def fit(filename, fitax, difax):
folder = P(filename).parent
_, data = read(filename)
field = str(P(filename).stem).split("data_")[-1]
if TESTING:
popt, pcov = cf(double_debye,
data[:, 0],
data[:, 1],
method='trf',
verbose=0)
print(field)
else:
popt, pcov = cf(double_debye,
data[:, 0],
data[:, 1],
method='trf',
verbose=2,
p0=[50, 10, 200, 10])
leg_popt = [f"{ii:.1f}" for ii in popt]
fitax.plot(data[:, 0],
double_debye(data[:, 0], *popt),
label=f'fit: {field}')
fitax.plot(data[:, 0], data[:, 1], label=f'raw: {field}')
fitax.legend()
difax.plot(data[:, 0],
data[:, 1] - double_debye(data[:, 0], *popt),
label=f'{field}')
difax.legend()
return popt
def pltfit(self, data, neg):
if neg:
self.params_neg, cov = cf(self.linearfunc, data[1, :], data[0, :],
sigma=self.sigma * np.ones(len(data[1, :])), p0=self.guess_neg, maxfev=10 ** 5)
chi2 = self.chisquared(self.params_neg, data[1, :], data[0, :])
dof = len(data[1, :]) - len(self.params_neg)
else:
self.params_pos, cov = cf(self.linearfunc, data[1, :], data[0, :],
sigma=self.sigma * np.ones(len(data[1, :])), p0=self.guess_pos, maxfev=10 ** 5)
chi2 = self.chisquared(self.params_pos, data[1, :], data[0, :])
dof = len(data[1, :]) - len(self.params_pos)
print("\nGoodness of fit - chi square measure:")
print("Chi2 = {}, Chi2/dof = {}\n".format(chi2, chi2 / dof))
cov = cov * dof / chi2
paramserr = np.sqrt(np.diag(cov))
print("Fit parameters:")
param_names = ['Slope', 'Offset']
if neg:
for i in range(len(self.params_neg)):
print('{} = {:.3e} +/- {:.3e}'.format(param_names[i], self.params_neg[i], paramserr[i]))
bfieldfit = np.linspace(min(data[1, :]), max(data[1, :]), len(data[1, :]) * 10)
rxyfit = self.linearfunc(bfieldfit, *self.params_neg)
else:
for i in range(len(self.params_pos)):
print('{} = {:.3e} +/- {:.3e}'.format(param_names[i], self.params_pos[i], paramserr[i]))
bfieldfit = np.linspace(min(data[1, :]), max(data[1, :]), len(data[1, :]) * 10)
rxyfit = self.linearfunc(bfieldfit, *self.params_pos)
plt.scatter(data[1, :], data[0, :], marker='.', label="measured data")
plt.plot(bfieldfit, rxyfit, marker="", linestyle="-", linewidth=2, color="r", label=" fit")
plt.xlabel('{} [{}]'.format(self.x_label, self.x_units))
plt.ylabel('{} [{}]'.format(self.y_label, self.y_units))
plt.title(self.title + " Rxx Fitted Guess")
plt.legend(loc='best', numpoints=1)
print('\nSaving plot 2 for ' + self.title)
if "OutPlane" in self.DataAddress:
if neg:
address = self.DataAddress[:90] + "Graphs/" + self.title + "_InPlane_Linear_Fitted_Neg" + ".png"
else:
address = self.DataAddress[:90] + "Graphs/" + self.title + "_InPlane_Linear_Fitted_Pos" + ".png"
elif neg:
address = self.DataAddress[:90] + "Graphs/" + self.title + "_Linear_Fitted_Neg" + ".png"
else:
address = self.DataAddress[:90] + "Graphs/" + self.title + "_Linear_Fitted_Pos" + ".png"
plt.savefig(address)
plt.clf()
def fitting(func,xdata,ydata,lb,ub,errors=None,Poisson=False,fixed_param=None):
params = -999. ; chi2n = -999.
# Check that the degrees of freedom is larger than 1
dof = len(xdata)-len(lb)
if (dof<=1):
sys.exit('HOD_FIT.py: The degrees of freedom should be >1')
# Find an adequate initial set of parameters
ntest = 50
chi0 = 999.
for i in range(ntest):
p1 = random.rand(len(lb))
p1 = lb + p1*(ub-lb)
if (fixed_param is None):
p2,cov = cf(func,xdata,ydata,p0=p1)
model = func(xdata,*p2)
else:
print 'working on fixing parameters'
#ia = fixed_param ; a = lb[ia]
#p2,cov = cf(func+bound([a,a],),xdata,ydata,p0=p1)
#model = func(xdata,*p2)
if (Poisson):
chi = abs(chi2_poisson(ydata,model)/dof -1.)
else:
chi = abs(chi2(ydata,model,errors)/dof -1.)
if (chi<=chi0 or i==0):
chi0 = chi
params = p2
chi2n = chi2(ydata,model,errors)/dof
return params,chi2n
def disparity_investigation(samplerate_name,shaping,datadate,n_box,n_delay,n_att,numhead):
phase_time = 1/20000000000 #sets timing between phases (initial sample rate of oscilloscope)
filedir = 'G:/data/watchman/'+str(datadate)+'_watchman_spe/studies/phase/'+samplerate_name+'/phase=0/phase_'+shaping+'/'
Nloops = len(os.listdir(filedir))
filedir = 'G:/data/watchman/'+str(datadate)+'_watchman_spe/studies/phase/' + samplerate_name + '/array_data/'
median_array = np.loadtxt(filedir+'median_array.csv', delimiter=',')
correction_median_array = np.loadtxt(filedir+'correction_median_array.csv', delimiter=',')
for i in range(29,40):
corrected_difference_list = [] #initializing lists (use python lists rather than np arrays when appending, faster)
for j in range(Nloops):
print(j) #printing value to show progress
#establishing directory and file names
filedir = 'G:/data/watchman/'+str(datadate)+'_watchman_spe/studies/phase/'+samplerate_name+'/phase='+str(i)+'/phase_'+shaping+'/'
filename = filedir + 'Phase--waveforms--%05d.txt' % j
#reading in waveform values and running CFD
(t,v,_) = rw(filename,numhead)
t_avg,v_avg = boxcar_wf(t,v,n_box)
v_delay = delay_wf(v_avg,n_delay)
v_att = attenuate_wf(v_avg,n_att)
v_sum = sum_wf(v_att,v_delay)
t_cross,_,_ = zc_locator(t_avg,v_sum)
t_cross = t_cross - median_array[0] #removing linear displacement
corrected_difference_list.append(-1*i*phase_time - (t_cross + correction_median_array[i])) #gathering timing difference
corrected_difference_list = np.asarray(corrected_difference_list) #turning to numpy array for better calculation
#calculating full mean and standard deviations
set_mean = np.mean(corrected_difference_list)
set_std = np.std(corrected_difference_list)
set_mean = '%.5g' % set_mean
set_std = '%.5g' % set_std
histo_mean,histo_std = gauss_histogram(corrected_difference_list) #gathering starting means/stds for fit
corrected_difference_list = corrected_difference_list[(corrected_difference_list >= histo_mean - 4*histo_std) & (corrected_difference_list <= histo_mean + 4*histo_std)] #cutting off outliers
histo_data, bins_data = np.histogram(corrected_difference_list, bins = 200)
binwidth = (bins_data[1] - bins_data[0]) #determining bin width
#determining bin centers
binscenters = np.array([0.5 * (bins_data[i] + bins_data[i+1]) for i in range(len(bins_data)-1)])
b_guess = (len(corrected_difference_list) * binwidth) #using area approximation to guess at B value
popt, _ = cf(fit_function,xdata = binscenters,ydata = histo_data, p0 = [b_guess,histo_mean,histo_std], maxfev = 10000)
gauss_mean = '%s' % float('%.5g' % popt[1])
gauss_std = '%s' % float('%.5g' % popt[2])
#establishing 5 significant figure versions of the mean and std from curve fit
x_values = np.linspace(popt[1] - 1.5*popt[2], popt[1] + 1.5*popt[2], 100000) #creating 100,000 x values to map curvefit gaussian to
fig,ax = plt.subplots()
ax.bar(binscenters, histo_data, width=binwidth) #plotting histogram
ax.plot(x_values, fit_function(x_values, *popt), color='darkorange') #plotting curve fit
ax.set_xlabel('True Timing - Recovered Timing')
ax.set_ylabel('Count')
ax.set_title('Corrected Timings for Phase=%d' %i +'\nGaussian Fit Values:\nMean = '+gauss_mean+' seconds, '+set_mean+'seconds\nStandard Deviation = '+gauss_std+' seconds, '+set_std+'seconds', fontdict={'fontsize': 14})
plt.get_current_fig_manager().window.showMaximized()
plt.show(block = False)
plt.pause(1)
filedir = 'G:/data/watchman/20190724_watchman_spe/studies/disparity/'
filename = 'Phase_%d.png' % i
savename = filedir + filename
fig.savefig(savename,dpi = 500)
plt.close()
def fit_CAB_powerlaw(sample_epochs_index, all_index,
sparse_data_averages_nonan, sparse_data_std_nonan, scale):
def plfunc(x, a, b):
return a * np.power(1 + x, -b)
#end
pfit, _ = cf(plfunc, sample_epochs_index, sparse_data_averages_nonan)
residuals = sparse_data_averages_nonan - plfunc(sample_epochs_index, *pfit)
squared_res = np.sum(np.power(residuals, 2))
sum_tot_squares = np.sum(
(sparse_data_averages_nonan - np.mean(sparse_data_averages_nonan))**2)
r_squared = 1 - (squared_res / sum_tot_squares)
all_data = plfunc(all_index, *pfit)
scatterplot(all_index,
all_data,
sample_epochs_index,
sparse_data_averages_nonan,
sparse_data_std_nonan,
pfit,
scale,
tag='CAB',
rsquare=r_squared)
return pfit
def gaussfit(self):
for idx, columnx in enumerate(df):
if boxDict[columnx + str(1)].isChecked():
pa = df[columnx].tolist()
for idy, columny in enumerate(df):
variablefit = str(idx) + str(idy) + "gauss_fit"
if boxDict[columny + str(2)].isChecked():
try:
fitDict[variablefit][0].remove()
except:
pass
pb = df[columny].tolist()
pstart = [1., 0., 1.]
coeff, var_matrix = cf(functions.gauss,
pa,
pb,
p0=pstart)
fitDict[variablefit] = plt.plot(
np.linspace(pa[0], pa[-1], 1000),
functions.gauss(np.linspace(pa[0], pa[-1], 1000),
coeff[0], coeff[1], coeff[2]),
"-",
color="red")
self.textBrowser.append("Line fit: " + "a = " +
str(coeff[0]) + ", mu = " +
str(coeff[1]) + ", sigma = " +
str(coeff[2]) + " for " +
str(columnx) + " x " +
str(columny))
self.reloadpictrue()
def process(filename):
header, data = read(filename)
data_array = np.array(data)
data_dict = {
'param': 1E6 * data_array[:, 0],
'echo': data_array[:, 3],
}
popt, pcov = cf(func, data_dict['param'], data_dict['echo'])
min_idx = np.argmin(func(data_dict['param'], *popt))
min_time = data_dict['param'][min_idx]
rabi_freq = 1 / (2 * min_time *
1E-6) / 1E6 # convert the us to s then get freq
# print(popt)
fig, ax = plt.subplots()
ax.plot(data_dict['param'], data_dict['echo'], label='Raw data', c='black')
ax.plot(data_dict['param'],
func(data_dict['param'], *popt),
label=f"Min time: {min_time:.2f} $\mu$s\nFreq: {popt[0]:.2f} MHz",
c='red')
ax.legend()
ax.set_ylabel('Echo intensity (arb. u)')
ax.set_yticks([])
ax.set_xlabel('$P_1$ length ($\mu$s)')
ax.set_title('Rabi echo intensity vs. inversion pulse length')
for s in ['top', 'right']:
ax.spines[s].set_visible(False)
plt.savefig(P(filename).parent.joinpath('fixedSourceRabi.png'), dpi=300)
plt.show()
def fitGaussianX(img, m, b, bright, offset, starX, starY, starR, gX, gY, gR, hotX, hotY):
parDist,perpDist = GT.getDistancesHorizontal(m, b, img.shape[1], img.shape[0], offset)
parF,perpF,imgF = getTrailBand(parDist, perpDist, img, 6)
x,y = GT.getXY(parF,perpF,m,b,offset)
trailScaled = imgF/bright(parF)
fig,axes = plt.subplots(1,2,sharex = True, sharey = True)
axes[0].plot(perpF,trailScaled,"bo")
axes[0].set_title("Trail Gaussian With Stars")
mask = getValueMask(img, x, y, starX, starY, starR, gX, gY, gR, hotX, hotY, 1)
perpF = perpF[mask]
trailScaled = trailScaled[mask]
axes[1].plot(perpF,trailScaled,"bo")
axes[1].set_title("Trail Gaussian Without Stars")
plt.show()
sDev = cf(gauss, perpF, trailScaled)[0][0]
x = np.arange(-5,5,0.1)
plt.plot(perpF,trailScaled,"bo",label = "Pixel Brightnesses")
plt.plot(x,gauss(x,sDev), label = "Gaussian Fit")
plt.title("Gaussian Fit")
plt.show()
return sDev
def crear_plot(self, sub_df, corr):
y_start, y_end = min(sub_df[y][sub_df['alpha'] == alpha_max]), max(sub_df[y][sub_df['alpha'] == alpha_max])
y_start -= 0.05 * (y_end - y_start)
y_end += 0.05 * (y_end - y_start)
scatter = figure(plot_height=400, plot_width=400,
tools='reset,box_zoom,pan,wheel_zoom,lasso_select,undo,redo',
sizing_mode='scale_width', output_backend="webgl", toolbar_location='above',
y_range=(y_start, y_end))
hover = HoverTool(
tooltips="""
<div><span style="font-size: 17px; font-weight: bold;">@municipio</span></div>
<div><span style="font-size: 12px;">@provincia (@autonomia), @poblacion</span></div>
<div><span style="font-size: 14px; font-weight: bold;">@partido</span>
<span style="font-size: 12px;">@porcentaje</span></div>
""")
scatter.add_tools(hover)
scatter.scatter(x=x, y=y, source=sub_df, color='color', alpha='alpha', **scatter_kwargs)
y_range=(y_start, y_end)
if corr: # Con esto añadimos las correlaciones.
for var_subor_i in self.subordinada_obj:
for var_indep_i in self.indepe_obj:
si_df = sub_df[(sub_df[var_indepe] == var_indep_i) &
(sub_df[var_subord] == var_subor_i)]
if len(si_df) > 1: # Nos aseguramos porque si no falla para Ceuta y Melilla
x_vals, y_vals = si_df[x].values, si_df[y].values
if corr_type == 'lineal':
def f(x, m, b):
return m * x + b
m, b, r, p, err = lr(x_vals, y_vals)
text_label = "r² = %.2f" % r**2
elif corr_type == 'exp':
def f(x, m, b):
return np.power(m * np.log10(x) + b, 10)
popt, pcor = cf(f, x_vals, y_vals)
m, b = popt
ss_res = np.sum((y_vals - f(x_vals, m, b)) ** 2)
ss_tot = np.sum((y_vals - np.mean(y_vals)) ** 2)
r_squared = 1 - (ss_res / ss_tot)
text_label = "r² = %.2f" % r_squared
x_arr = np.linspace(min(x_vals), max(x_vals), 100)
scatter.line(x_arr, [f(x_i, m, b) for x_i in x_arr], color=si_df['color'].iloc[0])
r_label = Label(x=1.05 * max(x_vals), y=f(max(x_vals), m, b),
text=text_label, text_align='left', text_color=si_df['color'].iloc[0],
render_mode='css')
scatter.add_layout(r_label)
if f(max(x_vals), m, b) > y_end: y_end = f(max(x_vals), m, b)
if f(max(x_vals), m, b) < y_start: y_start = f(max(x_vals), m, b)
else:
pass
scatter.y_range = Range1d(y_start, y_end)
return scatter
def polyfit6(landmarks):
a = np.array([m[0] for m in landmarks if 'contour_' in m[1]])
a = a[a[:, 0].argsort()]
x = a[:, 0]
y = a[:, 1]
cutoff = 7
popt, pcov = cf(_x6, x[cutoff:-cutoff], y[cutoff:-cutoff])
return list(popt)
def butterfly_catastrophe(landmarks):
a = np.array([m[0] for m in landmarks if 'contour_' in m[1]])
a = a[a[:, 0].argsort()]
x = a[:, 0]
y = a[:, 1]
cutoff = 7
popt, pcov = cf(_butterfly, x[cutoff:-cutoff], y[cutoff:-cutoff])
return list(popt)
def gauss_fit(data,
title='',
plot=True,
n_tot=[],
weights=None,
label='',
norm=None):
rng = max(data)
if n_tot == []:
n_tot = len(data)
bin_e, bin_edges = np.histogram(data,
bins=np.linspace(0, rng, 50),
density=False,
weights=weights)
err = np.sqrt(bin_e)
bin_mid = (bin_edges[1:] + bin_edges[:-1]) / 2
gauss_param = cf(gauss,
bin_mid,
bin_e, (max(bin_e), np.average(bin_mid, weights=bin_e),
np.average(bin_mid, weights=bin_e)),
sigma=1 / err)[0]
ex = np.linspace(min(data), rng, 400)
gauss_fit = gauss(ex, gauss_param[0], gauss_param[1], gauss_param[2])
width = abs(gauss_param[2] * 2 * np.sqrt(2 * np.log(2)))
width_locs = gauss_param[1] + np.array((-width / 2, width / 2))
if norm == 'peak':
gauss_fit = gauss(ex, gauss_param[0], gauss_param[1],
gauss_param[2]) / max(bin_e)
err = bin_e / max(bin_e) * np.sqrt(1 / bin_e + 1 / np.max(bin_e))
bin_e = bin_e / max(bin_e)
if type(norm) != str and norm != None:
bin_e = bin_e / norm
err = err / norm
gauss_fit = gauss(ex, gauss_param[0], gauss_param[1],
gauss_param[2]) / norm
if plot == True:
print('\nFit parmameters: ' + title)
print('[ a x0 sigma ]')
print(gauss_param)
print('\nthroughput(%): ' + str(len(data) / n_tot))
print('E: ' + str(gauss_param[1]))
print('FWHM: ' + str(width))
print('dE/E: ' + str(width / gauss_param[1]))
print('skewness: ' + str(stats.skew(data)))
line = plt.plot(ex, gauss_fit, alpha=.5, label=label)[0]
plt.errorbar(bin_mid, bin_e, err, fmt='.', color=line.get_color())
plt.axvline(width_locs[0], color=line.get_color())
plt.axvline(width_locs[1], color=line.get_color())
plt.ylabel('normalized count rate', fontsize=14)
plt.xlabel('Accepted Enterance Energy(ev)', fontsize=14)
plt.title(title)
plt.show()
return gauss_param, width / gauss_param[1]
def extrapolate_correlation(energies, basis):
"""
Extrapolate the correlation energy to the CBS limit.
Args: energies and basis are same length tuple-like, with the former
corresponding to the correlation (post-SCF) energy and basis the cardinal
values
Returns: the extrapolated energy, and the results of the fit.
"""
popt, pcov = cf(linear, basis, energies, p0=[1., np.min(energies)])
return popt[1], popt
def extrapolate_SCF(energies, basis):
# Function for extrapolating the SCF contribution
# to the CBS limit.
# Takes a list of SCF energies in order
# of T,Q,5-zeta quality, and returns the CBS energy.
popt, pcov = cf(exponential,
basis,
energies,
p0=[1., 1., np.min(energies)])
return popt[2], popt
def domass(Y, X, func = fit_log, p0 = [1, 2, 8], lim = False, loglim = False, sigma = True, absig = False, \
abund = False, retdata = False, nonzeroy = True, ranzero = 0):
'''Take in X(delta) & Y(loghalo) field and fit with function 'func' and starting parameter 'p0'
'''
xdata = X.flatten()
ydata = Y.flatten()
if nonzeroy:
pos = numpy.where(ydata > 0)[0]
if ranzero:
posz = numpy.where(ydata == 0)[0]
posz = numpy.random.permutation(posz)
pos = numpy.concatenate((pos, posz[:int(ranzero * Y.size / 100)]))
ydata = ydata[pos]
xdata = xdata[pos]
if abund:
#xdata = xdata[xdata > 0].flatten()
#ydata = ydata[ydata > 0].flatten()
xdata = numpy.sort(xdata)[::-1]
ydata = numpy.sort(ydata)[::-1]
if lim:
pos = numpy.where(ydata > (lim))[0]
ydata = ydata[pos]
xdata = xdata[pos]
if loglim:
pos = numpy.where(ydata > log10(lim))[0]
ydata = ydata[pos]
xdata = xdata[pos]
if sigma:
sigmaval = ydata.copy()
sigmaval[sigmaval == 0] = 1
poptall, dummy = cf(func, xdata, ydata, p0 = p0, sigma= 1/sigmaval, \
absolute_sigma= absig)
else:
poptall, dummy = cf(func, xdata, ydata, p0=p0)
sigmass = func(X, *poptall)
if retdata:
return sigmass, poptall, xdata, ydata
else:
return sigmass, poptall
def getfit(fn,
guess,
yfnm='align.csv',
xfnm='train_data.csv',
ykey='Align',
xkeys=['df2', 'df3'],
err=False,
bound=[]):
x, y, z = getxyz(yfnm=yfnm, xfnm=xfnm, ykey=ykey, xkeys=xkeys, err=err)
x = x.values
y = y.values
z = z.values
xy = np.row_stack([x, y])
if bound:
fit = cf(fn, xy, z, p0=guess, bounds=bound)
else:
fit = cf(fn, xy, z, p0=guess)
return (fit[0])
def _min_fit(self, Id, V):
"""
Calculates the best linear fit through the Id_saturation regime by
iterating through several potential peaks in the second derivative
"""
_residuals = np.array([])
_fits = np.array([0, 0])
# splines needs to be ascending
if V[2] < V[1]:
V = np.flip(V)
Id = np.flip(Id)
self.quadrant()
if self.quad == 'I': # top right
Id = np.flip(Id)
V = np.flip(-V)
mx_d2 = self._find_peak(Id * 1000,
V) # *1000 improves numerical spline accuracy
# sometimes for very small currents run into numerical issues
if not mx_d2:
mx_d2 = self._find_peak(Id * 1000, V, width=15)
# for each peak found, fits a line. Uses that to determine Vt, then residual up to that found Vt
for m in mx_d2:
# Id = Id - np.min(Id) # 0-offset
fit, _ = cf(self.line_f,
V[:m],
Id[:m],
bounds=([-np.inf, -np.inf], [0, np.inf]))
v_x = np.searchsorted(
V, -fit[1] /
fit[0]) # finds the Vt from this fit to determine residual
_res = np.sum(
np.array((Id[:v_x] - self.line_f(V[:v_x], fit[0], fit[1]))**2))
_fits = np.vstack((_fits, fit))
_residuals = np.append(_residuals, _res)
_fits = _fits[1:, :]
fit = _fits[np.argmin(_residuals), :]
if self.quad == 'I':
fit[0] *= -1
return fit
def fitBrightnessSDev(img, m, b, offset, starX, starY, starR, gX, gY, gR, hotX, hotY, trailSize):
parDist,perpDist = GT.getDistancesHorizontal(m, b, img.shape[1], img.shape[0], offset)
parDistF,perpDistF,imgF = getTrailBand(parDist, perpDist, img, trailSize)
x,y = GT.getXY(parDistF,perpDistF,m,b,offset)
mask = getValueMask(img, x, y, starX, starY, starR, gX, gY, gR, hotX, hotY, 1)
par = parDistF[mask]
perp = perpDistF[mask]
band = imgF[mask]
b1, b2, b3, b4, b5, sDev = cf(GT.gaussian2, [par, perp], band, bounds = ([-math.inf,-math.inf,-math.inf,-math.inf,-math.inf,0],[math.inf,math.inf,math.inf,math.inf,math.inf,trailSize]))[0]
return [np.poly1d([b1, b2, b3, b4, b5]), sDev]
def FitToDoubleGaussian(self):
"""
Fits the projected spectrum with a double gaussian
"""
if self.ok==1:
# Ok if we managed to do a guess on the fit parameters
self.x=np.arange(0,len(self.wf))
try:
self.fitresults,self.fitcov = cf(UXSDataPreProcessing.DoubleGaussianFunction,self.x+self.rangelim[0],self.wf,self.initparams)
#widths always positive
self.fitresults[2::3]=abs(self.fitresults[2::3])
except:
warnings.warn_explicit('Fit failed',UserWarning,'UXS',0)
def fit(x, y, error):
'''
Fits the data you give to it to the function you have previously defined
Arguments:
x, data fos the x axis
y, data for the y axis
error, relative error for the variable in the y axis
Return:
popt, slope of the fit
uncertainty for the slope
'''
popt, pcov = cf(function, x, y, sigma=error)
return popt, np.sqrt(np.diag(pcov))
def main():
streets_away = [0]
streets_to_check = [0]
check_time = [0]
walk_time = [0]
lines = 0
drive_time_per_street = 15 # s
walk_time_per_street = 90 # s
for i in range(7):
print(
f'{streets_away[-1]} streets away, {streets_to_check[-1]} streets to check, '
f'{streets_to_check[-1] * drive_time_per_street}s check time')
streets_to_check.append(streets_to_check[-1] + 4 * new_lines(lines))
check_time.append(streets_to_check[-1] * drive_time_per_street / 2 /
60) # in minutes
streets_away.append(streets_away[-1] + 1)
walk_time.append(streets_away[-1] * walk_time_per_street /
60) # in minutes
lines += 2
popt, pcov = cf(poly_2, streets_away, streets_to_check)
print(popt)
popt, pcov = cf(poly_2, streets_away, check_time)
print(popt)
fig, ax1 = plt.subplots()
ax1.plot(streets_away[1:], check_time[1:], 'bo')
x_plot = np.linspace(1, 7, 1000)
ax1.plot(x_plot,
poly_2(x_plot, *popt),
'r',
label='Average Time to Find Car')
ax1.set_xlabel('Distance of Car from Apartment (Blocks)')
ax1.set_ylabel('Time to Car (Minutes)')
ax1.plot(streets_away[1:], walk_time[1:], 'g', label='Time to Walk to Car')
plt.title('Average Time to Find Car Via Grid Search')
ax1.grid()
ax1.legend()
plt.show()
print('donzo')
def fit(data, guess, index):
params, cov = cf(function,
data[1, :],
data[0, :],
sigma=0.01 * np.ones(len(data[1, :])),
p0=guess,
maxfev=10**5)
residuals = data[0, :] - function(data[1, :], *params)
global Params
Params[index] = list(params[0:2])
return residuals
def stellar_relation():
x1 = 10**15 * 1.6
x2 = 10**12 * 4
y1 = x1 * 1.5 * 10**-3
y2 = x2 * 3.2 * 10**-2
line1, dummy = cf(line, numpy.array([log10(x1), log10(x2)]),
numpy.array([log10(y1), log10(y2)]))
y1 = x1 * 3.5 * 10**-4
y2 = x2 * 2.2 * 10**-2
line2, dummy = cf(line, numpy.array([log10(x1), log10(x2)]),
numpy.array([log10(y1), log10(y2)]))
#mean line
m = (line1[0] + line2[0]) * 0.5
c = (line1[1] + line2[1]) * 0.5
xval = numpy.linspace(log10(x2), log10(x1))
xline = line(xval, m, c)
stellar_sigma = interpolate(
xline, 0.01 + (line(xval, line1[0], line1[1]) - xline))
return stellar_sigma, m, c
def fit(filename, debye_T, approx=False, dims=False):
header, data = read(filename)
max_T = 15
data = data[data[:, 0] < max_T]
if not approx:
if dims:
popt, pcov = cf(debye_ndim, data[:,0], data[:, 1], bounds=(([55, 0, 1/2],[65,np.inf,4])))
else:
popt, pcov = cf(debye, data[:,0], data[:, 1], bounds=(([55, 0],[65,np.inf])))
else:
popt, pcov = cf(low_T_approx, data[:,0], data[:, 1], p0=[150, 10E-3])
fig, ax = plt.subplots()
if not approx:
if dims:
ax.plot(data[:,0], debye_ndim(data[:, 0], *popt),label=r"$T_D$" + f"={popt[0]:.1f} K\nA={popt[1]:.1e}\nn={popt[2]:.1f}")
else:
ax.plot(data[:,0], debye(data[:, 0], *popt),label=r"$T_D$" + f"={popt[0]:.1f} K\nA={popt[1]:.1e}")
else:
ax.plot(data[:,0], low_T_approx(data[:, 0], *popt),label=f"A={popt[0]:.3e}; B={popt[1]:.3e}")
ax.plot(data[:,0], data[:,1], label="raw")
ax.legend()
plt.savefig(P(filename).parent.joinpath('fit_to_0T.png'),dpi=300)
# ax.set_yscale('log')
figg, axx = plt.subplots()
for field in [0, 1, 3, 6, 9]:
_, data = read(f"/Users/Brad/Library/Containers/com.eltima.cloudmounter.mas/Data/.CMVolumes/Brad Price/Research/Data/2021/04/1/data_{field}T.dat")
data = data[data[:, 0] < max_T]
if not approx:
if dims:
plt.plot(data[:, 0], data[:, 1] - debye_ndim(data[:, 0], *popt), label=f"{field} T")
else:
plt.plot(data[:, 0], data[:, 1] - debye(data[:, 0], *popt), label=f"{field} T")
else:
plt.plot(data[:, 0], data[:, 1] - low_T_approx(data[:, 0], *popt), label=f"{field} T")
axx.legend()
plt.savefig(P(filename).parent.joinpath('all_fields_subtract_0T_fit.png'),dpi=300)
plt.show()
def fit(data, guess, neg, address):
params, cov = cf(linear,
data[1, :],
data[0, :],
sigma=0.01 * np.ones(len(data[1, :])),
p0=guess,
maxfev=10**5)
logfieldfit = np.linspace(min(data[1, :]), max(data[1, :]),
len(data[1, :]) * 10)
logrfit = linear(logfieldfit, *params)
plt.scatter(data[1, :], data[0, :], marker='.', label="Measured Data")
plt.plot(logfieldfit,
logrfit,
marker="",
linestyle="-",
linewidth=1,
color="r",
label="Initial Guess")
plt.xlabel('Log(B-Field)')
plt.ylabel('Log(Rxx)')
if address in [-2., -1., -0.5, 0.5, 1., 2., -10.]:
plt.title("Power {} Linearity Fitted Guess".format(address))
elif address == 'LogLogThickness':
plt.title('Log-Log Fitted Guess of Slope versus Thickness')
print('\nSaving plot 2 for Slope vs. Thickness')
else:
plt.title(address[90:99] + " Rxx Log-Log Fitted Guess")
print('\nSaving plot 2 for ' + address[90:99])
plt.legend(loc='best', numpoints=1)
if neg:
address1 = address[:90] + "Graphs/" + address[
90:99] + "_LogLog_Fitted_Neg" + ".png"
elif address in [-2., -1., -0.5, 0.5, 1., 2., -10.]:
address1 = "C:/Users/ryank/Desktop/Personal Files/Github/PythonCodes/EP3/Mobility and Carrier Density/Graphs/" \
"/LogLogs/Thickness/GraphFit{}.png".format(address)
elif address == 'LogLogThickness':
address1 = "C:/Users/ryank/Desktop/Personal Files/Github/PythonCodes/EP3/Mobility and Carrier Density/Graphs/" \
"LogLogThicknessFitted.png"
else:
address1 = address[:90] + "Graphs/LogLogs/" + address[
90:99] + "_LogLog_Fitted_Pos" + ".png"
plt.savefig(address1)
plt.clf()
return residual(data, params, neg, address)
def curve_fit(fit_eqn, X, Y, p0=None, sigma=None, absolute_sigma=False, plot=False, on_figs=None, **kw):
"""
Fit the two equal length arrays to a certain function Y = f(X).
Parameters
----------
X: array
Y: array
plot: bool
plot figures or not. Default to False.
on_figs: list/int
the current figure numbers to plot to, default to new figures
Returns
-------
a dict, containing
'params': fitting parameters
'r_squared': value for evaluating error
'fitted_data': a dict that has 2D array of fitted data
easily to Pandas DataFrame by pd.DataFrame(**returned_dict['fitted_data'])
'ax': the axes reference, if return_refs == True
"""
X = np.array(X)
Y = np.array(Y)
popt, pcov = cf(fit_eqn, X, Y, p0, sigma, absolute_sigma, **kw)
X_fit = np.linspace(sorted(X)[0], sorted(X)[-1], 1000)
Y_fit = fit_eqn(X_fit, *popt)
Y_fit_eqlen = fit_eqn(X, *popt)
r_squared = get_r_squared(Y, Y_fit_eqlen)
data = np.column_stack((X_fit, Y_fit))
col_names = ['X_fit', 'Y_fit']
return_dict = {'params': popt, 'r_squared': r_squared,
'fitted_data': {'columns': col_names, 'data': data}}
if plot:
initiate_figs(on_figs)
plt.plot(X, Y, 'o')
plt.plot(X_fit, Y_fit, '-')
axes = {'ax': plt.gca()}
plt.xlabel('X')
plt.ylabel('Y')
plt.tight_layout()
return_dict.update(axes)
return return_dict
def updateFit(self):
data = np.array(self.settings["saveData"])
fitX = data[:, 0]
fitY = data[:, 1]
fitY = fitY / fitY.max()
self.curveData.setData(fitX, fitY)
try:
p, pcov = cf(minir, fitX, fitY, p0=[22, 5, 0.1])
except TypeError:
return
angles = np.linspace(0, 90, 500)
fit = minir(angles, *p)
self.curveFit.setData(angles, fit)
self.textFit.setText("A={:.3f}, mu=\n {:.3f}, c={:.3f}".format(*p),
color=(0, 0, 0))
def gk_plot(name, winkel, gk, funktion, korr, fitgrenzen):
params, errors = cf(funktion,
np.cos(inrad(winkel[fitgrenzen[0]:fitgrenzen[1]]))**2,
noms(gk[fitgrenzen[0]:fitgrenzen[1]]))
g_plot = np.linspace(0, 1)
plt.errorbar(np.cos(inrad(winkel))**2,
noms(gk) * 1e10,
xerr=korr(winkel),
yerr=stds(gk) * 1e10,
fmt='x',
label=r'Messwert')
plt.plot(g_plot, funktion(g_plot, *params) * 1e10, label=r'Fit')
plt.xlabel(r'$\cos^2\left(\theta\right)$')
plt.ylabel(r'$a \:/\: \si{\angstrom}$')
plt.legend(loc='best')
plt.tight_layout()
plt.savefig("build/plot_" + name + ".pdf")
plt.close()
return (unp.uarray(params[1], np.sqrt(np.diag(errors)[1])))
def fit(data, guess, neg, address):
params, cov = cf(parabolicfunc, data[1, :], data[0, :], sigma=0.01 * np.ones(len(data[1, :])),
p0=guess, maxfev=10 ** 5)
chi2 = chisquared(params, data[1, :], data[0, :])
dof = len(data[1, :]) - len(params)
cov = cov * dof / chi2
paramserr = np.sqrt(np.diag(cov))
fieldfit = np.linspace(min(data[1, :]), max(data[1, :]), len(data[1, :]) * 10)
rfit = parabolicfunc(fieldfit, *params)
print('\nShowing plot 2 for ' + address[90:98])
plt.scatter(data[1, :], data[0, :], marker='.', label="Measured Data")
plt.plot(fieldfit, rfit, marker="", linestyle="-", linewidth=1, color="r", label="Initial Guess")
plt.xlabel('B-Field')
plt.ylabel('Rxx')
plt.title(address[90:98] + " Rxx Linearity Fitted Guess")
plt.legend(loc='best', numpoints=1)
plt.show()
plt.clf()
return residual(data, params, neg, address)
def fit_CABS_powerlaw(sample_epochs_index, all_index,
sparse_data_averages_nonan, sparse_data_std_nonan,
scale):
def plfunc(x, a, s, b):
x_ = np.ones(x.size) + s * x
return a * np.power(x_, -b)
#end
import warnings
warnings.simplefilter("ignore")
pfit, _ = cf(plfunc,
sample_epochs_index,
sparse_data_averages_nonan,
p0=[1., 1., 1.],
maxfev=2000)
residuals = sparse_data_averages_nonan - plfunc(sample_epochs_index, *pfit)
squared_res = np.sum(np.power(residuals, 2))
sum_tot_squares = np.sum(
(sparse_data_averages_nonan - np.mean(sparse_data_averages_nonan))**2)
r_squared = 1 - (squared_res / sum_tot_squares)
all_data = plfunc(all_index, *pfit)
scatterplot(all_index,
all_data,
sample_epochs_index,
sparse_data_averages_nonan,
sparse_data_std_nonan,
pfit,
scale,
tag='CABS',
rsquare=r_squared)
return pfit
#end
def estimateCaDecayKinetics(time, signals, p0 = None, thr = 2, preTime = 10,
postTime = 40):
"""
Given a time vector and Ca signal matrix of shape = (C,T), where
C = # of cells, and T = # of time points (must match length of time
vector), returns output of shape = (nSamples, 2), where the 1st and
2nd columns contain the fast and slow decay tau estimates after
fitting Ca2+ signals with double exponential
Parameters:
time - Time vector of length T
signals - Ca signals array of shape (nSamples,T)
p0 - Array-like, (tau_fast, tau_slow, wt_fast), where tau_fast is the
fast decay time constant (in sec), tau_slow is the slow decay
constant, and wt_fast is the weight of the fast exponential (<1)
for fitting the signal as a weighted sum of the fast and slow
exponential. Default is None, in which case fitting optimization
begins without initial estimate
thr - Threshold for peak detection in Ca signals, in units of zscore
preTime - Pre-peak time length of the Ca signals to include for segmentation
postTime - Post-peak " " " "
Avinash Pujala, JRC, 2017
"""
import numpy as np
from scipy.optimize import curve_fit as cf
import apCode.SignalProcessingTools as spt
import apCode.AnalyzeEphysData as aed
def doubleExp(time, tau1, tau2, wt1):
wt2 = 1-wt1
time = time - time[0]
e = wt1*np.exp(-time/tau1) + wt2*np.exp(-time/tau2)
return e
def listToArray(x):
lens = [len(item) for item in x]
lenOfLens = len(lens)
lens = lens[np.min((lenOfLens-1,2))]
a = np.zeros((len(x),lens))
delInds = []
for itemNum,item in enumerate(x):
if len(item) == lens:
a[itemNum,:] = item
else:
delInds.append(itemNum)
a = np.delete(a,delInds,axis = 0)
return a, delInds
if np.ndim(signals)==1:
signals = np.reshape(signals,(1,len(signals)))
dt = time[2]-time[1]
pts_post = np.round(postTime/dt).astype(int)
pts_pre = np.round(preTime/dt).astype(int)
x_norm = spt.zscore(signals,axis = 1)
x_seg, params, x_seg_fit = [],[],[]
nSamples = np.shape(signals)[0]
excludedSamples = np.zeros((nSamples,1))
for nSample in np.arange(nSamples):
inds_pk = spt.findPeaks(x_norm[nSample,:],thr = thr,ampType = 'rel')[0]
if len(inds_pk)==0:
print('Peak detection failed for sample #', nSample, '. Try lowering threshold')
excludedSamples[nSample] = 1
else:
blah = aed.SegmentDataByEvents(signals[nSample,:],inds_pk,pts_pre,pts_post,axis = 0)
blah = listToArray(blah)[0]
blah = np.mean(blah,axis=0)
x_seg.append(blah)
ind_max = np.where(blah == np.max(blah))[0][0]
y = spt.standardize(blah[ind_max:])
t = np.arange(len(y))*dt
popt,pcov = cf(doubleExp,t,y,p0 = [10,20, 0.5], bounds = (0,20))
if popt[0]> popt[1]:
popt[0:2] = popt[2:0:-1]
popt[-1] = 1-popt[-1]
params.append(popt)
foo = doubleExp(t,popt[0],popt[1],popt[2])
x_seg_fit.append(foo)
excludedSamples = np.where(excludedSamples)[0]
includedSamples = np.setdiff1d(np.arange(nSamples),excludedSamples)
x_seg,delInds = listToArray(x_seg)
params = np.delete(np.array(params),delInds,axis = 0)
delInds = includedSamples[delInds]
if len(delInds)>0:
print('Sample #', delInds, 'excluded for short segment length. Consider decreasing pre-peak time length')
excludedSamples = np.union1d(delInds,excludedSamples)
x_seg = spt.standardize(np.array(x_seg),axis = 1)
x_seg_fit = np.array(listToArray(x_seg_fit)[0])
out = {'raw': x_seg,'fit': x_seg_fit,'params': np.array(params),'excludedSamples': excludedSamples}
return out
interpArduinoTime = interp(dylosTime, arduinoTime, arduinoTime)#arduinoData['1um'])
interpArduinoP1Ratio = interp(dylosTime, arduinoTime, rawRollingArduinoP1Ratio)
interpArduinoP2Ratio = interp(dylosTime, arduinoTime, rawRollingArduinoP2Ratio)
rollingArduinoP1Ratio = pd.rolling_mean(np.array(interpArduinoP1Ratio), 20)
rollingArduinoP2Ratio = pd.rolling_mean(np.array(interpArduinoP2Ratio), 20)
### fitting and plotting
xData = interpArduinoP1Ratio
yData = dylosData['1um']
# fitting data
# linear, assumes intercept is 0
fitLineX = np.linspace(min(xData), max(xData), 1000)
linearpopt, linearpcov = cf(linearfunc, xData, yData)
print 'linear: ',linearpopt
fitLineYlinear = linearfunc(fitLineX, linearpopt[0])
# 2nd degree
fitLineX = np.linspace(min(xData), max(xData), 1000)
deg2popt, deg2pcov = cf(deg2func, xData, yData)
print '2nd degree: ', deg2popt
fitLineY2nd = deg2func(fitLineX, deg2popt[0], deg2popt[1], deg2popt[2])
# plotting
plt.scatter(xData, yData)
plt.plot(fitLineX, fitLineYlinear, linewidth=3, label='linear')
plt.plot(fitLineX, fitLineY2nd, linewidth=3, label='2nd degree')
plt.legend()
plt.xlabel('DSM501A P1 ratio')
with open('build/delta_f.tex', 'w') as f:
f.write(r'\SI{{{:L}}}{{\kilo\hertz}}'.format(delta_f / 1e3))
with open('build/m.tex', 'w') as f:
f.write(r'\num{{{:L}}}'.format(m))
# Teil e)
# Abhängigkeit phase-Spannung
T, U = np.genfromtxt('am-demodulation-e.txt', unpack=True)
# fit
def func(x, a, b, c, d):
""" Simple cosine function
"""
return a * np.cos(b * x + c) + d
popt, pocov = cf(func, T, U, p0=[150, 0.01, -1, 0])
plt.plot(T, U, 'r+', label='Messpunkte')
# plt.errorbar(T, U, yerr=0.1, label='Messpunkte', fmt='r+')
ts = np.linspace(np.amin(T), np.amax(T), 200)
plt.plot(ts, func(ts, *popt), label='Fit')
plt.xlabel(r'$T/\mathrm{ns}$')
plt.xlim(-5, 95)
plt.ylabel(r'$U/\mathrm{mV}$')
plt.legend(loc='best')
plt.savefig('build/demodulation-cosinus.pdf')
plt.clf()
def eos_fit(V, Y, eos='birch_murnaghan', B0_prime=None, plot=False, on_figs=None):
"""
Fit the volume and total energy, or pressure to the Birch-Murnaghan equation of state.
Note: bulk modulus B0 will be returned in the unit of GPa.
Parameters
----------
V: array
volume (Angstrom^3)
Y: array
total energy (eV), or pressure (GPa) if eos has '_p'
eos: string
chosen from ['birch_murnaghan', 'vinet']. Default to 'birch_murnaghan'
B0_prime: float
Keep B0_prime fixed to a given value or not. Default to None
plot: bool
whether to plot the data, default to False.
on_figs: list/int
the current figure numbers to plot to, default to new figures
Returns
-------
a dict, containing
'params': fitting parameters
'r_squared': value for evaluating error
'fitted_data': a dict that has 2D array of fitted data
easily to Pandas DataFrame by pd.DataFrame(**returned_dict['fitted_data'])
"""
V = np.array(V)
Y = np.array(Y)
if not B0_prime:
if '_p' not in eos:
initial_parameters = [V.mean(), 2.5, 4, Y.mean()]
fit_eqn = eval(eos)
else:
initial_parameters = [V.mean(), 2.5, 4]
fit_eqn = eval(eos)
else:
if '_p' not in eos:
initial_parameters = [V.mean(), 2.5, Y.mean()]
fit_eqn = fix_B0_prime(eval(eos), B0_prime)
else:
initial_parameters = [V.mean(), 2.5]
fit_eqn = fix_B0_prime(eval(eos), B0_prime)
popt, pcov = cf(fit_eqn, V, Y, initial_parameters)
V_fit = np.linspace(sorted(V)[0], sorted(V)[-1], 1000)
Y_fit = fit_eqn(V_fit, *popt)
Y_fit_eqlen = fit_eqn(V, *popt)
r_squared = get_r_squared(Y, Y_fit_eqlen)
data = np.column_stack((V_fit, Y_fit))
if '_p' not in eos:
col_names = ['V_fit', 'E_fit']
else:
col_names = ['V_fit', 'p_fit']
params = {'V0': popt[0], 'B0': popt[1] * 160.2}
if not B0_prime:
params['B0_prime'] = popt[2]
if '_p' not in eos:
params['E0'] = popt[3]
else:
if '_p' not in eos:
params['E0'] = popt[2]
return_dict = {'params': params, 'r_squared': r_squared,
'fitted_data': {'columns': col_names, 'data': data}}
if plot:
initiate_figs(on_figs)
plt.plot(V, Y, 'o')
plt.plot(V_fit, Y_fit, '-')
axes = {'ax': plt.gca()}
plt.xlabel(r'V ($\AA^{3}$)')
if '_p' not in eos:
plt.ylabel('E (eV)')
else:
plt.ylabel('P (GPa)')
plt.tight_layout()
return_dict.update(axes)
return return_dict
arduino1umData.append(interpArduinoData[each]*2.5)
arduinoP1ratio.append(interpArduinoRatio[each + mvaperiod/2])
rollingP1ratio = pd.rolling_mean(np.array(arduinoP1ratio),20)
for each in range(len(rollingP1ratio)):
if np.isnan(rollingP1ratio[each]):
rollingP1ratio[each] = arduinoP1ratio[each]
print arduinoP1ratio[each]
P1fit = np.polyfit(rollingP1ratio, dylos1umData, deg=4)
P1corr = np.poly1d(P1fit)
minRatio = min(rollingP1ratio)
maxRatio = max(rollingP1ratio)
fitLineX = np.linspace(minRatio, maxRatio, 1000)
fitLineY = P1corr(fitLineX)
print '4th order:',P1fit
popt, pcov = cf(func, rollingP1ratio, dylos1umData)
print '3rd order 0-intercept:',popt
fitLineY2 = func(fitLineX, popt[0], popt[1], popt[2])
popt3, pcov3 = cf(expfunc, rollingP1ratio, dylos1umData)
print 'exponential:',popt3
fitLineY3 = expfunc(fitLineX, popt3[0], popt3[1])
linearpopt, linearpcov = cf(linearfunc, rollingP1ratio, dylos1umData)
print 'linear:',linearpopt
fitLineYlinear = linearfunc(fitLineX, linearpopt[0])
allData = {}
allData['time'] = interpTimes
allData['dylos data'] = dylos1umData
allData['arduino data'] = arduino1umData
