# Source code for espressomd.accumulators

```
# Copyright (C) 2010-2022 The ESPResSo project
#
# This file is part of ESPResSo.
#
# ESPResSo is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# ESPResSo is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
from .script_interface import ScriptObjectList, ScriptInterfaceHelper, script_interface_register
import numpy as np
[docs]@script_interface_register
class MeanVarianceCalculator(ScriptInterfaceHelper):
"""
Accumulates results from observables.
Parameters
----------
obs : :class:`espressomd.observables.Observable`
delta_N : :obj:`int`
Number of timesteps between subsequent samples for the auto update mechanism.
Methods
-------
update()
Update the accumulator (get the current values from the observable).
"""
_so_name = "Accumulators::MeanVarianceCalculator"
_so_bind_methods = (
"update",
"shape",
)
_so_creation_policy = "LOCAL"
[docs] def mean(self):
"""
Returns the samples mean values of the respective observable with
which the accumulator was initialized.
"""
return np.array(self.call_method("mean")).reshape(self.shape())
[docs] def variance(self):
"""
Returns the samples variance for the observable.
"""
return np.array(self.call_method("variance")).reshape(self.shape())
[docs] def std_error(self):
"""
Returns the standard error calculated from the samples variance for the observable by
assuming uncorrelated samples.
"""
return np.array(self.call_method("std_error")).reshape(self.shape())
[docs]@script_interface_register
class TimeSeries(ScriptInterfaceHelper):
"""
Records results from observables.
Parameters
----------
obs : :class:`espressomd.observables.Observable`
delta_N : :obj:`int`
Number of timesteps between subsequent samples for the auto update mechanism.
Methods
-------
update()
Update the accumulator (get the current values from the observable).
clear()
Clear the data
"""
_so_name = "Accumulators::TimeSeries"
_so_bind_methods = (
"update",
"shape",
"clear"
)
_so_creation_policy = "LOCAL"
[docs] def time_series(self):
"""
Returns the recorded values of the observable.
"""
return np.array(self.call_method("time_series")).reshape(self.shape())
[docs]@script_interface_register
class Correlator(ScriptInterfaceHelper):
"""
Calculates the correlation of two observables :math:`A` and :math:`B`,
or of one observable against itself (i.e. :math:`B = A`).
The correlation can be compressed using the :ref:`multiple tau correlation
algorithm <Details of the multiple tau correlation algorithm>`.
The operation that is performed on :math:`A(t)` and :math:`B(t+\\tau)`
to obtain :math:`C(\\tau)` depends on the ``corr_operation`` argument:
* ``"scalar_product"``: Scalar product of :math:`A` and
:math:`B`, i.e., :math:`C=\\sum\\limits_{i} A_i B_i`
* ``"componentwise_product"``: Componentwise product of
:math:`A` and :math:`B`, i.e., :math:`C_i = A_i B_i`
* ``"square_distance_componentwise"``: Each component of
the correlation vector is the square of the difference
between the corresponding components of the observables, i.e.,
:math:`C_i = (A_i-B_i)^2`. Example: when :math:`A` is
:class:`espressomd.observables.ParticlePositions`, it produces the
mean square displacement (for each component separately).
* ``"tensor_product"``: Tensor product of :math:`A` and
:math:`B`, i.e., :math:`C_{i \\cdot l_B + j} = A_i B_j`
with :math:`l_B` the length of :math:`B`.
* ``"fcs_acf"``: Fluorescence Correlation Spectroscopy (FCS)
autocorrelation function, i.e.,
.. math::
G_i(\\tau) =
\\frac{1}{N} \\left< \\exp \\left(
- \\frac{\\Delta x_i^2(\\tau)}{w_x^2}
- \\frac{\\Delta y_i^2(\\tau)}{w_y^2}
- \\frac{\\Delta z_i^2(\\tau)}{w_z^2}
\\right) \\right>
where :math:`N` is the average number of fluorophores in the
illumination area,
.. math::
\\Delta x_i^2(\\tau) = \\left( x_i(0) - x_i(\\tau) \\right)^2
is the square displacement of particle
:math:`i` in the :math:`x` direction, and :math:`w_x`
is the beam waist of the intensity profile of the
exciting laser beam,
.. math::
W(x,y,z) = I_0 \\exp
\\left( - \\frac{2x^2}{w_x^2} - \\frac{2y^2}{w_y^2} -
\\frac{2z^2}{w_z^2} \\right).
The values of :math:`w_x`, :math:`w_y`, and :math:`w_z`
are passed to the correlator as ``args``. The correlator calculates
.. math::
C_i(\\tau) =
\\exp \\left(
- \\frac{\\Delta x_i^2(\\tau)}{w_x^2}
- \\frac{\\Delta y_i^2(\\tau)}{w_y^2}
- \\frac{\\Delta z_i^2(\\tau)}{w_z^2}
\\right)
Per each 3 dimensions of the observable, one dimension of the correlation
output is produced. If ``"fcs_acf"`` is used with other observables than
:class:`espressomd.observables.ParticlePositions`, the physical meaning
of the result is unclear.
The above equations are a generalization of the formula presented by
HÃ¶fling et al. :cite:`hofling11a`. For more information, see references
therein.
Parameters
----------
obs1 : :class:`espressomd.observables.Observable`
The observable :math:`A` to be correlated with :math:`B` (``obs2``).
If ``obs2`` is omitted, autocorrelation of ``obs1`` is calculated by
default.
obs2 : :class:`espressomd.observables.Observable`, optional
The observable :math:`B` to be correlated with :math:`A` (``obs1``).
corr_operation : :obj:`str`
The operation that is performed on :math:`A(t)` and :math:`B(t+\\tau)`.
delta_N : :obj:`int`
Number of timesteps between subsequent samples for the auto update mechanism.
tau_max : :obj:`float`
This is the maximum value of :math:`\\tau` for which the
correlation should be computed. Warning: Unless you are using
the multiple tau correlator, choosing ``tau_max`` of more than
``100 * dt`` will result in a huge computational overhead. In a
multiple tau correlator with reasonable parameters, ``tau_max``
can span the entire simulation without too much additional cpu time.
tau_lin : :obj:`int`
The number of data-points for which the results are linearly spaced
in ``tau``. This is a parameter of the multiple tau correlator. If you
want to use it, make sure that you know how it works. ``tau_lin`` must
be divisible by 2. By setting ``tau_lin`` such that
``tau_max >= dt * delta_N * tau_lin``, the
multiple tau correlator is used, otherwise the trivial linear
correlator is used. By setting ``tau_lin = 1``, the value will be
overridden by ``tau_lin = ceil(tau_max / (dt * delta_N))``, which
will result in either the multiple or linear tau correlator.
In many cases, ``tau_lin=16`` is a
good choice but this may strongly depend on the observables you are
correlating. For more information, we recommend to read
ref. :cite:`ramirez10a` or to perform your own tests.
compress1 : :obj:`str`
These functions are used to compress the data when
going to the next level of the multiple tau
correlator. This is done by producing one value out of two.
The following compression functions are available:
* ``"discard2"``: (default value) discard the second value from the time series, use the first value as the result
* ``"discard1"``: discard the first value from the time series, use the second value as the result
* ``"linear"``: make a linear combination (average) of the two values
If only ``compress1`` is specified, then
the same compression function is used for both
observables. If both ``compress1`` and ``compress2`` are specified,
then ``compress1`` is used for ``obs1`` and ``compress2`` for ``obs2``.
Both ``discard1`` and ``discard2`` are safe for all
observables but produce poor statistics in the
tail. For some observables, ``"linear"`` compression
can be used which makes an average of two
neighboring values but produces systematic
errors. Depending on the observable, the
systematic error using the ``"linear"`` compression
can be anything between harmless and disastrous.
For more information, we recommend to read ref.
:cite:`ramirez10a` or to perform your own tests.
compress2 : :obj:`str`, optional
See ``compress1``.
args: :obj:`float` of length 3
Three floats which are passed as arguments to the correlation
function. Currently it is only used by ``"fcs_acf"``, which
will square these values in the core; if you later decide to
update these weights with ``obs.args = [...]``, you'll have to
provide already squared values! Other correlation operations
will ignore these values.
"""
_so_name = "Accumulators::Correlator"
_so_bind_methods = (
"update",
"shape",
"finalize")
_so_creation_policy = "LOCAL"
[docs] def result(self):
"""
Get correlation.
Returns
-------
:obj:`ndarray` of :obj:`float`
The result of the correlation function. The shape of the array
is determined by the shape of the input observable(s) and the
correlation operation.
"""
return np.array(self.call_method(
"get_correlation")).reshape(self.shape())
[docs] def lag_times(self):
"""
Returns
-------
:obj:`ndarray` of :obj:`float`
Lag times of the correlation.
"""
return np.array(self.call_method("get_lag_times"))
[docs] def sample_sizes(self):
"""
Returns
-------
:obj:`ndarray` of :obj:`int`
Samples sizes for each lag time.
"""
return np.array(self.call_method("get_samples_sizes"), dtype=int)
[docs]@script_interface_register
class AutoUpdateAccumulators(ScriptObjectList):
"""
Class for handling the auto-update of accumulators used by
:class:`espressomd.system.System`.
"""
_so_name = "Accumulators::AutoUpdateAccumulators"
_so_creation_policy = "LOCAL"
[docs] def add(self, accumulator):
"""
Adds an accumulator instance to the auto-update list.
"""
self.call_method("add", object=accumulator)
[docs] def remove(self, accumulator):
"""
Removes an accumulator from the auto-update list.
"""
self.call_method("remove", object=accumulator)
[docs] def clear(self):
"""
Removes all accumulators from the auto-update list.
"""
self.call_method("clear")
```