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"""!
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3
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@brief Neural Network: Oscillatory Neural Network based on Kuramoto model
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@details Based on article description:
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- A.Arenas, Y.Moreno, C.Zhou. Synchronization in complex networks. 2008.
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6
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- X.B.Lu. Adaptive Cluster Synchronization in Coupled Phase Oscillators. 2009.
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7
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- X.Lou. Adaptive Synchronizability of Coupled Oscillators With Switching. 2012.
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8
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- A.Novikov, E.Benderskaya. Oscillatory Neural Networks Based on the Kuramoto Model. 2014.
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10
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@authors Andrei Novikov ([email protected])
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@date 2014-2016
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@copyright GNU Public License
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14
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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 matplotlib.pyplot as plt;
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import matplotlib.animation as animation;
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import numpy;
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import random;
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import pyclustering.core.sync_wrapper as wrapper;
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38
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from scipy import pi;
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from scipy.integrate import odeint;
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from scipy.integrate import ode;
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from pyclustering.nnet import *;
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44
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45
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from pyclustering.utils import draw_dynamics;
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47
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48
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class sync_dynamic:
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"""!
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@brief Represents output dynamic of Sync.
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51
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"""
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53
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@property
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def output(self):
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56
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"""!
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57
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@brief (list) Returns outputs of oscillator during simulation.
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58
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59
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"""
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if (self._ccore_sync_dynamic_pointer is not None):
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return wrapper.sync_dynamic_get_output(self._ccore_sync_dynamic_pointer);
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return self._dynamic;
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@property
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67
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def time(self):
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68
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"""!
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69
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@brief (list) Returns sampling times when dynamic is measured during simulation.
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70
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"""
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if (self._ccore_sync_dynamic_pointer is not None):
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return wrapper.sync_dynamic_get_time(self._ccore_sync_dynamic_pointer);
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return self._time;
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def __init__(self, phase, time, ccore = None):
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"""!
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@brief Constructor of Sync dynamic.
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@param[in] phase (list): Dynamic of oscillators on each step of simulation. If ccore pointer is specified than it can be ignored.
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@param[in] time (list): Simulation time.
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@param[in] ccore (ctypes.pointer): Pointer to CCORE sync_dynamic instance in memory.
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"""
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self._dynamic = phase;
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self._time = time;
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self._ccore_sync_dynamic_pointer = ccore;
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def __del__(self):
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"""!
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@brief Default destructor of Sync dynamic.
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"""
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if (self._ccore_sync_dynamic_pointer is not None):
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wrapper.sync_dynamic_destroy(self._ccore_sync_dynamic_pointer);
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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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if (self._ccore_sync_dynamic_pointer is not None):
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return wrapper.sync_dynamic_get_size(self._ccore_sync_dynamic_pointer);
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return len(self._dynamic);
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112
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def allocate_sync_ensembles(self, tolerance = 0.01):
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"""!
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@brief Allocate clusters in line with ensembles of synchronous oscillators where each
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synchronous ensemble corresponds to only one cluster.
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@param[in] tolerance (double): Maximum error for allocation of synchronous ensemble oscillators.
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@return (list) Grours (lists) of indexes of synchronous oscillators.
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For example [ [index_osc1, index_osc3], [index_osc2], [index_osc4, index_osc5] ].
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"""
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if (self._ccore_sync_dynamic_pointer is not None):
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return wrapper.sync_dynamic_allocate_sync_ensembles(self._ccore_sync_dynamic_pointer, tolerance);
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if ( (self._dynamic is None) or (len(self._dynamic) == 0) ):
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return [];
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number_oscillators = len(self._dynamic[0]);
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last_state = self._dynamic[len(self._dynamic) - 1];
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clusters = [];
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if (number_oscillators > 0):
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clusters.append([0]);
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138
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for i in range(1, number_oscillators, 1):
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cluster_allocated = False;
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for cluster in clusters:
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for neuron_index in cluster:
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last_state_shifted = abs(last_state[i] - 2 * pi);
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144
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if ( ( (last_state[i] < (last_state[neuron_index] + tolerance)) and (last_state[i] > (last_state[neuron_index] - tolerance)) ) or
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( (last_state_shifted < (last_state[neuron_index] + tolerance)) and (last_state_shifted > (last_state[neuron_index] - tolerance)) ) ):
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146
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cluster_allocated = True;
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cluster.append(i);
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148
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break;
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150
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if (cluster_allocated == True):
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break;
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153
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if (cluster_allocated == False):
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154
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clusters.append([i]);
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156
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return clusters;
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def allocate_correlation_matrix(self, iteration = None):
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"""!
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@brief Allocate correlation matrix between oscillators at the specified step of simulation.
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163
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@param[in] iteration (uint): Number of iteration of simulation for which correlation matrix should be allocated.
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If iternation number is not specified, the last step of simulation is used for the matrix allocation.
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166
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@return (list) Correlation matrix between oscillators with size [number_oscillators x number_oscillators].
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168
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"""
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169
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if ( (self._dynamic is None) or (len(self._dynamic) == 0) ):
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return [];
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173
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dynamic = self._dynamic;
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174
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current_dynamic = dynamic[len(dynamic) - 1];
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175
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176
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if (iteration is not None):
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current_dynamic = dynamic[iteration];
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179
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number_oscillators = len(dynamic[0]);
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affinity_matrix = [ [ 0.0 for i in range(number_oscillators) ] for j in range(number_oscillators) ];
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181
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182
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for i in range(number_oscillators):
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183
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for j in range(number_oscillators):
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184
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phase1 = current_dynamic[i];
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185
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phase2 = current_dynamic[j];
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187
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affinity_matrix[i][j] = math.sin(phase1 - phase2);
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188
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189
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return affinity_matrix;
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191
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192
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class sync_visualizer:
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193
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"""!
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194
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@brief Visualizer of output dynamic of sync network (Sync).
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195
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196
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"""
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197
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198
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@staticmethod
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199
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def show_output_dynamic(sync_output_dynamic):
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200
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"""!
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201
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@brief Shows output dynamic (output of each oscillator) during simulation.
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202
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203
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@param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network.
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204
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205
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"""
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207
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draw_dynamics(sync_output_dynamic.time, sync_output_dynamic.output, x_title = "t", y_title = "phase", y_lim = [0, 2 * 3.14]);
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208
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209
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210
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@staticmethod
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211
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def show_correlation_matrix(sync_output_dynamic, iteration = None):
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212
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"""!
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213
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@brief Shows correlation matrix between oscillators at the specified iteration.
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214
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215
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@param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network.
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216
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@param[in] iteration (uint): Number of interation of simulation for which correlation matrix should be allocated.
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217
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If iternation number is not specified, the last step of simulation is used for the matrix allocation.
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218
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219
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"""
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220
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221
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figure = plt.figure();
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222
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correlation_matrix = sync_output_dynamic.allocate_correlation_matrix(iteration);
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223
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224
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plt.imshow(correlation_matrix, cmap = plt.get_cmap('cool'), interpolation='kaiser');
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225
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plt.show();
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226
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227
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228
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@staticmethod
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229
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def animate_output_dynamic(sync_output_dynamic, animation_velocity = 75):
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230
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"""!
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231
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@brief Shows animation of output dynamic (output of each oscillator) during simulation on a circle from [0; 2pi].
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232
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233
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@param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network.
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234
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@param[in] animation_velocity (uint): Interval between frames in milliseconds.
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235
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236
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"""
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237
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238
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figure = plt.figure();
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239
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240
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xcircle = numpy.linspace(-1.0, 1.0, 500);
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241
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ycircle_positive = [ (1.0 - x ** 2) ** 0.5 for x in xcircle ];
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242
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ycircle_negative = [ -y for y in ycircle_positive ];
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243
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244
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def init_frame():
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245
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artist1, = plt.plot(xcircle, ycircle_positive, 'b-');
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246
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artist2, = plt.plot(xcircle, ycircle_negative, 'b-');
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247
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artist3, = plt.plot([-1.1, 1.1], [0.0, 0.0], 'b-');
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248
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artist4, = plt.plot([0.0, 0.0], [-1.1, 1.1], 'b-');
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249
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250
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|
text1 = plt.text(-1.1, 0.0, r'$\pi$');
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251
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|
text2 = plt.text(1.1, 0.0, r'0');
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252
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text3 = plt.text(0.0, 1.1, r'$\pi$/2');
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253
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text4 = plt.text(0.0, -1.1, r'3$\pi$/2');
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254
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255
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|
return [ artist1, artist2, artist3, artist4, text1, text2, text3, text4 ];
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256
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257
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def frame_generation(index_dynamic):
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258
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dynamic = sync_output_dynamic.output[index_dynamic];
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259
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260
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|
xdata = [];
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|
261
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ydata = [];
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262
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|
263
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|
for phase in dynamic:
|
|
264
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|
xcoord = math.cos(phase);
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265
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|
ycoord = math.sin(phase);
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266
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|
267
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|
xdata.append(xcoord);
|
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268
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|
ydata.append(ycoord);
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|
269
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|
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|
|
270
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|
|
artist5, = plt.plot(xdata, ydata, 'ro');
|
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271
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return [ artist5 ];
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|
272
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|
273
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|
im_ani = animation.FuncAnimation(figure, frame_generation, len(sync_output_dynamic), interval = 75, repeat_delay = 5000, init_func = init_frame, blit = True);
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|
274
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plt.show();
|
|
275
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|
276
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|
277
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|
@staticmethod
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|
278
|
|
|
def animate_correlation_matrix(sync_output_dynamic, animation_velocity = 75):
|
|
|
|
|
|
|
279
|
|
|
"""!
|
|
280
|
|
|
@brief Shows animation of correlation matrix between oscillators during simulation.
|
|
281
|
|
|
|
|
282
|
|
|
@param[in] sync_output_dynamic (sync_dynamic): Output dynamic of the Sync network.
|
|
283
|
|
|
@param[in] animation_velocity (uint): Interval between frames in milliseconds.
|
|
284
|
|
|
|
|
285
|
|
|
"""
|
|
286
|
|
|
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|
287
|
|
|
figure = plt.figure();
|
|
288
|
|
|
|
|
289
|
|
|
correlation_matrix = sync_output_dynamic.allocate_correlation_matrix(0);
|
|
290
|
|
|
|
|
291
|
|
|
def init_frame():
|
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292
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artist = plt.imshow(correlation_matrix, cmap = plt.get_cmap('cool'), interpolation='kaiser', hold = True);
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return [ artist ];
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def frame_generation(index_dynamic):
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correlation_matrix = sync_output_dynamic.allocate_correlation_matrix(index_dynamic);
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artist = plt.imshow(correlation_matrix, cmap = plt.get_cmap('cool'), interpolation='kaiser');
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return [ artist ];
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im_ani = animation.FuncAnimation(figure, frame_generation, len(sync_output_dynamic), init_func = init_frame, interval = 75, repeat_delay = 1000, blit = True);
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plt.show();
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class sync_network(network):
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"""!
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@brief Model of oscillatory network that is based on the Kuramoto model of synchronization.
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309
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"""
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# Protected members:
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_name = 'Phase Sync Network'
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_phases = None; # Current phases of oscillators.
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314
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_freq = None; # Own frequencies of oscillators.
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315
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_weight = 0; # Strength of connections between oscillators.
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317
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_ccore_network_pointer = None; # Pointer to CCORE Sync implementation of the network.
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318
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319
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320
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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 = False):
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321
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"""!
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322
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@brief Constructor of oscillatory network is based on Kuramoto model.
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324
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@param[in] num_osc (uint): Number of oscillators in the network.
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325
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@param[in] weight (double): Coupling strength of the links between oscillators.
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326
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@param[in] frequency (double): Multiplier of internal frequency of the oscillators.
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327
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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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328
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@param[in] representation (conn_represent): Internal representation of connection in the network: matrix or list.
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329
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@param[in] initial_phases (initial_type): Type of initialization of initial phases of oscillators (random, uniformly distributed, etc.).
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330
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@param[in] ccore (bool): If True simulation is performed by CCORE library (C++ implementation of pyclustering).
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331
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332
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"""
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333
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334
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if (ccore is True):
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335
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self._ccore_network_pointer = wrapper.sync_create_network(num_osc, weight, frequency, type_conn, initial_phases);
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else:
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337
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super().__init__(num_osc, type_conn, representation);
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338
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339
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self._weight = weight;
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340
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341
|
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self._phases = list();
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342
|
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self._freq = list();
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343
|
|
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344
|
|
|
for index in range(0, num_osc, 1):
|
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345
|
|
|
if (initial_phases == initial_type.RANDOM_GAUSSIAN):
|
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346
|
|
|
self._phases.append(random.random() * 2.0 * pi);
|
|
347
|
|
|
elif (initial_phases == initial_type.EQUIPARTITION):
|
|
348
|
|
|
self._phases.append( pi / num_osc * index);
|
|
349
|
|
|
|
|
350
|
|
|
self._freq.append(random.random() * frequency);
|
|
351
|
|
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|
352
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|
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353
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|
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def __del__(self):
|
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354
|
|
|
"""!
|
|
355
|
|
|
@brief Destructor of oscillatory network is based on Kuramoto model.
|
|
356
|
|
|
|
|
357
|
|
|
"""
|
|
358
|
|
|
|
|
359
|
|
|
if (self._ccore_network_pointer is not None):
|
|
360
|
|
|
wrapper.sync_destroy_network(self._ccore_network_pointer);
|
|
361
|
|
|
self._ccore_network_pointer = None;
|
|
362
|
|
|
|
|
363
|
|
|
|
|
364
|
|
|
def sync_order(self):
|
|
365
|
|
|
"""!
|
|
366
|
|
|
@brief Calculates level of global synchorization in the network.
|
|
367
|
|
|
|
|
368
|
|
|
@return (double) Level of global synchronization.
|
|
369
|
|
|
|
|
370
|
|
|
@see sync_local_order()
|
|
371
|
|
|
|
|
372
|
|
|
"""
|
|
373
|
|
|
|
|
374
|
|
|
if (self._ccore_network_pointer is not None):
|
|
375
|
|
|
return wrapper.sync_order(self._ccore_network_pointer);
|
|
376
|
|
|
|
|
377
|
|
|
exp_amount = 0;
|
|
378
|
|
|
average_phase = 0;
|
|
379
|
|
|
|
|
380
|
|
|
for index in range(0, self._num_osc, 1):
|
|
381
|
|
|
exp_amount += math.expm1( abs(1j * self._phases[index]) );
|
|
382
|
|
|
average_phase += self._phases[index];
|
|
383
|
|
|
|
|
384
|
|
|
exp_amount /= self._num_osc;
|
|
385
|
|
|
average_phase = math.expm1( abs(1j * (average_phase / self._num_osc)) );
|
|
386
|
|
|
|
|
387
|
|
|
return abs(average_phase) / abs(exp_amount);
|
|
388
|
|
|
|
|
389
|
|
|
|
|
390
|
|
|
def sync_local_order(self):
|
|
391
|
|
|
"""!
|
|
392
|
|
|
@brief Calculates level of local (partial) synchronization in the network.
|
|
393
|
|
|
|
|
394
|
|
|
@return (double) Level of local (partial) synchronization.
|
|
395
|
|
|
|
|
396
|
|
|
@see sync_order()
|
|
397
|
|
|
|
|
398
|
|
|
"""
|
|
399
|
|
|
|
|
400
|
|
|
if (self._ccore_network_pointer is not None):
|
|
401
|
|
|
return wrapper.sync_local_order(self._ccore_network_pointer);
|
|
402
|
|
|
|
|
403
|
|
|
exp_amount = 0.0;
|
|
404
|
|
|
num_neigh = 0;
|
|
405
|
|
|
|
|
406
|
|
|
for i in range(0, self._num_osc, 1):
|
|
407
|
|
|
for j in range(0, self._num_osc, 1):
|
|
408
|
|
|
if (self.has_connection(i, j) == True):
|
|
409
|
|
|
exp_amount += math.exp(-abs(self._phases[j] - self._phases[i]));
|
|
410
|
|
|
num_neigh += 1;
|
|
411
|
|
|
|
|
412
|
|
|
if (num_neigh == 0):
|
|
413
|
|
|
num_neigh = 1;
|
|
414
|
|
|
|
|
415
|
|
|
return exp_amount / num_neigh;
|
|
416
|
|
|
|
|
417
|
|
|
|
|
418
|
|
|
def _phase_kuramoto(self, teta, t, argv):
|
|
|
|
|
|
|
419
|
|
|
"""!
|
|
420
|
|
|
@brief Returns result of phase calculation for specified oscillator in the network.
|
|
421
|
|
|
|
|
422
|
|
|
@param[in] teta (double): Phase of the oscillator that is differentiated.
|
|
423
|
|
|
@param[in] t (double): Current time of simulation.
|
|
424
|
|
|
@param[in] argv (tuple): Index of the oscillator in the list.
|
|
425
|
|
|
|
|
426
|
|
|
@return (double) New phase for specified oscillator (don't assign here).
|
|
427
|
|
|
|
|
428
|
|
|
"""
|
|
429
|
|
|
|
|
430
|
|
|
index = argv;
|
|
431
|
|
|
phase = 0;
|
|
432
|
|
|
for k in range(0, self._num_osc):
|
|
433
|
|
|
if (self.has_connection(index, k) == True):
|
|
434
|
|
|
phase += math.sin(self._phases[k] - teta);
|
|
435
|
|
|
|
|
436
|
|
|
return ( self._freq[index] + (phase * self._weight / self._num_osc) );
|
|
437
|
|
|
|
|
438
|
|
|
|
|
439
|
|
|
def simulate(self, steps, time, solution = solve_type.FAST, collect_dynamic = True):
|
|
440
|
|
|
"""!
|
|
441
|
|
|
@brief Performs static simulation of Sync oscillatory network.
|
|
442
|
|
|
|
|
443
|
|
|
@param[in] steps (uint): Number steps of simulations during simulation.
|
|
444
|
|
|
@param[in] time (double): Time of simulation.
|
|
445
|
|
|
@param[in] solution (solve_type): Type of solution (solving).
|
|
446
|
|
|
@param[in] collect_dynamic (bool): If True - returns whole dynamic of oscillatory network, otherwise returns only last values of dynamics.
|
|
447
|
|
|
|
|
448
|
|
|
@return (list) Dynamic of oscillatory network. If argument 'collect_dynamic' = True, than return dynamic for the whole simulation time,
|
|
449
|
|
|
otherwise returns only last values (last step of simulation) of dynamic.
|
|
450
|
|
|
|
|
451
|
|
|
@see simulate_dynamic()
|
|
452
|
|
|
@see simulate_static()
|
|
453
|
|
|
|
|
454
|
|
|
"""
|
|
455
|
|
|
|
|
456
|
|
|
return self.simulate_static(steps, time, solution, collect_dynamic);
|
|
457
|
|
|
|
|
458
|
|
|
|
|
459
|
|
|
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):
|
|
460
|
|
|
"""!
|
|
461
|
|
|
@brief Performs dynamic simulation of the network until stop condition is not reached. Stop condition is defined by input argument 'order'.
|
|
462
|
|
|
|
|
463
|
|
|
@param[in] order (double): Order of process synchronization, distributed 0..1.
|
|
464
|
|
|
@param[in] solution (solve_type): Type of solution.
|
|
465
|
|
|
@param[in] collect_dynamic (bool): If True - returns whole dynamic of oscillatory network, otherwise returns only last values of dynamics.
|
|
466
|
|
|
@param[in] step (double): Time step of one iteration of simulation.
|
|
467
|
|
|
@param[in] int_step (double): Integration step, should be less than step.
|
|
468
|
|
|
@param[in] threshold_changes (double): Additional stop condition that helps prevent infinite simulation, defines limit of changes of oscillators between current and previous steps.
|
|
469
|
|
|
|
|
470
|
|
|
@return (list) Dynamic of oscillatory network. If argument 'collect_dynamic' = True, than return dynamic for the whole simulation time,
|
|
471
|
|
|
otherwise returns only last values (last step of simulation) of dynamic.
|
|
472
|
|
|
|
|
473
|
|
|
@see simulate()
|
|
474
|
|
|
@see simulate_static()
|
|
475
|
|
|
|
|
476
|
|
|
"""
|
|
477
|
|
|
|
|
478
|
|
|
if (self._ccore_network_pointer is not None):
|
|
479
|
|
|
ccore_instance_dynamic = wrapper.sync_simulate_dynamic(self._ccore_network_pointer, order, solution, collect_dynamic, step, int_step, threshold_changes);
|
|
480
|
|
|
return sync_dynamic(None, None, ccore_instance_dynamic);
|
|
481
|
|
|
|
|
482
|
|
|
# For statistics and integration
|
|
483
|
|
|
time_counter = 0;
|
|
484
|
|
|
|
|
485
|
|
|
# Prevent infinite loop. It's possible when required state cannot be reached.
|
|
486
|
|
|
previous_order = 0;
|
|
487
|
|
|
current_order = self.sync_local_order();
|
|
488
|
|
|
|
|
489
|
|
|
# If requested input dynamics
|
|
490
|
|
|
dyn_phase = [];
|
|
491
|
|
|
dyn_time = [];
|
|
492
|
|
|
if (collect_dynamic == True):
|
|
493
|
|
|
dyn_phase.append(self._phases);
|
|
494
|
|
|
dyn_time.append(0);
|
|
495
|
|
|
|
|
496
|
|
|
# Execute until sync state will be reached
|
|
497
|
|
|
while (current_order < order):
|
|
498
|
|
|
# update states of oscillators
|
|
499
|
|
|
self._phases = self._calculate_phases(solution, time_counter, step, int_step);
|
|
500
|
|
|
|
|
501
|
|
|
# update time
|
|
502
|
|
|
time_counter += step;
|
|
503
|
|
|
|
|
504
|
|
|
# if requested input dynamic
|
|
505
|
|
|
if (collect_dynamic == True):
|
|
506
|
|
|
dyn_phase.append(self._phases);
|
|
507
|
|
|
dyn_time.append(time_counter);
|
|
508
|
|
|
|
|
509
|
|
|
# update orders
|
|
510
|
|
|
previous_order = current_order;
|
|
511
|
|
|
current_order = self.sync_local_order();
|
|
512
|
|
|
|
|
513
|
|
|
# hang prevention
|
|
514
|
|
|
if (abs(current_order - previous_order) < threshold_changes):
|
|
515
|
|
|
# print("Warning: sync_network::simulate_dynamic - simulation is aborted due to low level of convergence rate (order = " + str(current_order) + ").");
|
|
516
|
|
|
break;
|
|
517
|
|
|
|
|
518
|
|
|
if (collect_dynamic != True):
|
|
519
|
|
|
dyn_phase.append(self._phases);
|
|
520
|
|
|
dyn_time.append(time_counter);
|
|
521
|
|
|
|
|
522
|
|
|
output_sync_dynamic = sync_dynamic(dyn_phase, dyn_time, None);
|
|
523
|
|
|
return output_sync_dynamic;
|
|
524
|
|
|
|
|
525
|
|
|
|
|
526
|
|
|
def simulate_static(self, steps, time, solution = solve_type.FAST, collect_dynamic = False):
|
|
527
|
|
|
"""!
|
|
528
|
|
|
@brief Performs static simulation of oscillatory network.
|
|
529
|
|
|
|
|
530
|
|
|
@param[in] steps (uint): Number steps of simulations during simulation.
|
|
531
|
|
|
@param[in] time (double): Time of simulation.
|
|
532
|
|
|
@param[in] solution (solve_type): Type of solution.
|
|
533
|
|
|
@param[in] collect_dynamic (bool): If True - returns whole dynamic of oscillatory network, otherwise returns only last values of dynamics.
|
|
534
|
|
|
|
|
535
|
|
|
@return (list) Dynamic of oscillatory network. If argument 'collect_dynamic' = True, than return dynamic for the whole simulation time,
|
|
536
|
|
|
otherwise returns only last values (last step of simulation) of dynamic.
|
|
537
|
|
|
|
|
538
|
|
|
@see simulate()
|
|
539
|
|
|
@see simulate_dynamic()
|
|
540
|
|
|
|
|
541
|
|
|
"""
|
|
542
|
|
|
|
|
543
|
|
|
if (self._ccore_network_pointer is not None):
|
|
544
|
|
|
ccore_instance_dynamic = wrapper.sync_simulate_static(self._ccore_network_pointer, steps, time, solution, collect_dynamic);
|
|
545
|
|
|
return sync_dynamic(None, None, ccore_instance_dynamic);
|
|
546
|
|
|
|
|
547
|
|
|
dyn_phase = [];
|
|
548
|
|
|
dyn_time = [];
|
|
549
|
|
|
|
|
550
|
|
|
if (collect_dynamic == True):
|
|
551
|
|
|
dyn_phase.append(self._phases);
|
|
552
|
|
|
dyn_time.append(0);
|
|
553
|
|
|
|
|
554
|
|
|
step = time / steps;
|
|
555
|
|
|
int_step = step / 10.0;
|
|
556
|
|
|
|
|
557
|
|
|
for t in numpy.arange(step, time + step, step):
|
|
558
|
|
|
# update states of oscillators
|
|
559
|
|
|
self._phases = self._calculate_phases(solution, t, step, int_step);
|
|
560
|
|
|
|
|
561
|
|
|
# update states of oscillators
|
|
562
|
|
|
if (collect_dynamic == True):
|
|
563
|
|
|
dyn_phase.append(self._phases);
|
|
564
|
|
|
dyn_time.append(t);
|
|
565
|
|
|
|
|
566
|
|
|
if (collect_dynamic != True):
|
|
567
|
|
|
dyn_phase.append(self._phases);
|
|
568
|
|
|
dyn_time.append(time);
|
|
569
|
|
|
|
|
570
|
|
|
output_sync_dynamic = sync_dynamic(dyn_phase, dyn_time);
|
|
571
|
|
|
return output_sync_dynamic;
|
|
572
|
|
|
|
|
573
|
|
|
|
|
574
|
|
|
def _calculate_phases(self, solution, t, step, int_step):
|
|
575
|
|
|
"""!
|
|
576
|
|
|
@brief Calculates new phases for oscillators in the network in line with current step.
|
|
577
|
|
|
|
|
578
|
|
|
@param[in] solution (solve_type): Type solver of the differential equation.
|
|
579
|
|
|
@param[in] t (double): Time of simulation.
|
|
580
|
|
|
@param[in] step (double): Step of solution at the end of which states of oscillators should be calculated.
|
|
581
|
|
|
@param[in] int_step (double): Step differentiation that is used for solving differential equation.
|
|
582
|
|
|
|
|
583
|
|
|
@return (list) New states (phases) for oscillators.
|
|
584
|
|
|
|
|
585
|
|
|
"""
|
|
586
|
|
|
|
|
587
|
|
|
next_phases = [0] * self._num_osc; # new oscillator _phases
|
|
588
|
|
|
|
|
589
|
|
|
for index in range (0, self._num_osc, 1):
|
|
590
|
|
|
if (solution == solve_type.FAST):
|
|
591
|
|
|
result = self._phases[index] + self._phase_kuramoto(self._phases[index], 0, index);
|
|
592
|
|
|
next_phases[index] = self._phase_normalization(result);
|
|
593
|
|
|
|
|
594
|
|
|
elif (solution == solve_type.RK4):
|
|
595
|
|
|
result = odeint(self._phase_kuramoto, self._phases[index], numpy.arange(t - step, t, int_step), (index , ));
|
|
596
|
|
|
next_phases[index] = self._phase_normalization(result[len(result) - 1][0]);
|
|
597
|
|
|
|
|
598
|
|
|
else:
|
|
599
|
|
|
raise NameError("Solver '" + solution + "' is not supported");
|
|
600
|
|
|
|
|
601
|
|
|
return next_phases;
|
|
602
|
|
|
|
|
603
|
|
|
|
|
604
|
|
|
def _phase_normalization(self, teta):
|
|
605
|
|
|
"""!
|
|
606
|
|
|
@brief Normalization of phase of oscillator that should be placed between [0; 2 * pi].
|
|
607
|
|
|
|
|
608
|
|
|
@param[in] teta (double): phase of oscillator.
|
|
609
|
|
|
|
|
610
|
|
|
@return (double) Normalized phase.
|
|
611
|
|
|
|
|
612
|
|
|
"""
|
|
613
|
|
|
|
|
614
|
|
|
norm_teta = teta;
|
|
615
|
|
|
while (norm_teta > (2.0 * pi)) or (norm_teta < 0):
|
|
616
|
|
|
if (norm_teta > (2.0 * pi)):
|
|
617
|
|
|
norm_teta -= 2.0 * pi;
|
|
618
|
|
|
else:
|
|
619
|
|
|
norm_teta += 2.0 * pi;
|
|
620
|
|
|
|
|
621
|
|
|
return norm_teta;
|
|
622
|
|
|
|
annoviko /
pyclustering
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