def asymptotic_areas(tres, roots, QAA, QFF, QAF, QFA, kA, kF, GAF, GFA):
"""
Find the areas of the asymptotic pdf (Eq. 58, HJC92).
Parameters
----------
tres : float
Time resolution (dead time).
roots : array_like, shape (1,kA)
Roots of the asymptotic pdf.
QAA : array_like, shape (kA, kA)
QFF : array_like, shape (kF, kF)
QAF : array_like, shape (kA, kF)
QFA : array_like, shape (kF, kA)
QAA, QFF, QAF, QFA - submatrices of Q.
kA : int
A number of open states in kinetic scheme.
kF : int
A number of shut states in kinetic scheme.
GAF : array_like, shape (kA, kB)
GFA : array_like, shape (kB, kA)
GAF, GFA- transition probabilities
Returns
-------
areas : ndarray, shape (1, kA)
"""
expQFF = qml.expQt(QFF, tres)
expQAA = qml.expQt(QAA, tres)
eGAF = qml.eGs(GAF, GFA, kA, kF, expQFF)
eGFA = qml.eGs(GFA, GAF, kF, kA, expQAA)
phiA = qml.phiHJC(eGAF, eGFA, kA)
R = qml.AR(roots, tres, QAA, QFF, QAF, QFA, kA, kF)
uF = np.ones((kF, 1))
areas = np.zeros(kA)
for i in range(kA):
areas[i] = (
(-1 / roots[i]) *
np.dot(phiA, np.dot(np.dot(R[i], np.dot(QAF, expQFF)), uF)))
# rowA = np.zeros((kA,kA))
# colA = np.zeros((kA,kA))
# for i in range(kA):
# WA = qml.W(roots[i], tres,
# QAA, QFF, QAF, QFA, kA, kF)
# rowA[i] = qml.pinf(WA)
# AW = np.transpose(WA)
# colA[i] = qml.pinf(AW)
#
# for i in range(kA):
# uF = np.ones((kF,1))
# nom = np.dot(np.dot(np.dot(np.dot(np.dot(phiA, colA[i]), rowA[i]),
# QAF), expQFF), uF)
# W1A = qml.dW(roots[i], tres, QAF, QFF, QFA, kA, kF)
# denom = -roots[i] * np.dot(np.dot(rowA[i], W1A), colA[i])
# areas[i] = nom / denom
return areas
def adjacent_open_to_shut_range_mean(u1, u2, QAA, QAF, QFF, QFA, phiA):
"""
Calculate mean (ideal- no missed events) open times adjacent to a
specified shut time range.
Parameters
----------
u1, u2 : floats
Shut time range.
QAA, QAF, QFF, QFA : array_like
Submatrices of Q.
phiA : array_like, shape (1, kA)
Initial vector for openings
Returns
-------
m : float
Mean open time.
"""
kA = QAA.shape[0]
uA = np.ones((kA))[:,np.newaxis]
invQAA, invQFF = -nplin.inv(QAA), nplin.inv(QFF)
expQFFr = qml.expQt(QFF, u2) - qml.expQt(QFF, u1)
col = np.dot(np.dot(np.dot(np.dot(QAF, invQFF), expQFFr), QFA), uA)
row1 = np.dot(phiA, qml.Qpow(invQAA, 2))
row2 = np.dot(phiA, invQAA)
m = np.dot(row1, col)[0, 0] / np.dot(row2, col)[0, 0]
return m
def adjacent_open_to_shut_range_mean(u1, u2, QAA, QAF, QFF, QFA, phiA):
"""
Calculate mean (ideal- no missed events) open times adjacent to a
specified shut time range.
Parameters
----------
u1, u2 : floats
Shut time range.
QAA, QAF, QFF, QFA : array_like
Submatrices of Q.
phiA : array_like, shape (1, kA)
Initial vector for openings
Returns
-------
m : float
Mean open time.
"""
kA = QAA.shape[0]
uA = np.ones((kA))[:, np.newaxis]
invQAA, invQFF = -nplin.inv(QAA), nplin.inv(QFF)
expQFFr = qml.expQt(QFF, u2) - qml.expQt(QFF, u1)
col = np.dot(np.dot(np.dot(np.dot(QAF, invQFF), expQFFr), QFA), uA)
row1 = np.dot(phiA, qml.Qpow(invQAA, 2))
row2 = np.dot(phiA, invQAA)
m = np.dot(row1, col)[0, 0] / np.dot(row2, col)[0, 0]
return m
def asymptotic_areas(tres, roots, QAA, QFF, QAF, QFA, kA, kF, GAF, GFA):
"""
Find the areas of the asymptotic pdf (Eq. 58, HJC92).
Parameters
----------
tres : float
Time resolution (dead time).
roots : array_like, shape (1,kA)
Roots of the asymptotic pdf.
QAA : array_like, shape (kA, kA)
QFF : array_like, shape (kF, kF)
QAF : array_like, shape (kA, kF)
QFA : array_like, shape (kF, kA)
QAA, QFF, QAF, QFA - submatrices of Q.
kA : int
A number of open states in kinetic scheme.
kF : int
A number of shut states in kinetic scheme.
GAF : array_like, shape (kA, kB)
GFA : array_like, shape (kB, kA)
GAF, GFA- transition probabilities
Returns
-------
areas : ndarray, shape (1, kA)
"""
expQFF = qml.expQt(QFF, tres)
expQAA = qml.expQt(QAA, tres)
eGAF = qml.eGs(GAF, GFA, kA, kF, expQFF)
eGFA = qml.eGs(GFA, GAF, kF, kA, expQAA)
phiA = qml.phiHJC(eGAF, eGFA, kA)
R = qml.AR(roots, tres, QAA, QFF, QAF, QFA, kA, kF)
uF = np.ones((kF,1))
areas = np.zeros(kA)
for i in range(kA):
areas[i] = ((-1 / roots[i]) *
np.dot(phiA, np.dot(np.dot(R[i], np.dot(QAF, expQFF)), uF)))
# rowA = np.zeros((kA,kA))
# colA = np.zeros((kA,kA))
# for i in range(kA):
# WA = qml.W(roots[i], tres,
# QAA, QFF, QAF, QFA, kA, kF)
# rowA[i] = qml.pinf(WA)
# AW = np.transpose(WA)
# colA[i] = qml.pinf(AW)
#
# for i in range(kA):
# uF = np.ones((kF,1))
# nom = np.dot(np.dot(np.dot(np.dot(np.dot(phiA, colA[i]), rowA[i]),
# QAF), expQFF), uF)
# W1A = qml.dW(roots[i], tres, QAF, QFF, QFA, kA, kF)
# denom = -roots[i] * np.dot(np.dot(rowA[i], W1A), colA[i])
# areas[i] = nom / denom
return areas
def HJC_adjacent_mean_open_to_shut_time_pdf(sht, tres, Q, QAA, QAF, QFF, QFA):
"""
Calculate theoretical HJC (with missed events correction) mean open time
given previous/next gap length (continuous function; CHS96 Eq.3.5).
Parameters
----------
sht : array of floats
Shut time interval.
tres : float
Time resolution.
Q : array, shape (k,k)
Q matrix.
QAA, QAF, QFF, QFA : array_like
Submatrices of Q.
Returns
-------
mp : ndarray of floats
Mean open time given previous gap length.
mn : ndarray of floats
Mean open time given next gap length.
"""
kA, kF = QAA.shape[0], QFF.shape[0]
uA = np.ones((kA))[:, np.newaxis]
uF = np.ones((kF))[:, np.newaxis]
expQFF = qml.expQt(QFF, tres)
expQAA = qml.expQt(QAA, tres)
GAF, GFA = qml.iGs(Q, kA, kF)
eGAF = qml.eGs(GAF, GFA, kA, kF, expQFF)
eGFA = qml.eGs(GFA, GAF, kF, kA, expQAA)
phiA = qml.phiHJC(eGAF, eGFA, kA)
phiF = qml.phiHJC(eGFA, eGAF, kF)
DARS = qml.dARSdS(tres, QAA, QFF, GAF, GFA, expQFF, kA, kF)
eigs, A = qml.eigs(-Q)
Feigvals, FZ00, FZ10, FZ11 = qml.Zxx(Q, eigs, A, kA, QAA, QFA, QAF, expQAA,
False)
Froots = asymptotic_roots(tres, QFF, QAA, QFA, QAF, kF, kA)
FR = qml.AR(Froots, tres, QFF, QAA, QFA, QAF, kF, kA)
Q1 = np.dot(np.dot(DARS, QAF), expQFF)
col1 = np.dot(Q1, uF)
row1 = np.dot(phiA, Q1)
mp = []
mn = []
for t in sht:
eGFAt = qml.eGAF(t, tres, Feigvals, FZ00, FZ10, FZ11, Froots, FR, QFA,
expQAA)
denom = np.dot(np.dot(phiF, eGFAt), uA)[0]
nom1 = np.dot(np.dot(phiF, eGFAt), col1)[0]
nom2 = np.dot(np.dot(row1, eGFAt), uA)[0]
mp.append(nom1 / denom)
mn.append(nom2 / denom)
return np.array(mp), np.array(mn)
def HJC_adjacent_mean_open_to_shut_time_pdf(sht, tres, Q, QAA, QAF, QFF, QFA):
"""
Calculate theoretical HJC (with missed events correction) mean open time
given previous/next gap length (continuous function; CHS96 Eq.3.5).
Parameters
----------
sht : array of floats
Shut time interval.
tres : float
Time resolution.
Q : array, shape (k,k)
Q matrix.
QAA, QAF, QFF, QFA : array_like
Submatrices of Q.
Returns
-------
mp : ndarray of floats
Mean open time given previous gap length.
mn : ndarray of floats
Mean open time given next gap length.
"""
kA, kF = QAA.shape[0], QFF.shape[0]
uA = np.ones((kA))[:,np.newaxis]
uF = np.ones((kF))[:,np.newaxis]
expQFF = qml.expQt(QFF, tres)
expQAA = qml.expQt(QAA, tres)
GAF, GFA = qml.iGs(Q, kA, kF)
eGAF = qml.eGs(GAF, GFA, kA, kF, expQFF)
eGFA = qml.eGs(GFA, GAF, kF, kA, expQAA)
phiA = qml.phiHJC(eGAF, eGFA, kA)
phiF = qml.phiHJC(eGFA, eGAF, kF)
DARS = qml.dARSdS(tres, QAA, QFF, GAF, GFA, expQFF, kA, kF)
eigs, A = qml.eigs(-Q)
Feigvals, FZ00, FZ10, FZ11 = qml.Zxx(Q, eigs, A, kA, QAA, QFA, QAF, expQAA, False)
Froots = asymptotic_roots(tres, QFF, QAA, QFA, QAF, kF, kA)
FR = qml.AR(Froots, tres, QFF, QAA, QFA, QAF, kF, kA)
Q1 = np.dot(np.dot(DARS, QAF), expQFF)
col1 = np.dot(Q1, uF)
row1 = np.dot(phiA, Q1)
mp = []
mn = []
for t in sht:
eGFAt = qml.eGAF(t, tres, Feigvals, FZ00, FZ10, FZ11, Froots,
FR, QFA, expQAA)
denom = np.dot(np.dot(phiF, eGFAt), uA)[0]
nom1 = np.dot(np.dot(phiF, eGFAt), col1)[0]
nom2 = np.dot(np.dot(row1, eGFAt), uA)[0]
mp.append(nom1 / denom)
mn.append(nom2 / denom)
return np.array(mp), np.array(mn)
def HJC_dependency(top, tsh, tres, Q, QAA, QAF, QFF, QFA):
"""
Calculate normalised joint distribution (CHS96, Eq. 3.22) of an open time
and the following shut time as proposed by Magleby & Song 1992.
Parameters
----------
top, tsh : array_like of floats
Open and shut tims.
tres : float
Time resolution.
Q : array, shape (k,k)
Q matrix.
QAA, QAF, QFF, QFA : array_like
Submatrices of Q.
Returns
-------
dependency : ndarray
"""
kA, kF = QAA.shape[0], QFF.shape[0]
uA = np.ones((kA))[:, np.newaxis]
uF = np.ones((kF))[:, np.newaxis]
expQFF = qml.expQt(QFF, tres)
expQAA = qml.expQt(QAA, tres)
GAF, GFA = qml.iGs(Q, kA, kF)
eGAF = qml.eGs(GAF, GFA, kA, kF, expQFF)
eGFA = qml.eGs(GFA, GAF, kF, kA, expQAA)
phiA = qml.phiHJC(eGAF, eGFA, kA)
phiF = qml.phiHJC(eGFA, eGAF, kF)
eigs, A = qml.eigs(-Q)
Feigvals, FZ00, FZ10, FZ11 = qml.Zxx(Q, eigs, A, kA, QAA, QFA, QAF, expQAA,
False)
Froots = asymptotic_roots(tres, QFF, QAA, QFA, QAF, kF, kA)
FR = qml.AR(Froots, tres, QFF, QAA, QFA, QAF, kF, kA)
Aeigvals, AZ00, AZ10, AZ11 = qml.Zxx(Q, eigs, A, kA, QFF, QAF, QFA, expQFF,
True)
Aroots = asymptotic_roots(tres, QAA, QFF, QAF, QFA, kA, kF)
AR = qml.AR(Aroots, tres, QAA, QFF, QAF, QFA, kA, kF)
dependency = np.zeros((top.shape[0], tsh.shape[0]))
for i in range(top.shape[0]):
eGAFt = qml.eGAF(top[i], tres, Aeigvals, AZ00, AZ10, AZ11, Aroots, AR,
QAF, expQFF)
fo = np.dot(np.dot(phiA, eGAFt), uF)[0]
for j in range(tsh.shape[0]):
eGFAt = qml.eGAF(tsh[j], tres, Feigvals, FZ00, FZ10, FZ11, Froots,
FR, QFA, expQAA)
fs = np.dot(np.dot(phiF, eGFAt), uA)[0]
fos = np.dot(np.dot(np.dot(phiA, eGAFt), eGFAt), uA)[0]
dependency[i, j] = (fos - (fo * fs)) / (fo * fs)
return dependency
def HJC_dependency(top, tsh, tres, Q, QAA, QAF, QFF, QFA):
"""
Calculate normalised joint distribution (CHS96, Eq. 3.22) of an open time
and the following shut time as proposed by Magleby & Song 1992.
Parameters
----------
top, tsh : array_like of floats
Open and shut tims.
tres : float
Time resolution.
Q : array, shape (k,k)
Q matrix.
QAA, QAF, QFF, QFA : array_like
Submatrices of Q.
Returns
-------
dependency : ndarray
"""
kA, kF = QAA.shape[0], QFF.shape[0]
uA = np.ones((kA))[:,np.newaxis]
uF = np.ones((kF))[:,np.newaxis]
expQFF = qml.expQt(QFF, tres)
expQAA = qml.expQt(QAA, tres)
GAF, GFA = qml.iGs(Q, kA, kF)
eGAF = qml.eGs(GAF, GFA, kA, kF, expQFF)
eGFA = qml.eGs(GFA, GAF, kF, kA, expQAA)
phiA = qml.phiHJC(eGAF, eGFA, kA)
phiF = qml.phiHJC(eGFA, eGAF, kF)
eigs, A = qml.eigs(-Q)
Feigvals, FZ00, FZ10, FZ11 = qml.Zxx(Q, eigs, A, kA, QAA, QFA, QAF, expQAA, False)
Froots = asymptotic_roots(tres, QFF, QAA, QFA, QAF, kF, kA)
FR = qml.AR(Froots, tres, QFF, QAA, QFA, QAF, kF, kA)
Aeigvals, AZ00, AZ10, AZ11 = qml.Zxx(Q, eigs, A, kA, QFF, QAF, QFA, expQFF, True)
Aroots = asymptotic_roots(tres, QAA, QFF, QAF, QFA, kA, kF)
AR = qml.AR(Aroots, tres, QAA, QFF, QAF, QFA, kA, kF)
dependency = np.zeros((top.shape[0], tsh.shape[0]))
for i in range(top.shape[0]):
eGAFt = qml.eGAF(top[i], tres, Aeigvals, AZ00, AZ10, AZ11, Aroots,
AR, QAF, expQFF)
fo = np.dot(np.dot(phiA, eGAFt), uF)[0]
for j in range(tsh.shape[0]):
eGFAt = qml.eGAF(tsh[j], tres, Feigvals, FZ00, FZ10, FZ11, Froots,
FR, QFA, expQAA)
fs = np.dot(np.dot(phiF, eGFAt), uA)[0]
fos = np.dot(np.dot(np.dot(phiA, eGAFt), eGFAt), uA)[0]
dependency[i, j] = (fos - (fo * fs)) / (fo * fs)
return dependency
def ideal_dwell_time_pdf(t, QAA, phiA):
"""
Probability density function of the open time.
f(t) = phiOp * exp(-QAA * t) * (-QAA) * uA
For shut time pdf A by F in function call.
Parameters
----------
t : float
Time (sec).
QAA : array_like, shape (kA, kA)
Submatrix of Q.
phiA : array_like, shape (1, kA)
Initial vector for openings
Returns
-------
f : float
"""
kA = QAA.shape[0]
uA = np.ones((kA, 1))
expQAA = qml.expQt(QAA, t)
f = np.dot(np.dot(np.dot(phiA, expQAA), -QAA), uA)
return f
def ideal_dwell_time_pdf(t, QAA, phiA):
"""
Probability density function of the open time.
f(t) = phiOp * exp(-QAA * t) * (-QAA) * uA
For shut time pdf A by F in function call.
Parameters
----------
t : float
Time (sec).
QAA : array_like, shape (kA, kA)
Submatrix of Q.
phiA : array_like, shape (1, kA)
Initial vector for openings
Returns
-------
f : float
"""
kA = QAA.shape[0]
uA = np.ones((kA, 1))
expQAA = qml.expQt(QAA, t)
f = np.dot(np.dot(np.dot(phiA, expQAA), -QAA), uA)
return f
def exact_mean_open_shut_time(mec, tres):
"""
Calculate exact mean open or shut time from HJC probability density
function.
Parameters
----------
tres : float
Time resolution (dead time).
QAA : array_like, shape (kA, kA)
QFF : array_like, shape (kF, kF)
QAF : array_like, shape (kA, kF)
QAA, QFF, QAF - submatrices of Q.
kA : int
A number of open states in kinetic scheme.
kF : int
A number of shut states in kinetic scheme.
GAF : array_like, shape (kA, kB)
GFA : array_like, shape (kB, kA)
GAF, GFA- transition probabilities
Returns
-------
mean : float
Apparent mean open/shut time.
"""
GAF, GFA = qml.iGs(mec.Q, mec.kA, mec.kF)
expQFF = qml.expQt(mec.QFF, tres)
expQAA = qml.expQt(mec.QAA, tres)
eGAF = qml.eGs(GAF, GFA, mec.kA, mec.kF, expQFF)
eGFA = qml.eGs(GFA, GAF, mec.kF, mec.kA, expQAA)
phiA = qml.phiHJC(eGAF, eGFA, mec.kA)
phiF = qml.phiHJC(eGFA, eGAF, mec.kF)
QexpQF = np.dot(mec.QAF, expQFF)
QexpQA = np.dot(mec.QFA, expQAA)
DARS = qml.dARSdS(tres, mec.QAA, mec.QFF, GAF, GFA, expQFF, mec.kA, mec.kF)
DFRS = qml.dARSdS(tres, mec.QFF, mec.QAA, GFA, GAF, expQAA, mec.kF, mec.kA)
uF, uA = np.ones((mec.kF, 1)), np.ones((mec.kA, 1))
# meanOpenTime = tres + phiA * DARS * QexpQF * uF
meanA = tres + np.dot(phiA, np.dot(np.dot(DARS, QexpQF), uF))[0]
meanF = tres + np.dot(phiF, np.dot(np.dot(DFRS, QexpQA), uA))[0]
return meanA, meanF
def exact_mean_open_shut_time(mec, tres):
"""
Calculate exact mean open or shut time from HJC probability density
function.
Parameters
----------
tres : float
Time resolution (dead time).
QAA : array_like, shape (kA, kA)
QFF : array_like, shape (kF, kF)
QAF : array_like, shape (kA, kF)
QAA, QFF, QAF - submatrices of Q.
kA : int
A number of open states in kinetic scheme.
kF : int
A number of shut states in kinetic scheme.
GAF : array_like, shape (kA, kB)
GFA : array_like, shape (kB, kA)
GAF, GFA- transition probabilities
Returns
-------
mean : float
Apparent mean open/shut time.
"""
GAF, GFA = qml.iGs(mec.Q, mec.kA, mec.kF)
expQFF = qml.expQt(mec.QFF, tres)
expQAA = qml.expQt(mec.QAA, tres)
eGAF = qml.eGs(GAF, GFA, mec.kA, mec.kF, expQFF)
eGFA = qml.eGs(GFA, GAF, mec.kF, mec.kA, expQAA)
phiA = qml.phiHJC(eGAF, eGFA, mec.kA)
phiF = qml.phiHJC(eGFA, eGAF, mec.kF)
QexpQF = np.dot(mec.QAF, expQFF)
QexpQA = np.dot(mec.QFA, expQAA)
DARS = qml.dARSdS(tres, mec.QAA, mec.QFF, GAF, GFA, expQFF, mec.kA, mec.kF)
DFRS = qml.dARSdS(tres, mec.QFF, mec.QAA, GFA, GAF, expQAA, mec.kF, mec.kA)
uF, uA = np.ones((mec.kF, 1)), np.ones((mec.kA, 1))
# meanOpenTime = tres + phiA * DARS * QexpQF * uF
meanA = tres + np.dot(phiA, np.dot(np.dot(DARS, QexpQF), uF))[0]
meanF = tres + np.dot(phiF, np.dot(np.dot(DFRS, QexpQA), uA))[0]
return meanA, meanF
def exact_GAMAxx(mec, tres, open):
"""
Calculate gama coeficients for the exact open time pdf (Eq. 3.22, HJC90).
Parameters
----------
tres : float
mec : dcpyps.Mechanism
The mechanism to be analysed.
open : bool
True for open time pdf and False for shut time pdf.
Returns
-------
eigen : ndarray, shape (k,)
Eigenvalues of -Q matrix.
gama00, gama10, gama11 : ndarrays
Constants for the exact open/shut time pdf.
"""
expQFF = qml.expQt(mec.QII, tres)
expQAA = qml.expQt(mec.QAA, tres)
GAF, GFA = qml.iGs(mec.Q, mec.kA, mec.kI)
eGAF = qml.eGs(GAF, GFA, mec.kA, mec.kI, expQFF)
eGFA = qml.eGs(GFA, GAF, mec.kI, mec.kA, expQAA)
eigs, A = qml.eigs_sorted(-mec.Q)
if open:
phi = qml.phiHJC(eGAF, eGFA, mec.kA)
eigen, Z00, Z10, Z11 = qml.Zxx(mec.Q, eigs, A, mec.kA,
mec.QII, mec.QAI, mec.QIA, expQFF, open)
u = np.ones((mec.kI,1))
else:
phi = qml.phiHJC(eGFA, eGAF, mec.kI)
eigen, Z00, Z10, Z11 = qml.Zxx(mec.Q, eigs, A, mec.kA,
mec.QAA, mec.QIA, mec.QAI, expQAA, open)
u = np.ones((mec.kA, 1))
gama00 = (np.dot(np.dot(phi, Z00), u)).T[0]
gama10 = (np.dot(np.dot(phi, Z10), u)).T[0]
gama11 = (np.dot(np.dot(phi, Z11), u)).T[0]
return eigen, gama00, gama10, gama11
def ideal_subset_time_pdf(Q, k1, k2, t):
"""
"""
u = np.ones((k2 - k1 + 1, 1))
phi, QSub = qml.phiSub(Q, k1, k2)
expQSub = qml.expQt(QSub, t)
f = np.dot(np.dot(np.dot(phi, expQSub), -QSub), u)
return f
def exact_GAMAxx(mec, tres, open):
"""
Calculate gama coeficients for the exact open time pdf (Eq. 3.22, HJC90).
Parameters
----------
tres : float
mec : dcpyps.Mechanism
The mechanism to be analysed.
open : bool
True for open time pdf and False for shut time pdf.
Returns
-------
eigen : ndarray, shape (k,)
Eigenvalues of -Q matrix.
gama00, gama10, gama11 : ndarrays
Constants for the exact open/shut time pdf.
"""
expQFF = qml.expQt(mec.QII, tres)
expQAA = qml.expQt(mec.QAA, tres)
GAF, GFA = qml.iGs(mec.Q, mec.kA, mec.kI)
eGAF = qml.eGs(GAF, GFA, mec.kA, mec.kI, expQFF)
eGFA = qml.eGs(GFA, GAF, mec.kI, mec.kA, expQAA)
eigs, A = qml.eigs_sorted(-mec.Q)
if open:
phi = qml.phiHJC(eGAF, eGFA, mec.kA)
eigen, Z00, Z10, Z11 = qml.Zxx(mec.Q, eigs, A, mec.kA, mec.QII,
mec.QAI, mec.QIA, expQFF, open)
u = np.ones((mec.kI, 1))
else:
phi = qml.phiHJC(eGFA, eGAF, mec.kI)
eigen, Z00, Z10, Z11 = qml.Zxx(mec.Q, eigs, A, mec.kA, mec.QAA,
mec.QIA, mec.QAI, expQAA, open)
u = np.ones((mec.kA, 1))
gama00 = (np.dot(np.dot(phi, Z00), u)).T[0]
gama10 = (np.dot(np.dot(phi, Z10), u)).T[0]
gama11 = (np.dot(np.dot(phi, Z11), u)).T[0]
return eigen, gama00, gama10, gama11
def ideal_subset_time_pdf(Q, k1, k2, t):
"""
"""
u = np.ones((k2 - k1 + 1, 1))
phi, QSub = qml.phiSub(Q, k1, k2)
expQSub = qml.expQt(QSub, t)
f = np.dot(np.dot(np.dot(phi, expQSub), -QSub), u)
return f
def adjacent_open_to_shut_range_pdf_components(u1, u2, QAA, QAF, QFF, QFA,
phiA):
"""
Calculate time constants and areas for an ideal (no missed events)
exponential probability density function of open times adjacent to a
specified shut time range.
Parameters
----------
t : float
Time (sec).
QAA : array_like, shape (kA, kA)
Submatrix of Q.
phiA : array_like, shape (1, kA)
Initial vector for openings
Returns
-------
taus : ndarray, shape(k, 1)
Time constants.
areas : ndarray, shape(k, 1)
Component relative areas.
"""
kA = QAA.shape[0]
uA = np.ones((kA))[:, np.newaxis]
invQAA, invQFF = -nplin.inv(QAA), nplin.inv(QFF)
expQFFr = qml.expQt(QFF, u2) - qml.expQt(QFF, u1)
col = np.dot(np.dot(np.dot(np.dot(QAF, invQFF), expQFFr), QFA), uA)
w = np.zeros(kA)
eigs, A = qml.eigs(-QAA)
row = np.dot(phiA, invQAA)
den = np.dot(row, col)[0, 0]
#TODO: remove 'for'
for i in range(kA):
w[i] = np.dot(np.dot(phiA, A[i]), col) / den
return eigs, w
def adjacent_open_to_shut_range_pdf_components(u1, u2, QAA, QAF, QFF, QFA, phiA):
"""
Calculate time constants and areas for an ideal (no missed events)
exponential probability density function of open times adjacent to a
specified shut time range.
Parameters
----------
t : float
Time (sec).
QAA : array_like, shape (kA, kA)
Submatrix of Q.
phiA : array_like, shape (1, kA)
Initial vector for openings
Returns
-------
taus : ndarray, shape(k, 1)
Time constants.
areas : ndarray, shape(k, 1)
Component relative areas.
"""
kA = QAA.shape[0]
uA = np.ones((kA))[:,np.newaxis]
invQAA, invQFF = -nplin.inv(QAA), nplin.inv(QFF)
expQFFr = qml.expQt(QFF, u2) - qml.expQt(QFF, u1)
col = np.dot(np.dot(np.dot(np.dot(QAF, invQFF), expQFFr), QFA), uA)
w = np.zeros(kA)
eigs, A = qml.eigs(-QAA)
row = np.dot(phiA, invQAA)
den = np.dot(row, col)[0, 0]
#TODO: remove 'for'
for i in range(kA):
w[i] = np.dot(np.dot(phiA, A[i]), col) / den
return eigs, w
def length_pdf(mec, t):
"""
Probability density function of the burst length (Eq. 3.17, CH82).
f(t) = phiB * [PEE(t)]AA * (-QAA) * eB, where PEE(t) = exp(QEE * t)
Parameters
----------
mec : dcpyps.Mechanism
The mechanism to be analysed.
Returns
-------
f : float
"""
expQEEA = qml.expQt(mec.QEE, t)[:mec.kA, :mec.kA]
f = np.dot(np.dot(np.dot(phiBurst(mec), expQEEA), -mec.QAA), endBurst(mec))
return f
def length_pdf(mec, t):
"""
Probability density function of the burst length (Eq. 3.17, CH82).
f(t) = phiB * [PEE(t)]AA * (-QAA) * eB, where PEE(t) = exp(QEE * t)
Parameters
----------
mec : dcpyps.Mechanism
The mechanism to be analysed.
Returns
-------
f : float
"""
expQEEA = qml.expQt(mec.QEE, t)[:mec.kA, :mec.kA]
f = np.dot(np.dot(np.dot(phiBurst(mec), expQEEA), -mec.QAA),
endBurst(mec))
return f
def length_cond_pdf(mec, t):
"""
The distribution of burst length coditional on starting state.
Parameters
----------
mec : dcpyps.Mechanism
The mechanism to be analysed.
t : float
Length.
Returns
-------
vec : array_like, shape (kA, 1)
Probability of seeing burst length t depending on starting state.
"""
expQEEA = qml.expQt(mec.QEE, t)[:mec.kA, :mec.kA]
vec = np.dot(np.dot(expQEEA, -mec.QAA), endBurst(mec))
vec = vec.transpose()
return vec
def length_cond_pdf(mec, t):
"""
The distribution of burst length coditional on starting state.
Parameters
----------
mec : dcpyps.Mechanism
The mechanism to be analysed.
t : float
Length.
Returns
-------
vec : array_like, shape (kA, 1)
Probability of seeing burst length t depending on starting state.
"""
expQEEA = qml.expQt(mec.QEE, t)[:mec.kA, :mec.kA]
vec = np.dot(np.dot(expQEEA, -mec.QAA), endBurst(mec))
vec = vec.transpose()
return vec
def printout_occupancies(mec, tres):
"""
"""
str = ('\n\n\n*******************************************\n\n' +
'Open\tEquilibrium\tMean life\tMean latency (ms)\n' +
'state\toccupancy\t(ms)\tto next shutting\n' +
'\t\t\tgiven start in this state\n')
pinf = qml.pinf(mec.Q)
for i in range(mec.k):
if i == 0:
mean_life_A = ideal_subset_mean_life_time(mec.Q, 1, mec.kA)
str += ('Subset A ' + '\t{0:.5g}'.format(np.sum(pinf[:mec.kA])) +
'\t{0:.5g}\n'.format(mean_life_A * 1000))
if i == mec.kA:
mean_life_B = ideal_subset_mean_life_time(mec.Q, mec.kA + 1,
mec.kE)
str += ('\nShut\tEquilibrium\tMean life\tMean latency (ms)\n' +
'state\toccupancy\t(ms)\tto next opening\n' +
'\t\t\tgiven start in this state\n' + 'Subset B ' +
'\t{0:.5g}'.format(np.sum(pinf[mec.kA:mec.kE])) +
'\t{0:.5g}\n'.format(mean_life_B * 1000))
if i == mec.kE:
mean_life_C = ideal_subset_mean_life_time(mec.Q, mec.kE + 1,
mec.kG)
str += ('\nSubset C ' +
'\t{0:.5g}'.format(np.sum(pinf[mec.kE:mec.kG])) +
'\t{0:.5g}\n'.format(mean_life_C * 1000))
if i == mec.kG:
mean_life_D = ideal_subset_mean_life_time(mec.Q, mec.kG + 1, mec.k)
str += ('\nSubset D ' +
'\t{0:.5g}'.format(np.sum(pinf[mec.kG:mec.k])) +
'\t{0:.5g}\n'.format(mean_life_D * 1000))
mean = ideal_mean_latency_given_start_state(mec, i + 1)
str += ('{0:d}'.format(i + 1) + '\t{0:.5g}'.format(pinf[i]) +
'\t{0:.5g}'.format(-1 / mec.Q[i, i] * 1000) +
'\t{0:.5g}\n'.format(mean * 1000))
expQFF = qml.expQt(mec.QFF, tres)
expQAA = qml.expQt(mec.QAA, tres)
GAF, GFA = qml.iGs(mec.Q, mec.kA, mec.kF)
eGAF = qml.eGs(GAF, GFA, mec.kA, mec.kF, expQFF)
eGFA = qml.eGs(GFA, GAF, mec.kF, mec.kA, expQAA)
phiA = qml.phiHJC(eGAF, eGFA, mec.kA)
phiF = qml.phiHJC(eGFA, eGAF, mec.kF)
str += ('\n\nInitial vector for HJC openings phiOp =\n')
for i in range(phiA.shape[0]):
str += ('\t{0:.5g}'.format(phiA[i]))
str += ('\nInitial vector for ideal openings phiOp =\n')
phiAi = qml.phiA(mec)
for i in range(phiA.shape[0]):
str += ('\t{0:.5g}'.format(phiAi[i]))
str += ('\nInitial vector for HJC shuttings phiSh =\n')
for i in range(phiF.shape[0]):
str += ('\t{0:.5g}'.format(phiF[i]))
str += ('\nInitial vector for ideal shuttings phiSh =\n')
phiFi = qml.phiF(mec)
for i in range(phiF.shape[0]):
str += ('\t{0:.5g}'.format(phiFi[i]))
str += '\n'
return str
def test_openshut(self):
# # # Initial HJC vectors.
expQFF = qml.expQt(self.mec.QFF, self.tres)
expQAA = qml.expQt(self.mec.QAA, self.tres)
GAF, GFA = qml.iGs(self.mec.Q, self.mec.kA, self.mec.kF)
eGAF = qml.eGs(GAF, GFA, self.mec.kA, self.mec.kF, expQFF)
eGFA = qml.eGs(GFA, GAF, self.mec.kF, self.mec.kA, expQAA)
phiA = qml.phiHJC(eGAF, eGFA, self.mec.kA)
phiF = qml.phiHJC(eGFA, eGAF, self.mec.kF)
self.assertAlmostEqual(phiA[0], 0.153966, 6)
self.assertAlmostEqual(phiA[1], 0.846034, 6)
self.assertAlmostEqual(phiF[0], 0.530369, 6)
self.assertAlmostEqual(phiF[1], 0.386116, 6)
self.assertAlmostEqual(phiF[2], 0.0835153, 6)
# Ideal shut time pdf
eigs, w = scl.ideal_dwell_time_pdf_components(self.mec.QFF,
qml.phiF(self.mec))
self.assertAlmostEqual(eigs[0], 0.263895, 6)
self.assertAlmostEqual(eigs[1], 2062.93, 2)
self.assertAlmostEqual(eigs[2], 19011.8, 1)
self.assertAlmostEqual(w[0], 0.0691263, 6)
self.assertAlmostEqual(w[1], 17.2607, 4)
self.assertAlmostEqual(w[2], 13872.7, 1)
# Asymptotic shut time pdf
roots = scl.asymptotic_roots(self.tres, self.mec.QFF, self.mec.QAA,
self.mec.QFA, self.mec.QAF, self.mec.kF,
self.mec.kA)
areas = scl.asymptotic_areas(self.tres, roots, self.mec.QFF,
self.mec.QAA, self.mec.QFA, self.mec.QAF,
self.mec.kF, self.mec.kA, GFA, GAF)
mean = scl.exact_mean_time(self.tres, self.mec.QFF, self.mec.QAA,
self.mec.QFA, self.mec.kF, self.mec.kA, GFA,
GAF)
self.assertAlmostEqual(-roots[0], 17090.2, 1)
self.assertAlmostEqual(-roots[1], 2058.08, 2)
self.assertAlmostEqual(-roots[2], 0.243565, 6)
self.assertAlmostEqual(areas[0] * 100, 28.5815, 4)
self.assertAlmostEqual(areas[1] * 100, 1.67311, 5)
self.assertAlmostEqual(areas[2] * 100, 68.3542, 4)
# Exact pdf
eigvals, gamma00, gamma10, gamma11 = scl.exact_GAMAxx(
self.mec, self.tres, False)
self.assertAlmostEqual(gamma00[0], 0.940819, 6)
self.assertAlmostEqual(gamma00[1], 117.816, 3)
self.assertAlmostEqual(gamma00[2], 24.8962, 4)
self.assertAlmostEqual(gamma00[3], 1.28843, 5)
self.assertAlmostEqual(gamma00[4], 5370.18, 2)
self.assertAlmostEqual(gamma10[0], 4.57792, 5)
self.assertAlmostEqual(gamma10[1], 100.211, 3)
self.assertAlmostEqual(gamma10[2], -5.49855, 4)
self.assertAlmostEqual(gamma10[3], 0.671548, 6)
self.assertAlmostEqual(gamma10[4], -99.9617, 4)
self.assertAlmostEqual(gamma11[0], 0.885141, 6)
self.assertAlmostEqual(gamma11[1], 43634.99, 1)
self.assertAlmostEqual(gamma11[2], 718.068, 3)
self.assertAlmostEqual(gamma11[3], -39.7437, 3)
self.assertAlmostEqual(gamma11[4], -1.9832288e+06, 0)
def HJClik(theta, opts):
"""
Calculate likelihood for a series of open and shut times using HJC missed
events probability density functions (first two dead time intervals- exact
solution, then- asymptotic).
Lik = phi * eGAF(t1) * eGFA(t2) * eGAF(t3) * ... * eGAF(tn) * uF
where t1, t3,..., tn are open times; t2, t4,..., t(n-1) are shut times.
Gaps > tcrit are treated as unusable (e.g. contain double or bad bit of
record, or desens gaps that are not in the model, or gaps so long that
next opening may not be from the same channel). However this calculation
DOES assume that all the shut times predicted by the model are present
within each group. The series of multiplied likelihoods is terminated at
the end of the opening before an unusable gap. A new series is then
started, using appropriate initial vector to give Lik(2), ... At end
these are multiplied to give final likelihood.
Parameters
----------
theta : array_like
Guesses.
bursts : dictionary
A dictionary containing lists of open and shut intervals.
opts : dictionary
opts['mec'] : instance of type Mechanism
opts['tres'] : float
Time resolution (dead time).
opts['tcrit'] : float
Ctritical time interval.
opts['isCHS'] : bool
True if CHS vectors should be used (Eq. 5.7, CHS96).
Returns
-------
loglik : float
Log-likelihood.
newrates : array_like
Updated rates/guesses.
"""
# TODO: Errors.
mec = opts['mec']
conc = opts['conc']
tres = opts['tres']
tcrit = opts['tcrit']
is_chsvec = opts['isCHS']
bursts = opts['data']
mec.theta_unsqueeze(np.exp(theta))
mec.set_eff('c', conc)
GAF, GFA = qml.iGs(mec.Q, mec.kA, mec.kF)
expQFF = qml.expQt(mec.QFF, tres)
expQAA = qml.expQt(mec.QAA, tres)
eGAF = qml.eGs(GAF, GFA, mec.kA, mec.kF, expQFF)
eGFA = qml.eGs(GFA, GAF, mec.kF, mec.kA, expQAA)
phiF = qml.phiHJC(eGFA, eGAF, mec.kF)
startB = qml.phiHJC(eGAF, eGFA, mec.kA)
endB = np.ones((mec.kF, 1))
eigen, A = qml.eigs(-mec.Q)
Aeigvals, AZ00, AZ10, AZ11 = qml.Zxx(mec.Q, eigen, A, mec.kA, mec.QFF,
mec.QAF, mec.QFA, expQFF, True)
Aroots = asymptotic_roots(tres,
mec.QAA, mec.QFF, mec.QAF, mec.QFA, mec.kA, mec.kF)
AR = qml.AR(Aroots, tres, mec.QAA, mec.QFF, mec.QAF, mec.QFA, mec.kA, mec.kF)
Feigvals, FZ00, FZ10, FZ11 = qml.Zxx(mec.Q, eigen, A, mec.kA, mec.QAA,
mec.QFA, mec.QAF, expQAA, False)
Froots = asymptotic_roots(tres,
mec.QFF, mec.QAA, mec.QFA, mec.QAF, mec.kF, mec.kA)
FR = qml.AR(Froots, tres, mec.QFF, mec.QAA, mec.QFA, mec.QAF, mec.kF, mec.kA)
if is_chsvec:
startB, endB = qml.CHSvec(Froots, tres, tcrit,
mec.QFA, mec.kA, expQAA, phiF, FR)
loglik = 0
for ind in range(len(bursts)):
burst = bursts[ind]
grouplik = startB
for i in range(len(burst)):
t = burst[i]
if i % 2 == 0: # open time
eGAFt = qml.eGAF(t, tres, Aeigvals, AZ00, AZ10, AZ11, Aroots,
AR, mec.QAF, expQFF)
else: # shut
eGAFt = qml.eGAF(t, tres, Feigvals, FZ00, FZ10, FZ11, Froots,
FR, mec.QFA, expQAA)
grouplik = np.dot(grouplik, eGAFt)
if grouplik.max() > 1e50:
grouplik = grouplik * 1e-100
#print 'grouplik was scaled down'
grouplik = np.dot(grouplik, endB)
try:
loglik += log(grouplik[0])
except:
print ('HJClik: Warning: likelihood has been set to 0')
print ('likelihood=', grouplik[0])
print ('rates=', mec.unit_rates())
loglik = 0
break
newrates = np.log(mec.theta())
return -loglik, newrates
def HJClik(theta, opts):
"""
Calculate likelihood for a series of open and shut times using HJC missed
events probability density functions (first two dead time intervals- exact
solution, then- asymptotic).
Lik = phi * eGAF(t1) * eGFA(t2) * eGAF(t3) * ... * eGAF(tn) * uF
where t1, t3,..., tn are open times; t2, t4,..., t(n-1) are shut times.
Gaps > tcrit are treated as unusable (e.g. contain double or bad bit of
record, or desens gaps that are not in the model, or gaps so long that
next opening may not be from the same channel). However this calculation
DOES assume that all the shut times predicted by the model are present
within each group. The series of multiplied likelihoods is terminated at
the end of the opening before an unusable gap. A new series is then
started, using appropriate initial vector to give Lik(2), ... At end
these are multiplied to give final likelihood.
Parameters
----------
theta : array_like
Guesses.
bursts : dictionary
A dictionary containing lists of open and shut intervals.
opts : dictionary
opts['mec'] : instance of type Mechanism
opts['tres'] : float
Time resolution (dead time).
opts['tcrit'] : float
Ctritical time interval.
opts['isCHS'] : bool
True if CHS vectors should be used (Eq. 5.7, CHS96).
Returns
-------
loglik : float
Log-likelihood.
newrates : array_like
Updated rates/guesses.
"""
# TODO: Errors.
mec = opts['mec']
conc = opts['conc']
tres = opts['tres']
tcrit = opts['tcrit']
is_chsvec = opts['isCHS']
bursts = opts['data']
mec.theta_unsqueeze(np.exp(theta))
mec.set_eff('c', conc)
GAF, GFA = qml.iGs(mec.Q, mec.kA, mec.kF)
expQFF = qml.expQt(mec.QFF, tres)
expQAA = qml.expQt(mec.QAA, tres)
eGAF = qml.eGs(GAF, GFA, mec.kA, mec.kF, expQFF)
eGFA = qml.eGs(GFA, GAF, mec.kF, mec.kA, expQAA)
phiF = qml.phiHJC(eGFA, eGAF, mec.kF)
startB = qml.phiHJC(eGAF, eGFA, mec.kA)
endB = np.ones((mec.kF, 1))
eigen, A = qml.eigs(-mec.Q)
Aeigvals, AZ00, AZ10, AZ11 = qml.Zxx(mec.Q, eigen, A, mec.kA, mec.QFF,
mec.QAF, mec.QFA, expQFF, True)
Aroots = asymptotic_roots(tres, mec.QAA, mec.QFF, mec.QAF, mec.QFA, mec.kA,
mec.kF)
AR = qml.AR(Aroots, tres, mec.QAA, mec.QFF, mec.QAF, mec.QFA, mec.kA,
mec.kF)
Feigvals, FZ00, FZ10, FZ11 = qml.Zxx(mec.Q, eigen, A, mec.kA, mec.QAA,
mec.QFA, mec.QAF, expQAA, False)
Froots = asymptotic_roots(tres, mec.QFF, mec.QAA, mec.QFA, mec.QAF, mec.kF,
mec.kA)
FR = qml.AR(Froots, tres, mec.QFF, mec.QAA, mec.QFA, mec.QAF, mec.kF,
mec.kA)
if is_chsvec:
startB, endB = qml.CHSvec(Froots, tres, tcrit, mec.QFA, mec.kA, expQAA,
phiF, FR)
loglik = 0
for ind in range(len(bursts)):
burst = bursts[ind]
grouplik = startB
for i in range(len(burst)):
t = burst[i]
if i % 2 == 0: # open time
eGAFt = qml.eGAF(t, tres, Aeigvals, AZ00, AZ10, AZ11, Aroots,
AR, mec.QAF, expQFF)
else: # shut
eGAFt = qml.eGAF(t, tres, Feigvals, FZ00, FZ10, FZ11, Froots,
FR, mec.QFA, expQAA)
grouplik = np.dot(grouplik, eGAFt)
if grouplik.max() > 1e50:
grouplik = grouplik * 1e-100
#print 'grouplik was scaled down'
grouplik = np.dot(grouplik, endB)
try:
loglik += log(grouplik[0])
except:
print('HJClik: Warning: likelihood has been set to 0')
print('likelihood=', grouplik[0])
print('rates=', mec.unit_rates())
loglik = 0
break
newrates = np.log(mec.theta())
return -loglik, newrates
def printout_occupancies(mec, tres):
"""
"""
str = ('\n\n\n*******************************************\n\n' +
'Open\tEquilibrium\tMean life\tMean latency (ms)\n' +
'state\toccupancy\t(ms)\tto next shutting\n' +
'\t\t\tgiven start in this state\n')
pinf = qml.pinf(mec.Q)
for i in range(mec.k):
if i == 0:
mean_life_A = ideal_subset_mean_life_time(mec.Q, 1, mec.kA)
str += ('Subset A ' +
'\t{0:.5g}'.format(np.sum(pinf[:mec.kA])) +
'\t{0:.5g}\n'.format(mean_life_A * 1000))
if i == mec.kA:
mean_life_B = ideal_subset_mean_life_time(mec.Q, mec.kA + 1, mec.kE)
str += ('\nShut\tEquilibrium\tMean life\tMean latency (ms)\n' +
'state\toccupancy\t(ms)\tto next opening\n' +
'\t\t\tgiven start in this state\n' +
'Subset B ' +
'\t{0:.5g}'.format(np.sum(pinf[mec.kA : mec.kE])) +
'\t{0:.5g}\n'.format(mean_life_B * 1000))
if i == mec.kE:
mean_life_C = ideal_subset_mean_life_time(mec.Q, mec.kE + 1, mec.kG)
str += ('\nSubset C ' +
'\t{0:.5g}'.format(np.sum(pinf[mec.kE : mec.kG])) +
'\t{0:.5g}\n'.format(mean_life_C * 1000))
if i == mec.kG:
mean_life_D = ideal_subset_mean_life_time(mec.Q, mec.kG + 1, mec.k)
str += ('\nSubset D ' +
'\t{0:.5g}'.format(np.sum(pinf[mec.kG : mec.k])) +
'\t{0:.5g}\n'.format(mean_life_D * 1000))
mean = ideal_mean_latency_given_start_state(mec, i+1)
str += ('{0:d}'.format(i+1) +
'\t{0:.5g}'.format(pinf[i]) +
'\t{0:.5g}'.format(-1 / mec.Q[i,i] * 1000) +
'\t{0:.5g}\n'.format(mean * 1000))
expQFF = qml.expQt(mec.QFF, tres)
expQAA = qml.expQt(mec.QAA, tres)
GAF, GFA = qml.iGs(mec.Q, mec.kA, mec.kF)
eGAF = qml.eGs(GAF, GFA, mec.kA, mec.kF, expQFF)
eGFA = qml.eGs(GFA, GAF, mec.kF, mec.kA, expQAA)
phiA = qml.phiHJC(eGAF, eGFA, mec.kA)
phiF = qml.phiHJC(eGFA, eGAF, mec.kF)
str += ('\n\nInitial vector for HJC openings phiOp =\n')
for i in range(phiA.shape[0]):
str += ('\t{0:.5g}'.format(phiA[i]))
str += ('\nInitial vector for ideal openings phiOp =\n')
phiAi = qml.phiA(mec)
for i in range(phiA.shape[0]):
str += ('\t{0:.5g}'.format(phiAi[i]))
str += ('\nInitial vector for HJC shuttings phiSh =\n')
for i in range(phiF.shape[0]):
str += ('\t{0:.5g}'.format(phiF[i]))
str += ('\nInitial vector for ideal shuttings phiSh =\n')
phiFi = qml.phiF(mec)
for i in range(phiF.shape[0]):
str += ('\t{0:.5g}'.format(phiFi[i]))
str += '\n'
return str