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
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# ESPResSo is distributed in the hope that it will be useful,
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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)