peak_mean(-1)
else:
stf.set_peak_direction(peakmode)
# Set peak computation to single sampling point
stf.set_peak_mean(1)
if peakwindow is not None:
stf.peak.cursor_time = peakwindow
stf.measure()
if basewindow is not None:
ipeaks.append(stf.peak.value-stf.base.value)
else:
ipeaks.append(stf.peak.value)
# Measure pulse amplitude
stf.set_channel(vchannel)
trace = stf.get_trace()
ax_voltages.plot(np.arange(len(trace))*dt, trace)
stf.set_peak_direction("up")
stf.set_peak_mean(-1)
if pulsewindow is not None:
stf.peak.cursor_time = pulsewindow
stf.measure()
v_commands.append(stf.peak.value)
stfio_plot.plot_scalebars(
ax_currents, xunits=stf.get_xunits(), yunits=stf.get_yunits(channel=0))
stfio_plot.plot_scalebars(
ax_voltages, xunits=stf.get_xunits(), yunits=stf.get_yunits(channel=1))
v_commands = np.array(v_commands)
ipeaks = np.array(ipeaks)
if erev is None:
# Find first zero crossing in ipeaks:
for npulse in range(ipeaks.shape[0]-1):
if np.sign(ipeaks[npulse]) != np.sign(ipeaks[npulse+1]):
# linear interpolation
m1 = (ipeaks[npulse+1]-ipeaks[npulse]) / (
v_commands[npulse+1]-v_commands[npulse])
c1 = ipeaks[npulse] - m1*v_commands[npulse]
erev = -c1/m1
break
if erev is None:
sys.stderr.write(
"Could not determine reversal potential. Aborting now\n")
return None
# Reset peak computation to single sampling point
stf.set_peak_mean(1)
stf.set_peak_direction(olddirection)
# Reset active channel
stf.set_channel(ichannel)
# Compute conductances:
gpeaks, g_fit = gv(ipeaks, v_commands, erev)
ax_ipeaks = plot_iv(
ipeaks, v_commands, stf.get_yunits(channel=ichannel),
stf.get_yunits(channel=1), fig, 222)
ax_ipeaks.set_title("Peak current")
ax_gpeaks = plot_gv(
gpeaks, v_commands, stf.get_yunits(channel=vchannel),
g_fit, fig, 224)
ax_gpeaks.set_title("Peak conductance")
stf.show_table_dictlist({
"Voltage ({0})".format(
stf.get_yunits(channel=vchannel)): v_commands.tolist(),
"Peak current ({0})".format(
stf.get_yunits(channel=ichannel)): ipeaks.tolist(),
"Peak conductance (g/g_max)": gpeaks.tolist(),
})
return v_commands, ipeaks, gpeaks, g_fit
def count_events(start, delta, threshold=0, up=True, trace=None, mark=True):
"""
Counts the number of events (e.g action potentials (AP)) in the current trace.
Arguments:
start -- starting time (in ms) to look for events.
delta -- time interval (in ms) to look for events.
threshold -- (optional) detection threshold (default = 0).
up -- (optional) True (default) will look for upward events,
False downwards.
trace -- (optional) zero-based index of the trace in the current
channel, if None, the current trace is selected.
mark -- (optional) if True (default), set a mark at the point
of threshold crossing
Returns:
An integer with the number of events.
Examples:
count_events(500,1000) returns the number of events found between t=500
ms and t=1500 ms above 0 in the current trace and shows a stf
marker.
count_events(500,1000,0,False,-10,i) returns the number of events found
below -10 in the trace i and shows the corresponding stf markers.
"""
# sets the current trace or the one given in trace.
if trace is None:
sweep = stf.get_trace_index()
else:
if type(trace) !=int:
print('trace argument admits only integers')
return False
sweep = trace
# set the trace described in sweep
stf.set_trace(sweep)
# transform time into sampling points
dt = stf.get_sampling_interval()
pstart = int( round(start/dt) )
pdelta = int( round(delta/dt) )
# select the section of interest within the trace
selection = stf.get_trace()[pstart:(pstart+pdelta)]
# algorithm to detect events
event_counter, i = 0, 0 # set counter and index to zero
# choose comparator according to direction:
if up:
comp = lambda a, b: a > b
else:
comp = lambda a, b: a < b
# run the loop
while i < len(selection):
if comp(selection[i], threshold):
event_counter += 1
if mark:
stf.set_marker(pstart+i, selection[i])
while i < len(selection) and comp(selection[i], threshold):
i += 1 # skip until value is below/above threshold
else:
i += 1
return event_counter
def savemat():
"""
Save electrophysiology recordings to ephysIO HDF5-based Matlab
v7.3 (.mat) files
"""
# Import required modules for file IO
from Tkinter import Tk
import tkFileDialog
from gc import collect
# Use file save dialog to obtain file path
root = Tk()
opt = dict(defaultextension='.mat',
filetypes=[('MATLAB v7.3 (HDF5) file', '*.mat'),
('All files', '*.*')])
if 'savecwd' not in globals():
global savecwd
else:
opt['initialdir'] = savecwd
filepath = tkFileDialog.asksaveasfilename(**opt)
root.destroy()
if filepath != '':
# Move to file directoty
savecwd = filepath.rsplit('/', 1)[0]
import os
print filepath
os.chdir(savecwd)
filename = filepath.rsplit('/', 1)[1]
# Get data from active Stimfit window
import stf
import numpy as np
n = stf.get_size_channel()
array = np.array([stf.get_trace(i).tolist() for i in range(n)])
if np.any(np.isnan(array)) | np.any(np.isinf(array)):
raise ValueError(
"nan and inf values cannot be parsed into ephysIO")
if stf.get_yunits() == 'pA':
yunit = 'A'
array = 1.0e-12 * array
elif stf.get_yunits() == 'mV':
yunit = 'V'
array = 1.0e-03 * array
else:
yunit = stf.get_yunits()
#print "Warning: Expected Y dimension units to be either pA or mV"
# Create X dimension properties
if stf.get_xunits() == 'ms':
xunit = 's'
xdiff = np.array([[1.0e-03 * stf.get_sampling_interval()]])
else:
raise ValueError("Expected X dimension units to be ms")
# Calculate X dimension and add to array
x = xdiff * np.arange(0.0, np.shape(array)[1], 1, 'float64')
array = np.concatenate((np.array(x, ndmin=2), array), 0)
# Get data recording notes
notes = stf.get_recording_comment().split('\n')
names = None
import ephysIO
ephysIO.MATsave(filepath, array, xunit, yunit, names, notes)
collect()
return
def chebexp(n, Tn=20):
"""
Fits sums of exponentials with offset to the current trace in the
active channel using the Chebyshev tranform algorithm. The maximum
order of the Chebyshev polynomials can be set using Tn.
Reference:
Malachowski, Clegg and Redford (2007) J Microsc 228(3): 282-95
"""
# Get data trace between fit/decay cursors
y = stf.get_trace()[stf.get_fit_start():stf.get_fit_end()].astype(
np.double)
si = np.double(stf.get_sampling_interval())
l = len(y)
N = np.double(l - 1)
# Calculate time dimension with unit 1
t = np.arange(0, l, 1, np.double)
# Check the maximum order Chebyshev polynomials to generate
if l < Tn:
raise ValueError('Tn exceeds the number of data points')
# Generate the polynomials T and coefficients d
T0 = np.ones((l), np.double)
R0 = np.sum(T0**2)
d0 = np.sum((T0 * y) / R0)
T = np.zeros((l, Tn), np.double)
T[:, 0] = 1 - 2 * t / N
T[:, 1] = 1 - 6 * t / (N - 1) + 6 * t**2 / (N * (N - 1))
R = np.zeros((Tn), np.double)
d = np.zeros((Tn), np.double)
for j in range(Tn):
if j > 1:
A = (j + 1) * (N - j)
B = 2 * (j + 1) - 1
C = j * (N + j + 1)
T[:, j] = (B * (N - 2 * t) * T[:, j - 1] - C * T[:, j - 2]) / A
R[j] = np.sum(T[:, j]**2)
d[j] = np.sum(T[:, j] * y / R[j])
# Generate additional coefficients dn that describe the relationship
# between the Chebyshev coefficients d and the constant k, which is
# directly related to the exponent time constant
dn = np.zeros((n, Tn), np.double)
for i in range(1, n + 1):
for j in range(1 + i, Tn - i + 1):
if i > 1:
dn[i - 1, j - 1] = (((N + j + 2) * dn[i - 2, j] /
(2 * j + 3)) - dn[i - 2, j - 1] -
((N - j + 1) * dn[i - 2, j - 2] /
(2 * j - 1))) / 2
else:
dn[i - 1,
j - 1] = (((N + j + 2) * d[j] / (2 * j + 3)) - d[j - 1] -
((N - j + 1) * d[j - 2] / (2 * j - 1))) / 2
for i in range(n):
dn[i, :] = dn[i, :] * np.double(np.all(dn, 0))
# Form the regression model to find the time constants of each exponent
Mn = np.zeros((n, n), np.double)
b = np.zeros(n, np.double)
for i in range(n):
b[i] = np.sum(d * dn[i, :])
for m in range(n):
Mn[i, m] = -np.sum(dn[i, :] * dn[m, :])
# Solve the linear problem
try:
x = np.linalg.solve(Mn, b)
except:
x = np.linalg.lstsq(Mn, b)[0]
k = np.roots(np.hstack((1, x)))
if any(k != np.real(k)):
raise ValueError("Result is not a sum of %d real exponents" % n)
tau = -1 / np.log(1 + k)
# Generate the Chebyshev coefficients df for each exponent
df0 = np.zeros(n, np.double)
df = np.zeros((n, Tn), np.double)
for i in range(n):
for j in range(Tn):
df[i, j] = np.sum(np.exp(-t / tau[i]) * T[:, j] / R[j])
df0[i] = np.sum(np.exp(-t / tau[i]) * T0 / R0)
# Form the regression model to find the amplitude of each exponent
Mf = np.zeros((n, n), np.double)
b = np.zeros(n, np.double)
for i in range(n):
b[i] = np.sum(d * df[i, :])
for m in range(n):
Mf[i, m] = np.sum(df[i, :] * df[m, :])
# Solve the linear problem
try:
a = np.linalg.solve(Mf, b)
except:
a = np.linalg.lstsq(Mf, b)[0]
# Calculate the offset for the fit
offset = d0 - np.sum(df0 * a.T)
# Prepare output
retval = [("Amp_%d" % i, a[i]) for i in range(n)]
retval += [("Tau_%d" % i, si * tau[i]) for i in range(n)]
retval += [("Offset", np.double(offset))]
retval = dict(retval)
return retval
