```
# -*- coding: utf-8 -*-
# Copyright (c) 2015, PyRETIS Development Team.
# Distributed under the LGPLv2.1+ License. See LICENSE for more info.
"""Methods for analysis of path ensembles.
Important methods defined here
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
analyse_path_ensemble (:py:func:`.analyse_path_ensemble`)
Method to analyse a path ensemble, it will calculate crossing
probabilities and information about moves etc. This method
can be applied to files as well as path ensemble objects.
analyse_path_ensemble_object (:py:func:`.analyse_path_ensemble_object`)
Method to analyse a path ensemble, it will calculate crossing
probabilities and information about moves etc. This method is
intended to work directly on path ensemble objects.
match_probabilities (:py:func:`.match_probabilities`)
Match probabilities from several path ensembles and calculate
efficiencies and the error for the matched probability.
retis_flux (:py:func:`.retis_flux`)
Calculate the initial flux with errors for a RETIS simulation.
retis_rate (:py:func:`.retis_rate`)
Calculate the rate constant with errors for a RETIS simulation.
"""
import logging
import numpy as np
from pyretis.analysis.analysis import running_average, block_error_corr
from pyretis.analysis.histogram import histogram, histogram_and_avg
logger = logging.getLogger(__name__) # pylint: disable=C0103
logger.addHandler(logging.NullHandler())
__all__ = ['analyse_path_ensemble', 'analyse_path_ensemble_object',
'match_probabilities', 'retis_flux', 'retis_rate']
def _get_successful(path_ensemble, idetect):
"""Build the data of accepted (successful) paths.
In the `PathEnsemble` object all paths are stored, both accepted and
rejected and the `PathEnsemble.get_accepted()` is used here to
iterate over accepted paths. Successful paths are defined as paths
which are able to reach the interface specified with `idetect`. For
each accepted path, this function will give a value of `1` if the
path was successful and `0` otherwise.
Parameters
----------
path_ensemble : object :py:class:`.PathEnsemble`
This is the path ensemble we will analyse.
idetect : float
This is the interface used for detecting if a path is successful
or not.
Returns
-------
out : numpy.array
``out[i] = 1`` if path no. `i` is successful 0 otherwise.
"""
data = []
for path in path_ensemble.get_accepted():
value = 1 if path['ordermax'][0] > idetect else 0
data.append(value)
data = np.array(data)
return data
def _running_pcross(path_ensemble, idetect, data=None):
"""Create a running average of the crossing probability.
The running average is created as a function of the cycle number.
Note that the accepted paths are used to create an array which is
then averaged. This could possibly be replaced by a simple
'on-the-fly' calculation of the running average,
as detailed in: http://en.wikipedia.org/wiki/Moving_average
Parameters
----------
path_ensemble : object like :py:class:`.PathEnsemble`
This is the path ensemble we will analyse.
idetect : float
This is the interface used for detecting if a path is successful
or not.
data : numpy.array
This is the data created by `_get_successful(path_ensemble)`
If this function has been executed, the result can be re-used
here by specifying data. If not, it will be generated.
Returns
-------
out[0] : numpy.array
The running average of the crossing probability
out[1] : numpy.array
The original data, can be further put to use in the other
analysis functions.
See Also
--------
`_get_successful`
"""
if data is None:
data = _get_successful(path_ensemble, idetect)
return running_average(data), data
def _pcross_lambda(path_ensemble, ngrid=1000):
"""Calculate crossing probability for an ensemble.
The crossing probability is here obtained as a function of the order
parameter. The actual calculation is performed by
`_pcross_lambda_cumulative` and this function is just a wrapper in
order to handle input objects like :py:class:`.PathEnsemble`.
Parameters
----------
path_ensemble : object like :py:class:`.PathEnsemble`
This is the path ensemble we will analyse.
ngrid : int
This is the number of grid points.
Returns
-------
out[0] : numpy.array
The crossing probability.
out[1] : numpy.array
The order parameters.
See Also
--------
`_pcross_lambda_cumulative`
Notes
-----
This routine could perhaps be made shorter by making use of
`numpy.digitize` etc.
"""
# first, get the boundaries and order parameters of the
# accepted paths
orderparam = []
ordermax = None
for path in path_ensemble.get_accepted():
orderp = path['ordermax'][0]
if ordermax is None or orderp > ordermax:
ordermax = orderp
orderparam.append(orderp)
orderparam = np.array(orderparam)
# next create the ``cumulative histogram'':
ordermax = min(ordermax, max(path_ensemble.interfaces))
ordermin = path_ensemble.interfaces[1]
pcross, lamb = _pcross_lambda_cumulative(orderparam, ordermin, ordermax,
ngrid)
return pcross, lamb
def _pcross_lambda_cumulative(orderparam, ordermin, ordermax, ngrid,
weights=None):
"""Obtain crossing probability as a function of the order parameter.
It will do the actual calculation of the crossing probability as
a function of order parameter. It is split off from `pcross_lambda`
since the analysis is intended to be backwards compatible with the
output/results from the old ``TISMOL FORTRAN`` program.
Parameters
----------
orderparam : numpy.array
Array containing the order parameters.
ordermin : float
Minimum allowed order parameter.
ordermax : float
Maximum allowed order parameter.
ngrid : int
This is the number of grid points.
weights : numpy.array, optional
The weight of each order parameter. This is used in order to
count a specific order parameter more than once. If not given,
the values in `orderparam` will be weighted equally.
"""
lamb = np.linspace(ordermin, ordermax, ngrid)
pcross = np.zeros(ngrid)
delta_l = lamb[1] - lamb[0]
sumw = 0.0
for i, orderp in enumerate(orderparam):
idx = np.floor((orderp - ordermin) / delta_l)
idx = int(idx) + 1
# +1: idx is here defined so that lamb[idx-1] <= orderp < lamb[idx]
# further this lambda will contribute up to and including lamb[idx]
# this is accomplished by the idx+1 when summing weights below
if weights is None:
weight = 1
else:
weight = weights[i]
sumw += weight
if idx >= ngrid:
pcross += weight
elif idx < 0:
pass
else:
pcross[:idx + 1] += weight # +1 to include up to idx
pcross /= sumw # normalisation
return pcross, lamb
def _get_path_distribution(path_ensemble, bins=1000):
"""Calculate the distribution of path lengths.
Parameters
----------
path_ensemble : object like :py:class:`.PathEnsemble`
This is the path ensemble we will analyse.
bins : int, optional
The number of bins to use for the histograms for the
distribution.
Returns
-------
out[0] : list, [numpy.array, numpy.array, tuple]
Result for accepted paths (distribution). `out[0][0]` is the
histogram and `out[0][1]` are the mid points for bins.
`out[0][2]` is a tuple with the average and standard deviation
for the length.
out[1] : list, [numpy.array, numpy.array, tuple]
Result for all paths (distribution). `out[1][0]` is the
histogram and `out[1][1]` are the mid points for bins.
`out[1][2]` is a tuple with the average and standard deviation
for the length.
out[2] : numpy.array
The length of the accepted paths, in case we want to analyse it
further.
See Also
--------
:py:func:`.histogram_and_avg` in :py:mod:`.histogram`.
"""
# first get lengths of accepted paths:
length_acc = [path['length'] for path in path_ensemble.get_accepted()]
length_acc = np.array(length_acc)
length_all = []
for path in path_ensemble.paths:
length = _get_path_length(path, path_ensemble.ensemble_number)
if length is not None:
length_all.append(length)
length_all = np.array(length_all)
hist_acc = histogram_and_avg(length_acc, bins, density=True)
hist_all = histogram_and_avg(length_all, bins, density=True)
return hist_acc, hist_all, length_acc
def _get_path_length(path, ensemble_number):
"""Return the path length for different moves.
Different moves may have a different way of obtaining the path
length. (Example: time-reversal vs. shooting move).
Parameters
----------
path : dict
This is the dict containing the information about the path.
It can typically be obtained by iterating over the path
ensemble object, e.g. with a
`for path in path_ensemble.get_paths():`.
ensemble : int
This integer identifies the ensemble. This is used for
the swapping moves in [0^-] and [0^+].
Returns
-------
out : int
The path length
"""
move = path['generated'][0]
return_table = {'tr': 0, 's+': 0, 's-': 0, '00': 0}
if move in return_table:
if move == 's+' and ensemble_number == 0:
return path['length'] - 2
elif move == 's-' and ensemble_number == 1:
return path['length'] - 2
return return_table[move]
if move == 'sh':
return path['length'] - 1
elif move == 'ki':
msg = 'Skipped initial path: {}'.format(move)
logger.info(msg)
return None
msg = 'Skipped unknown mc move: {}'.format(move)
logger.warning(msg)
return None
def _shoot_analysis(path_ensemble, bins=1000):
"""Analyse the shooting performed in the path ensemble.
Parameters
----------
path_ensemble : object like :py:class:`.PathEnsemble`
This is the path ensemble we will analyse.
bins : int, optional
The number of bins to use for the histograms for the
distribution.
Returns
-------
out[0] : dict
For each possible status ('ACC, 'BWI', etc) this dict will
contain a histogram as returned by the histogram function.
It will also contain a 'REJ' key which is the concatenation
of all rejections and a 'ALL' key which is simply all the
values.
out[1] : dict
For each possible status ('ACC, 'BWI', etc) this dict will
contain the scale factors for the histograms. The scale
factors are obtained by dividing with the 'ALL' value.
See Also
--------
:py:func:`._create_shoot_histograms`.
"""
shoot_stats = {'REJ': [], 'ALL': []}
for path in path_ensemble.paths:
_update_shoot_stats(shoot_stats, path)
histograms, scale = _create_shoot_histograms(shoot_stats, bins)
return histograms, scale
def _update_shoot_stats(shoot_stats, path):
"""Update the shooting statistics with the status of the given path.
Parameters
----------
shoot_stats : dict
This dict contains the results from the shoot analysis, e.g.
`shoot_stats[key]` contain the order parameters for the status
`key` which can be the different statuses defined in
`pyretis.core.path._STATUS` or 'REJ' (for rejected).
path : dict
This is the path information, represented as a dictionary.
Returns
-------
out : None
Returns `None` but will update `shoot_stats` for shooting moves.
"""
move = path['generated'][0]
if move == 'sh':
orderp = path['generated'][1]
status = path['status']
if status not in shoot_stats:
shoot_stats[status] = []
shoot_stats[status].append(orderp)
if status != 'ACC':
shoot_stats['REJ'].append(orderp)
shoot_stats['ALL'].append(orderp)
def _create_shoot_histograms(shoot_stats, bins):
"""Create histograms and scale for the shoot analysis.
Parameters
----------
shoot_stats : dict
This dict contains the results from the shoot analysis, e.g.
`shoot_stats[key]` contain the order parameters for the status
`key` which can be the different statuses defined in
`pyretis.core.path._STATUS` or 'REJ' (for rejected).
bins : int
The number of bins to use for the histograms.
Returns
-------
out[0] : dict
For each possible status ('ACC, 'BWI', etc) this dict will
contain a histogram as returned by the histogram function.
It will also contain a 'REJ' key which is the concatenation of
all rejections and a 'ALL' key which is simply all the values.
out[1] : dict
For each possible status ('ACC, 'BWI', etc) this dict will
contain the scale factors for the histograms. The scale factors
are obtained by dividing with the 'ALL' value.
See Also
--------
:py:func:`.histogram` in :py:mod:`.histogram`.
"""
histograms = {}
scale = {}
for key in shoot_stats:
shoot_stats[key] = np.array(shoot_stats[key])
if len(shoot_stats[key]) < 1:
logger.warning('No shoots data found for %s (empty histogram)',
key)
mind = 0.0
maxd = 0.1
else:
mind = shoot_stats[key].min()
maxd = shoot_stats[key].max()
histograms[key] = histogram(shoot_stats[key], bins=bins,
limits=(mind, maxd), density=True)
scale[key] = (float(len(shoot_stats[key])) /
float(len(shoot_stats['ALL'])))
return histograms, scale
[docs]def analyse_path_ensemble_object(path_ensemble, settings):
"""Analyse a path ensemble object.
This function will make use of the different analysis functions and
analyse a path ensemble. This analysis function assumes that the
given path ensemble is an object like :py:class:`.PathEnsemble`
and that this path ensemble contains all the paths that are needed.
Parameters
----------
path_ensemble : object like :py:class:`.PathEnsemble`
The path ensemble to analyse.
settings : dict
This dictionary contains settings for the analysis.
Here we make use of the following keys from the
analysis section:
* `ngrid`: The number of grid points for calculating the
crossing probability as a function of the order parameter.
* `maxblock`: The max length of the blocks for the block error
analysis. Note that this will maximum be equal the half the
length of the data, see `block_error` in `.analysis`.
* `blockskip`: Can be used to skip certain block lengths.
A `blockskip` equal to `n` will consider every n'th block up
to `maxblock`, i.e. it will use block lengths equal to `1`,
`1+n`, `1+2n`, etc.
* `bins`: The number of bins to use for creating histograms.
Returns
-------
out : dict
This dictionary contains the main results for the analysis
which can be used for plotting or other kinds of output.
See Also
--------
:py:func:`._pcross_lambda`, :py:func:`._running_pcross`,
:py:func:`._get_path_distribution` and :py:func:`._shoot_analysis`.
"""
result = {}
analysis = settings['analysis']
if path_ensemble.nstats['npath'] != len(path_ensemble.paths):
msg = ' '.join(['The number of paths stored in path ensemble does not',
'correspond to the number of paths seen by the path',
'ensemble! Consider re-running the analysis using',
'the path ensemble file!'])
logger.warning(msg)
# first analysis is pcross as a function of lambda:
pcross, lamb = _pcross_lambda(path_ensemble,
ngrid=analysis['ngrid'])
result['pcross'] = [lamb, pcross]
# next get the running average of the crossing probability
prun, pdata = _running_pcross(path_ensemble, path_ensemble.detect)
result['prun'] = prun
try:
result['cycle'] = np.array(
[path['cycle'] for path in path_ensemble.get_paths()]
)
except KeyError:
msg = 'Could not obtain cycle number! Will assume (1, 2, ..., len(p))'
logger.warning(msg)
result['cycle'] = np.arange(len(prun))
# next, the error analysis:
result['blockerror'] = block_error_corr(pdata,
maxblock=analysis['maxblock'],
blockskip=analysis['blockskip'])
# next length-analysis:
hist1, hist2, _ = _get_path_distribution(path_ensemble,
bins=analysis['bins'])
result['pathlength'] = (hist1, hist2)
# next, shoots:
# move so that the analysis returns histograms and scale...
hist3, scale = _shoot_analysis(path_ensemble,
bins=analysis['bins'])
result['shoots'] = [hist3, scale]
# finally add some simple efficiency metrics:
result['efficiency'] = [path_ensemble.get_acceptance_rate(),
path_ensemble.nstats['npath'] * hist2[2][0]]
result['efficiency'].append(result['efficiency'][1] *
result['blockerror'][4]**2)
result['tis-cycles'] = path_ensemble.nstats['npath']
# results['efficiency'] is [acceptance rate, totsim , tis-eff]
return result
[docs]def analyse_path_ensemble(path_ensemble, settings):
"""Analyse a path ensemble.
This function will make use of the different analysis functions and
analyse a path ensemble. This function is more general than the
`analyse_path_ensemble_object` function in that it should work on
both `PathEnsemble` and `PathEnsembleFile` objects. The running
average is updated on-the-fly, see Wikipedia for
details [wikimov]_.
Parameters
----------
path_ensemble : object like :py:class:`.PathEnsemble`
This is the path ensemble to analyse.
settings : dict
This dictionary contains settings for the analysis.
We make use of the following keys:
* `ngrid`: The number of grid points for calculating the
crossing probability as a function of the order parameter.
* `maxblock`: The max length of the blocks for the block error
analysis. Note that this will maximum be equal the half the
length of the data, see `block_error` in `.analysis`.
* `blockskip`: Can be used to skip certain block lengths.
A `blockskip` equal to `n` will consider every n'th block up
to `maxblock`, i.e. it will use block lengths equal to `1`,
`1+n`, `1+2n`, etc.
* `bins`: The number of bins to use for creating histograms.
Returns
-------
out : dict
This dictionary contains the main results for the analysis which
can be used for plotting or other kinds of output.
See Also
--------
:py:func:`._update_shoot_stats`, :py:func:`.pcross_lambda_cumulative`
and :py:func:`._create_shoot_histograms`.
References
----------
.. [wikimov] Wikipedia, "Moving Average",
http://en.wikipedia.org/wiki/Moving_average
"""
detect = path_ensemble.detect
if path_ensemble.ensemble_number == 0:
return analyse_path_ensemble0(path_ensemble, settings)
ensemble_number = path_ensemble.ensemble_number
result = {'prun': [],
'cycle': [],
'detect': detect,
'ensemble': path_ensemble.ensemble_name,
'ensembleid': ensemble_number,
'interfaces': [i for i in path_ensemble.interfaces]}
orderparam = [] # list of all accepted order parameters
weights = []
success = 0 # determines if the current path is successful or not
pdata = []
length_acc = []
length_all = []
shoot_stats = {'REJ': [], 'ALL': []}
nacc = 0
npath = 0
for path in path_ensemble.get_paths(): # loop over all paths
npath += 1
if path['status'] == 'ACC':
nacc += 1
weights.append(1)
orderparam.append(path['ordermax'][0])
length_acc.append(path['length'])
success = 1 if path['ordermax'][0] > detect else 0
pdata.append(success) # Store data for block analysis
else: # just increase the weights
weights[-1] += 1
# we also update the running average of the probability here:
if not result['prun']:
result['prun'] = [success]
else: # update average
result['prun'].append(float(success +
result['prun'][-1] * (npath - 1)) /
float(npath))
result['cycle'].append(path['cycle'])
# get the length - note that this length depends on the type of move
# see the `_get_path_length` function.
length = _get_path_length(path, ensemble_number)
if length is not None:
length_all.append(length)
# update the shoot stats, this will only be done for shooting moves
_update_shoot_stats(shoot_stats, path)
# Perform the different analysis tasks:
# 1) result['prun'] is already calculated.
result['cycle'] = np.array(result['cycle'])
result['prun'] = np.array(result['prun'])
# 2) lambda pcross:
analysis = settings['analysis']
orderparam = np.array(orderparam)
ordermax = min(orderparam.max(), max(path_ensemble.interfaces))
pcross, lamb = _pcross_lambda_cumulative(orderparam,
path_ensemble.interfaces[1],
ordermax,
analysis['ngrid'],
weights=weights)
result['pcross'] = [lamb, pcross]
# 3) block error analysis:
result['blockerror'] = block_error_corr(data=np.repeat(pdata, weights),
maxblock=analysis['maxblock'],
blockskip=analysis['blockskip'])
# 4) length analysis:
hist1 = histogram_and_avg(np.repeat(length_acc, weights),
analysis['bins'], density=True)
hist2 = histogram_and_avg(np.array(length_all),
analysis['bins'], density=True)
result['pathlength'] = (hist1, hist2)
# 5) shoots analysis:
result['shoots'] = _create_shoot_histograms(shoot_stats,
analysis['bins'])
# 6) Add some simple efficiency metrics:
result['efficiency'] = [float(nacc) / float(npath),
float(npath) * hist2[2][0]]
result['efficiency'].append(result['efficiency'][1] *
result['blockerror'][4]**2)
result['tis-cycles'] = npath
# extra analysis for the [0^+] ensemble in case we will determine
# the initial flux:
if ensemble_number == 1:
lengtherr = block_error_corr(data=np.repeat(length_acc,
weights),
maxblock=analysis['maxblock'],
blockskip=analysis['blockskip'])
result['lengtherror'] = lengtherr
lenge2 = result['lengtherror'][4] * hist1[2][0] / (hist1[2][0]-2.)
result['fluxlength'] = [hist1[2][0]-2.0, lenge2,
lenge2 * (hist1[2][0]-2.)]
result['fluxlength'].append(result['efficiency'][1] * lenge2**2)
# results['efficiency'] is [acceptance rate, totsim , tis-eff]
return result
def analyse_path_ensemble0(path_ensemble, settings):
"""Analyse the [0^-] ensemble.
Parameters
----------
path_ensemble : object like :py:class:`.PathEnsemble`
This is the path ensemble to analyse.
settings : dict
This dictionary contains settings for the analysis.
We make use of the following keys:
* `ngrid`: The number of grid points for calculating the
crossing probability as a function of the order parameter.
* `maxblock`: The max length of the blocks for the block error
analysis. Note that this will maximum be equal the half the
length of the data, see `block_error` in `.analysis`.
* `blockskip`: Can be used to skip certain block lengths.
A `blockskip` equal to `n` will consider every n'th block up
to `maxblock`, i.e. it will use block lengths equal to `1`,
`1+n`, `1+2n`, etc.
* `bins`: The number of bins to use for creating histograms.
Returns
-------
result : dict
The results from the analysis on this ensemble.
"""
detect = path_ensemble.detect
ensemble_number = path_ensemble.ensemble_number
result = {'cycle': [],
'detect': detect,
'ensemble': path_ensemble.ensemble_name,
'ensembleid': ensemble_number,
'interfaces': [i for i in path_ensemble.interfaces]}
length_acc, length_all, weights = [], [], []
shoot_stats = {'REJ': [], 'ALL': []}
nacc, npath = 0, 0
for path in path_ensemble.get_paths(): # loop over all paths
npath += 1
if path['status'] == 'ACC':
nacc += 1
weights.append(1)
length_acc.append(path['length'])
else: # just increase the weights
weights[-1] += 1
result['cycle'].append(path['cycle'])
length = _get_path_length(path, ensemble_number)
if length is not None:
length_all.append(length)
# update the shoot stats, this will only be done for shooting moves
_update_shoot_stats(shoot_stats, path)
# Perform the different analysis tasks:
analysis = settings['analysis']
result['cycle'] = np.array(result['cycle'])
# 1) length analysis:
hist1 = histogram_and_avg(np.repeat(length_acc, weights),
analysis['bins'], density=True)
hist2 = histogram_and_avg(np.array(length_all),
analysis['bins'], density=True)
result['pathlength'] = (hist1, hist2)
# 2) block error of lengths:
result['lengtherror'] = block_error_corr(data=np.repeat(length_acc,
weights),
maxblock=analysis['maxblock'],
blockskip=analysis['blockskip'])
# 3) shoots analysis:
result['shoots'] = _create_shoot_histograms(shoot_stats,
analysis['bins'])
# 4) Add some simple efficiency metrics:
result['efficiency'] = [float(nacc) / float(npath),
float(npath) * hist2[2][0]]
result['efficiency'].append(result['efficiency'][1] *
result['lengtherror'][4]**2)
lenge2 = result['lengtherror'][4] * hist1[2][0] / (hist1[2][0]-2.)
result['fluxlength'] = [hist1[2][0]-2.0, lenge2, lenge2 * (hist1[2][0]-2.)]
result['fluxlength'].append(result['efficiency'][1] * lenge2**2)
result['tis-cycles'] = npath
return result
[docs]def match_probabilities(path_results, detect):
"""Match probabilities from several path ensembles.
It will also calculate efficiencies and error for the matched
probability.
Parameters
----------
path_results : list
These are the results from the path analysis. `path_results[i]`
contains the output from `analyse_path_ensemble` applied to
ensemble no. `i`. Here we make use of the following keys from
`path_results[i]`:
* `pcross`: The crossing probability.
* `prun`: The running average of the crossing probability.
* `blockerror`: The output from the block error analysis.
* `efficiency`: The output from the efficiency analysis.
detect : list of floats
These are the detect interfaces used in the analysis.
Returns
-------
results : dict
These are results for the over-all probability and error
and also some over-all TIS efficiencies.
"""
results = {'matched-prob': [],
'overall-prob': [[], []]}
accprob = 1.0
accprob_err = 0.0
prob_simtime = 0.0
prob_opt_eff = 0.0
for idet, result in zip(detect, path_results):
# do matching only in part left of idetect:
idx = np.where(result['pcross'][0] <= idet)[0]
results['overall-prob'][0].extend(result['pcross'][0][idx])
results['overall-prob'][1].extend(result['pcross'][1][idx] * accprob)
# update probabilities, error and efficiency:
mat = np.column_stack((result['pcross'][0], result['pcross'][1]))
mat[:, 1] *= accprob
results['matched-prob'].append(mat)
accprob *= result['prun'][-1]
accprob_err += result['blockerror'][4]**2
prob_simtime += result['efficiency'][1]
prob_opt_eff += np.sqrt(result['efficiency'][2])
results['overall-prob'] = np.transpose(results['overall-prob'])
results['prob'] = accprob
results['relerror'] = np.sqrt(accprob_err)
# simulation time: cycles * path-length:
results['simtime'] = prob_simtime
# optimised TIS efficiency:
results['opteff'] = prob_opt_eff**2
# over-all TIS efficiency:
results['eff'] = accprob_err * prob_simtime
return results
[docs]def retis_flux(results0, results1, timestep):
"""Calculate the initial flux for RETIS.
Parameters
----------
results0 : dict
Results from the analysis of ensemble [0^-]
results1 : dict
Results from the analysis of ensemble [0^+]
timestep : float
The simulation timestep.
Returns
-------
flux : float
The initial flux.
flux_error : float
The relative error in the initial flux.
"""
flux0 = results0['fluxlength']
flux1 = results1['fluxlength']
tsum = flux0[0] + flux1[0]
flux = 1.0 / (tsum * timestep)
flux_error = (np.sqrt((flux0[1]*flux0[0])**2 + (flux1[1]*flux1[0])**2) /
tsum)
return flux, flux_error
[docs]def retis_rate(pcross, pcross_relerror, flux, flux_relerror):
"""Calculate the rate constant for RETIS.
Parameters
----------
pcross : float
Estimated crossing probability
pcross_relerror : float
Relative error in crossing probability.
flux : float
The initial flux.
flux_relerror : float
Relative error in the initial flux.
Returns
-------
rate : float
The rate constant
rate_error : float
The relative error in the rate constant.
"""
rate = pcross * flux
rate_error = np.sqrt(pcross_relerror**2 + flux_relerror**2)
return rate, rate_error
```

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