def meanSterr(self, remove=False, max=None):
"""
Returns array of mean and standard error of measured data.
Parameters
----------
remove : bool
Remove inf and -inf as well as nan. (default: False)
NOTE: A warning will be issued if remove == False and such objects are
encountered.
max : float or None
Remove data which is strictly above max in absolute value.
(default: None)
NOTE: max != None will trigger remove = True.
Returns
-------
SCGF : (self.sValues.size, 3) float Numpy array
Scaled cumulant generating function.
orderParameter : (self.sValues.size, 3) float Numpy array.
Order parameter.
orderParameterSq : (self.sValues.size, 3) float Numpy array.
Squared order parameter.
NOTE: (0) Biasing parameter.
(1) Mean.
(2) Standard error.
I : (self.sValues.size, 4) float Numpy array
Rate function.
NOTE: (0) (Squared) order parameter.
(1) Standard error on (squared) order parameter.
(2) Rate function.
(3) Standard error on rate function.
"""
SCGF = np.empty((self.sValues.size, 3))
orderParameter = np.empty((self.sValues.size, 3))
orderParameterSq = np.empty((self.sValues.size, 3))
I = np.empty((self.sValues.size, 4))
for i in range(self.sValues.size):
SCGF[i] = [
self.sValues[i],
*mean_sterr(self.SCGF[i], remove=remove, max=max)
]
orderParameter[i] = [
self.sValues[i],
*mean_sterr(self.orderParameter[i], remove=remove, max=max)
]
orderParameterSq[i] = [
self.sValues[i],
*mean_sterr(self.orderParameterSq[i], remove=remove, max=max)
]
I[i] = [
*mean_sterr(self.I[i, :, 0], remove=remove, max=max),
*mean_sterr(self.I[i, :, 1], remove=remove, max=max)
]
return SCGF, orderParameter, orderParameterSq, I
def msd(self, n_max=100, int_max=100, min=None, max=None, jump=1):
"""
Compute mean square displacement.
Parameters
----------
n_max : int
Maximum number of times at which to compute the mean square
displacement. (default: 100)
int_max : int
Maximum number of different intervals to consider when averaging
the mean square displacement. (default: 100)
min : int or None
Minimum time at which to compute the displacement. (default: None)
NOTE: if min == None, then min = 1.
max : int or None
Maximum time at which to compute the displacement. (default: None)
NOTE: if max == None, then max is taken to be the maximum according
to the choice of int_max.
jump : int
Compute displacements by treating frames in packs of `jump'. This
can speed up calculation but also give unaccuracies if
`jump'*self.dt is of the order of the system size. (default: 1)
Returns
-------
msd_sterr : (3, *) float numpy array
Array of:
(0) lag time at which the mean square displacement is computed,
(1) mean square displacement,
(2) standard error of the computed mean square displacement.
"""
min = 1 if min == None else int(min)
max = ((self.frames - self.skip - 1) //
int_max if max == None else int(max))
# COMPUTE RELEVANT DISPLACEMENTS FROM DATA
dt = logspace(min, max, n_max) # array of lag times
displacements = self.dtDisplacements(
dt, # array of displacements for different initial times and lag times
int_max=int_max,
jump=jump,
norm=False)
# COMPUTE MEAN SQUARE DISPLACEMENTS
msd_sterr = []
for i in range(dt.size):
disp = displacements[:, i]
if self.N > 1:
disp -= disp.mean(axis=1).reshape(
displacements.shape[0], 1, 2
) # substract mean displacement of particles during each considered intervals
disp.reshape(displacements.shape[0] * self.N, 2)
msd_sterr += [[
dt[i], *mean_sterr(np.sum(disp**2, axis=-1).flatten())
]]
return np.array(msd_sterr)
def corWorkOrderAve(self,
n_max=100,
int_max=None,
min=None,
max=None,
log=False):
"""
Compute correlations of the fluctuations of the work averaged over an
interval of length `tau' and the fluctuations of the order parameter norm
at the beginning of the interval.
Parameters
----------
n_max : int
Maximum number of values at which to evaluate the correlation.
(default: 100)
int_max : int or None
Maximum number of different intervals to consider in order to
compute the mean which appears in the correlation expression.
(default: None)
NOTE: if int_max == None, then a maximum number of disjoint
intervals will be considered.
min : int or None
Minimum value at which to compute the correlation. (default: None)
NOTE: this value is passed as `min' to self.n.
max : int or None
Maximum value at which to compute the correlation. (default: None)
NOTE: this value is passed as `max' to self.n.
log : bool
Logarithmically space values at which the correlations are
computed. (default: True)
Returns
-------
cor : (5, *) numpy array
Array of:
(0) value at which the correlation is computed,
(1) mean of the computed correlation,
(2) standard error of the computed correlation,
(3) standard deviation of the active work,
(4) standard deviation of the order parameter norm.
"""
cor = []
for n in self._n(n_max=n_max, min=min, max=max, log=log):
works = (lambda l: l - np.mean(l))(
self.nWork(n, int_max=int_max)
) # fluctuations of the active wok on intervals of size n
orders = (lambda l: l - np.mean(l))(
np.array(
list(
map( # fluctuations of the order parameter norm at the beginning of these intervals
lambda t: self.getOrderParameter(t, norm=True),
self.framesWork *
self._time0(n, int_max=int_max)))))
workOrder = works * orders
cor += [[n, *mean_sterr(workOrder), np.std(works), np.std(orders)]]
return np.array(cor)
def corForceForce(self,
n_max=100, int_max=None, min=1, max=None, log=False):
"""
Returns fluctuations of the force autocorrelations.
Parameters
----------
n_max : int
Maximum number of values at which to evaluate the correlation.
(default: 100)
int_max : int or None
Maximum number of different intervals to consider in order to
compute the mean which appears in the correlation expression.
(default: None)
NOTE: if int_max == None, then a maximum number of disjoint
intervals will be considered.
min : int or None
Minimum value at which to compute the correlation. (default: 1)
max : int or None
Maximum value at which to compute the correlation. (default: None)
NOTE: if max == None, then n_max = self.frames - self.skip - 1.
log : bool
Logarithmically space values at which the correlations are
computed. (default: False)
Returns
-------
cor : (3, *) numpy array
Array of:
(0) value at which the correlation is computed,
(1) mean of the computed correlation,
(2) standard error of the computed correlation,
(3) mean of the squared norm of the flucuations of the force.
"""
min = 1 if min == None else int(min)
max = self.frames - self.skip - 1 if max == None else int(max)
int_max = ((self.frames - self.skip - 1)//max if int_max == None
else int(int_max))
if log: space = logspace
else: space = linspace
dt = space(min, max, n_max)
time0 = linspace(self.skip, self.frames - max - 1, int_max)
cor = []
forcesIni = (
(lambda l: (np.array(l)
- np.mean(l, axis=1).reshape(time0.size, 1)).flatten())( # fluctuations of the force scalar the orientation at t0
list(map(
lambda t: self._ForceOrientation(t),
time0))))
for tau in dt:
forcesFin = (
(lambda l:
np.array(l) - np.mean(l, axis=1).reshape(time0.size, 1, 2))( # fluctuations of the force at t0 + tau
list(map(lambda t: self.getForce(t + tau), time0)))).reshape(
(self.N*time0.size, 2))
forcesForces = list(map(lambda x, y: np.dot(x, y),
*(forcesIni, forcesFin)))
forcesNormSq = (list(map(lambda x, y: np.dot(x, y),
*(forcesIni, forcesIni)))
+ list(map(lambda x, y: np.dot(x, y),
*(forcesFin, forcesFin))))
cor += [[tau, *mean_sterr(forcesForces), np.mean(forcesNormSq)]]
return np.array(cor)
def corForceVelocity(self,
n_max=100, int_max=None, min=1, max=None, log=False):
"""
Returns correlations of the scalar product of force and velocity.
Parameters
----------
n_max : int
Maximum number of values at which to evaluate the correlation.
(default: 100)
int_max : int or None
Maximum number of different intervals to consider in order to
compute the mean which appears in the correlation expression.
(default: None)
NOTE: if int_max == None, then a maximum number of disjoint
intervals will be considered.
min : int or None
Minimum value at which to compute the correlation. (default: 1)
max : int or None
Maximum value at which to compute the correlation. (default: None)
NOTE: if max == None, then n_max = self.frames - self.skip - 1.
log : bool
Logarithmically space values at which the correlations are
computed. (default: False)
Returns
-------
cor : (3, *) numpy array
Array of:
(0) value at which the correlation is computed,
(1) mean of the computed correlation,
(2) standard error of the computed correlation,
(3) product of the standard deviations of the scalar product
at initial and final times.
"""
min = 1 if min == None else int(min)
max = self.frames - self.skip - 1 if max == None else int(max)
int_max = ((self.frames - self.skip - 1)//max if int_max == None
else int(int_max))
if log: space = logspace
else: space = linspace
dt = space(min, max, n_max)
time0 = linspace(self.skip, self.frames - max - 1, int_max)
cor = []
forcesVelocitesIni = (
(lambda l:
np.array(l) - np.mean(l, axis=1).reshape(time0.size, 1))( # fluctuations of the scalar product of force and velocity at t0
list(map(
lambda t: list(map(
lambda f, v: np.dot(f, v),
*(self.getForce(t),
self.getVelocities(t, norm=False)))),
time0)))).flatten()
print(forcesVelocitesIni)
for tau in dt:
forcesVelocitesFin = (
(lambda l:
np.array(l) - np.mean(l, axis=1).reshape(time0.size, 1))( # fluctuations of the scalar product of force and velocity at t0 + tau
list(map(
lambda t: list(map(
lambda f, v: np.dot(f, v),
*(self.getForce(t),
self.getVelocities(t, norm=False)))),
time0 + tau)))).flatten()
print(forcesVelocitesFin)
cor += [[
tau,
*mean_sterr(forcesVelocitesIni*forcesVelocitesFin),
forcesVelocitesIni.std()*forcesVelocitesFin.std()]]
return np.array(cor)
def meanSterr(self, remove=False, max=None):
"""
Returns array of mean and standard error of measured data.
Parameters
----------
remove : bool
Remove inf and -inf as well as nan. (default: False)
NOTE: A warning will be issued if remove == False and such objects
are encountered.
max : float or None
Remove data which is strictly above max in absolute value.
(default: None)
NOTE: max != None will trigger remove = True.
Returns
-------
activeWork : (self.gValues.size, 3) float Numpy array
Normalised rate of active work.
activeWorkForce : (self.gValues.size, 3) float Numpy array
Force part of the normalised rate of active work.
activeWorkOri : (self.gValues.size, 3) float Numpy array
Orientation part of the normalised rate of active work.
orderParameter : (self.gValues.size, 3) float Numpy array
Order parameter.
torqueIntegral1 : (self.gValues.size, 3) float Numpy array
First torque integral.
torqueIntegral2 : (self.gValues.size, 3) float Numpy array
Second torque integral.
NOTE: (0) Torque parameter.
(1) Mean.
(2) Standard error.
Lambda : (self.gValues.size, 4) float Numpy array
Bound to the rate function.
NOTE: (0) Active work.
(1) Standard error on active work.
(2) Bound to the rate function.
(3) Standard error on the boudn to the function.
"""
activeWork = np.empty((self.gValues.size, 3))
activeWorkForce = np.empty((self.gValues.size, 3))
activeWorkOri = np.empty((self.gValues.size, 3))
orderParameter = np.empty((self.gValues.size, 3))
torqueIntegral1 = np.empty((self.gValues.size, 3))
torqueIntegral2 = np.empty((self.gValues.size, 3))
Lambda = np.empty((self.gValues.size, 4))
for i in range(self.gValues.size):
activeWork[i] = [
self.gValues[i],
*mean_sterr(self.activeWork[i], remove=remove, max=max)]
activeWorkForce[i] = [
self.gValues[i],
*mean_sterr(self.activeWorkForce[i], remove=remove, max=max)]
activeWorkOri[i] = [
self.gValues[i],
*mean_sterr(self.activeWorkOri[i], remove=remove, max=max)]
orderParameter[i] = [
self.gValues[i],
*mean_sterr(self.orderParameter[i], remove=remove, max=max)]
torqueIntegral1[i] = [
self.gValues[i],
*mean_sterr(self.torqueIntegral1[i], remove=remove, max=max)]
torqueIntegral2[i] = [
self.gValues[i],
*mean_sterr(self.torqueIntegral2[i], remove=remove, max=max)]
Lambda[i] = [
*mean_sterr(self.Lambda[i, :, 0], remove=remove, max=max),
*mean_sterr(self.Lambda[i, :, 1], remove=remove, max=max)]
return (activeWork, activeWorkForce, activeWorkOri, orderParameter,
torqueIntegral1, torqueIntegral2, Lambda)
def meanSterr(self, remove=False, max=None):
"""
Returns array of mean and standard error of measured data.
Parameters
----------
remove : bool
Remove inf and -inf as well as nan. (default: False)
NOTE: A warning will be issued if remove == False and such objects
are encountered.
max : float or None
Remove data which is strictly above max in absolute value.
(default: None)
NOTE: max != None will trigger remove = True.
Returns
-------
SCGF : (self.sValues.size, 3) float Numpy array
Scaled cumulant generating function.
activeWork : (self.sValues.size, 3) float Numpy array
Normalised rate of active work.
activeWorkForce : (self.sValues.size, 3) float Numpy array
Force part of the normalised rate of active work.
activeWorkOri : (self.sValues.size, 3) float Numpy array
Orientation part of the normalised rate of active work.
orderParameter : (self.sValues.size, 3) float Numpy array
Order parameter.
NOTE: (0) Biasing parameter.
(1) Mean.
(2) Standard error.
I : (self.sValues.size, 4) float Numpy array
Rate function.
NOTE: (0) Active work.
(1) Standard error on active work.
(2) Rate function.
(3) Standard error on rate function.
"""
if max != None: remove = True
SCGF = np.empty((self.sValues.size, 3))
activeWork = np.empty((self.sValues.size, 3))
activeWorkForce = np.empty((self.sValues.size, 3))
activeWorkOri = np.empty((self.sValues.size, 3))
orderParameter = np.empty((self.sValues.size, 3))
I = np.empty((self.sValues.size, 4))
for i in range(self.sValues.size):
SCGF[i] = [
self.sValues[i],
*mean_sterr(self.SCGF[i], remove=remove, max=max)
]
activeWork[i] = [
self.sValues[i],
*mean_sterr(self.activeWork[i], remove=remove, max=max)
]
activeWorkForce[i] = [
self.sValues[i],
*mean_sterr(self.activeWorkForce[i], remove=remove, max=max)
]
activeWorkOri[i] = [
self.sValues[i],
*mean_sterr(self.activeWorkOri[i], remove=remove, max=max)
]
orderParameter[i] = [
self.sValues[i],
*mean_sterr(self.orderParameter[i], remove=remove, max=max)
]
I[i] = [
*mean_sterr(self.I[i, :, 0], remove=remove, max=max),
*mean_sterr(self.I[i, :, 1], remove=remove, max=max)
]
return (SCGF, activeWork, activeWorkForce, activeWorkOri,
orderParameter, I)
def corOrderOrder(self,
n_max=100,
int_max=100,
max=None,
norm=False,
log=False):
"""
Compute autocorrelations of the fluctuations of the order parameter.
Parameters
----------
n_max : int
Maximum number of values at which to evaluate the correlation.
(default: 100)
int_max : int
Maximum number of different intervals to consider in order to
compute the mean which appears in the correlation expression.
(default: 100)
max : int or None
Maximum value at which to compute the correlation. (default: None)
NOTE: if max == None, then max = self.frames - 1.
norm : bool
Consider the norm of the order parameter rather than its vector
form. (default: False)
log : bool
Logarithmically space values at which the correlations are
computed. (default: True)
Returns
-------
cor : (3, *) numpy array
Array of:
(0) value at which the correlation is computed,
(1) mean of the computed correlation,
(2) standard error of the computed correlation.
"""
if max == None: max = self.frames - 1
if log: space = logspace
else: space = linspace
cor = []
for tau in space(1, max, n_max):
time0 = list(
OrderedDict.fromkeys(
np.linspace(self.skip * self.framesWork,
self.frames - tau - 1,
int_max,
endpoint=True,
dtype=int)))
ordersIni = (lambda l: np.array(l) - np.mean(l, axis=0))(list(
map(lambda t: self.getOrderParameter(t, norm=norm), time0)))
ordersFin = (lambda l: np.array(l) - np.mean(l, axis=0))(list(
map(lambda t: self.getOrderParameter(t + tau, norm=norm),
time0)))
orderOrder = list(
map(lambda x, y: np.dot(x, y), *(ordersIni, ordersFin)))
cor += [[tau, *mean_sterr(orderOrder)]]
return np.array(cor)
def corWorkOrderIns(self,
tau0=1,
n_max=100,
int_max=None,
min=None,
max=None,
log=False):
"""
Compute correlations of the fluctuations of the order parameter norm
at a given time and the fluctuations of the active work averaged over
a time `tau0' at a later time.
Parameters
----------
tau0 : int
Number of consecutive individual active works on which to average
it. (default: 1)
n_max : int
Maximum number of values at which to evaluate the correlation.
(default: 100)
int_max : int or None
Maximum number of different intervals to consider in order to
compute the mean which appears in the correlation expression.
(default: None)
NOTE: if int_max == None, then a maximum number of disjoint
intervals will be considered.
min : int or None
Minimum value at which to compute the correlation. (default: None)
NOTE: if min == None then min = `tau0', otherwise the minimum of
`tau0' and `min' is taken.
max : int or None
Maximum value at which to compute the correlation. (default: None)
NOTE: this value is passed as `max' to self.n.
log : bool
Logarithmically space values at which the correlations are
computed. (default: True)
Returns
-------
cor : (5, *) numpy array
Array of:
(0) value at which the correlation is computed,
(1) mean of the computed correlation,
(2) standard error of the computed correlation,
(3) standard deviation of the active work,
(4) standard deviation of the order parameter norm.
"""
cor = []
for n in self._n(
n_max=n_max,
log=log,
min=(2 *
tau0 if min == None else np.max([tau0 + min, 2 * tau0])),
max=(None if max == None else tau0 + max)):
ordersIni = (lambda l: l - np.mean(l))(
list(
map(
lambda t: self.getOrderParameter(
t, norm=True
), # fluctuations of the active work averaged between t0 and t0 + tau0
self._time0(n, int_max=int_max))))
worksFin = (lambda l: l - np.mean(l))(
list(
map(
lambda t: self.workArray[t + n - tau0:t + n].mean(
), # fluctuations of the active work averaged between t0 and t0 + tau0
self._time0(n, int_max=int_max))))
workOrder = ordersIni * worksFin
cor += [[
n - tau0, *mean_sterr(workOrder),
np.std(ordersIni),
np.std(worksFin)
]]
return np.array(cor)
def varWorkFromCorWork(self, tau0=1, n=100, int_max=None, bruteForce=True):
"""
Compute variance of the active work from its "instantaneous"
fluctuations correlations.
This function is primarily for consistency testing of
the correlations functions.
Parameters
----------
tau0 : int
Number of consecutive individual active works on which to average
it, and for which correlations will be computed. (default: 1)
n : int
Compute variance for tau = i*tau0 with i in {1, ..., n}.
(default: 100)
int_max : int or None
Maximum number of different intervals to consider in order to
compute the mean which appears in the correlation expression.
(default: None)
NOTE: if int_max == None, then a maximum number of intervals will
intervals will be considered (joint if bruteForce else
disjoint).
bruteForce : bool
Use self.corWorkWorkInsBruteForce rather than self.corWorkWorkIns.
(default: True)
Returns
-------
var : (3, *) numpy array
Array of:
(0) value at which the variance is computed,
(1) mean of the computed variance,
(2) standard error of the computed variance.
"""
if bruteForce: corWorkWorkIns = self.corWorkWorkInsBruteForce
else: corWorkWorkIns = self.corWorkWorkIns
if bruteForce:
cor = self.corWorkWorkInsBruteForce(tau0,
n_max=n,
int_max=int_max,
max=n - 1,
log=False)
else:
cor = self.corWorkWorkIns(tau0,
n_max=n,
int_max=int_max,
min=tau0,
max=(n - 1) * tau0,
log=False)
var0 = mean_sterr(
(lambda l: (l - l.mean())**2)(self.nWork(tau0, int_max=int_max)))
var = []
for n0 in range(1, n + 1):
var += [[n0 * tau0, var0[0] / n0, (var0[1] / n0)**2]]
for i in range(1, n0):
var[-1][1] += 2 * (n0 - i) * cor[i - 1, 1] / (n0**2)
var[-1][2] += (2 * (n0 - i) * cor[i - 1, 2] / (n0**2))**2
var[-1][2] = np.sqrt(var[-1][2])
return np.array(var)
def corWorkWorkInsBruteForce(self,
workPart1=None,
workPart2=None,
tau0=1,
n_max=100,
int_max=None,
max=None,
log=True):
"""
Compute (cross) correlations of the fluctuations of the work averaged
over `tau0' between different times.
This algorithm computes the correlations more quickly by averaging over
successive couples of initial and final values of the active work.
Results of this function should then be taken with care as some other
unwanted low-time correlations could be picked.
Parameters
----------
workPart1 : string
Part of the active work to consider at the beginning of the
interval:
* 'all': active work,
* 'force': force part of the active work,
* 'orientation': orientation part of the active work,
* 'noise': noise part of the active work.
(default: None)
NOTE: if workPart1 == None, then self.workArray is taken.
workPart2 : string
Part of the active work to consider at the end of the interval.
(default: None)
NOTE: if workPart2 == None, then self.workArray is taken.
tau0 : int
Number of consecutive individual active works on which to average
it. (default: 1)
n_max : int
Maximum number of values at which to evaluate the correlation.
(default: 100)
int_max : int or None
Maximum number of different intervals to consider in order to
compute the mean which appears in the correlation expression.
(default: None)
NOTE: if int_max == None, then a maximum number of intervals will
intervals will be considered.
max : int or None
Maximum value at which to compute the correlation in units of tau0.
(default: None)
NOTE: if max == None, the maximum number of values is computed.
log : bool
Logarithmically space values at which the correlations are
computed. (default: True)
Returns
-------
cor : (3, *) numpy array
Array of:
(0) value at which the correlation is computed,
(1) mean of the computed correlation,
(2) standard error of the computed correlation.
"""
work1 = (self.workArray
if workPart1 == None else self.workDict[workPart1])
work2 = (self.workArray
if workPart2 == None else self.workDict[workPart2])
if log: space = logspace
else: space = linspace
if int_max == None: int_max = (self.numberWork - self.skip) // tau0
Nsample = int(
np.min([(self.numberWork - self.skip) // tau0, int_max * tau0])
) # size of the sample of consecutive normalised rates of active work to consider
workArray1 = np.array(
list(
map( # array of consecutive normalised rate of active work averaged of time tau0
lambda t: work1[self.skip + t * tau0:self.skip + t * tau0 +
tau0].mean(), range(Nsample))))
workArray1 -= workArray1.mean(
) # only considering fluctuations to the mean
if workPart1 == workPart2: workArray2 = workArray1
else:
workArray2 = np.array(
list(
map( # array of consecutive normalised rate of active work averaged of time tau0
lambda t: work2[self.skip + t * tau0:self.skip + t *
tau0 + tau0].mean(), range(Nsample))))
workArray2 -= workArray2.mean(
) # only considering fluctuations to the mean
lagTimes = space( # array of lag times considered
1,
(Nsample - 1) if max == None else int(np.min([max, Nsample - 1])),
n_max)
cor = list(
map(
lambda dt: [
tau0 * dt, *mean_sterr(
(workArray1 * np.roll(workArray2, -dt))[:Nsample - dt])
], lagTimes))
return np.array(cor)
def corWorkWorkIns(self,
workPart1=None,
workPart2=None,
tau0=1,
n_max=100,
int_max=None,
min=None,
max=None,
log=True):
"""
Compute (cross) correlations of the fluctuations of the work averaged
over `tau0' between different times.
Parameters
----------
workPart1 : string
Part of the active work to consider at the beginning of the
interval:
* 'all': active work,
* 'force': force part of the active work,
* 'orientation': orientation part of the active work,
* 'noise': noise part of the active work.
(default: None)
NOTE: if workPart1 == None, then self.workArray is taken.
workPart2 : string
Part of the active work to consider at the end of the interval.
(default: None)
NOTE: if workPart2 == None, then self.workArray is taken.
tau0 : int
Number of consecutive individual active works on which to average
it. (default: 1)
n_max : int
Maximum number of values at which to evaluate the correlation.
(default: 100)
int_max : int or None
Maximum number of different intervals to consider in order to
compute the mean which appears in the correlation expression.
(default: None)
NOTE: if int_max == None, then a maximum number of disjoint
intervals will be considered.
min : int or None
Minimum value at which to compute the correlation. (default: None)
NOTE: if min == None then min = `tau0', otherwise the minimum of
`tau0' and `min' is taken.
max : int or None
Maximum value at which to compute the correlation. (default: None)
NOTE: this value is passed as `max' to self.n.
log : bool
Logarithmically space values at which the correlations are
computed. (default: True)
Returns
-------
cor : (5, *) numpy array
Array of:
(0) value at which the correlation is computed,
(1) mean of the computed correlation,
(2) standard error of the computed correlation,
(3) standard deviation of the active work computed at the
beginning of the interval,
(4) standard deviation of the active work computed at the end
of the interval.
"""
work1 = (self.workArray
if workPart1 == None else self.workDict[workPart1])
work2 = (self.workArray
if workPart2 == None else self.workDict[workPart2])
cor = []
for n in self._n(
n_max=n_max,
log=log,
min=(2 *
tau0 if min == None else np.max([tau0 + min, 2 * tau0])),
max=(None if max == None else tau0 + max)):
worksIni = (lambda l: l - np.mean(l))(
list(
map(
lambda t: work1[t:t + tau0].mean(
), # fluctuations of the active work averaged between t0 and t0 + tau0
self._time0(n, int_max=int_max))))
worksFin = (lambda l: l - np.mean(l))(
list(
map(
lambda t: work2[t + n - tau0:t + n].mean(
), # fluctuations of the active work averaged between t0 and t0 + tau0
self._time0(n, int_max=int_max))))
workWork = worksIni * worksFin
cor += [[
n - tau0, *mean_sterr(workWork),
np.std(worksIni),
np.std(worksFin)
]]
return np.array(cor)
def corWorkWorkAve(self,
tau0=1,
n_max=100,
int_max=None,
min=None,
max=None,
log=True):
"""
Compute correlations of the fluctuations of the work averaged over
`tau0' at the beginning of an interval and the fluctuations of the work
averaged over the whole interval.
Parameters
----------
tau0 : int
Number of consecutive individual active works on which to average
it. (default: 1)
n_max : int
Maximum number of values at which to evaluate the correlation.
(default: 100)
int_max : int or None
Maximum number of different intervals to consider in order to
compute the mean which appears in the correlation expression.
(default: None)
NOTE: if int_max == None, then a maximum number of disjoint
intervals will be considered.
min : int or None
Minimum value at which to compute the correlation. (default: None)
NOTE: if min == None then this value is passed as `min' to self.n,
otherwise the minimum of `tau0' and `min' is taken.
max : int or None
Maximum value at which to compute the correlation. (default: None)
NOTE: this value is passed as `max' to self.n.
log : bool
Logarithmically space values at which the correlations are
computed. (default: True)
Returns
-------
cor : (5, *) numpy array
Array of:
(0) value at which the correlation is computed,
(1) mean of the computed correlation,
(2) standard error of the computed correlation,
(3) standard deviation of the active work computed at the
beginning of the interval,
(4) standard deviation of the active work computed over the
interval.
"""
cor = []
for n in self._n(n_max=n_max,
max=max,
log=log,
min=(None if min == None else np.max([min, tau0]))):
worksTot = (lambda l: l - np.mean(l))(
self.nWork(n, int_max=int_max)
) # fluctuations of the active wok on intervals of size n
worksIni = (lambda l: l - np.mean(l))(
list(
map(
lambda t: self.workArray[t:t + tau0].mean(
), # fluctuations of the active work averaged on tau0 at the beginning of these intervals
self._time0(n, int_max=int_max))))
workWork = worksTot * worksIni
cor += [[
n, *mean_sterr(workWork),
np.std(worksTot),
np.std(worksIni)
]]
return np.array(cor)