sync.py

"""!

@brief Neural Network: Oscillatory Neural Network based on Kuramoto model
@details Implementation based on paper @cite article::syncnet::1, @cite article::nnet::sync::1, @cite inproceedings::net::sync::1.

@authors Andrei Novikov (pyclustering@yandex.ru)
@date 2014-2020
@copyright GNU Public License

@cond GNU_PUBLIC_LICENSE
    PyClustering 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.
    
    PyClustering 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/>.
@endcond

"""

import math
import numpy
import random
import warnings

try:
    import matplotlib.pyplot as plt
    import matplotlib.animation as animation
except Exception as error_instance:
    warnings.warn("Impossible to import matplotlib (please, install 'matplotlib'), pyclustering's visualization "
                  "functionality is not available (details: '%s')." % str(error_instance))

import pyclustering.core.sync_wrapper as wrapper

from pyclustering.core.wrapper import ccore_library

from scipy.integrate import odeint

from pyclustering.nnet import network, conn_represent, conn_type, initial_type, solve_type
from pyclustering.utils import pi, draw_dynamics, draw_dynamics_set, set_ax_param


class order_estimator:
    """!
    @brief Provides services to calculate order parameter and local order parameter that are used
            for synchronization level estimation.

    """
    @staticmethod
    def calculate_sync_order(oscillator_phases):
        """!
        @brief Calculates level of global synchronization (order parameter) for input phases.
        @details This parameter is tend 1.0 when the oscillatory network close to global synchronization and it tend to 0.0 when 
                  desynchronization is observed in the network.
        
        @param[in] oscillator_phases (list): List of oscillator phases that are used for level of global synchronization.
        
        @return (double) Level of global synchronization (order parameter).
        
        @see calculate_order_parameter()
        
        """

        exp_amount = 0.0
        average_phase = 0.0

        for phase in oscillator_phases:
            exp_amount += math.expm1(abs(1j * phase))
            average_phase += phase

        exp_amount /= len(oscillator_phases)
        average_phase = math.expm1(abs(1j * (average_phase / len(oscillator_phases))))

        return abs(average_phase) / abs(exp_amount)


    @staticmethod
    def calculate_local_sync_order(oscillator_phases, oscillatory_network):
        """!
        @brief Calculates level of local synchorization (local order parameter) for input phases for the specified network.
        @details This parameter is tend 1.0 when the oscillatory network close to local synchronization and it tend to 0.0 when 
                  desynchronization is observed in the network.
        
        @param[in] oscillator_phases (list): List of oscillator phases that are used for level of local (partial) synchronization.
        @param[in] oscillatory_network (sync): Instance of oscillatory network whose connections are required for calculation.
        
        @return (double) Level of local synchronization (local order parameter).
        
        """

        exp_amount = 0.0
        num_neigh = 0.0

        for i in range(0, len(oscillatory_network), 1):
            for j in range(0, len(oscillatory_network), 1):
                if oscillatory_network.has_connection(i, j) is True:
                    exp_amount += math.exp(-abs(oscillator_phases[j] - oscillator_phases[i]))
                    num_neigh += 1.0

        if num_neigh == 0:
            num_neigh = 1.0

        return exp_amount / num_neigh



class sync_dynamic:
    """!
    @brief Represents output dynamic of Sync.
    
    """

    @property
    def output(self):
        """!
        @brief (list) Returns output dynamic of the Sync network (phase coordinates of each oscillator in the network) during simulation.
        
        """
        if (self._ccore_sync_dynamic_pointer is not None) and ((self._dynamic is None) or (len(self._dynamic) == 0)):
            self._dynamic = wrapper.sync_dynamic_get_output(self._ccore_sync_dynamic_pointer)

        return self._dynamic


    @property
    def time(self):
        """!
        @brief (list) Returns sampling times when dynamic is measured during simulation.
        
        """
        if (self._ccore_sync_dynamic_pointer is not None) and ((self._time is None) or (len(self._time) == 0)):
            self._time = wrapper.sync_dynamic_get_time(self._ccore_sync_dynamic_pointer)

        return self._time


    def __init__(self, phase, time, ccore=None):
        """!
        @brief Constructor of Sync dynamic.
        
        @param[in] phase (list): Dynamic of oscillators on each step of simulation. If ccore pointer is specified than it can be ignored.
        @param[in] time (list): Simulation time.
        @param[in] ccore (ctypes.pointer): Pointer to CCORE sync_dynamic instance in memory.
        
        """

        self._dynamic = phase
        self._time = time
        self._ccore_sync_dynamic_pointer = ccore


    def __del__(self):
        """!
        @brief Default destructor of Sync dynamic.
        
        """
        if self._ccore_sync_dynamic_pointer is not None:
            wrapper.sync_dynamic_destroy(self._ccore_sync_dynamic_pointer)


    def __len__(self):
        """!
        @brief Returns number of simulation steps that are stored in dynamic.
        @return (uint) Number of simulation steps that are stored in dynamic.
        
        """
        if (self._ccore_sync_dynamic_pointer is not None):
            return wrapper.sync_dynamic_get_size(self._ccore_sync_dynamic_pointer)

        return len(self._dynamic)


    def __getitem__(self, index):
        """!
        @brief Indexing of the dynamic.
        
        """
        if index == 0:
            return self.time

        elif index == 1:
            return self.output

        else:
            raise NameError('Out of range ' + index + ': only indexes 0 and 1 are supported.')


    def allocate_sync_ensembles(self, tolerance = 0.01, indexes = None, iteration = None):
        """!
        @brief Allocate clusters in line with ensembles of synchronous oscillators where each synchronous ensemble corresponds to only one cluster.
               
        @param[in] tolerance (double): Maximum error for allocation of synchronous ensemble oscillators.
        @param[in] indexes (list): List of real object indexes and it should be equal to amount of oscillators (in case of 'None' - indexes are in range [0; amount_oscillators]).
        @param[in] iteration (uint): Iteration of simulation that should be used for allocation.
        
        @return (list) Groups (lists) of indexes of synchronous oscillators.
                For example [ [index_osc1, index_osc3], [index_osc2], [index_osc4, index_osc5] ].
        
        """

        if self._ccore_sync_dynamic_pointer is not None:
            ensembles = wrapper.sync_dynamic_allocate_sync_ensembles(self._ccore_sync_dynamic_pointer, tolerance, iteration)

            if indexes is not None:
                for ensemble in ensembles:
                    for index in range(len(ensemble)):
                        ensemble[index] = indexes[ensemble[index]]

            return ensembles

        if (self._dynamic is None) or (len(self._dynamic) == 0):
            return []

        number_oscillators = len(self._dynamic[0])
        last_state = None

        if iteration is None:
            last_state = self._dynamic[len(self._dynamic) - 1]
        else:
            last_state = self._dynamic[iteration]

        clusters = []
        if number_oscillators > 0:
            clusters.append([0])

        for i in range(1, number_oscillators, 1):
            cluster_allocated = False
            for cluster in clusters:
                for neuron_index in cluster:
                    last_state_shifted = abs(last_state[i] - 2 * pi)

                    if ( ( (last_state[i] < (last_state[neuron_index] + tolerance)) and (last_state[i] > (last_state[neuron_index] - tolerance)) ) or
                         ( (last_state_shifted < (last_state[neuron_index] + tolerance)) and (last_state_shifted > (last_state[neuron_index] - tolerance)) ) ):
                        cluster_allocated = True

                        real_index = i
                        if indexes is not None:
                            real_index = indexes[i]

                        cluster.append(real_index)
                        break

                if cluster_allocated is True:
                    break

            if cluster_allocated is False:
                clusters.append([i])

        return clusters


    def allocate_phase_matrix(self, grid_width = None, grid_height = None, iteration = None):
        """!
        @brief Returns 2D matrix of phase values of oscillators at the specified iteration of simulation.
        @details User should ensure correct matrix sizes in line with following expression grid_width x grid_height that should be equal to 
                  amount of oscillators otherwise exception is thrown. If grid_width or grid_height are not specified than phase matrix size 
                  will by calculated automatically by square root.
        
        @param[in] grid_width (uint): Width of the allocated matrix.
        @param[in] grid_height (uint): Height of the allocated matrix.
        @param[in] iteration (uint): Number of iteration of simulation for which correlation matrix should be allocated.
                    If iternation number is not specified, the last step of simulation is used for the matrix allocation.
        
        @return (list) Phase value matrix of oscillators with size [number_oscillators x number_oscillators].
        
        """

        output_dynamic = self.output

        if (output_dynamic is None) or (len(output_dynamic) == 0):
            return []

        current_dynamic = output_dynamic[len(output_dynamic) - 1]
        if iteration is not None:
            current_dynamic = output_dynamic[iteration]

        width_matrix = grid_width
        height_matrix = grid_height
        number_oscillators = len(current_dynamic)
        if (width_matrix is None) or (height_matrix is None):
            width_matrix = int(math.ceil(math.sqrt(number_oscillators)))
            height_matrix = width_matrix

        if (number_oscillators != width_matrix * height_matrix):
            raise NameError("Impossible to allocate phase matrix with specified sizes, amout of neurons should be equal to grid_width * grid_height.");

        phase_matrix = [[0.0 for _ in range(width_matrix)] for _ in range(height_matrix)]
        for i in range(height_matrix):
            for j in range(width_matrix):
                phase_matrix[i][j] = current_dynamic[j + i * width_matrix]

        return phase_matrix


    def allocate_correlation_matrix(self, iteration = None):
        """!
        @brief Allocate correlation matrix between oscillators at the specified step of simulation.
               
        @param[in] iteration (uint): Number of iteration of simulation for which correlation matrix should be allocated.
                    If iternation number is not specified, the last step of simulation is used for the matrix allocation.
        
        @return (list) Correlation matrix between oscillators with size [number_oscillators x number_oscillators].
        
        """

        if self._ccore_sync_dynamic_pointer is not None:
            return wrapper.sync_dynamic_allocate_correlation_matrix(self._ccore_sync_dynamic_pointer, iteration)

        if (self._dynamic is None) or (len(self._dynamic) == 0):
            return []

        dynamic = self._dynamic
        current_dynamic = dynamic[len(dynamic) - 1]

        if iteration is not None:
            current_dynamic = dynamic[iteration]

        number_oscillators = len(dynamic[0])
        affinity_matrix = [[0.0 for i in range(number_oscillators)] for j in range(number_oscillators)]

        for i in range(number_oscillators):
            for j in range(number_oscillators):
                phase1 = current_dynamic[i]
                phase2 = current_dynamic[j]

                affinity_matrix[i][j] = abs(math.sin(phase1 - phase2))

        return affinity_matrix


    def calculate_order_parameter(self, start_iteration=None, stop_iteration=None):
        """!
        @brief Calculates level of global synchorization (order parameter).
        @details This parameter is tend 1.0 when the oscillatory network close to global synchronization and it tend to 0.0 when 
                  desynchronization is observed in the network. Order parameter is calculated using following equation:
                  
                  \f[
                  r_{c}=\frac{1}{Ne^{i\varphi }}\sum_{j=0}^{N}e^{i\theta_{j}};
                  \f]
                  
                  where \f$\varphi\f$ is a average phase coordinate in the network, \f$N\f$ is an amount of oscillators in the network.
        
        @param[in] start_iteration (uint): The first iteration that is used for calculation, if 'None' then the last iteration is used.
        @param[in] stop_iteration (uint): The last iteration that is used for calculation, if 'None' then 'start_iteration' + 1 is used.
        
        Example:
        @code
            oscillatory_network = sync(16, type_conn = conn_type.ALL_TO_ALL);
            output_dynamic = oscillatory_network.simulate_static(100, 10);
            
            print("Order parameter at the last step: ", output_dynamic.calculate_order_parameter());
            print("Order parameter at the first step:", output_dynamic.calculate_order_parameter(0));
            print("Order parameter evolution between 40 and 50 steps:", output_dynamic.calculate_order_parameter(40, 50));
        @endcode
        
        @return (list) List of levels of global synchronization (order parameter evolution).
        
        @see order_estimator
        
        """

        (start_iteration, stop_iteration) = self.__get_start_stop_iterations(start_iteration, stop_iteration)

        if self._ccore_sync_dynamic_pointer is not None:
            return wrapper.sync_dynamic_calculate_order(self._ccore_sync_dynamic_pointer, start_iteration, stop_iteration)

        sequence_order = []
        for index in range(start_iteration, stop_iteration):
            sequence_order.append(order_estimator.calculate_sync_order(self.output[index]))

        return sequence_order


    def calculate_local_order_parameter(self, oscillatory_network, start_iteration = None, stop_iteration = None):
        """!
        @brief Calculates local order parameter.
        @details Local order parameter or so-called level of local or partial synchronization is calculated by following expression:
        
        \f[
        r_{c}=\left | \sum_{i=0}^{N} \frac{1}{N_{i}} \sum_{j=0}e^{ \theta_{j} - \theta_{i} } \right |;
        \f]
        
        where N - total amount of oscillators in the network and \f$N_{i}\f$ - amount of neighbors of oscillator with index \f$i\f$.
        
        @param[in] oscillatory_network (sync): Sync oscillatory network whose structure of connections is required for calculation.
        @param[in] start_iteration (uint): The first iteration that is used for calculation, if 'None' then the last iteration is used.
        @param[in] stop_iteration (uint): The last iteration that is used for calculation, if 'None' then 'start_iteration' + 1 is used.
        
        @return (list) List of levels of local (partial) synchronization (local order parameter evolution).
        
        """

        (start_iteration, stop_iteration) = self.__get_start_stop_iterations(start_iteration, stop_iteration)

        if self._ccore_sync_dynamic_pointer is not None:
            network_pointer = oscillatory_network._ccore_network_pointer
            return wrapper.sync_dynamic_calculate_local_order(self._ccore_sync_dynamic_pointer, network_pointer, start_iteration, stop_iteration)

        sequence_local_order = []
        for index in range(start_iteration, stop_iteration):
            sequence_local_order.append(order_estimator.calculate_local_sync_order(self.output[index], oscillatory_network))

        return sequence_local_order


    def __get_start_stop_iterations(self, start_iteration, stop_iteration):
        """!
        @brief Aplly rules for start_iteration and stop_iteration parameters.

        @param[in] start_iteration (uint): The first iteration that is used for calculation.
        @param[in] stop_iteration (uint): The last iteration that is used for calculation.
        
        @return (tuple) New the first iteration and the last.
        
        """
        if start_iteration is None:
            start_iteration = len(self) - 1

        if stop_iteration is None:
            stop_iteration = start_iteration + 1

        return start_iteration, stop_iteration



class sync_visualizer:
    """!
    @brief Visualizer of output dynamic of sync network (Sync).
    
    """

    @staticmethod
    def show_output_dynamic(sync_output_dynamic):
        """!
        @brief Shows output dynamic (output of each oscillator) during simulation.
        
        @param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network.
        
        @see show_output_dynamics
        
        """

        draw_dynamics(sync_output_dynamic.time, sync_output_dynamic.output, x_title="t", y_title="phase", y_lim=[0, 2 * 3.14])


    @staticmethod
    def show_output_dynamics(sync_output_dynamics):
        """!
        @brief Shows several output dynamics (output of each oscillator) during simulation.
        @details Each dynamic is presented on separate plot.
        
        @param[in] sync_output_dynamics (list): list of output dynamics 'sync_dynamic' of the Sync network.
        
        @see show_output_dynamic
        
        """

        draw_dynamics_set(sync_output_dynamics, "t", "phase", None, [0, 2 * 3.14], False, False)


    @staticmethod
    def show_correlation_matrix(sync_output_dynamic, iteration=None):
        """!
        @brief Shows correlation matrix between oscillators at the specified iteration.
        
        @param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network.
        @param[in] iteration (uint): Number of iteration of simulation for which correlation matrix should be
                    allocated. If iteration number is not specified, the last step of simulation is used for the matrix
                    allocation.
        
        """

        _ = plt.figure()
        correlation_matrix = sync_output_dynamic.allocate_correlation_matrix(iteration)

        plt.imshow(correlation_matrix, cmap = plt.get_cmap('cool'), interpolation='kaiser', vmin=0.0, vmax=1.0)
        plt.show()


    @staticmethod
    def show_phase_matrix(sync_output_dynamic, grid_width=None, grid_height=None, iteration=None):
        """!
        @brief Shows 2D matrix of phase values of oscillators at the specified iteration.
        @details User should ensure correct matrix sizes in line with following expression grid_width x grid_height that should be equal to 
                  amount of oscillators otherwise exception is thrown. If grid_width or grid_height are not specified than phase matrix size 
                  will by calculated automatically by square root.
        
        @param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network whose phase matrix should be shown.
        @param[in] grid_width (uint): Width of the phase matrix.
        @param[in] grid_height (uint): Height of the phase matrix.
        @param[in] iteration (uint): Number of iteration of simulation for which correlation matrix should be allocated.
                    If iternation number is not specified, the last step of simulation is used for the matrix allocation.
        
        """

        _ = plt.figure()
        phase_matrix = sync_output_dynamic.allocate_phase_matrix(grid_width, grid_height, iteration)

        plt.imshow(phase_matrix, cmap = plt.get_cmap('jet'), interpolation='kaiser', vmin=0.0, vmax=2.0 * math.pi)
        plt.show()


    @staticmethod
    def show_order_parameter(sync_output_dynamic, start_iteration=None, stop_iteration=None):
        """!
        @brief Shows evolution of order parameter (level of global synchronization in the network).
        
        @param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network whose evolution of global synchronization should be visualized.
        @param[in] start_iteration (uint): The first iteration that is used for calculation, if 'None' then the first is used
        @param[in] stop_iteration (uint): The last iteration that is used for calculation, if 'None' then the last is used.
        
        """

        (start_iteration, stop_iteration) = sync_visualizer.__get_start_stop_iterations(sync_output_dynamic, start_iteration, stop_iteration)

        order_parameter = sync_output_dynamic.calculate_order_parameter(start_iteration, stop_iteration)
        axis = plt.subplot(111)
        plt.plot(sync_output_dynamic.time[start_iteration:stop_iteration], order_parameter, 'b-', linewidth=2.0)
        set_ax_param(axis, "t", "R (order parameter)", None, [0.0, 1.05])

        plt.show()


    @staticmethod
    def show_local_order_parameter(sync_output_dynamic, oscillatory_network, start_iteration=None, stop_iteration=None):
        """!
        @brief Shows evolution of local order parameter (level of local synchronization in the network).
        
        @param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network whose evolution of global synchronization should be visualized.
        @param[in] oscillatory_network (sync): Sync oscillatory network whose structure of connections is required for calculation.
        @param[in] start_iteration (uint): The first iteration that is used for calculation, if 'None' then the first is used
        @param[in] stop_iteration (uint): The last iteration that is used for calculation, if 'None' then the last is used.
        
        """
        (start_iteration, stop_iteration) = sync_visualizer.__get_start_stop_iterations(sync_output_dynamic, start_iteration, stop_iteration)

        order_parameter = sync_output_dynamic.calculate_local_order_parameter(oscillatory_network, start_iteration, stop_iteration)
        axis = plt.subplot(111)
        plt.plot(sync_output_dynamic.time[start_iteration:stop_iteration], order_parameter, 'b-', linewidth=2.0)
        set_ax_param(axis, "t", "R (local order parameter)", None, [0.0, 1.05])

        plt.show()


    @staticmethod
    def animate_output_dynamic(sync_output_dynamic, animation_velocity = 75, save_movie = None):
        """!
        @brief Shows animation of output dynamic (output of each oscillator) during simulation on a circle from [0; 2pi].
        
        @param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network.
        @param[in] animation_velocity (uint): Interval between frames in milliseconds.
        @param[in] save_movie (string): If it is specified then animation will be stored to file that is specified in this parameter.
        
        """

        figure = plt.figure()

        dynamic = sync_output_dynamic.output[0]
        artist, = plt.polar(dynamic, [1.0] * len(dynamic), 'o', color='blue')

        def init_frame():
            return [artist]

        def frame_generation(index_dynamic):
            dynamic = sync_output_dynamic.output[index_dynamic]
            artist.set_data(dynamic, [1.0] * len(dynamic))

            return [artist]

        phase_animation = animation.FuncAnimation(figure, frame_generation, len(sync_output_dynamic), interval = animation_velocity, init_func = init_frame, repeat_delay = 5000);

        if save_movie is not None:
            phase_animation.save(save_movie, writer='ffmpeg', fps=15, bitrate=1500)
        else:
            plt.show()


    @staticmethod
    def animate_correlation_matrix(sync_output_dynamic, animation_velocity = 75, colormap = 'cool', save_movie = None):
        """!
        @brief Shows animation of correlation matrix between oscillators during simulation.
        
        @param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network.
        @param[in] animation_velocity (uint): Interval between frames in milliseconds.
        @param[in] colormap (string): Name of colormap that is used by matplotlib ('gray', 'pink', 'cool', spring', etc.).
        @param[in] save_movie (string): If it is specified then animation will be stored to file that is specified in this parameter.
        
        """

        figure = plt.figure()

        correlation_matrix = sync_output_dynamic.allocate_correlation_matrix(0)
        artist = plt.imshow(correlation_matrix, cmap = plt.get_cmap(colormap), interpolation='kaiser', vmin = 0.0, vmax = 1.0)

        def init_frame():
            return [ artist ]

        def frame_generation(index_dynamic):
            correlation_matrix = sync_output_dynamic.allocate_correlation_matrix(index_dynamic)
            artist.set_data(correlation_matrix)

            return [artist]

        correlation_animation = animation.FuncAnimation(figure, frame_generation, len(sync_output_dynamic), init_func = init_frame, interval = animation_velocity , repeat_delay = 1000, blit = True)

        if save_movie is not None:
            correlation_animation.save(save_movie, writer='ffmpeg', fps=15, bitrate=1500)
        else:
            plt.show()


    @staticmethod
    def animate_phase_matrix(sync_output_dynamic, grid_width=None, grid_height=None, animation_velocity=75, colormap='jet', save_movie=None):
        """!
        @brief Shows animation of phase matrix between oscillators during simulation on 2D stage.
        @details If grid_width or grid_height are not specified than phase matrix size will by calculated automatically by square root.
        
        @param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network.
        @param[in] grid_width (uint): Width of the phase matrix.
        @param[in] grid_height (uint): Height of the phase matrix.
        @param[in] animation_velocity (uint): Interval between frames in milliseconds.
        @param[in] colormap (string): Name of colormap that is used by matplotlib ('gray', 'pink', 'cool', spring', etc.).
        @param[in] save_movie (string): If it is specified then animation will be stored to file that is specified in this parameter.
        
        """

        figure = plt.figure()

        def init_frame():
            return frame_generation(0)

        def frame_generation(index_dynamic):
            figure.clf()
            axis = figure.add_subplot(111)

            phase_matrix = sync_output_dynamic.allocate_phase_matrix(grid_width, grid_height, index_dynamic)
            axis.imshow(phase_matrix, cmap=plt.get_cmap(colormap), interpolation='kaiser', vmin=0.0, vmax=2.0 * math.pi)
            artist = figure.gca()

            return [artist]

        phase_animation = animation.FuncAnimation(figure, frame_generation, len(sync_output_dynamic), init_func = init_frame, interval = animation_velocity , repeat_delay = 1000);

        if save_movie is not None:
            phase_animation.save(save_movie, writer='ffmpeg', fps=15, bitrate=1500)
        else:
            plt.show()


    @staticmethod
    def __get_start_stop_iterations(sync_output_dynamic, start_iteration, stop_iteration):
        """!
        @brief Apply rule of preparation for start iteration and stop iteration values.
        
        @param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network.
        @param[in] start_iteration (uint): The first iteration that is used for calculation.
        @param[in] stop_iteration (uint): The last iteration that is used for calculation.
        
        @return (tuple) New values of start and stop iterations.
        
        """
        if start_iteration is None:
            start_iteration = 0

        if stop_iteration is None:
            stop_iteration = len(sync_output_dynamic)

        return start_iteration, stop_iteration


    @staticmethod
    def animate(sync_output_dynamic, title=None, save_movie=None):
        """!
        @brief Shows animation of phase coordinates and animation of correlation matrix together for the Sync dynamic output on the same figure.
        
        @param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network.
        @param[in] title (string): Title of the animation that is displayed on a figure if it is specified.
        @param[in] save_movie (string): If it is specified then animation will be stored to file that is specified in this parameter.
        
        """

        dynamic = sync_output_dynamic.output[0]
        correlation_matrix = sync_output_dynamic.allocate_correlation_matrix(0)

        figure = plt.figure(1)
        if title is not None:
            figure.suptitle(title, fontsize = 26, fontweight = 'bold')

        ax1 = figure.add_subplot(121, projection='polar')
        ax2 = figure.add_subplot(122)

        artist1, = ax1.plot(dynamic, [1.0] * len(dynamic), marker='o', color='blue', ls='')
        artist2 = ax2.imshow(correlation_matrix, cmap = plt.get_cmap('Accent'), interpolation='kaiser')

        def init_frame():
            return [artist1, artist2]

        def frame_generation(index_dynamic):
            dynamic = sync_output_dynamic.output[index_dynamic]
            artist1.set_data(dynamic, [1.0] * len(dynamic))

            correlation_matrix = sync_output_dynamic.allocate_correlation_matrix(index_dynamic)
            artist2.set_data(correlation_matrix)

            return [artist1, artist2]

        dynamic_animation = animation.FuncAnimation(figure, frame_generation, len(sync_output_dynamic), interval=75, init_func=init_frame, repeat_delay=5000)

        if save_movie is not None:
            dynamic_animation.save(save_movie, writer='ffmpeg', fps=15, bitrate=1500)
        else:
            plt.show()



class sync_network(network):
    """!
    @brief Model of oscillatory network that is based on the Kuramoto model of synchronization.
    
    @details CCORE option can be used to use the pyclustering core - C/C++ shared library for processing that significantly increases performance.
    
    """

    def __init__(self, num_osc, weight = 1, frequency = 0, type_conn = conn_type.ALL_TO_ALL, representation = conn_represent.MATRIX, initial_phases = initial_type.RANDOM_GAUSSIAN, ccore = True):
        """!
        @brief Constructor of oscillatory network is based on Kuramoto model.
        
        @param[in] num_osc (uint): Number of oscillators in the network.
        @param[in] weight (double): Coupling strength of the links between oscillators.
        @param[in] frequency (double): Multiplier of internal frequency of the oscillators.
        @param[in] type_conn (conn_type): Type of connection between oscillators in the network (all-to-all, grid, bidirectional list, etc.).
        @param[in] representation (conn_represent): Internal representation of connection in the network: matrix or list.
        @param[in] initial_phases (initial_type): Type of initialization of initial phases of oscillators (random, uniformly distributed, etc.).
        @param[in] ccore (bool): If True simulation is performed by CCORE library (C++ implementation of pyclustering).
        
        """

        self._ccore_network_pointer = None;      # Pointer to CCORE Sync implementation of the network.

        if ( (ccore is True) and ccore_library.workable() ):
            self._ccore_network_pointer = wrapper.sync_create_network(num_osc, weight, frequency, type_conn, initial_phases);
            self._num_osc = num_osc;
            self._conn_represent = conn_represent.MATRIX;

        else:
            super().__init__(num_osc, type_conn, representation);

            self._weight = weight;

            self._phases = list();
            self._freq = list();

            random.seed();
            for index in range(0, num_osc, 1):
                if (initial_phases == initial_type.RANDOM_GAUSSIAN):
                    self._phases.append(random.random() * 2 * pi);

                elif (initial_phases == initial_type.EQUIPARTITION):
                    self._phases.append( pi / num_osc * index);

                self._freq.append(random.random() * frequency);


    def __del__(self):
        """!
        @brief Destructor of oscillatory network is based on Kuramoto model.
        
        """

        if (self._ccore_network_pointer is not None):
            wrapper.sync_destroy_network(self._ccore_network_pointer);
            self._ccore_network_pointer = None;


    def sync_order(self):
        """!
        @brief Calculates current level of global synchorization (order parameter) in the network.
        @details This parameter is tend 1.0 when the oscillatory network close to global synchronization and it tend to 0.0 when 
                  desynchronization is observed in the network. Order parameter is calculated using following equation:
                  
                  \f[
                  r_{c}=\frac{1}{Ne^{i\varphi }}\sum_{j=0}^{N}e^{i\theta_{j}};
                  \f]
                  
                  where \f$\varphi\f$ is a average phase coordinate in the network, \f$N\f$ is an amount of oscillators in the network.
        
        Example:
        @code
            oscillatory_network = sync(16, type_conn = conn_type.ALL_TO_ALL);
            output_dynamic = oscillatory_network.simulate_static(100, 10);
            
            if (oscillatory_network.sync_order() < 0.9): print("Global synchronization is not reached yet.");
            else: print("Global synchronization is reached.");
        @endcode
        
        @return (double) Level of global synchronization (order parameter).
        
        @see sync_local_order()
        
        """

        if (self._ccore_network_pointer is not None):
            return wrapper.sync_order(self._ccore_network_pointer);

        return order_estimator.calculate_sync_order(self._phases);


    def sync_local_order(self):
        """!
        @brief Calculates current level of local (partial) synchronization in the network.
        
        @return (double) Level of local (partial) synchronization.
        
        @see sync_order()
        
        """

        if (self._ccore_network_pointer is not None):
            return wrapper.sync_local_order(self._ccore_network_pointer);

        return order_estimator.calculate_local_sync_order(self._phases, self);


    def _phase_kuramoto(self, teta, t, argv):
        """!
        @brief Returns result of phase calculation for specified oscillator in the network.
        
        @param[in] teta (double): Phase of the oscillator that is differentiated.
        @param[in] t (double): Current time of simulation.
        @param[in] argv (tuple): Index of the oscillator in the list.
        
        @return (double) New phase for specified oscillator (don't assign here).
        
        """

        index = argv;
        phase = 0;
        for k in range(0, self._num_osc):
            if (self.has_connection(index, k) == True):
                phase += math.sin(self._phases[k] - teta);

        return ( self._freq[index] + (phase * self._weight / self._num_osc) );


    def simulate(self, steps, time, solution = solve_type.FAST, collect_dynamic = True):
        """!
        @brief Performs static simulation of Sync oscillatory network.
        
        @param[in] steps (uint): Number steps of simulations during simulation.
        @param[in] time (double): Time of simulation.
        @param[in] solution (solve_type): Type of solution (solving).
        @param[in] collect_dynamic (bool): If True - returns whole dynamic of oscillatory network, otherwise returns only last values of dynamics.
        
        @return (list) Dynamic of oscillatory network. If argument 'collect_dynamic' = True, than return dynamic for the whole simulation time,
                otherwise returns only last values (last step of simulation) of dynamic.
        
        @see simulate_dynamic()
        @see simulate_static()
        
        """

        return self.simulate_static(steps, time, solution, collect_dynamic);


    def simulate_dynamic(self, order = 0.998, solution = solve_type.FAST, collect_dynamic = False, step = 0.1, int_step = 0.01, threshold_changes = 0.0000001):
        """!
        @brief Performs dynamic simulation of the network until stop condition is not reached. Stop condition is defined by input argument 'order'.
        
        @param[in] order (double): Order of process synchronization, distributed 0..1.
        @param[in] solution (solve_type): Type of solution.
        @param[in] collect_dynamic (bool): If True - returns whole dynamic of oscillatory network, otherwise returns only last values of dynamics.
        @param[in] step (double): Time step of one iteration of simulation.
        @param[in] int_step (double): Integration step, should be less than step.
        @param[in] threshold_changes (double): Additional stop condition that helps prevent infinite simulation, defines limit of changes of oscillators between current and previous steps.
        
        @return (list) Dynamic of oscillatory network. If argument 'collect_dynamic' = True, than return dynamic for the whole simulation time,
                otherwise returns only last values (last step of simulation) of dynamic.
        
        @see simulate()
        @see simulate_static()
        
        """

        if (self._ccore_network_pointer is not None):
            ccore_instance_dynamic = wrapper.sync_simulate_dynamic(self._ccore_network_pointer, order, solution, collect_dynamic, step, int_step, threshold_changes);
            return sync_dynamic(None, None, ccore_instance_dynamic);

        # For statistics and integration
        time_counter = 0;

        # Prevent infinite loop. It's possible when required state cannot be reached.
        previous_order = 0;
        current_order = self.sync_local_order();

        # If requested input dynamics
        dyn_phase = [];
        dyn_time = [];
        if (collect_dynamic == True):
            dyn_phase.append(self._phases);
            dyn_time.append(0);

        # Execute until sync state will be reached
        while (current_order < order):
            # update states of oscillators
            self._phases = self._calculate_phases(solution, time_counter, step, int_step);

            # update time
            time_counter += step;

            # if requested input dynamic
            if (collect_dynamic == True):
                dyn_phase.append(self._phases);
                dyn_time.append(time_counter);

            # update orders
            previous_order = current_order;
            current_order = self.sync_local_order();

            # hang prevention
            if (abs(current_order - previous_order) < threshold_changes):
                # print("Warning: sync_network::simulate_dynamic - simulation is aborted due to low level of convergence rate (order = " + str(current_order) + ").");
                break;

        if (collect_dynamic != True):
            dyn_phase.append(self._phases);
            dyn_time.append(time_counter);

        output_sync_dynamic = sync_dynamic(dyn_phase, dyn_time, None);
        return output_sync_dynamic;


    def simulate_static(self, steps, time, solution = solve_type.FAST, collect_dynamic = False):
        """!
        @brief Performs static simulation of oscillatory network.
        
        @param[in] steps (uint): Number steps of simulations during simulation.
        @param[in] time (double): Time of simulation.
        @param[in] solution (solve_type): Type of solution.
        @param[in] collect_dynamic (bool): If True - returns whole dynamic of oscillatory network, otherwise returns only last values of dynamics.
        
        @return (list) Dynamic of oscillatory network. If argument 'collect_dynamic' = True, than return dynamic for the whole simulation time,
                otherwise returns only last values (last step of simulation) of dynamic.
        
        @see simulate()
        @see simulate_dynamic()
        
        """

        if (self._ccore_network_pointer is not None):
            ccore_instance_dynamic = wrapper.sync_simulate_static(self._ccore_network_pointer, steps, time, solution, collect_dynamic);
            return sync_dynamic(None, None, ccore_instance_dynamic);

        dyn_phase = [];
        dyn_time = [];

        if (collect_dynamic == True):
            dyn_phase.append(self._phases);
            dyn_time.append(0);

        step = time / steps;
        int_step = step / 10.0;

        for t in numpy.arange(step, time + step, step):
            # update states of oscillators
            self._phases = self._calculate_phases(solution, t, step, int_step);

            # update states of oscillators
            if (collect_dynamic == True):
                dyn_phase.append(self._phases);
                dyn_time.append(t);

        if (collect_dynamic != True):
            dyn_phase.append(self._phases);
            dyn_time.append(time);

        output_sync_dynamic = sync_dynamic(dyn_phase, dyn_time);
        return output_sync_dynamic;


    def _calculate_phases(self, solution, t, step, int_step):
        """!
        @brief Calculates new phases for oscillators in the network in line with current step.
        
        @param[in] solution (solve_type): Type solver of the differential equation.
        @param[in] t (double): Time of simulation.
        @param[in] step (double): Step of solution at the end of which states of oscillators should be calculated.
        @param[in] int_step (double): Step differentiation that is used for solving differential equation.
        
        @return (list) New states (phases) for oscillators.
        
        """

        next_phases = [0.0] * self._num_osc;    # new oscillator _phases

        for index in range (0, self._num_osc, 1):
            if (solution == solve_type.FAST):
                result = self._phases[index] + self._phase_kuramoto(self._phases[index], 0, index);
                next_phases[index] = self._phase_normalization(result);

            elif ( (solution == solve_type.RK4) or (solution == solve_type.RKF45) ):
                result = odeint(self._phase_kuramoto, self._phases[index], numpy.arange(t - step, t, int_step), (index , ));
                next_phases[index] = self._phase_normalization(result[len(result) - 1][0]);

            else:
                raise NameError("Solver '" + str(solution) + "' is not supported");

        return next_phases;


    def _phase_normalization(self, teta):
        """!
        @brief Normalization of phase of oscillator that should be placed between [0; 2 * pi].
        
        @param[in] teta (double): phase of oscillator.
        
        @return (double) Normalized phase.
        
        """

        norm_teta = teta;
        while (norm_teta > (2.0 * pi)) or (norm_teta < 0):
            if (norm_teta > (2.0 * pi)):
                norm_teta -= 2.0 * pi;
            else:
                norm_teta += 2.0 * pi;

        return norm_teta;


    def get_neighbors(self, index):
        """!
        @brief Finds neighbors of the oscillator with specified index.
        
        @param[in] index (uint): index of oscillator for which neighbors should be found in the network.
        
        @return (list) Indexes of neighbors of the specified oscillator.
        
        """

        if ( (self._ccore_network_pointer is not None) and (self._osc_conn is None) ):
            self._osc_conn = wrapper.sync_connectivity_matrix(self._ccore_network_pointer);

        return super().get_neighbors(index);


    def has_connection(self, i, j):
        """!
        @brief Returns True if there is connection between i and j oscillators and False - if connection doesn't exist.
        
        @param[in] i (uint): index of an oscillator in the network.
        @param[in] j (uint): index of an oscillator in the network.
        
        """

        if ( (self._ccore_network_pointer is not None) and (self._osc_conn is None) ):
            self._osc_conn = wrapper.sync_connectivity_matrix(self._ccore_network_pointer);

        return super().has_connection(i, j);