# Source code for espressomd.accumulators

```
# Copyright (C) 2010-2018 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 __future__ import print_function, absolute_import
from .script_interface import ScriptInterfaceHelper, script_interface_register
import numpy as np
[docs]@script_interface_register
class MeanVarianceCalculator(ScriptInterfaceHelper):
"""
Accumulates results from observables.
Parameters
----------
obs : Instance of :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).
get_mean
Returns the samples mean values of the respective observable with which the
accumulator was initialized.
get_variance
Returns the samples variance for the observable.
"""
_so_name = "Accumulators::MeanVarianceCalculator"
_so_bind_methods = (
"update",
"get_mean",
"get_variance"
)
_so_creation_policy = "LOCAL"
[docs]@script_interface_register
class Correlator(ScriptInterfaceHelper):
"""
Calculates correlations based on results from observables.
Parameters
----------
obs1, obs2 : Instances of :class:`espressomd.observables.Observable`.
The observables A and B that are to be correlated. If `obs2`
is omitted, autocorrelation of `obs1` is calculated by
default.
corr_operation : :obj:`str`
The operation that is performed on :math:`A(t)` and
:math:`B(t+\\tau)` to obtain :math:`C(\\tau)`. The
following operations are currently available:
* `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 `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`.
* `complex_conjugate_product`: assuming that the observables
consist of a complex and real part
:math:`A=(A_x+iA_y)`, and :math:`B=(B_x+iB_y)`, this
operation computes the result :math:`C=(C_x+iC_y)`,
as:
.. math::
C_x = A_xB_x + A_yB_y\\\\
C_y = A_yB_x - A_xB_y
* `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::
\\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 above equations are a
generalization of the formula presented by Hoefling
et. al. :cite:`hofling11a`. For more information, see
references therein. Per each 3 dimensions of the
observable, one dimension of the correlation output
is produced. If `fcs_acf` is used with other
observables than `ParticlePositions`, the physical
meaning of the result is unclear.
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. By default, it
is set equal to `tau_max` which results in the trivial linear
correlator. By setting `tau_lin` < `tau_max` the multiple
tau correlator is switched on. 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 and compress2 : :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.
args: :obj:`float[3]`
Three floats which are passed as arguments to the
correlation function. Currently it is only used by
fcs_acf. Other correlation operations will ignore these
values.
"""
_so_name = "Accumulators::Correlator"
_so_bind_methods = (
"update",
"finalize")
_so_creation_policy = "LOCAL"
[docs] def result(self):
res = np.array(self.call_method("get_correlation"))
return res.reshape((self.n_result, 2 + self.dim_corr))
[docs]@script_interface_register
class AutoUpdateAccumulators(ScriptInterfaceHelper):
"""
Class for handling auto-update of Accumulators used by
:class:`espressomd.System`.
"""
_so_name = "Accumulators::AutoUpdateAccumulators"
_so_creation_policy = "LOCAL"
[docs] def add(self, Accumulator):
"""
Adds a Accumulator instance to the auto-update list in the system.
"""
self.call_method("add", object=Accumulator)
[docs] def remove(self, Accumulator):
"""
Removes an MeanVarianceCalculator from the auto-update list.
"""
self.call_method("remove", object=Accumulator)
```