Source code for espressomd.accumulators

# Copyright (C) 2010-2019 The ESPResSo project
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# ESPResSo is free software: you can redistribute it and/or modify
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from .script_interface import ScriptObjectRegistry, 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 get_mean(self): """ Returns the samples mean values of the respective observable with which the accumulator was initialized. """ return np.array(self.call_method("get_mean")).reshape(self.shape())
[docs] def get_variance(self): """ Returns the samples variance for the observable. """ return np.array(self.call_method("get_variance")).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 correlations based on results from observables. 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)` 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 :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 Hoefling et. al. :cite:`hofling11a`. For more information, see references therein. 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(ScriptObjectRegistry): """ 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")