def asymptotic_pdf(t, tres, tau, area):
"""
Calculate asymptotic probabolity density function.
Parameters
----------
t : ndarray.
Time.
tres : float
Time resolution.
tau : ndarray, shape(k, 1)
Time constants.
area : ndarray, shape(k, 1)
Component relative area.
Returns
-------
apdf : ndarray.
"""
t1 = np.extract(t[:] < tres, t)
t2 = np.extract(t[:] >= tres, t)
apdf2 = t2 * pdfs.expPDF(t2 - tres, tau, area)
apdf = np.append(t1 * 0.0, apdf2)
return apdf
def exact_pdf(t, tres, roots, areas, eigvals, gamma00, gamma10, gamma11):
r"""
Calculate exponential probabolity density function with exact solution for
missed events correction (Eq. 21, HJC92).
.. math::
:nowrap:
\begin{align*}
f(t) =
\begin{cases}
f_0(t) & \text{for}\; 0 \leq t \leq t_\text{res} \\
f_0(t) - f_1(t - t_\text{res}) & \text{for}\; t_\text{res} \leq t \leq 2 t_\text{res}
\end{cases}
\end{align*}
Parameters
----------
t : float
Time.
tres : float
Time resolution (dead time).
roots : array_like, shape (k,)
areas : array_like, shape (k,)
eigvals : array_like, shape (k,)
Eigenvalues of -Q matrix.
gama00, gama10, gama11 : lists of floats
Coeficients for the exact open/shut time pdf.
Returns
-------
f : float
"""
if t < tres:
f = 0
elif ((tres < t) and (t < (2 * tres))):
f = qml.f0((t - tres), eigvals, gamma00)
elif ((tres * 2) < t) and (t < (3 * tres)):
f = (qml.f0((t - tres), eigvals, gamma00) -
qml.f1((t - 2 * tres), eigvals, gamma10, gamma11))
else:
f = pdfs.expPDF(t - tres, -1 / roots, areas)
return f
