def test_logistic_and_linear_function(self):
x_data = np.arange(-10, 10, 0.1)
_ = logistic(x_data, x0=0, alpha=1)
self.assertTrue(logistic(0, x0=0, alpha=1) == 0.5)
_ = linear_function(x_data, 1, 2)
self.assertTrue(linear_function(0, 1, 2) == 2)
self.assertTrue(linear_function(3, 1, 2) == 5)
def test_initial_estimate_fermi_linear(self, fig=None):
expected_parameters = [0.01000295, 0.51806569, -4.88800525, 0.12838861, 0.25382811]
x_data = np.arange(-20, 10, 0.1)
y_data = FermiLinear(x_data, *expected_parameters)
y_data += 0.005 * np.random.rand(y_data.size)
linear_part, fermi_part = initFermiLinear(x_data, y_data, fig=fig)
ylin = linear_function(x_data, *linear_part)
yr = y_data - ylin
cc, A = _estimate_fermi_model_center_amplitude(x_data, yr, fig=fig)
np.testing.assert_almost_equal(cc, expected_parameters[2], decimal=1)
np.testing.assert_almost_equal(A, expected_parameters[3], decimal=1)
self.assertTrue(fermi_part is not None)
plt.close('all')
def initFermiLinear(x_data, y_data, fig=None):
""" Initialization of fitting a FermiLinear function.
First the linear part is estimated, then the Fermi part of the function.
Args:
x_data (array): data for independent variable
y_data (array): dependent variable
fig (int) : figure number
Returns:
linear_part (array)
fermi_part (array)
"""
xdata = np.array(x_data)
ydata = np.array(y_data)
n = xdata.size
nx = int(np.ceil(n / 5))
if nx < 4:
p1, _ = scipy.optimize.curve_fit(linear_function,
np.array(xdata[0:100]),
np.array(ydata[0:100]))
a = p1[0]
b = p1[1]
linear_part = [a, b]
ylin = linear_function(xdata, linear_part[0], linear_part[1])
cc = np.mean(xdata)
A = 0
T = np.std(xdata) / 10
fermi_part = [cc, A, T]
else:
# guess initial linear part
mx = np.mean(xdata)
my = np.mean(ydata)
dx = np.hstack((np.diff(xdata[0:nx]), np.diff(xdata[-nx:])))
dx = np.mean(dx)
dd = np.hstack((np.diff(ydata[0:nx]), np.diff(ydata[-nx:])))
dd = np.convolve(dd, np.array([1., 1, 1]) / 3) # smooth
if dd.size > 15:
dd = np.array(sorted(dd))
w = int(dd.size / 10)
a = np.mean(dd[w:-w]) / dx
else:
a = np.mean(dd) / dx
b = my - a * mx
linear_part = [a, b]
ylin = linear_function(xdata, *linear_part)
# subtract linear part
yr = ydata - ylin
cc, A = _estimate_fermi_model_center_amplitude(xdata, yr)
T = np.std(xdata) / 100
linear_part[1] = linear_part[1] - A / 2 # correction
fermi_part = [cc, A, T]
yr = ydata - linear_function(xdata, *linear_part)
if fig is not None:
yf = FermiLinear(xdata, *linear_part, *fermi_part)
xx = np.hstack((xdata[0:nx], xdata[-nx:]))
yy = np.hstack((ydata[0:nx], ydata[-nx:]))
plt.figure(fig)
plt.clf()
plt.plot(xdata, ydata, '.b', label='raw data')
plt.plot(xx, yy, 'ok')
qtt.pgeometry.plot2Dline([-1, 0, cc], ':c', label='center')
plt.plot(xdata, ylin, '-c', alpha=.5, label='fitted linear function')
plt.plot(xdata, yf, '-m', label='fitted FermiLinear function')
plt.title('initFermiLinear', fontsize=12)
plt.legend(numpoints=1)
plt.figure(fig + 1)
plt.clf()
# TODO: When nx < 4 and fig is not None -> yr is undefined
plt.plot(xdata, yr, '.b', label='Fermi part')
fermi_part_values = Fermi(xdata, cc, A, T)
plt.plot(xdata, fermi_part_values, '-m', label='initial estimate')
plt.legend()
return linear_part, fermi_part
def initFermiLinear(x_data, y_data, fig=None):
""" Initalization of fitting a FermiLinear function.
First the linear part is estimated, then the Fermi part of the function.
"""
xdata = np.array(x_data)
ydata = np.array(y_data)
n = xdata.size
nx = int(np.ceil(n / 5))
if nx < 4:
p1, _ = scipy.optimize.curve_fit(linear_function, np.array(xdata[0:100]),
np.array(ydata[0:100]))
a = p1[0]
b = p1[1]
ab = [a, b]
y = linear_function(xdata, ab[0], ab[1])
cc = np.mean(xdata)
A = 0
T = np.std(xdata) / 10
ff = [cc, A, T]
else:
# guess initial linear part
mx = np.mean(xdata)
my = np.mean(ydata)
dx = np.hstack((np.diff(xdata[0:nx]), np.diff(xdata[-nx:])))
dx = np.mean(dx)
dd = np.hstack((np.diff(ydata[0:nx]), np.diff(ydata[-nx:])))
dd = np.convolve(dd, np.array([1., 1, 1]) / 3) # smooth
if dd.size > 15:
dd = np.array(sorted(dd))
w = int(dd.size / 10)
a = np.mean(dd[w:-w]) / dx
else:
a = np.mean(dd) / dx
b = my - a * mx
xx = np.hstack((xdata[0:nx], xdata[-nx:]))
ab = [a, b]
y = linear_function(xdata, ab[0], ab[1])
# subtract linear part
yr = ydata - y
cc = np.mean(xdata)
h = int(xdata.size / 2)
A = -(np.mean(yr[h:]) - np.mean(yr[:h]))
T = np.std(xdata) / 10
ab[1] = ab[1] - A / 2 # correction
ylin = linear_function(xdata, ab[0], ab[1])
# subtract linear part
yr = ydata - ylin
ff = [cc, A, T]
if fig is not None:
yf = FermiLinear(xdata, ab[0], ab[1], *ff)
xx = np.hstack((xdata[0:nx], xdata[-nx:]))
yy = np.hstack((ydata[0:nx], ydata[-nx:]))
plt.figure(fig)
plt.clf()
plt.plot(xdata, ydata, '.b', label='raw data')
plt.plot(xx, yy, 'ok')
qtt.pgeometry.plot2Dline([-1, 0, cc], ':c', label='center')
plt.plot(xdata, ylin, '-m', label='fitted linear function')
plt.plot(xdata, yf, '-m', label='fitted FermiLinear function')
plt.title('initFermiLinear', fontsize=12)
plt.legend(numpoints=1)
plt.figure(fig + 1)
plt.clf()
plt.plot(xdata, yr, '.b', label='Fermi part')
f = Fermi(xdata, cc, A, T)
plt.plot(xdata, f, '-m', label='estimated')
plt.plot(xdata, f, '-m', label='estimated')
# plt.plot(xdata, yr, '.b', label='Fermi part')
plt.legend()
return ab, ff
