def adjacent_open_time_pdf(mec,
tres,
u1,
u2,
tmin=0.00001,
tmax=1000,
points=512,
unit='ms'):
"""
Calculate pdf's of ideal all open time and open time adjacent to specified shut
time range.
Parameters
----------
mec : instance of type Mechanism
tres : float
Time resolution.
tmin, tmax : floats
Time range for burst length ditribution.
points : int
Number of points per plot.
unit : str
'ms'- milliseconds.
Returns
-------
t : ndarray of floats, shape (num of points)
Time in millisec.
ipdf, ajpdf : ndarrays of floats, shape (num of points)
Ideal all and adjacent open time distributions.
"""
# Ideal pdf.
eigs, w = scl.ideal_dwell_time_pdf_components(mec.QAA, qml.phiA(mec))
tmax = (1 / eigs.max()) * 100
t = np.logspace(math.log10(tmin), math.log10(tmax), points)
fac = 1 / np.sum((w / eigs) * np.exp(-tres * eigs)) # Scale factor
ipdf = t * pdfs.expPDF(t, 1 / eigs, w / eigs) * fac
# Ajacent open time pdf
eigs, w = scl.adjacent_open_to_shut_range_pdf_components(
u1, u2, mec.QAA, mec.QAI, mec.QII, mec.QIA,
qml.phiA(mec).reshape((1, mec.kA)))
# fac = 1 / np.sum((w / eigs) * np.exp(-tres * eigs)) # Scale factor
ajpdf = t * pdfs.expPDF(t, 1 / eigs, w / eigs) * fac
if unit == 'ms':
t = t * 1000 # x scale in millisec
return t, ipdf, ajpdf
def open_time_pdf(mec, tres, tmin=0.00001, tmax=1000, points=512, unit='ms'):
"""
Calculate ideal asymptotic and exact open time distributions.
Parameters
----------
mec : instance of type Mechanism
tres : float
Time resolution.
tmin, tmax : floats
Time range for burst length ditribution.
points : int
Number of points per plot.
unit : str
'ms'- milliseconds.
Returns
-------
t : ndarray of floats, shape (num of points)
Time in millisec.
ipdf, epdf, apdf : ndarrays of floats, shape (num of points)
Ideal, exact and asymptotic open time distributions.
"""
open = True
# Asymptotic pdf
roots = scl.asymptotic_roots(tres,
mec.QAA, mec.QII, mec.QAI, mec.QIA, mec.kA, mec.kI)
tmax = (-1 / roots.max()) * 20
t = np.logspace(math.log10(tmin), math.log10(tmax), points)
# Ideal pdf.
eigs, w = scl.ideal_dwell_time_pdf_components(mec.QAA, qml.phiA(mec))
fac = 1 / np.sum((w / eigs) * np.exp(-tres * eigs)) # Scale factor
ipdf = t * pdfs.expPDF(t, 1 / eigs, w / eigs) * fac
# Asymptotic pdf
GAF, GFA = qml.iGs(mec.Q, mec.kA, mec.kI)
areas = scl.asymptotic_areas(tres, roots,
mec.QAA, mec.QII, mec.QAI, mec.QIA,
mec.kA, mec.kI, GAF, GFA)
apdf = scl.asymptotic_pdf(t, tres, -1 / roots, areas)
# Exact pdf
eigvals, gamma00, gamma10, gamma11 = scl.exact_GAMAxx(mec,
tres, open)
epdf = np.zeros(points)
for i in range(points):
epdf[i] = (t[i] * scl.exact_pdf(t[i], tres,
roots, areas, eigvals, gamma00, gamma10, gamma11))
if unit == 'ms':
t = t * 1000 # x scale in millisec
return t, ipdf, epdf, apdf
def adjacent_open_time_pdf(mec, tres, u1, u2,
tmin=0.00001, tmax=1000, points=512, unit='ms'):
"""
Calculate pdf's of ideal all open time and open time adjacent to specified shut
time range.
Parameters
----------
mec : instance of type Mechanism
tres : float
Time resolution.
tmin, tmax : floats
Time range for burst length ditribution.
points : int
Number of points per plot.
unit : str
'ms'- milliseconds.
Returns
-------
t : ndarray of floats, shape (num of points)
Time in millisec.
ipdf, ajpdf : ndarrays of floats, shape (num of points)
Ideal all and adjacent open time distributions.
"""
# Ideal pdf.
eigs, w = scl.ideal_dwell_time_pdf_components(mec.QAA, qml.phiA(mec))
tmax = (1 / eigs.max()) * 100
t = np.logspace(math.log10(tmin), math.log10(tmax), points)
fac = 1 / np.sum((w / eigs) * np.exp(-tres * eigs)) # Scale factor
ipdf = t * pdfs.expPDF(t, 1 / eigs, w / eigs) * fac
# Ajacent open time pdf
eigs, w = scl.adjacent_open_to_shut_range_pdf_components(u1, u2,
mec.QAA, mec.QAI, mec.QII, mec.QIA, qml.phiA(mec).reshape((1,mec.kA)))
# fac = 1 / np.sum((w / eigs) * np.exp(-tres * eigs)) # Scale factor
ajpdf = t * pdfs.expPDF(t, 1 / eigs, w / eigs) * fac
if unit == 'ms':
t = t * 1000 # x scale in millisec
return t, ipdf, ajpdf
def open_time_pdf(mec, tres, tmin=0.00001, tmax=1000, points=512, unit='ms'):
"""
Calculate ideal asymptotic and exact open time distributions.
Parameters
----------
mec : instance of type Mechanism
tres : float
Time resolution.
tmin, tmax : floats
Time range for burst length ditribution.
points : int
Number of points per plot.
unit : str
'ms'- milliseconds.
Returns
-------
t : ndarray of floats, shape (num of points)
Time in millisec.
ipdf, epdf, apdf : ndarrays of floats, shape (num of points)
Ideal, exact and asymptotic open time distributions.
"""
open = True
# Asymptotic pdf
roots = scl.asymptotic_roots(tres, mec.QAA, mec.QII, mec.QAI, mec.QIA,
mec.kA, mec.kI)
tmax = (-1 / roots.max()) * 20
t = np.logspace(math.log10(tmin), math.log10(tmax), points)
# Ideal pdf.
eigs, w = scl.ideal_dwell_time_pdf_components(mec.QAA, qml.phiA(mec))
fac = 1 / np.sum((w / eigs) * np.exp(-tres * eigs)) # Scale factor
ipdf = t * pdfs.expPDF(t, 1 / eigs, w / eigs) * fac
# Asymptotic pdf
GAF, GFA = qml.iGs(mec.Q, mec.kA, mec.kI)
areas = scl.asymptotic_areas(tres, roots, mec.QAA, mec.QII, mec.QAI,
mec.QIA, mec.kA, mec.kI, GAF, GFA)
apdf = scl.asymptotic_pdf(t, tres, -1 / roots, areas)
# Exact pdf
eigvals, gamma00, gamma10, gamma11 = scl.exact_GAMAxx(mec, tres, open)
epdf = np.zeros(points)
for i in range(points):
epdf[i] = (t[i] * scl.exact_pdf(t[i], tres, roots, areas, eigvals,
gamma00, gamma10, gamma11))
if unit == 'ms':
t = t * 1000 # x scale in millisec
return t, ipdf, epdf, apdf
def subset_time_pdf(mec,
tres,
state1,
state2,
tmin=0.00001,
tmax=1000,
points=512,
unit='ms'):
"""
Calculate ideal pdf of any subset dwell times.
Parameters
----------
mec : instance of type Mechanism
tres : float
Time resolution.
state1, state2 : ints
tmin, tmax : floats
Time range for burst length ditribution.
points : int
Number of points per plot.
unit : str
'ms'- milliseconds.
Returns
-------
t : ndarray of floats, shape (num of points)
Time in millisec.
spdf : ndarray of floats, shape (num of points)
Subset dwell time pdf.
"""
open = False
if open:
eigs, w = scl.ideal_dwell_time_pdf_components(mec.QAA, qml.phiA(mec))
else:
eigs, w = scl.ideal_dwell_time_pdf_components(mec.QII, qml.phiF(mec))
tmax = tau.max() * 20
t = np.logspace(math.log10(tmin), math.log10(tmax), points)
# Ideal pdf.
fac = 1 / np.sum((w / eigs) * np.exp(-tres * eigs)) # Scale factor
ipdf = t * pdfs.expPDF(t, 1 / eigs, w / eigs) * fac
spdf = np.zeros(points)
for i in range(points):
spdf[i] = t[i] * scl.ideal_subset_time_pdf(mec.Q, state1, state2,
t[i]) * fac
if unit == 'ms':
t = t * 1000 # x scale in millisec
return t, ipdf, spdf
def subset_time_pdf(mec, tres, state1, state2,
tmin=0.00001, tmax=1000, points=512, unit='ms'):
"""
Calculate ideal pdf of any subset dwell times.
Parameters
----------
mec : instance of type Mechanism
tres : float
Time resolution.
state1, state2 : ints
tmin, tmax : floats
Time range for burst length ditribution.
points : int
Number of points per plot.
unit : str
'ms'- milliseconds.
Returns
-------
t : ndarray of floats, shape (num of points)
Time in millisec.
spdf : ndarray of floats, shape (num of points)
Subset dwell time pdf.
"""
open = False
if open:
eigs, w = scl.ideal_dwell_time_pdf_components(mec.QAA, qml.phiA(mec))
else:
eigs, w = scl.ideal_dwell_time_pdf_components(mec.QII, qml.phiF(mec))
tmax = tau.max() * 20
t = np.logspace(math.log10(tmin), math.log10(tmax), points)
# Ideal pdf.
fac = 1 / np.sum((w / eigs) * np.exp(-tres * eigs)) # Scale factor
ipdf = t * pdfs.expPDF(t, 1 / eigs, w / eigs) * fac
spdf = np.zeros(points)
for i in range(points):
spdf[i] = t[i] * scl.ideal_subset_time_pdf(mec.Q,
state1, state2, t[i]) * fac
if unit == 'ms':
t = t * 1000 # x scale in millisec
return t, ipdf, spdf
def corr_open_shut(mec, lag):
"""
Calculate data for the plot of open, shut and open-shut time correlations.
Parameters
----------
mec : instance of type Mechanism
lag : int
Number of lags.
Returns
-------
c : ndarray of floats, shape (num of points,)
Concentration in mikroM
br : ndarray of floats, shape (num of points,)
Mean burst length in millisec.
brblk : ndarray of floats, shape (num of points,)
Mean burst length in millisec corrected for fast block.
"""
kA, kF = mec.kA, mec.kI
GAF, GFA = qml.iGs(mec.Q, kA, kF)
XAA, XFF = np.dot(GAF, GFA), np.dot(GFA, GAF)
phiA, phiF = qml.phiA(mec).reshape((1, kA)), qml.phiF(mec).reshape((1, kF))
varA = scl.corr_variance_A(phiA, mec.QAA, kA)
varF = scl.corr_variance_A(phiF, mec.QII, kF)
r = np.arange(1, lag + 1)
roA, roF, roAF = np.zeros(lag), np.zeros(lag), np.zeros(lag)
for i in range(lag):
covA = scl.corr_covariance_A(i + 1, phiA, mec.QAA, XAA, kA)
roA[i] = scl.correlation_coefficient(covA, varA, varA)
covF = scl.corr_covariance_A(i + 1, phiF, mec.QII, XFF, kF)
roF[i] = scl.correlation_coefficient(covF, varF, varF)
covAF = scl.corr_covariance_AF(i + 1, phiA, mec.QAA, mec.QII, XAA, GAF,
kA, kF)
roAF[i] = scl.correlation_coefficient(covAF, varA, varF)
return r, roA, roF, roAF
def corr_open_shut(mec, lag):
"""
Calculate data for the plot of open, shut and open-shut time correlations.
Parameters
----------
mec : instance of type Mechanism
lag : int
Number of lags.
Returns
-------
c : ndarray of floats, shape (num of points,)
Concentration in mikroM
br : ndarray of floats, shape (num of points,)
Mean burst length in millisec.
brblk : ndarray of floats, shape (num of points,)
Mean burst length in millisec corrected for fast block.
"""
kA, kF = mec.kA, mec.kI
GAF, GFA = qml.iGs(mec.Q, kA, kF)
XAA, XFF = np.dot(GAF, GFA), np.dot(GFA, GAF)
phiA, phiF = qml.phiA(mec).reshape((1,kA)), qml.phiF(mec).reshape((1,kF))
varA = scl.corr_variance_A(phiA, mec.QAA, kA)
varF = scl.corr_variance_A(phiF, mec.QII, kF)
r = np.arange(1, lag + 1)
roA, roF, roAF = np.zeros(lag), np.zeros(lag), np.zeros(lag)
for i in range(lag):
covA = scl.corr_covariance_A(i+1, phiA, mec.QAA, XAA, kA)
roA[i] = scl.correlation_coefficient(covA, varA, varA)
covF = scl.corr_covariance_A(i+1, phiF, mec.QII, XFF, kF)
roF[i] = scl.correlation_coefficient(covF, varF, varF)
covAF = scl.corr_covariance_AF(i+1, phiA, mec.QAA, mec.QII,
XAA, GAF, kA, kF)
roAF[i] = scl.correlation_coefficient(covAF, varA, varF)
return r, roA, roF, roAF
def printout_adjacent(mec, t1, t2):
"""
"""
str = ('\n*************************************\n' +
' OPEN TIMES ADJACENT TO SPECIFIED SHUT TIME RANGE\n')
kA = mec.kA
phiA = qml.phiA(mec).reshape((1,kA))
str += ('PDF of open times that precede shut times between {0:.3f}\
and {1:.3f} ms\n'.format(t1 * 1000, t2 * 1000))
eigs, w = adjacent_open_to_shut_range_pdf_components(t1, t2,
mec.QAA, mec.QAF, mec.QFF, mec.QFA, phiA)
str += pdfs.expPDF_printout(eigs, w)
mean = adjacent_open_to_shut_range_mean(t1, t2,
mec.QAA, mec.QAF, mec.QFF, mec.QFA, phiA)
str += ('Mean from direct calculation (ms) = {0:.6f}\n'.format(mean * 1000))
return str
def printout_adjacent(mec, t1, t2):
"""
"""
str = ('\n*************************************\n' +
' OPEN TIMES ADJACENT TO SPECIFIED SHUT TIME RANGE\n')
kA = mec.kA
phiA = qml.phiA(mec).reshape((1, kA))
str += ('PDF of open times that precede shut times between {0:.3f}\
and {1:.3f} ms\n'.format(t1 * 1000, t2 * 1000))
eigs, w = adjacent_open_to_shut_range_pdf_components(
t1, t2, mec.QAA, mec.QAF, mec.QFF, mec.QFA, phiA)
str += pdfs.expPDF_printout(eigs, w)
mean = adjacent_open_to_shut_range_mean(t1, t2, mec.QAA, mec.QAF, mec.QFF,
mec.QFA, phiA)
str += ('Mean from direct calculation (ms) = {0:.6f}\n'.format(mean *
1000))
return str
def likelihood(theta, opts):
"""
Calculate likelihood for a series of open and shut times using ideal
probability density functions.
"""
mec = opts['mec']
conc = opts['conc']
bursts = opts['data']
#mec.set_rateconstants(np.exp(theta))
mec.theta_unsqueeze(np.exp(theta))
mec.set_eff('c', conc)
startB = qml.phiA(mec)
endB = np.ones((mec.kF, 1))
loglik = 0
for ind in bursts:
burst = bursts[ind]
grouplik = startB
for i in range(len(burst)):
t = burst[i]
if i % 2 == 0: # open time
GAFt = qml.iGt(t, mec.QAA, mec.QAF)
else: # shut
GAFt = qml.iGt(t, mec.QFF, mec.QFA)
grouplik = np.dot(grouplik, GAFt)
if grouplik.max() > 1e50:
grouplik = grouplik * 1e-100
print ('grouplik was scaled down')
grouplik = np.dot(grouplik, endB)
loglik += log(grouplik[0])
newrates = np.log(mec.theta())
return -loglik, newrates
def likelihood(theta, opts):
"""
Calculate likelihood for a series of open and shut times using ideal
probability density functions.
"""
mec = opts['mec']
conc = opts['conc']
bursts = opts['data']
#mec.set_rateconstants(np.exp(theta))
mec.theta_unsqueeze(np.exp(theta))
mec.set_eff('c', conc)
startB = qml.phiA(mec)
endB = np.ones((mec.kF, 1))
loglik = 0
for ind in bursts:
burst = bursts[ind]
grouplik = startB
for i in range(len(burst)):
t = burst[i]
if i % 2 == 0: # open time
GAFt = qml.iGt(t, mec.QAA, mec.QAF)
else: # shut
GAFt = qml.iGt(t, mec.QFF, mec.QFA)
grouplik = np.dot(grouplik, GAFt)
if grouplik.max() > 1e50:
grouplik = grouplik * 1e-100
print('grouplik was scaled down')
grouplik = np.dot(grouplik, endB)
loglik += log(grouplik[0])
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
def printout_correlations(mec, output=sys.stdout, eff='c'):
"""
"""
str = ('\n\n*************************************\n' +
'CORRELATIONS\n')
kA, kI = mec.kA, mec.kI
str += ('kA, kF = {0:d}, {1:d}\n'.format(kA, kI))
GAF, GFA = qml.iGs(mec.Q, kA, kI)
rGAF, rGFA = np.rank(GAF), np.rank(GFA)
str += ('Ranks of GAF, GFA = {0:d}, {1:d}\n'.format(rGAF, rGFA))
XFF = np.dot(GFA, GAF)
rXFF = np.rank(XFF)
str += ('Rank of GFA * GAF = {0:d}\n'.format(rXFF))
ncF = rXFF - 1
eigXFF, AXFF = qml.eigs(XFF)
str += ('Eigenvalues of GFA * GAF:\n')
str1 = ''
for i in range(kI):
str1 += '\t{0:.5g}'.format(eigXFF[i])
str += str1 + '\n'
XAA = np.dot(GAF, GFA)
rXAA = np.rank(XAA)
str += ('Rank of GAF * GFA = {0:d}\n'.format(rXAA))
ncA = rXAA - 1
eigXAA, AXAA = qml.eigs(XAA)
str += ('Eigenvalues of GAF * GFA:\n')
str1 = ''
for i in range(kA):
str1 += '\t{0:.5g}'.format(eigXAA[i])
str += str1 + '\n'
phiA, phiF = qml.phiA(mec).reshape((1,kA)), qml.phiF(mec).reshape((1,kI))
varA = corr_variance_A(phiA, mec.QAA, kA)
varF = corr_variance_A(phiF, mec.QII, kI)
# open - open time correlations
str += ('\n OPEN - OPEN TIME CORRELATIONS')
str += ('Variance of open time = {0:.5g}\n'.format(varA))
SDA = sqrt(varA)
str += ('SD of all open times = {0:.5g} ms\n'.format(SDA * 1000))
n = 50
SDA_mean_n = SDA / sqrt(float(n))
str += ('SD of means of {0:d} open times if'.format(n) +
'uncorrelated = {0:.5g} ms\n'.format(SDA_mean_n * 1000))
covAtot = 0
for i in range(1, n):
covA = corr_covariance_A(i+1, phiA, mec.QAA, XAA, kA)
ro = correlation_coefficient(covA, varA, varA)
covAtot += (n - i) * ro * varA
vtot = n * varA + 2. * covAtot
actSDA = sqrt(vtot / (n * n))
str += ('Actual SD of mean = {0:.5g} ms\n'.format(actSDA * 1000))
pA = 100 * (actSDA - SDA_mean_n) / SDA_mean_n
str += ('Percent difference as result of correlation = {0:.5g}\n'.
format(pA))
v2A = corr_limit_A(phiA, mec.QAA, AXAA, eigXAA, kA)
pmaxA = 100 * (sqrt(1 + 2 * v2A / varA) - 1)
str += ('Limiting value of percent difference for large n = {0:.5g}\n'.
format(pmaxA))
str += ('Correlation coefficients, r(k), for up to lag k = 5:\n')
for i in range(5):
covA = corr_covariance_A(i+1, phiA, mec.QAA, XAA, kA)
ro = correlation_coefficient(covA, varA, varA)
str += ('r({0:d}) = {1:.5g}\n'.format(i+1, ro))
# shut - shut time correlations
str += ('\n SHUT - SHUT TIME CORRELATIONS\n')
str += ('Variance of shut time = {0:.5g}\n'.format(varF))
SDF = sqrt(varF)
str += ('SD of all shut times = {0:.5g} ms\n'.format(SDF * 1000))
n = 50
SDF_mean_n = SDF / sqrt(float(n))
str += ('SD of means of {0:d} shut times if'.format(n) +
'uncorrelated = {0:.5g} ms\n'.format(SDF_mean_n * 1000))
covFtot = 0
for i in range(1, n):
covF = corr_covariance_A(i+1, phiF, mec.QII, XFF, kI)
ro = correlation_coefficient(covF, varF, varF)
covFtot += (n - i) * ro * varF
vtotF = 50 * varF + 2. * covFtot
actSDF = sqrt(vtotF / (50. * 50.))
str += ('Actual SD of mean = {0:.5g} ms\n'.format(actSDF * 1000))
pF = 100 * (actSDF - SDF_mean_n) / SDF_mean_n
str += ('Percent difference as result of correlation = {0:.5g}\n'.
format(pF))
v2F = corr_limit_A(phiF, mec.QII, AXFF, eigXFF, kI)
pmaxF = 100 * (sqrt(1 + 2 * v2F / varF) - 1)
str += ('Limiting value of percent difference for large n = {0:.5g}\n'.
format(pmaxF))
str += ('Correlation coefficients, r(k), for up to k = 5 lags:\n')
for i in range(5):
covF = corr_covariance_A(i+1, phiF, mec.QII, XFF, kI)
ro = correlation_coefficient(covF, varF, varF)
str += ('r({0:d}) = {1:.5g}\n'.format(i+1, ro))
# open - shut time correlations
str += ('\n OPEN - SHUT TIME CORRELATIONS\n')
str += ('Correlation coefficients, r(k), for up to k= 5 lags:\n')
for i in range(5):
covAF = corr_covariance_AF(i+1, phiA, mec.QAA, mec.QII, XAA, GAF, kA, kI)
ro = correlation_coefficient(covAF, varA, varF)
str += ('r({0:d}) = {1:.5g}\n'.format(i+1, ro))
return str
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 printout_distributions(mec, tres, eff='c'):
"""
"""
str = '\n*******************************************\n'
GAI, GIA = qml.iGs(mec.Q, mec.kA, mec.kI)
# OPEN TIME DISTRIBUTIONS
open = True
# Ideal pdf
eigs, w = ideal_dwell_time_pdf_components(mec.QAA, qml.phiA(mec))
str += 'IDEAL OPEN TIME DISTRIBUTION\n'
str += pdfs.expPDF_printout(eigs, w)
# Asymptotic pdf
#roots = asymptotic_roots(mec, tres, open)
roots = asymptotic_roots(tres, mec.QAA, mec.QII, mec.QAI, mec.QIA, mec.kA,
mec.kI)
#areas = asymptotic_areas(mec, tres, roots, open)
areas = asymptotic_areas(tres, roots, mec.QAA, mec.QII, mec.QAI, mec.QIA,
mec.kA, mec.kI, GAI, GIA)
str += '\nASYMPTOTIC OPEN TIME DISTRIBUTION\n'
str += 'term\ttau (ms)\tarea (%)\trate const (1/sec)\n'
for i in range(mec.kA):
str += ('{0:d}'.format(i + 1) +
'\t{0:.5g}'.format(-1.0 / roots[i] * 1000) +
'\t{0:.5g}'.format(areas[i] * 100) +
'\t{0:.5g}\n'.format(-roots[i]))
areast0 = np.zeros(mec.kA)
for i in range(mec.kA):
areast0[i] = areas[i] * np.exp(-tres * roots[i])
areast0 = areast0 / np.sum(areast0)
str += ('Areas for asymptotic pdf renormalised for t=0 to\
infinity (and sum=1), so areas can be compared with ideal pdf.\n')
for i in range(mec.kA):
str += ('{0:d}'.format(i + 1) + '\t{0:.5g}\n'.format(areast0[i] * 100))
mean = exact_mean_time(tres, mec.QAA, mec.QII, mec.QAI, mec.kA, mec.kI,
GAI, GIA)
str += ('Mean open time (ms) = {0:.5g}\n'.format(mean * 1000))
# Exact pdf
eigvals, gamma00, gamma10, gamma11 = exact_GAMAxx(mec, tres, open)
str += ('\nEXACT OPEN TIME DISTRIBUTION\n')
str += ('eigen\tg00(m)\tg10(m)\tg11(m)\n')
for i in range(mec.k):
str += ('{0:.5g}'.format(eigvals[i]) + '\t{0:.5g}'.format(gamma00[i]) +
'\t{0:.5g}'.format(gamma10[i]) +
'\t{0:.5g}\n'.format(gamma11[i]))
str += ('\n\n*******************************************\n')
# SHUT TIME DISTRIBUTIONS
open = False
# Ideal pdf
eigs, w = ideal_dwell_time_pdf_components(mec.QII, qml.phiF(mec))
str += ('IDEAL SHUT TIME DISTRIBUTION\n')
str += pdfs.expPDF_printout(eigs, w)
# Asymptotic pdf
#roots = asymptotic_roots(mec, tres, open)
roots = asymptotic_roots(tres, mec.QII, mec.QAA, mec.QIA, mec.QAI, mec.kI,
mec.kA)
#areas = asymptotic_areas(mec, tres, roots, open)
areas = asymptotic_areas(tres, roots, mec.QII, mec.QAA, mec.QIA, mec.QAI,
mec.kI, mec.kA, GIA, GAI)
str += ('\nASYMPTOTIC SHUT TIME DISTRIBUTION\n')
str += ('term\ttau (ms)\tarea (%)\trate const (1/sec)\n')
for i in range(mec.kI):
str += ('{0:d}'.format(i + 1) +
'\t{0:.5g}'.format(-1.0 / roots[i] * 1000) +
'\t{0:.5g}'.format(areas[i] * 100) +
'\t{0:.5g}\n'.format(-roots[i]))
areast0 = np.zeros(mec.kI)
for i in range(mec.kI):
areast0[i] = areas[i] * np.exp(-tres * roots[i])
areast0 = areast0 / np.sum(areast0)
str += ('Areas for asymptotic pdf renormalised for t=0 to\
infinity (and sum=1), so areas can be compared with ideal pdf.\n')
for i in range(mec.kI):
str += ('{0:d}'.format(i + 1) + '\t{0:.5g}\n'.format(areast0[i] * 100))
mean = exact_mean_time(tres, mec.QII, mec.QAA, mec.QIA, mec.kI, mec.kA,
GIA, GAI)
str += ('Mean shut time (ms) = {0:.6f}\n'.format(mean * 1000))
# Exact pdf
eigvals, gamma00, gamma10, gamma11 = exact_GAMAxx(mec, tres, open)
str += ('\nEXACT SHUT TIME DISTRIBUTION\n' +
'eigen\tg00(m)\tg10(m)\tg11(m)\n')
for i in range(mec.k):
str += ('{0:.5g}'.format(eigvals[i]) + '\t{0:.5g}'.format(gamma00[i]) +
'\t{0:.5g}'.format(gamma10[i]) +
'\t{0:.5g}\n'.format(gamma11[i]))
# Transition probabilities
pi = transition_probability(mec.Q)
str += ('\nProbability of transitions regardless of time:\n')
for i in range(mec.k):
str1 = '['
for j in range(mec.k):
str1 += '{0:.4g}\t'.format(pi[i, j])
str1 += ']\n'
str += str1
# Transition frequency
f = transition_frequency(mec.Q)
str += ('\nFrequency of transitions (per second):\n')
for i in range(mec.k):
str1 = '['
for j in range(mec.k):
str1 += '{0:.4g}\t'.format(f[i, j])
str1 += ']\n'
str += str1
return str
def printout_correlations(mec, output=sys.stdout, eff='c'):
"""
"""
str = ('\n\n*************************************\n' + 'CORRELATIONS\n')
kA, kI = mec.kA, mec.kI
str += ('kA, kF = {0:d}, {1:d}\n'.format(kA, kI))
GAF, GFA = qml.iGs(mec.Q, kA, kI)
rGAF, rGFA = np.rank(GAF), np.rank(GFA)
str += ('Ranks of GAF, GFA = {0:d}, {1:d}\n'.format(rGAF, rGFA))
XFF = np.dot(GFA, GAF)
rXFF = np.rank(XFF)
str += ('Rank of GFA * GAF = {0:d}\n'.format(rXFF))
ncF = rXFF - 1
eigXFF, AXFF = qml.eigs(XFF)
str += ('Eigenvalues of GFA * GAF:\n')
str1 = ''
for i in range(kI):
str1 += '\t{0:.5g}'.format(eigXFF[i])
str += str1 + '\n'
XAA = np.dot(GAF, GFA)
rXAA = np.rank(XAA)
str += ('Rank of GAF * GFA = {0:d}\n'.format(rXAA))
ncA = rXAA - 1
eigXAA, AXAA = qml.eigs(XAA)
str += ('Eigenvalues of GAF * GFA:\n')
str1 = ''
for i in range(kA):
str1 += '\t{0:.5g}'.format(eigXAA[i])
str += str1 + '\n'
phiA, phiF = qml.phiA(mec).reshape((1, kA)), qml.phiF(mec).reshape((1, kI))
varA = corr_variance_A(phiA, mec.QAA, kA)
varF = corr_variance_A(phiF, mec.QII, kI)
# open - open time correlations
str += ('\n OPEN - OPEN TIME CORRELATIONS')
str += ('Variance of open time = {0:.5g}\n'.format(varA))
SDA = sqrt(varA)
str += ('SD of all open times = {0:.5g} ms\n'.format(SDA * 1000))
n = 50
SDA_mean_n = SDA / sqrt(float(n))
str += ('SD of means of {0:d} open times if'.format(n) +
'uncorrelated = {0:.5g} ms\n'.format(SDA_mean_n * 1000))
covAtot = 0
for i in range(1, n):
covA = corr_covariance_A(i + 1, phiA, mec.QAA, XAA, kA)
ro = correlation_coefficient(covA, varA, varA)
covAtot += (n - i) * ro * varA
vtot = n * varA + 2. * covAtot
actSDA = sqrt(vtot / (n * n))
str += ('Actual SD of mean = {0:.5g} ms\n'.format(actSDA * 1000))
pA = 100 * (actSDA - SDA_mean_n) / SDA_mean_n
str += (
'Percent difference as result of correlation = {0:.5g}\n'.format(pA))
v2A = corr_limit_A(phiA, mec.QAA, AXAA, eigXAA, kA)
pmaxA = 100 * (sqrt(1 + 2 * v2A / varA) - 1)
str += ('Limiting value of percent difference for large n = {0:.5g}\n'.
format(pmaxA))
str += ('Correlation coefficients, r(k), for up to lag k = 5:\n')
for i in range(5):
covA = corr_covariance_A(i + 1, phiA, mec.QAA, XAA, kA)
ro = correlation_coefficient(covA, varA, varA)
str += ('r({0:d}) = {1:.5g}\n'.format(i + 1, ro))
# shut - shut time correlations
str += ('\n SHUT - SHUT TIME CORRELATIONS\n')
str += ('Variance of shut time = {0:.5g}\n'.format(varF))
SDF = sqrt(varF)
str += ('SD of all shut times = {0:.5g} ms\n'.format(SDF * 1000))
n = 50
SDF_mean_n = SDF / sqrt(float(n))
str += ('SD of means of {0:d} shut times if'.format(n) +
'uncorrelated = {0:.5g} ms\n'.format(SDF_mean_n * 1000))
covFtot = 0
for i in range(1, n):
covF = corr_covariance_A(i + 1, phiF, mec.QII, XFF, kI)
ro = correlation_coefficient(covF, varF, varF)
covFtot += (n - i) * ro * varF
vtotF = 50 * varF + 2. * covFtot
actSDF = sqrt(vtotF / (50. * 50.))
str += ('Actual SD of mean = {0:.5g} ms\n'.format(actSDF * 1000))
pF = 100 * (actSDF - SDF_mean_n) / SDF_mean_n
str += (
'Percent difference as result of correlation = {0:.5g}\n'.format(pF))
v2F = corr_limit_A(phiF, mec.QII, AXFF, eigXFF, kI)
pmaxF = 100 * (sqrt(1 + 2 * v2F / varF) - 1)
str += ('Limiting value of percent difference for large n = {0:.5g}\n'.
format(pmaxF))
str += ('Correlation coefficients, r(k), for up to k = 5 lags:\n')
for i in range(5):
covF = corr_covariance_A(i + 1, phiF, mec.QII, XFF, kI)
ro = correlation_coefficient(covF, varF, varF)
str += ('r({0:d}) = {1:.5g}\n'.format(i + 1, ro))
# open - shut time correlations
str += ('\n OPEN - SHUT TIME CORRELATIONS\n')
str += ('Correlation coefficients, r(k), for up to k= 5 lags:\n')
for i in range(5):
covAF = corr_covariance_AF(i + 1, phiA, mec.QAA, mec.QII, XAA, GAF, kA,
kI)
ro = correlation_coefficient(covAF, varA, varF)
str += ('r({0:d}) = {1:.5g}\n'.format(i + 1, ro))
return str
def printout_distributions(mec, tres, eff='c'):
"""
"""
str = '\n*******************************************\n'
GAI, GIA = qml.iGs(mec.Q, mec.kA, mec.kI)
# OPEN TIME DISTRIBUTIONS
open = True
# Ideal pdf
eigs, w = ideal_dwell_time_pdf_components(mec.QAA,
qml.phiA(mec))
str += 'IDEAL OPEN TIME DISTRIBUTION\n'
str += pdfs.expPDF_printout(eigs, w)
# Asymptotic pdf
#roots = asymptotic_roots(mec, tres, open)
roots = asymptotic_roots(tres,
mec.QAA, mec.QII, mec.QAI, mec.QIA, mec.kA, mec.kI)
#areas = asymptotic_areas(mec, tres, roots, open)
areas = asymptotic_areas(tres, roots,
mec.QAA, mec.QII, mec.QAI, mec.QIA, mec.kA, mec.kI, GAI, GIA)
str += '\nASYMPTOTIC OPEN TIME DISTRIBUTION\n'
str += 'term\ttau (ms)\tarea (%)\trate const (1/sec)\n'
for i in range(mec.kA):
str += ('{0:d}'.format(i+1) +
'\t{0:.5g}'.format(-1.0 / roots[i] * 1000) +
'\t{0:.5g}'.format(areas[i] * 100) +
'\t{0:.5g}\n'.format(- roots[i]))
areast0 = np.zeros(mec.kA)
for i in range(mec.kA):
areast0[i] = areas[i] * np.exp(- tres * roots[i])
areast0 = areast0 / np.sum(areast0)
str += ('Areas for asymptotic pdf renormalised for t=0 to\
infinity (and sum=1), so areas can be compared with ideal pdf.\n')
for i in range(mec.kA):
str += ('{0:d}'.format(i+1) +
'\t{0:.5g}\n'.format(areast0[i] * 100))
mean = exact_mean_time(tres,
mec.QAA, mec.QII, mec.QAI, mec.kA, mec.kI, GAI, GIA)
str += ('Mean open time (ms) = {0:.5g}\n'.format(mean * 1000))
# Exact pdf
eigvals, gamma00, gamma10, gamma11 = exact_GAMAxx(mec, tres, open)
str += ('\nEXACT OPEN TIME DISTRIBUTION\n')
str += ('eigen\tg00(m)\tg10(m)\tg11(m)\n')
for i in range(mec.k):
str += ('{0:.5g}'.format(eigvals[i]) +
'\t{0:.5g}'.format(gamma00[i]) +
'\t{0:.5g}'.format(gamma10[i]) +
'\t{0:.5g}\n'.format(gamma11[i]))
str += ('\n\n*******************************************\n')
# SHUT TIME DISTRIBUTIONS
open = False
# Ideal pdf
eigs, w = ideal_dwell_time_pdf_components(mec.QII, qml.phiF(mec))
str += ('IDEAL SHUT TIME DISTRIBUTION\n')
str += pdfs.expPDF_printout(eigs, w)
# Asymptotic pdf
#roots = asymptotic_roots(mec, tres, open)
roots = asymptotic_roots(tres,
mec.QII, mec.QAA, mec.QIA, mec.QAI, mec.kI, mec.kA)
#areas = asymptotic_areas(mec, tres, roots, open)
areas = asymptotic_areas(tres, roots,
mec.QII, mec.QAA, mec.QIA, mec.QAI, mec.kI, mec.kA, GIA, GAI)
str += ('\nASYMPTOTIC SHUT TIME DISTRIBUTION\n')
str += ('term\ttau (ms)\tarea (%)\trate const (1/sec)\n')
for i in range(mec.kI):
str += ('{0:d}'.format(i+1) +
'\t{0:.5g}'.format(-1.0 / roots[i] * 1000) +
'\t{0:.5g}'.format(areas[i] * 100) +
'\t{0:.5g}\n'.format(- roots[i]))
areast0 = np.zeros(mec.kI)
for i in range(mec.kI):
areast0[i] = areas[i] * np.exp(- tres * roots[i])
areast0 = areast0 / np.sum(areast0)
str += ('Areas for asymptotic pdf renormalised for t=0 to\
infinity (and sum=1), so areas can be compared with ideal pdf.\n')
for i in range(mec.kI):
str += ('{0:d}'.format(i+1) +
'\t{0:.5g}\n'.format(areast0[i] * 100))
mean = exact_mean_time(tres,
mec.QII, mec.QAA, mec.QIA, mec.kI, mec.kA, GIA, GAI)
str += ('Mean shut time (ms) = {0:.6f}\n'.format(mean * 1000))
# Exact pdf
eigvals, gamma00, gamma10, gamma11 = exact_GAMAxx(mec, tres, open)
str += ('\nEXACT SHUT TIME DISTRIBUTION\n' +
'eigen\tg00(m)\tg10(m)\tg11(m)\n')
for i in range(mec.k):
str += ('{0:.5g}'.format(eigvals[i]) +
'\t{0:.5g}'.format(gamma00[i]) +
'\t{0:.5g}'.format(gamma10[i]) +
'\t{0:.5g}\n'.format(gamma11[i]))
# Transition probabilities
pi = transition_probability(mec.Q)
str += ('\nProbability of transitions regardless of time:\n')
for i in range(mec.k):
str1 = '['
for j in range(mec.k):
str1 += '{0:.4g}\t'.format(pi[i,j])
str1 += ']\n'
str += str1
# Transition frequency
f = transition_frequency(mec.Q)
str += ('\nFrequency of transitions (per second):\n')
for i in range(mec.k):
str1 = '['
for j in range(mec.k):
str1 += '{0:.4g}\t'.format(f[i,j])
str1 += ']\n'
str += str1
return str