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"""!
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@brief Oscillatory Neural Network based on Kuramoto model in frequency domain.
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@details Based on article description:
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- Y.Kuramoto. Chemical Oscillations, Waves, and Turbulence. 1984.
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@authors Andrei Novikov ([email protected])
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@date 2014-2017
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@copyright GNU Public License
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@cond GNU_PUBLIC_LICENSE
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PyClustering is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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PyClustering is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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@endcond
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"""
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import numpy;
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import random;
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from scipy.integrate import odeint;
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from pyclustering.nnet import network, conn_type, conn_represent;
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from pyclustering.utils import draw_dynamics, draw_dynamics_set;
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class fsync_dynamic:
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"""!
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@brief Represents output dynamic of Sync in frequency domain.
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"""
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def __init__(self, amplitude, time):
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"""!
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@brief Constructor of Sync dynamic in frequency domain.
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@param[in] amplitude (list): Dynamic of oscillators on each step of simulation.
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@param[in] time (list): Simulation time where each time-point corresponds to amplitude-point.
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"""
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self.__amplitude = amplitude;
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self.__time = time;
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@property
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def output(self):
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"""!
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@brief (list) Returns output dynamic of the Sync network (amplitudes of each oscillator in the network) during simulation.
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"""
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return self.__amplitude;
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@property
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def time(self):
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"""!
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@brief (list) Returns time-points corresponds to dynamic-points points.
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"""
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return self.__time;
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def __len__(self):
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"""!
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@brief (uint) Returns number of simulation steps that are stored in dynamic.
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"""
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return len(self.__amplitude);
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87
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class fsync_visualizer:
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"""!
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@brief Visualizer of output dynamic of sync network in frequency domain.
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"""
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@staticmethod
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def show_output_dynamic(fsync_output_dynamic):
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"""!
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@brief Shows output dynamic (output of each oscillator) during simulation.
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@param[in] fsync_output_dynamic (fsync_dynamic): Output dynamic of the fSync network.
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@see show_output_dynamics
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"""
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draw_dynamics(fsync_output_dynamic.time, fsync_output_dynamic.output, x_title = "t", y_title = "amplitude");
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@staticmethod
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def show_output_dynamics(sync_output_dynamics):
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"""!
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@brief Shows several output dynamics (output of each oscillator) during simulation.
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@details Each dynamic is presented on separate plot.
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@param[in] sync_output_dynamics (list): list of output dynamics 'fsync_dynamic' of the fSync network.
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116
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@see show_output_dynamic
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"""
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draw_dynamics_set(sync_output_dynamics, "t", "amplitude", None, None, False, False);
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class fsync_network(network):
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"""!
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@brief Model of oscillatory network that uses Landau-Stuart oscillator and Kuramoto model as a synchronization mechanism.
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@details Dynamic of each oscillator in the network is described by following differential equation:
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129
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\f[
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\dot{z}_{i} = (i\omega_{i} + \rho^{2}_{i} - |z_{i}|^{2} )z_{i} + \sum_{j=0}^{N}k_{ij}(z_{j} - z_{i})
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\f]
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"""
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__DEFAULT_FREQUENCY_VALUE = 1.0;
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__DEFAULT_RADIUS_VALUE = 1.0;
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__DEFAULT_COUPLING_STRENGTH = 1.0;
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def __init__(self, num_osc, factor_frequency = 1.0, factor_radius = 1.0, factor_coupling = 1.0, type_conn = conn_type.ALL_TO_ALL, representation = conn_represent.MATRIX):
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141
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"""!
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@brief Constructor of oscillatory network based on synchronization Kuramoto model and Landau-Stuart oscillator.
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144
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@param[in] num_osc (uint): Amount oscillators in the network.
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@param[in] type_conn (conn_type): Type of connection between oscillators in the network (all-to-all, grid, bidirectional list, etc.).
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@param[in] representation (conn_represent): Internal representation of connection in the network: matrix or list.
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"""
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super().__init__(num_osc, type_conn, representation);
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152
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self.__frequency = fsync_network.__DEFAULT_FREQUENCY_VALUE * factor_frequency;
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self.__radius = fsync_network.__DEFAULT_RADIUS_VALUE * factor_radius;
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self.__coupling_strength = fsync_network.__DEFAULT_COUPLING_STRENGTH * factor_coupling;
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156
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self.__landau_contant = numpy.array(1j * self.__frequency + self.__radius**2, dtype = numpy.complex128, ndmin = 1);
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158
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random.seed();
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self.__amplitude = [ random.random() for _ in range(num_osc) ];
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def simulate_static(self, steps, time, collect_dynamic = False):
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"""!
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@brief Performs static simulation of oscillatory network.
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166
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@param[in] steps (uint): Number simulation steps.
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167
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@param[in] time (double): Time of simulation.
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168
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@param[in] collect_dynamic (bool): If True - returns whole dynamic of oscillatory network, otherwise returns only last values of dynamics.
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169
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170
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@return (list) Dynamic of oscillatory network. If argument 'collect_dynamic' is True, than return dynamic for the whole simulation time,
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otherwise returns only last values (last step of simulation) of output dynamic.
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173
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@see simulate()
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@see simulate_dynamic()
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176
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"""
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178
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dynamic_amplitude, dynamic_time = ([], []) if collect_dynamic is False else ([self.__amplitude], [0]);
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180
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step = time / steps;
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181
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int_step = step / 10.0;
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183
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for t in numpy.arange(step, time + step, step):
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self.__amplitude = self.__calculate(t, step, int_step);
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if (collect_dynamic == True):
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dynamic_amplitude.append([ numpy.real(amplitude) for amplitude in self.__amplitude ]);
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dynamic_time.append(t);
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if (collect_dynamic != True):
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dynamic_amplitude.append([ numpy.real(amplitude) for amplitude in self.__amplitude ]);
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dynamic_time.append(time);
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194
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output_sync_dynamic = fsync_dynamic(dynamic_amplitude, dynamic_time);
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return output_sync_dynamic;
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197
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198
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def __calculate(self, t, step, int_step):
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"""!
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@brief Calculates new amplitudes for oscillators in the network in line with current step.
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@param[in] t (double): Time of simulation.
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@param[in] step (double): Step of solution at the end of which states of oscillators should be calculated.
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@param[in] int_step (double): Step differentiation that is used for solving differential equation.
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206
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@return (list) New states (phases) for oscillators.
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207
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208
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"""
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210
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next_amplitudes = [0.0] * self._num_osc;
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for index in range (0, self._num_osc, 1):
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z = numpy.array(self.__amplitude[index], dtype = numpy.complex128, ndmin = 1);
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214
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result = odeint(self.__calculate_amplitude, z.view(numpy.float64), numpy.arange(t - step, t, int_step), (index , ));
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215
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next_amplitudes[index] = (result[len(result) - 1]).view(numpy.complex128);
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216
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217
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return next_amplitudes;
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218
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219
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220
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def __landau_stuart(self, amplitude, index):
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221
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"""!
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222
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@brief Calculate Landau-Stuart state.
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223
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224
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@param[in] amplitude (double): Current amplitude of oscillator.
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225
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@param[in] index (uint): Oscillator index whose state is calculated.
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226
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227
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@return (double) Landau-Stuart state.
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228
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229
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"""
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230
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231
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return (self.__landau_contant - numpy.absolute(amplitude) ** 2) * amplitude;
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232
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233
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234
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def __synchronization_mechanism(self, amplitude, index):
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235
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"""!
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236
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@brief Calculate synchronization part using Kuramoto synchronization mechanism.
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237
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238
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@param[in] amplitude (double): Current amplitude of oscillator.
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239
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@param[in] index (uint): Oscillator index whose synchronization influence is calculated.
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240
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241
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@return (double) Synchronization influence for the specified oscillator.
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242
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243
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"""
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244
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245
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sync_influence = 0.0;
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246
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247
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for k in range(self._num_osc):
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248
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if (self.has_connection(index, k) == True):
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249
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amplitude_neighbor = numpy.array(self.__amplitude[k], dtype = numpy.complex128, ndmin = 1);
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250
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sync_influence += amplitude_neighbor - amplitude;
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251
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252
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return sync_influence * self.__coupling_strength / self._num_osc;
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253
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254
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255
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def __calculate_amplitude(self, amplitude, t, argv):
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256
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"""!
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257
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@brief Returns new amplitude value for particular oscillator that is defined by index that is in 'argv' argument.
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258
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@details The method is used for differential calculation.
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259
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260
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@param[in] amplitude (double): Current amplitude of oscillator.
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261
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@param[in] t (double): Current time of simulation.
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262
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@param[in] argv (uint): Index of the current oscillator.
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263
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264
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@return (double) New amplitude of the oscillator.
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265
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266
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"""
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267
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268
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z = amplitude.view(numpy.complex);
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269
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dzdt = self.__landau_stuart(z, argv) + self.__synchronization_mechanism(z, argv);
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270
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271
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return dzdt.view(numpy.float64); |
annoviko /
pyclustering
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