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dependencies = [ "cellpylib", "pysindy", "pydmd", - "seaborn" + "seaborn", + "dysts>=0.85", + "neurokit2>=0.2.9", + "nolds>=0.6.0", + "EntropyHub>=2.0", + "juliacall>=0.9.22", + "juliapkg>=0.1.13", + "julia>=0.6.2", + "fathon>=1.3.3.post1", ] requires-python = ">=3.10,<=3.11" readme = "README.md" diff --git a/src/dynadojo/systems/gilpin_flows.py b/src/dynadojo/systems/gilpin_flows.py new file mode 100644 index 00000000..60a6771f --- /dev/null +++ b/src/dynadojo/systems/gilpin_flows.py @@ -0,0 +1,170 @@ +import numpy as np +from ..abstractions import AbstractSystem +import importlib +import warnings +import os +import json +import dysts +from dysts.utils import generate_ic_ensemble + +class GilpinFlowsSystem(AbstractSystem): + """ + Gilpin Flows System for modeling chaotic attractors using systems from the dysts library. + + Attributes + ---------- + base_path : str + Base path for the dysts library. + json_file_path : str + Path to the JSON file containing chaotic attractors data. + all_systems : list + List of all available systems from the chaotic attractors data. + + Example + ------- + >>> from dynadojo.systems.gilpin_flows import GilpinFlowsSystem + >>> latent_dim = 3 + >>> embed_dim = 3 + >>> system_name = 'Lorenz' + >>> system = GilpinFlowsSystem(latent_dim, embed_dim, system_name) + >>> n = 10 + >>> init_conds = system.make_init_conds(n, in_dist=True) + >>> timesteps = 100 + >>> trajectories = system.make_data(init_conds, timesteps) + >>> error = system.calc_error(trajectories[0], trajectories[1]) + >>> control_cost = system.calc_control_cost(np.zeros((n, timesteps, embed_dim))) + + Methods + ------- + __init__(self, latent_dim, embed_dim, system_name: str, seed=None) + Initializes the system with given dimensions and system name. + make_init_conds(self, n: int, in_dist=True) -> np.ndarray + Generates initial conditions for the system. + make_data(self, init_conds: np.ndarray, timesteps: int, control=None, noisy=False) -> np.ndarray + Generates trajectories from initial conditions. + calc_error(self, x: np.ndarray, y: np.ndarray) -> float + Calculates the mean squared error between two arrays. + calc_control_cost(self, control: np.ndarray) -> float + Calculates the control cost. + """ + base_path = os.path.dirname(dysts.__file__) + json_file_path = os.path.join(base_path, 'data', 'chaotic_attractors.json') + + with open(json_file_path, 'r') as file: + systems_data = json.load(file) + + all_systems = list(systems_data.keys()) + + def __init__(self, latent_dim, embed_dim, system_name: str, seed=None): + """ + Initialize the GilpinFlowsSystem class. + + Parameters + ---------- + latent_dim : int + Dimension of the latent space. + embed_dim : int + Embedding dimension of the system. Fixed to Gilpin's set dimensionality for the particular system. + system_name : str + The name of the system to be used. + seed : int or None, optional + Seed for random number generation. Default is None. + """ + super().__init__(latent_dim, embed_dim, seed=seed) + self.system_name = system_name + + try: + module = importlib.import_module('dysts.flows') + SystemClass = getattr(module, system_name) + self.system = SystemClass() + except (ModuleNotFoundError, AttributeError) as e: + raise ValueError(f"Unsupported system: {self.system_name}") from e + + setattr(self, 'rhs', self.system.rhs) + #setattr(self, 'jac', self.system.jac) + data = self.system._load_data() + self._embed_dim = data.get("embedding_dimension") + self._latent_dim = self._embed_dim + + attributes = [ + "embedding_dimension", "bifurcation_parameter", "citation", + "correlation_dimension", "delay", "description", "dt", + "hamiltonian", "initial_conditions", "kaplan_yorke_dimension", + "lyapunov_spectrum_estimated", "maximum_lyapunov_estimated", + "multiscale_entropy", "nonautonomous", "parameters", "period", + "pesin_entropy", "unbounded_indices", + ] + + for attr in attributes: + value = data.get(attr, 'NA') + setattr(self, attr, value) + if value == 'NA': + warnings.warn( + f"Attribute '{attr}' not found for system '{self.system_name}'", + UserWarning + ) + + def make_init_conds(self, n: int, in_dist=True) -> np.ndarray: + if in_dist: + tpts0 = np.arange(0, 2, 1) + trajectories = generate_ic_ensemble(self.system, tpts0, n, random_state=self._seed) + x0 = trajectories[:, :, 0] + return x0 + + x = self.system.make_trajectory(10000, resample = True) + + mean = np.mean(x, axis=0) + x_centered = x - mean + U, s, _ = np.linalg.svd(x_centered, full_matrices=False) + + variance_explained = np.cumsum(s**2) / np.sum(s**2) + num_components = np.argmax(variance_explained >= 0.90) + 1 + num_components = min(num_components, x.shape[1] - 1) + + U_remaining = U[:, num_components:] + + scale = 10.0 + ood_points = [] + + for _ in range(n): + random_projection = np.random.randn(x.shape[1] - num_components) + projection = U_remaining @ random_projection + ood_point = mean + scale * projection[:mean.shape[0]] + ood_points.append(ood_point) + + return np.array(ood_points) + + def make_data(self, init_conds: np.ndarray, timesteps: int, pts_per_period=100, control=None, noisy=False, return_times=False): + n = init_conds.shape[0] + trajectories = np.zeros((n, timesteps, self._embed_dim)) + + if return_times: + timepoints = np.zeros((n, timesteps)) + for i in range(n): + self.system.ic = init_conds[i] + timepoint, trajectory = self.system.make_trajectory(timesteps, resample=True, pts_per_period = pts_per_period, return_times=True) + if trajectory.shape[0] < timesteps: + timepoint, trajectory = self.system.make_trajectory(timesteps, resample=False, pts_per_period = pts_per_period, return_times=True) + assert trajectory.shape == (timesteps, self._embed_dim) + trajectories[i] = trajectory + timepoints[i] = timepoint + + + return timepoints, trajectories + + for i in range(n): + self.system.ic = init_conds[i] + trajectory = self.system.make_trajectory(timesteps, resample=True, pts_per_period = pts_per_period) + if trajectory.shape[0] < timesteps: + trajectory = self.system.make_trajectory(timesteps, resample=False, pts_per_period = pts_per_period) + assert trajectory.shape == (timesteps, self._embed_dim) + trajectories[i] = trajectory + + return trajectories + + def calc_error(self, x, y) -> float: + error = x - y + return np.mean(error ** 2) + + def calc_control_cost(self, control: np.ndarray) -> float: + return np.linalg.norm(control, axis=(1, 2), ord=2) / self._embed_dim \ No newline at end of file diff --git a/src/dynadojo/systems/gilpin_lds.py b/src/dynadojo/systems/gilpin_lds.py new file mode 100644 index 00000000..eb2fa9a2 --- /dev/null +++ b/src/dynadojo/systems/gilpin_lds.py @@ -0,0 +1,24 @@ +from dysts.base import BaseDyn, staticjit + +class DynSys: + def __init__(self, alpha): + self.alpha = alpha + + def rhs(self, X, t): + """The right hand side of a dynamical equation""" + out = self._rhs(*X.T, t, alpha=self.alpha) + return out + def jac(self, X, t): + """The Jacobian of the dynamical system""" + out = self._jac(*X.T, t, alpha=self.alpha) + return out + +class LDS(DynSys): + @staticjit + def _rhs(x, t, alpha): + xdot = alpha * x + return xdot + @staticjit + def _jac(x, t, alpha): + row1 = [alpha] + return row1 \ No newline at end of file diff --git a/src/dynadojo/systems/utils/simple.py b/src/dynadojo/systems/utils/simple.py index ff6c73b9..4eba4831 100644 --- a/src/dynadojo/systems/utils/simple.py +++ b/src/dynadojo/systems/utils/simple.py @@ -134,7 +134,7 @@ def calc_dynamics(self, t, x): """ raise NotImplementedError - def make_data(self, init_conds: np.ndarray, control: np.ndarray, timesteps: int, noisy=False) -> np.ndarray: + def make_data(self, init_conds: np.ndarray, control: np.ndarray, timesteps: int, dt = 0.015, noisy=False) -> np.ndarray: r""" Uses the :func:`~calc_dynamics` method to generate data. Mathematically, data is generated like :math:`\dot{x} = f(x) + Bu`. Where :math:`f(x)` is given by :func:`~calc_dynamics`. @@ -147,6 +147,8 @@ def make_data(self, init_conds: np.ndarray, control: np.ndarray, timesteps: int, (n, timesteps, embed_dim) Controls tensor. timesteps : int Timesteps per training trajectory (per action horizon). + dt: float, optional + If specified, changes the size of dt between each timestep. noisy : bool, optional If True, add noise to trajectories. Defaults to False. If False, no noise is added. @@ -157,7 +159,7 @@ def make_data(self, init_conds: np.ndarray, control: np.ndarray, timesteps: int, """ data = [] init_conds = init_conds @ np.linalg.pinv(self.embedder) - time = np.linspace(self._t_range[0], self._t_range[1], num=timesteps) + time = np.linspace(self._t_range[0], self._t_range[1] * dt * timesteps, num=timesteps) def dynamics(t, x, u): i = np.argmin(np.abs(t - time)) @@ -167,7 +169,7 @@ def dynamics(t, x, u): return dx for x0, u in zip(init_conds, control): - sol = solve_ivp(dynamics, t_span=[self._t_range[0], self._t_range[1]], y0=x0, t_eval=time, + sol = solve_ivp(dynamics, t_span=[self._t_range[0], self._t_range[1] * dt * timesteps], y0=x0, t_eval=time, dense_output=True, args=(u,)) data.append(sol.y) diff --git a/src/dynadojo/utils/complexity_calculations/dyna_datagen.py b/src/dynadojo/utils/complexity_calculations/dyna_datagen.py new file mode 100644 index 00000000..93337b2e --- /dev/null +++ b/src/dynadojo/utils/complexity_calculations/dyna_datagen.py @@ -0,0 +1,90 @@ +from dynadojo.wrappers import SystemChecker +from dynadojo.utils.complexity_measures import gp_dim, mse_mv, pca +import pandas as pd +import os + +# NOTE: very similar to data generation for Gilpin systems + +# only Lorenz is standardized in timesteps definiton (i.e. number of timesteps) +# can use others, but timesteps will be ill-defined +from dynadojo.systems.lorenz import LorenzSystem +all_systems = ["LorenzSystem"] +def system_selector (system, dimension, seed): + if system == "LorenzSystem": + return SystemChecker(LorenzSystem(latent_dim=dimension, embed_dim=dimension, seed=seed)) + +# prep dataframe columns +column_names = ["system", "D", "seed", "x0", "OOD", "timesteps", + "gp_dim", "mse_mv", "pca", "lyapunov_spectrum", "kaplan_yorke_dimension", "pesin"] # noise? + +# NOTE: specify sweep parameters here +seeds = [2] +dimensions = [3, 5, 7] +timesteps_list = [100, 500, 1000] +max_timesteps = 1000 + +data = [] +save_interval = 10 +int_counter = 0 + +file_path = 'docs/dyna_complexity_data.JSON' +if os.path.isfile(file_path): + df_old = pd.read_json(file_path, orient='records', lines=True) # loads pre-existing data +else: + pd.DataFrame(columns=column_names).to_json(file_path, orient='records', lines=True) + df_old = pd.read_json(file_path, orient='records', lines=True) # loads newly created data file + +for system_name in all_systems: + + print() + print("### WORKING ON:", system_name, "###") + print() + + for dimension in dimensions: + for seed in seeds: + system = system_selector(system_name, dimension, seed) + + x0 = system.make_init_conds(1) + x = system.make_data(x0, timesteps=max_timesteps) + x0 = x0[0] + x = x[0] + + y0 = system.make_init_conds(1, in_dist=False) + y = system.make_data(y0, timesteps=max_timesteps) + y0 = y0[0] + y = y[0] + + for timesteps in timesteps_list: + + print() + print(" ### CURRENTLY: dimension = ", dimension, ", seed = ", seed, ", timestep =", + timesteps, "###") + print() + + if df_old.empty == False: # guard against indexing into empty file + exists = ((df_old['system'] == system_name) & (df_old['D'] == dimension) & + (df_old['seed'] == seed) & (df_old['timesteps'] == timesteps)).any() + if exists: # skips calculation if already exists in pre-existing data + continue + + X = x[:timesteps] + Y = y[:timesteps] + + data.append([system_name, dimension, seed, x0, False, timesteps, gp_dim(X), + mse_mv(X), pca(X), None, None, None]) + data.append([system_name, dimension, seed, y0, True, timesteps, gp_dim(Y), + mse_mv(Y), pca(Y), None, None, None]) + + if int_counter % save_interval == 0: + temp_df = pd.DataFrame(data, columns=column_names) + temp_df.to_json(file_path, mode='a', orient='records', lines=True) + data = [] + int_counter += 1 + +if data: + temp_df = pd.DataFrame(data, columns=column_names) + temp_df.to_json(file_path, mode='a', orient='records', lines=True) + +df_unsorted = pd.read_json(file_path, orient='records', lines=True) +df = df_unsorted.sort_values(by=['system', 'seed', 'D', 'OOD']) +df.to_json(file_path, orient='records', lines=True) \ No newline at end of file diff --git a/src/dynadojo/utils/complexity_calculations/dyna_grapher.py b/src/dynadojo/utils/complexity_calculations/dyna_grapher.py new file mode 100644 index 00000000..44e99751 --- /dev/null +++ b/src/dynadojo/utils/complexity_calculations/dyna_grapher.py @@ -0,0 +1,48 @@ +import pandas as pd +import matplotlib.pyplot as plt + +df = pd.read_json('/home/vigith/dynadojo/docs/dyna_complexity_data.JSON', orient='records', lines=True) +OOD = [True, False] +timesteps_list = [100, 500, 1000, 2500, 5000, 10000] +#dimensions = [4, 8, 12] +dimensions = [3, 5, 7] +all_systems = ["LorenzSystem", "KuramotoSystem", "CompetitiveLVSystem", "PreyPredatorSystem", "NBodySystem"] +bin_edges = [] +for i in range(10): + bin_edges.append(0.05*i) +for timesteps in timesteps_list: + filter = df['timesteps'] == timesteps + filtered_df = df[filter] + plt.hist(filtered_df['mse_mv'], bins=bin_edges, edgecolor='black') + plt.title(f"Histogram of mse_mv at timesteps {timesteps}") + plt.xlabel('Value') + plt.ylabel('Frequency') + plt.ylim(0, 20) + plt.savefig(f"mse_mv_timesteps_{timesteps}.png") + plt.clf() +bin_edges = [] +for i in range(10): + bin_edges.append(0.1*i) +for dimension in dimensions: + filter = df['D'] == dimension + filtered_df = df[filter] + plt.hist(filtered_df['mse_mv'], bins=bin_edges, edgecolor='black') + plt.title(f"Histogram of mse_mv at dimension {dimension}") + plt.xlabel('Value') + plt.ylabel('Frequency') + plt.ylim(0, 40) + plt.savefig(f"mse_mv_dimension_{dimension}.png") + plt.clf() +bin_edges = [] +for i in range(10): + bin_edges.append(0.1*i) +for state in OOD: + filter = df['OOD'] == state + filtered_df = df[filter] + plt.hist(filtered_df['mse_mv'], bins=10, edgecolor='black') + plt.title(f"Histogram of mse_mv if OOD {state}") + plt.xlabel('Value') + plt.ylabel('Frequency') + plt.ylim(0, 60) + plt.savefig(f"mse_mv_OOD_{state}.png") + plt.clf() \ No newline at end of file diff --git a/src/dynadojo/utils/complexity_calculations/gilpin_datagen.py b/src/dynadojo/utils/complexity_calculations/gilpin_datagen.py new file mode 100644 index 00000000..92fb23bd --- /dev/null +++ b/src/dynadojo/utils/complexity_calculations/gilpin_datagen.py @@ -0,0 +1,111 @@ +from dynadojo.wrappers import SystemChecker +from dynadojo.systems.gilpin_flows import GilpinFlowsSystem +from dynadojo.utils.complexity_measures import corr_dim, multi_en, pca, find_lyapunov_exponents, find_max_lyapunov, kaplan_yorke_dimension, pesin + +import pandas as pd +import os +import dysts +import json + +# pull Gilpin's system info json +base_path = os.path.dirname(dysts.__file__) +json_file_path = os.path.join(base_path, 'data', 'chaotic_attractors.json') +with open(json_file_path, 'r') as file: + systems_data = json.load(file) +all_systems = list(systems_data.keys()) + +# Systems that crashed the code when generating some seeds +problematic_systems = ["IkedaDelay", "MackeyGlass", "PiecewiseCircuit", "RabinovichFabrikant", + "ScrollDelay", "SprottDelay", "SprottJerk", "SprottL", "SprottM", "SprottQ", "VossDelay", "Torus", "TurchinHanski"] + +for problematic_system in problematic_systems: + all_systems.remove(problematic_system) + +# prep dataframe columns +column_names = ["system", "D", "seed", "x0", "OOD", "timesteps", + "gp_dim", "mse_mv", "pca", "lyapunov_spectrum", "kaplan_yorke_dimension", "pesin"] + +# NOTE: specify sweep parameters here, as well as how often the code should save to JSON +seeds = [1, 2, 3, 4, 5] +dimensions = [3] +timesteps_list = [100, 500, 1000, 2500] +max_timesteps = 2500 + +data = [] +save_interval = 2 # Save every "save_interval" number of seeds +int_counter = 0 + +# Checkpointing system to reduce redundancy if partial data already exists +file_path = 'docs/gilpin_complexity_data.JSON' +if os.path.isfile(file_path): + df_old = pd.read_json(file_path, orient='records', lines=True) # loads pre-existing data +else: + pd.DataFrame(columns=column_names).to_json(file_path, orient='records', lines=True) + df_old = pd.read_json(file_path, orient='records', lines=True) # loads newly created data file + +# Loop to sweep and generate code +for system_name in all_systems: + print() + print("### WORKING ON:", system_name, "###") + print() + for dimension in dimensions: + for seed in seeds: + system = SystemChecker(GilpinFlowsSystem(latent_dim=dimension, embed_dim=dimension, system_name=system_name, seed=seed)) + unwrapped_system = system._system # Reach under SystemChecker to enable "return_times" kwarg to GilpinFlowsSystem's "make_data" method + model = unwrapped_system.system # Reach under GilpinFlowsSystem to access the model for Lyapunov + + # Generate in distribution trajectory data + x0 = system.make_init_conds(1) + xtpts, x = unwrapped_system.make_data(x0, timesteps=max_timesteps, return_times=True) + x0 = x0[0] + x = x[0] + + # Generate out of distribution trajectory data + y0 = system.make_init_conds(1, in_dist=False) + ytpts, y = unwrapped_system.make_data(y0, timesteps=max_timesteps, return_times=True) + y0 = y0[0] + y = y[0] + + # Calculate the measures for each "timesteps" sub-slice of the overall trajectory + for timesteps in timesteps_list: + print() + print(" ### CURRENTLY: dimension = ", dimension, ", seed = ", seed, ", timestep =", + timesteps, "###") + print() + + if df_old.empty == False: # guard against indexing into empty file + exists = ((df_old['system'] == system_name) & (df_old['D'] == dimension) & + (df_old['seed'] == seed) & (df_old['timesteps'] == timesteps)).any() + if exists: # skips calculation if already exists in pre-existing data + continue + + # Aforementioned subsets of trajectories + X = x[:timesteps] + Y = y[:timesteps] + + xlyapunov_spectrum = find_lyapunov_exponents(X, xtpts, timesteps, model) + ylyapunov_spectrum = find_lyapunov_exponents(Y, ytpts, timesteps, model) + data.append([system_name, dimension, seed, x0, False, timesteps, corr_dim(X), + multi_en(X), pca(X), xlyapunov_spectrum, + kaplan_yorke_dimension(xlyapunov_spectrum), pesin(xlyapunov_spectrum)]) + data.append([system_name, dimension, seed, y0, True, timesteps, corr_dim(Y), + multi_en(Y), pca(Y), ylyapunov_spectrum, + kaplan_yorke_dimension(ylyapunov_spectrum), pesin(ylyapunov_spectrum)]) + + # Code to append & save to existing JSON periodically + if int_counter % save_interval == 0: + temp_df = pd.DataFrame(data, columns=column_names) + temp_df.to_json(file_path, mode='a', orient='records', lines=True) + data = [] + + int_counter += 1 + +# Check and append any remaining data +if data: + temp_df = pd.DataFrame(data, columns=column_names) + temp_df.to_json(file_path, mode='a', orient='records', lines=True) + +# Re-sort the JSON +df_unsorted = pd.read_json(file_path, orient='records', lines=True) +df = df_unsorted.sort_values(by=['system', 'seed', 'D']) +df.to_json(file_path, orient='records', lines=True) \ No newline at end of file diff --git a/src/dynadojo/utils/complexity_calculations/gilpin_grapher.py b/src/dynadojo/utils/complexity_calculations/gilpin_grapher.py new file mode 100644 index 00000000..22a101fd --- /dev/null +++ b/src/dynadojo/utils/complexity_calculations/gilpin_grapher.py @@ -0,0 +1,69 @@ +import pandas as pd +import matplotlib.pyplot as plt + +import os +import dysts +import json + +df = pd.read_json('/home/vigith/dynadojo/docs/dyna_complexity_data.JSON', orient='records', lines=True) +OOD = [True, False] +timesteps_list = [100, 500, 1000, 2500, 5000, 10000] +#dimensions = [4, 8, 12] +dimensions = [3]#, 5, 7] + +base_path = os.path.dirname(dysts.__file__) +json_file_path = os.path.join(base_path, 'data', 'chaotic_attractors.json') +with open(json_file_path, 'r') as file: + systems_data = json.load(file) +all_systems = list(systems_data.keys()) + +problematic_systems = ["IkedaDelay", "MackeyGlass", "PiecewiseCircuit", "ScrollDelay", "SprottDelay", "SprottJerk", "VossDelay", "Torus"] +for problematic_system in problematic_systems: + all_systems.remove(problematic_system) + +measures = ["gp_dim", "mse_mv", "pca", "lyapunov_spectrum", "kaplan_yorke_dimension", "pesin"] +for measure in measures: + #Sweep Timesteps + bin_edges = [] + for i in range(10): + bin_edges.append(0.05*i) + for timesteps in timesteps_list: + filter = df['timesteps'] == timesteps + filtered_df = df[filter] + plt.hist(filtered_df[measure], bins=bin_edges, edgecolor='black') + plt.title(f"Histogram of {measure} at timesteps {timesteps}") + plt.xlabel('Value') + plt.ylabel('Frequency') + #plt.ylim(0, 20) + plt.savefig(f"{measure}_timesteps_{timesteps}.png") + plt.clf() + + #Sweep Dimension + bin_edges = [] + for i in range(10): + bin_edges.append(0.1*i) + for dimension in dimensions: + filter = df['D'] == dimension + filtered_df = df[filter] + plt.hist(filtered_df[measure], bins=bin_edges, edgecolor='black') + plt.title(f"Histogram of {measure} at dimension {dimension}") + plt.xlabel('Value') + plt.ylabel('Frequency') + #plt.ylim(0, 40) + plt.savefig(f"{measure}_dimension_{dimension}.png") + plt.clf() + + #Sweep In/Out + bin_edges = [] + for i in range(10): + bin_edges.append(0.1*i) + for state in OOD: + filter = df['OOD'] == state + filtered_df = df[filter] + plt.hist(filtered_df[measure], bins=10, edgecolor='black') + plt.title(f"Histogram of {measure} if OOD {state}") + plt.xlabel('Value') + plt.ylabel('Frequency') + #plt.ylim(0, 60) + plt.savefig(f"{measure}_OOD_{state}.png") + plt.clf() \ No newline at end of file diff --git a/src/dynadojo/utils/complexity_calculations/jl_datagen.py b/src/dynadojo/utils/complexity_calculations/jl_datagen.py new file mode 100644 index 00000000..ac5dc574 --- /dev/null +++ b/src/dynadojo/utils/complexity_calculations/jl_datagen.py @@ -0,0 +1,125 @@ +from dynadojo.wrappers import SystemChecker +from dynadojo.systems.gilpin_flows import GilpinFlowsSystem + +import dynadojo.utils.julia_complexity_measures as jl + +import pandas as pd +import os +import dysts +import json + +# pull Gilpin's system info json +base_path = os.path.dirname(dysts.__file__) +json_file_path = os.path.join(base_path, 'data', 'chaotic_attractors.json') +with open(json_file_path, 'r') as file: + systems_data = json.load(file) +all_systems = list(systems_data.keys()) + +# # Systems that crashed the code when generating some seeds +# problematic_systems = ['AnishchenkoAstakhov', 'ArnoldBeltramiChildress', 'ArnoldWeb', 'BeerRNN', 'BelousovZhabotinsky', 'BickleyJet', 'BlinkingRotlet', 'BlinkingVortex', 'CaTwoPlus', 'CaTwoPlusQuasiperiodic', 'CellCycle', 'CellularNeuralNetwork', 'Chua', 'CircadianRhythm', 'Colpitts', 'DoubleGyre', 'DoublePendulum', 'Duffing', 'ExcitableCell', 'FluidTrampoline', 'ForcedBrusselator', 'ForcedFitzHughNagumo', 'ForcedVanDerPol', 'Hopfield', 'HyperLu', 'IkedaDelay', 'InteriorSquirmer', 'JerkCircuit', 'LidDrivenCavityFlow', 'Lorenz96', 'MacArthur', 'MackeyGlass', 'MultiChua', 'NuclearQuadrupole', 'OscillatingFlow', 'PiecewiseCircuit', 'SanUmSrisuchinwong', 'ScrollDelay', 'SprottDelay', 'SprottMore', 'StickSlipOscillator', 'SwingingAtwood', 'Thomas', 'ThomasLabyrinth', 'TurchinHanski', 'VossDelay', 'WindmiReduced', 'YuWang', 'YuWang2'] +# +# for problematic_system in problematic_systems: +# all_systems.remove(problematic_system) + +# prep dataframe columns +column_names = ["system", "D", "seed", "x0", "OOD", "timesteps", + "corr_dim", "generalized_dim", "shannon_en", "perm_en", "lyapunov_spectrum", "lyapunov_max", "ky_dim"] + +# NOTE: specify sweep parameters here, as well as how often the code should save to JSON +seeds = [1] +dimensions = [3] +timesteps_list = [1000] +max_timesteps = 1000 + +data = [] +save_interval = 2 # Save every "save_interval" number of seeds +int_counter = 0 + +# Checkpointing system to reduce redundancy if partial data already exists +file_path = 'docs/jl_complexity_data.JSON' +if os.path.isfile(file_path): + df_old = pd.read_json(file_path, orient='records', lines=True) # loads pre-existing data +else: + pd.DataFrame(columns=column_names).to_json(file_path, orient='records', lines=True) + df_old = pd.read_json(file_path, orient='records', lines=True) # loads newly created data file + +# Loop to sweep and generate code +for system_name in all_systems: + print() + print("### WORKING ON:", system_name, "###") + print() + for dimension in dimensions: + for seed in seeds: + system = SystemChecker(GilpinFlowsSystem(latent_dim=dimension, embed_dim=dimension, system_name=system_name, seed=seed)) + unwrapped_system = system._system # Reach under SystemChecker to enable "return_times" kwarg to GilpinFlowsSystem's "make_data" method + model = unwrapped_system.system # Reach under GilpinFlowsSystem to access the model for Lyapunov + + # Generate in distribution trajectory data + x0 = system.make_init_conds(1) + xtpts, x = unwrapped_system.make_data(x0, timesteps=max_timesteps, return_times=True) + x0 = x0[0] + x = x[0] + + # Generate out of distribution trajectory data + y0 = system.make_init_conds(1, in_dist=False) + ytpts, y = unwrapped_system.make_data(y0, timesteps=max_timesteps, return_times=True) + y0 = y0[0] + y = y[0] + + # Calculate the measures for each "timesteps" sub-slice of the overall trajectory + for timesteps in timesteps_list: + print() + print(" ### CURRENTLY: dimension = ", dimension, ", seed = ", seed, ", timestep =", + timesteps, "###") + print() + + if df_old.empty == False: # guard against indexing into empty file + exists = ((df_old['system'] == system_name) & (df_old['D'] == dimension) & + (df_old['seed'] == seed) & (df_old['timesteps'] == timesteps)).any() + if exists: # skips calculation if already exists in pre-existing data + continue + + # Aforementioned subsets of trajectories + X = x[:timesteps] + Y = y[:timesteps] + + try: + lyapunov_spectrum = jl.find_lyapunov(system_name, timesteps) + max_lyapunov = jl.find_lyapunov(system_name, timesteps, max=True) + kaplan_yorke_dim = jl.ky_dim(lyapunov_spectrum) + lyapunov_spectrum = [i for i in lyapunov_spectrum] + except: + # Handle the exception + print(f"THERE WAS AN ERROR WITH {system_name}") + problematic_systems.append(system_name) + lyapunov_spectrum = None + max_lyapunov = None + kaplan_yorke_dim = None # Provide a default value or take corrective action + + data.append([system_name, dimension, seed, x0, False, timesteps, + jl.corr_dim(X), jl.generalized_dim(X), jl.shannon_en(X), jl.perm_en(X), + lyapunov_spectrum, max_lyapunov, kaplan_yorke_dim]) + data.append([system_name, dimension, seed, x0, False, timesteps, + jl.corr_dim(Y), jl.generalized_dim(Y), jl.shannon_en(Y), jl.perm_en(Y), + lyapunov_spectrum, max_lyapunov, kaplan_yorke_dim]) + + # Code to append & save to existing JSON periodically + if int_counter % save_interval == 0: + temp_df = pd.DataFrame(data, columns=column_names) + temp_df.to_json(file_path, mode='a', orient='records', lines=True) + data = [] + + int_counter += 1 + +# Check and append any remaining data +if data: + temp_df = pd.DataFrame(data, columns=column_names) + temp_df.to_json(file_path, mode='a', orient='records', lines=True) + +print("PROBLEMATIC SYSTEMS:") +# print(problematic_systems) + +# Re-sort the JSON +df_unsorted = pd.read_json(file_path, orient='records', lines=True) +df = df_unsorted.sort_values(by=['system', 'seed', 'D']) +df.to_json(file_path, orient='records', lines=True) \ No newline at end of file diff --git a/src/dynadojo/utils/complexity_calculations/lyapunov_gilpin_tester.py b/src/dynadojo/utils/complexity_calculations/lyapunov_gilpin_tester.py new file mode 100644 index 00000000..b6964ec0 --- /dev/null +++ b/src/dynadojo/utils/complexity_calculations/lyapunov_gilpin_tester.py @@ -0,0 +1,94 @@ +from dynadojo.wrappers import SystemChecker +from dynadojo.systems.gilpin_flows import GilpinFlowsSystem +from dynadojo.utils.complexity_measures import find_lyapunov_exponents +import numpy as np + +system = SystemChecker(GilpinFlowsSystem(latent_dim=3, embed_dim=3, system_name="Lorenz", seed=1)) +unwrapped_system = system._system +model = unwrapped_system.system + +model.beta = 8/3 +model.rho = 28 +model.sigma = 10 +timesteps = 1000 +x0 = np.array([[-9.7869288, -15.03852, 20.533978]]) + +xtpts, x = unwrapped_system.make_data(x0, timesteps=timesteps, return_times=True) +spectrum = find_lyapunov_exponents(x[0], xtpts, timesteps, model) + +print("Lorenz:", spectrum) + +""" + +"parameters": { + "beta": 2.667, + "rho": 28, + "sigma": 10 + } +"initial_conditions": [ + -9.7869288, + -15.03852, + 20.533978 + ], +"dt": 0.0003002100350058257, + +class Lorenz(DynSys): +@staticjit +def _rhs(x, y, z, t, beta, rho, sigma): + xdot = sigma * y - sigma * x + ydot = rho * x - x * z - y + zdot = x * y - beta * z + return xdot, ydot, zdot +@staticjit +def _jac(x, y, z, t, beta, rho, sigma): + row1 = [-sigma, sigma, 0] + row2 = [rho - z, -1, -x] + row3 = [y, x, -beta] + return row1, row2, row3 + +""" + +system = SystemChecker(GilpinFlowsSystem(latent_dim=3, embed_dim=3, system_name="Rossler", seed=1)) +unwrapped_system = system._system +model = unwrapped_system.system + +model.beta = 8/3 +model.rho = 28 +model.sigma = 10 +timesteps = 1000 +x0 = np.array([[6.5134412, 6.5134412, 0.34164294]]) + +xtpts, x = unwrapped_system.make_data(x0, timesteps=timesteps, return_times=True) +spectrum = find_lyapunov_exponents(x[0], xtpts, timesteps, model) + +print("Rossler:", spectrum) + +""" + +"parameters": { + "a": 0.2, + "b": 0.2, + "c": 5.7 + }, +"initial_conditions": [ + 6.5134412, + 6.5134412, + 0.34164294 + ], +"dt": 0.001181916986164424, + +class Rossler(DynSys): + @staticjit + def _rhs(x, y, z, t, a, b, c): + xdot = -y - z + ydot = x + a * y + zdot = b + z * x - c * z + return xdot, ydot, zdot + @staticjit + def _jac(x, y, z, t, a, b, c): + row1 = [0, -1, -1] + row2 = [1, a, 0] + row3 = [z, 0, x - c] + return row1, row2, row3 + +""" \ No newline at end of file diff --git a/src/dynadojo/utils/complexity_calculations/lyapunov_julia_tester.jl b/src/dynadojo/utils/complexity_calculations/lyapunov_julia_tester.jl new file mode 100644 index 00000000..bb293c9a --- /dev/null +++ b/src/dynadojo/utils/complexity_calculations/lyapunov_julia_tester.jl @@ -0,0 +1,35 @@ +using DynamicalSystems + +## LORENZ ## + +@inline @inbounds function new_lorenz(u, p, t) + σ = p[1]; ρ = p[2]; β = p[3] + du1 = σ*(u[2]-u[1]) + du2 = u[1]*(ρ-u[3]) - u[2] + du3 = u[1]*u[2] - β*u[3] + return SVector{3}(du1, du2, du3) +end + +lu0 = [-9.7869288, -15.03852, 20.533978] +lp = [10, 28, 8/3] +lds = ContinuousDynamicalSystem(new_lorenz, lu0, lp) +lλs = lyapunovspectrum(lds, 1000, Ttr = 0.0003002100350058257) + +println("Lorenz:", lλs) + +## ROSSLER ## + +@inline @inbounds function new_rossler(u, p, t) + a = p[1]; b = p[2]; c = p[3] + du1 = -u[2] -u[3] + du2 = u[1] + a*u[2] + du3 = b + u[3]*(u[1] - c) + return SVector{3}(du1, du2, du3) +end + +ru0 = [6.5134412, 6.5134412, 0.34164294] +rp = [0.2, 0.2, 5.7] +rds = ContinuousDynamicalSystem(new_rossler, ru0, rp) +rλs = lyapunovspectrum(rds, 1000, Ttr = 0.001181916986164424) + +println("Rossler:", rλs) \ No newline at end of file diff --git a/src/dynadojo/utils/complexity_calculations/verify_against_gilpin.py b/src/dynadojo/utils/complexity_calculations/verify_against_gilpin.py new file mode 100644 index 00000000..51b1e6e1 --- /dev/null +++ b/src/dynadojo/utils/complexity_calculations/verify_against_gilpin.py @@ -0,0 +1,106 @@ +from dynadojo.wrappers import SystemChecker +import numpy as np +import pandas as pd +import json +import os +import dysts +from dynadojo.systems.gilpin_flows import GilpinFlowsSystem +from dynadojo.utils.complexity_measures import gp_dim, mse_mv, pca, find_lyapunov_exponents, find_max_lyapunov, kaplan_yorke_dimension, pesin + +base_path = os.path.dirname(dysts.__file__) +json_file_path = os.path.join(base_path, 'data', 'chaotic_attractors.json') +with open(json_file_path, 'r') as file: + systems_data = json.load(file) +all_systems = list(systems_data.keys()) + +problematic_systems = ["IkedaDelay", "MackeyGlass", "PiecewiseCircuit", "RabinovichFabrikant", + "ScrollDelay", "SprottDelay", "SprottJerk", "SprottL", "SprottM", "SprottQ", "VossDelay", "Torus", "TurchinHanski"] + +for problematic_system in problematic_systems: + all_systems.remove(problematic_system) + +"""For all mathematical properties we perform 20 replicate computations from different initial conditions, and record +the average in our database. To ensure high-quality estimates, we compute trajectories at high granularity of 500 +points per period (as determined by the dominant frequency in the power spectrum), and we use trajectories with +length 2500, corresponding to five complete periods.""" + +timesteps = 2500 +pts_per_period = 500 + +# prep dataframe columns +column_names = ["system", "calc_correlation_dimension", "calc_multiscale_entropy", "calc_lyapunov_spectrum_estimated", "calc_pesin_entropy", "calc_kaplan_yorke_dimension", + "og_correlation_dimension", "og_multiscale_entropy", "og_lyapunov_spectrum_estimated", "og_pesin_entropy", "og_kaplan_yorke_dimension", + "diff_correlation_dimension", "diff_multiscale_entropy", "diff_lyapunov_spectrum_estimated", "diff_pesin_entropy", "diff_kaplan_yorke_dimension" + ] + +# Checkpointing system to reduce redundancy if partial data already exists +file_path = 'docs/complexity_comparison.JSON' +pd.DataFrame(columns=column_names).to_json(file_path, orient='records', lines=True) +df = pd.read_json(file_path, orient='records', lines=True) # loads newly created data file + +for system_name in all_systems: + system_dict = systems_data[system_name] + embedding_dimension = system_dict["embedding_dimension"] + initial_conditions = np.asarray([system_dict["initial_conditions"]]) + + system = SystemChecker(GilpinFlowsSystem(latent_dim=embedding_dimension, embed_dim=embedding_dimension, system_name=system_name)) + model = system._system.system + + tpts, x = system._system.make_data(initial_conditions, pts_per_period=pts_per_period, timesteps=timesteps, return_times=True) + x = x[0] + + lyapunov_spectrum = find_lyapunov_exponents(x, tpts, timesteps, model) + + # Values calculated with Dynadojo utils + calc_correlation_dimension = gp_dim(x) + calc_multiscale_entropy = mse_mv(x) + calc_lyapunov_spectrum_estimated = pca(x) + # calc_maximum_lyapunov_estimated = find_max_lyapunov(lyapunov_spectrum) + calc_pesin_entropy = kaplan_yorke_dimension(lyapunov_spectrum) + calc_kaplan_yorke_dimension = pesin(lyapunov_spectrum) + + # Values pulled from Gilpin JSON + og_correlation_dimension = system_dict.get("correlation_dimension") + og_multiscale_entropy = system_dict.get("multiscale_entropy") + og_lyapunov_spectrum_estimated = system_dict.get("lyapunov_spectrum_estimated") + # og_maximum_lyapunov_estimated = system_dict.get("maximum_lyapunov_estimated") + og_pesin_entropy = system_dict.get("pesin_entropy") + og_kaplan_yorke_dimension = system_dict.get("kaplan_yorke_dimension") + + # Difference between values + if og_correlation_dimension != None: + diff_correlation_dimension = calc_correlation_dimension - og_correlation_dimension + else: + diff_correlation_dimension = None + if og_multiscale_entropy != None: + diff_multiscale_entropy = calc_multiscale_entropy - og_multiscale_entropy + else: + diff_multiscale_entropy = None + if og_lyapunov_spectrum_estimated != None: + diff_lyapunov_spectrum_estimated = calc_lyapunov_spectrum_estimated - og_lyapunov_spectrum_estimated + else: + og_lyapunov_spectrum_estimated = None + # diff_maximum_lyapunov_estimated = calc_maximum_lyapunov_estimated - og_maximum_lyapunov_estimated + if og_pesin_entropy != None: + diff_pesin_entropy = calc_pesin_entropy - og_pesin_entropy + else: + diff_pesin_entropy = None + if og_kaplan_yorke_dimension != None: + diff_kaplan_yorke_dimension = calc_kaplan_yorke_dimension - og_kaplan_yorke_dimension + else: + diff_kaplan_yorke_dimension = None + + # Throw the values into a list and then into pandas dataframe + data = [[system_name, calc_correlation_dimension, calc_multiscale_entropy, calc_lyapunov_spectrum_estimated, calc_pesin_entropy, calc_kaplan_yorke_dimension, + og_correlation_dimension, og_multiscale_entropy, og_lyapunov_spectrum_estimated, og_pesin_entropy, og_kaplan_yorke_dimension, + diff_correlation_dimension, diff_multiscale_entropy, diff_lyapunov_spectrum_estimated, diff_pesin_entropy, diff_kaplan_yorke_dimension + ]] + temp_df = pd.DataFrame(data, columns=column_names) + temp_df.to_json(file_path, mode='a', orient='records', lines=True) + +df_unsorted = pd.read_json(file_path, orient='records', lines=True) +df = df_unsorted.sort_values(by=['system', 'seed', 'D']) +df.to_json(file_path, orient='records', lines=True) + + + diff --git a/src/dynadojo/utils/complexity_measures.py b/src/dynadojo/utils/complexity_measures.py new file mode 100644 index 00000000..469fe4aa --- /dev/null +++ b/src/dynadojo/utils/complexity_measures.py @@ -0,0 +1,415 @@ +import numpy as np +import pandas as pd +import warnings +import neurokit2 +from sklearn.decomposition import PCA +from dysts.utils import jac_fd +from scipy.spatial.distance import cdist +from scipy.optimize import curve_fit +import EntropyHub as EH + +## Helper function for correlation dimension +def estimate_powerlaw(data0): + """ + Given a 1D array of continuous-valued data, estimate the power law exponent using the + maximum likelihood estimator proposed by Clauset, Shalizi, Newman (2009). + + Args: + data0 (np.ndarray): An array of continuous-valued data + + Returns: + float: The estimated power law exponent + """ + data = np.sort(data0, axis=0).copy() + xmin = np.min(data, axis=0) + n = data.shape[0] + ahat = 1 + n / np.sum(np.log(data / xmin), axis=0) + return ahat + +### Correlation dimension (Outdated) +#def gp_dim(data, y_data=None, rvals=None, nmax=100): +# """ +# Estimate the Grassberger-Procaccia dimension for a numpy array using the +# empirical correlation integral. +# +# Args: +# data (np.array): T x D, where T is the number of datapoints/timepoints, and D +# is the number of features/dimensions +# y_data (np.array, Optional): A second dataset of shape T2 x D, for +# computing cross-correlation. +# rvals (np.array): A list of radii +# nmax (int): The number of points at which to evaluate the correlation integral +# +# Returns: +# rvals (np.array): The discrete bins at which the correlation integral is +# estimated +# corr_sum (np.array): The estimates of the correlation integral at each bin +# +# """ +# data = np.asarray(data) +# +# # Makes a copy of original data for self correlation +# if y_data is None: +# y_data = data.copy() +# +# if rvals is None: +# std = np.std(data) +# rvals = np.logspace(np.log10(0.1 * std), np.log10(0.5 * std), nmax) +# +# n = len(data) +# +# dists = cdist(data, y_data) +# rvals = dists.ravel() +# +# ## Truncate the distance distribution to the linear scaling range +# std = np.std(data) +# rvals = rvals[rvals > 0] +# rvals = rvals[rvals > np.percentile(rvals, 5)] +# rvals = rvals[rvals < np.percentile(rvals, 50)] +# +# return estimate_powerlaw(rvals) + +## Correlation Dimension +def corr_dim(data, y_data=None, rvals=None, nmax=100): + """ + Estimate the Grassberger-Procaccia dimension for a numpy array using the + empirical correlation integral. + + Args: + data (np.array): T x D, where T is the number of datapoints/timepoints, and D + is the number of features/dimensions + y_data (np.array, Optional): A second dataset of shape T2 x D, for + computing cross-correlation. + rvals (np.array): A list of radii + nmax (int): The number of points at which to evaluate the correlation integral + + Returns: + rvals (np.array): The discrete bins at which the correlation integral is + estimated + corr_sum (np.array): The estimates of the correlation integral at each bin + + """ + + data = np.asarray(data) + + ## For self-correlation + if y_data is None: + y_data = data.copy() + + if rvals is None: + std = np.std(data) + rvals = np.logspace(np.log10(0.1 * std), np.log10(0.5 * std), nmax) + + n = len(data) + + # For Gilpin Flows + if len(data[0]) > 2: + dists = cdist(data, y_data) + rvals = dists.ravel() + + ## Truncate the distance distribution to the linear scaling range + std = np.std(data) + rvals = rvals[rvals > 0] + rvals = rvals[rvals > np.percentile(rvals, 5)] + rvals = rvals[rvals < np.percentile(rvals, 50)] + + return estimate_powerlaw(rvals) + + # For Gilpin Maps + if len(data[0]) <= 2: + dists = cdist(data, y_data) + rvals = np.sort(dists.ravel()) + corr_sum = np.arange(len(rvals)).astype(float) + corr_sum /= n * (n - 1) + std = np.std(data) + sel_inds = rvals > 0.1 * std + rvals = rvals[sel_inds] + corr_sum = corr_sum[sel_inds] + sel_inds = rvals < 0.5 * std + rvals = rvals[sel_inds] + corr_sum = corr_sum[sel_inds] + + ## Drop zeros before regression + sel_inds = corr_sum > 0 + rvals = rvals[sel_inds] + corr_sum = corr_sum[sel_inds] + + power_law = lambda x, a, b: a * (x ** b) + fit_vals = curve_fit(power_law, rvals, corr_sum) + return fit_vals[0][1] + +### Multiscale Entropy (Outdated) +#def mse_mv(traj, return_info=False, gilpin=False): +# """ +# Generate an estimate of the multivariate multiscale entropy. The current version +# computes the entropy separately for each channel and then averages. It therefore +# represents an upper-bound on the true multivariate multiscale entropy +# +# Args: +# traj (ndarray): a trajectory of shape (n_timesteps, n_channels) +# +# Returns: +# mmse (float): the multivariate multiscale entropy +# +# TODO: +# Implement algorithm from Ahmed and Mandic PRE 2011 +# """ +# mmse_opts = {"composite": True, "fuzzy": True} +# +# # For univariate data, just calculates once +# if len(traj.shape) == 1: +# mmse, info = neurokit2.entropy_multiscale(traj, dimension=2, **mmse_opts) +# return mmse, info +# +# # traj has shape T by D +# traj = standardize_ts(traj) +# all_mse = list() +# all_info = [] +# +# # Now D by T, where sol_coord is one dimension across all timepoints +# for sol_coord in traj.T: +# all_mse.append( +# neurokit2.entropy_multiscale(sol_coord, dimension=2, **mmse_opts)[0] +# ) +# all_info.append( +# neurokit2.entropy_multiscale(sol_coord, dimension=2, **mmse_opts)[1]["Value"] +# ) +# +# if return_info == True: +# # Additionally returns a dataframe containing all SampEn values across all dimensions and coarse grainings +# return np.sum(all_mse), pd.DataFrame(all_info) +# +# if gilpin == True: +# # If we want to return Gilpin's original version +# return np.median(all_mse) +# +# return np.sum(all_mse) + +## Multivariate/Univariate Multiscale Entropy +def multi_en(data, Scales=5, return_info=False): + """ + Generate an estimate of the multivariate multiscale entropy by summing the + (fuzzy) sample entropy at 5 coarse graining levels and normalizing. + note. manually increasing scale will increase multi_en value + + Args: + data (ndarray): a trajectory of shape (n_timesteps, n_channels) + + Returns: + mmse (float): the multivariate multiscale entropy + MSx (optional): the individual sample entropy values for each coarse graining level + """ + # For univariate data + if len(data[0]) == 1: + EnType = 'FuzzEn' + Mobj = EH.MSobject(EnType, Fx = 'constgaussian', r = 1.75, Norm = True) + MSx, CI = EH.cMvMSEn(data, Mobj, Scales = Scales) + + # For multivariate data + else: + EnType='MvFuzzEn' + Mobj = EH.MSobject(EnType, Fx = 'constgaussian', r = 1.75, Norm = True) + MSx, CI = EH.cMvMSEn(data, Mobj, Scales = Scales, Refined = True) + + if return_info == True: + return CI, MSx + + return CI + +## Principal Component Analysis +def pca(data, threshold=0.80): + """ + Calculates the minimum number of components needed to explain 80% of the data's variance + + Args: + data (ndarray): a trajectory of shape (n_timesteps, n_channels) + + Returns: + n_components (int): minimum number of components + """ + # Perform PCA + pca = PCA() + pca.fit(data) + + # Calculate cumulative explained variance + cumulative_explained_variance = np.cumsum(pca.explained_variance_ratio_) + + # Find the number of components that explain at least 80% of the variance + n_components = np.argmax(cumulative_explained_variance >= threshold) + 1 + + return n_components + +## Lyapunov Spectrum +def find_lyapunov_exponents( + model, traj_length, ic, pts_per_period=500, tol=1e-8, min_tpts=10, **kwargs): + """ + Given a dynamical system, compute its spectrum of Lyapunov exponents. + Args: + model (callable): a python object representing a system, with specified RHS, + parameters, and length of timestep + initial condition (nparray): double nested NxD array. An array of N arrays that are + initial conditions with D dimensions. The function will only return the spectrum of + the first initial condition. + traj_length (int): the length of each trajectory used to calulate Lyapunov + exponents + pts_per_period (int): the sampling density of the trajectory; set to 500 to match + William Gilpin's sampling density. + kwargs: additional keyword arguments to pass to the model's make_trajectory + method. Currently unused + + Returns: + final_lyap (ndarray): A list of computed Lyapunov exponents + + References: + William Gilpin + Christiansen & Rugh (1997). Computing Lyapunov spectra with continuous + Gram-Schmidt orthonormalization + """ + try: + rhs = model.rhs + except AttributeError: + raise ValueError(f"Calculation unavailable. System does not have a method for an RHS") + + try: + jac = model.jac + except AttributeError: + jac = None + + # make arrays for the trajectory and its corresponding timepoints + tpts, traj = model.make_data(ic, traj_length, pts_per_period=pts_per_period, return_times=True) + # traj has shape (traj_length, d), where d is the dimension of the system + # tpts has shape (traj_length,) and is used for: + # 1. calculating an average timestep dt for Euler + # 2. accessing the RHS/Jacobian at a trajectory point + # 3. normalizing the sum of each dimension's lyapunov exponent over time to find an average + + # get the dimensionality of the system from the trajectory (Gilpin's gets it from the model) + d = np.asarray(traj).shape[-1] + + # dt is the average timestep of the system used for Backward Euler + dt = np.median(np.diff(tpts)) + + # make an identity matrix of dimension d + u = np.identity(d) + + # Contains all full lyapunov spectrums for every point along trajectory + # a list/vector of subvectors; subvectors contain lyapunov spectrum of a point in time + all_lyap = list() + + # iterates over each time point t and corresponding state X. + # If the model does not provide a Jacobian (model.jac), + # it computes the Jacobian numerically using jac_fd + # using the righthand side (Gilpin's systems have an RHS property) + # This code is modified from Gilpin, who originally used his model's Jacobian method + # directly when it was available (Dynadojo does not have a Jacobian method so this was removed) + + for i in range(traj_length): # Compute the Jacobian numerically at time t and state x + t = tpts[0][i] # For the make_data function (at least the GilpinFlows one), tpts and traj are arrays of trajectories, + x = traj[0][i] # so the first indices of tpts and traj correspond to different trajectories and the second to points + # within one given trajectory + + if jac is None or jac(ic, 0) is None: # calculate analytically the jacobian from the RHS + rhsy = lambda a: np.array(rhs(a, t)) # define a function 'rhsy', using the model's right hand side diffeq + jacval = jac_fd(rhsy, x) # 'a' is a dummy variable that jac_fd plugs values into when it calls rhys. + else: + jacval = np.array(jac(x, t)) # use the jacobian if already defined + + # NOTE: no idea what this does. Unmodified from Gilpin. + # If postprocessing is applied to a trajectory, transform the jacobian into the + # new coordinates. + if hasattr(model, "_postprocessing"): + x0 = np.copy(x) + y2h = lambda y: model._postprocessing(*y) + dhdy = jac_fd(y2h, x0) + dydh = np.linalg.inv(dhdy) # dy/dh + ## Alternate version if good second-order fd is ever available + # dydh = jac_fd(y2h, X0, m=2, eps=1e-2) @ rhsy(X0) + jac_fd(y2h, y0) @ jac_fd(rhsy, X0)) + jacval = dhdy @ jacval @ dydh + + ## Forward Euler update (unused) + # u_n = np.matmul(np.eye(d) + jacval * dt, u) + + ## Backward Euler update + if i < 1: continue + u_n = np.matmul(np.linalg.inv(np.eye(d) - jacval * dt), u) + + q, r = np.linalg.qr(u_n) + lyap_estimate = np.log(abs(r.diagonal())) + all_lyap.append(lyap_estimate) + u = q # post-iteration update axes + + ## early stopping if middle exponents are close to zero, a requirement for + ## continuous-time dynamical systems + if (np.min(np.abs(lyap_estimate)) < tol) and (i > min_tpts): + traj_length = i + + all_lyap = np.array(all_lyap) # convert list of lists into nparray + # average each dimension's lyapunov over time (axis = 0) + # by summing lyapunov at each point/time for a given dimension, and then normalizing over total time elapsed + # results in a single vector that is the spectrum of average lyapunov exponents + final_lyap = np.sum(all_lyap, axis=0) / (dt * traj_length) + return np.sort(final_lyap)[::-1] # return the average exponents in descending order + +## Maximum Lyapunov Exponent +def find_max_lyapunov(spectrum0): + """ + Given a spectrum of Lyapunov exponents, find the maximum exponent + Args: + spectrum0 (ndarray): A list of computed Lyapunov exponents + + Returns: + max_exp (float): Maximum Lyapunov exponent + """ + max_exp = spectrum0[0] + for exp in spectrum0[1:]: + if exp > max_exp: + max_exp = exp + return max_exp + +## Kaplan Yorke Dimension +def kaplan_yorke_dimension(spectrum0): + """ + Calculate the Kaplan-Yorke dimension, given a list of + Lyapunov exponents + Args: + spectrum0 (ndarray): A list of computed Lyapunov exponents + + Returns: + dky (float): Kaplan Yorke dimension + """ + if np.all(spectrum0 < 0): + return 0 + + spectrum = np.sort(spectrum0)[::-1] + d = len(spectrum) + cspec = np.cumsum(spectrum) + j = np.max(np.where(cspec >= 0)) + if j > d - 2: + j = d - 2 + warnings.warn( + "Cumulative sum of Lyapunov exponents never crosses zero. System may be ill-posed or undersampled." + ) + dky = 1 + j + cspec[j] / np.abs(spectrum[j + 1]) + + return dky + +## Pesin Entropy +def pesin(spectrum0): + """ + Calculate the pesin entropy, given a list of + Lyapunov exponents + Args: + spectrum0 (ndarray): A list of computed Lyapunov exponents + + Returns: + pesin_entropy (float): Pesin entropy + """ + all_estimates_lyap = list() + all_estimates_lyap.append(spectrum0) + + all_estimates_pesin = list() + all_estimates_pesin.append(np.sum(np.array(spectrum0)[np.array(spectrum0) > 0])) + + pesin_entropy = np.median(all_estimates_pesin) + + return pesin_entropy \ No newline at end of file diff --git a/src/dynadojo/utils/dfa_complexity_measures.py b/src/dynadojo/utils/dfa_complexity_measures.py new file mode 100644 index 00000000..7273b151 --- /dev/null +++ b/src/dynadojo/utils/dfa_complexity_measures.py @@ -0,0 +1,102 @@ +import numpy as np +import fathon +from fathon import fathonUtils as fu + +## FROM FATHON ## + +def dfa(data, windows=[[10,2000]], detailed = False): + """ + Detrended Fluctuation Analysis: Given a trajectory and window range(s), compute its Hurst exponent(s) + Args: + data (matrix): D x T vector of data points + windows (list of lists): each element in the format [start,end] + detailed (bool): returns slope (aka exponent), intercept, window sizes, fluation of each window + Returns: + float/list: Hurst exponent(s) + """ + # zero-mean cumulative sum + data = fu.toAggregated(data) + # initialize dfa object + pydfa = fathon.DFA(data) + # compute fluctuation function and Hurst exponent + wins = fu.linRangeByStep(windows[0][0], windows[0][1]) + n, F = pydfa.computeFlucVec(wins, revSeg=True, polOrd=3) + H, H_intercept = pydfa.fitFlucVec() + + # if multiple windows are provided, returns list of exponent, one for each window + if len(windows) > 1: + limits_list = np.array(windows, dtype=int) + list_H, list_H_intercept = pydfa.multiFitFlucVec(limits_list) + if detailed == True: + return list_H, list_H_intercept, n, F + return list_H + + # in the case that there was just one window, returns just that one exponent + if detailed == True: + return H, H_intercept, n, F + return H + +def multi_dfa(data, detailed = False): + """ + MultiFractal Detrended Fluctuation Analysis: Computation of the fluctuations in each window for each q-order + Args: + data (matrix): D x T vector of data points + detailed (bool): returns slope (aka exponent), intercept, window sizes, fluation of each window + Returns: + list: Hurst exponent(s) + """ + # zero-mean cumulative sum + data = fu.toAggregated(data) + # initialize mfdfa object + pymfdfa = fathon.MFDFA(data) + # compute fluctuation function and generalized Hurst exponents + wins = fu.linRangeByStep(10, 2000) + n, F = pymfdfa.computeFlucVec(wins, np.arange(-3, 4, 0.1), revSeg=True, polOrd=1) + list_H, list_H_intercept = pymfdfa.fitFlucVec() + + if detailed == True: + return list_H, list_H_intercept, n, F + return list_H + +def mass_exponents(data): + """ + Computation of the mass exponents. + Args: + data (matrix): D x T vector of data points + Returns: + list: mass exponents + """ + # zero-mean cumulative sum + data = fu.toAggregated(data) + # initialize mfdfa object + pymfdfa = fathon.MFDFA(data) + # compute fluctuation function and generalized Hurst exponents + wins = fu.linRangeByStep(10, 2000) + n, F = pymfdfa.computeFlucVec(wins, np.arange(-3, 4, 0.1), revSeg=True, polOrd=1) + list_H, list_H_intercept = pymfdfa.fitFlucVec() + + tau = pymfdfa.computeMassExponents() + return tau + +def multifractal_spectrum(data, detailed = False): + """ + Computation of the multifractal spectrum + Args: + data (matrix): D x T vector of data points + detailed (bool): returns multifractal spectrum and singularity strengths + Returns: + list: multifractal spectrum + """ + # zero-mean cumulative sum + data = fu.toAggregated(data) + # initialize mfdfa object + pymfdfa = fathon.MFDFA(data) + # compute fluctuation function and generalized Hurst exponents + wins = fu.linRangeByStep(10, 2000) + n, F = pymfdfa.computeFlucVec(wins, np.arange(-3, 4, 0.1), revSeg=True, polOrd=1) + list_H, list_H_intercept = pymfdfa.fitFlucVec() + alpha, mfSpect = pymfdfa.computeMultifractalSpectrum() + + if detailed == True: + return mfSpect, alpha + return mfSpect \ No newline at end of file diff --git a/src/dynadojo/utils/json_visualizer.ipynb b/src/dynadojo/utils/json_visualizer.ipynb new file mode 100644 index 00000000..664934a5 --- /dev/null +++ b/src/dynadojo/utils/json_visualizer.ipynb @@ -0,0 +1,316 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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systemDseedx0OODtimestepsgp_dimmse_mvpcalyapunov_spectrumkaplan_yorke_dimensionpesin
0Aizawa31[-0.7714825128, -0.6565881090000001, -0.158586...False1001.6934450.4825833[0.43246514550000004, -0.5952530629, -0.702256...1.7265230.432465
1Aizawa31[-0.7714825128, -0.6565881090000001, -0.158586...True1001.7040090.4769743[0.5866091364, 0.5763447507, -1.3347709728]2.8712761.162954
2AnishchenkoAstakhov31[3.5624624915, 3.4690454262, 1.7976284685000001]False1001.6738910.1994722[-0.047867626600000004, -0.1960088915, -0.6360...0.0000000.000000
3AnishchenkoAstakhov31[3.5624624915, 3.4690454262, 1.7976284685000001]True1001.6705400.3221472[0.2698103699, 0.0764179847, -0.2485843804]3.3928000.346228
4Arneodo31[-2.7059058508, 0.1992056825, 3.1234059944]False1001.7404130.4990572[0.7221296291, 0.0389029295, -1.884395636]2.4038600.761033
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249YuWang31[-0.2106683917, -0.1872582077, 12.6952870632]True1001.7551920.5082531[4.7275321433, -7.806748716, -11.9029365876]1.6055704.727532
250YuWang231[0.12372685750000001, 1.3016720427, 16.5231311...False1001.6716750.2614041[0.2823311261, -1.3720157489, -12.7015190655]1.2057780.282331
251YuWang231[0.12372685750000001, 1.3016720427, 16.5231311...True1001.6640860.2364621[6.0084112936, -6.9707206595999995, -10.927709...1.8619506.008411
252ZhouChen31[-0.5938799140000001, 0.012645665, 0.000749520...False1001.5948050.2168981[2.9795473821, -1.5975323813, -9.6048936178]2.1438872.979547
253ZhouChen31[-0.5938799140000001, 0.012645665, 0.000749520...True1001.6559650.2042691[2.9527196396, -1.4346015393, -10.0275127797]2.1513952.952720
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254 rows × 12 columns

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" + ], + "text/plain": [ + " system D seed \\\n", + "0 Aizawa 3 1 \n", + "1 Aizawa 3 1 \n", + "2 AnishchenkoAstakhov 3 1 \n", + "3 AnishchenkoAstakhov 3 1 \n", + "4 Arneodo 3 1 \n", + ".. ... .. ... \n", + "249 YuWang 3 1 \n", + "250 YuWang2 3 1 \n", + "251 YuWang2 3 1 \n", + "252 ZhouChen 3 1 \n", + "253 ZhouChen 3 1 \n", + "\n", + " x0 OOD timesteps \\\n", + "0 [-0.7714825128, -0.6565881090000001, -0.158586... False 100 \n", + "1 [-0.7714825128, -0.6565881090000001, -0.158586... True 100 \n", + "2 [3.5624624915, 3.4690454262, 1.7976284685000001] False 100 \n", + "3 [3.5624624915, 3.4690454262, 1.7976284685000001] True 100 \n", + "4 [-2.7059058508, 0.1992056825, 3.1234059944] False 100 \n", + ".. ... ... ... \n", + "249 [-0.2106683917, -0.1872582077, 12.6952870632] True 100 \n", + "250 [0.12372685750000001, 1.3016720427, 16.5231311... False 100 \n", + "251 [0.12372685750000001, 1.3016720427, 16.5231311... True 100 \n", + "252 [-0.5938799140000001, 0.012645665, 0.000749520... False 100 \n", + "253 [-0.5938799140000001, 0.012645665, 0.000749520... True 100 \n", + "\n", + " gp_dim mse_mv pca \\\n", + "0 1.693445 0.482583 3 \n", + "1 1.704009 0.476974 3 \n", + "2 1.673891 0.199472 2 \n", + "3 1.670540 0.322147 2 \n", + "4 1.740413 0.499057 2 \n", + ".. ... ... ... \n", + "249 1.755192 0.508253 1 \n", + "250 1.671675 0.261404 1 \n", + "251 1.664086 0.236462 1 \n", + "252 1.594805 0.216898 1 \n", + "253 1.655965 0.204269 1 \n", + "\n", + " lyapunov_spectrum \\\n", + "0 [0.43246514550000004, -0.5952530629, -0.702256... \n", + "1 [0.5866091364, 0.5763447507, -1.3347709728] \n", + "2 [-0.047867626600000004, -0.1960088915, -0.6360... \n", + "3 [0.2698103699, 0.0764179847, -0.2485843804] \n", + "4 [0.7221296291, 0.0389029295, -1.884395636] \n", + ".. ... \n", + "249 [4.7275321433, -7.806748716, -11.9029365876] \n", + "250 [0.2823311261, -1.3720157489, -12.7015190655] \n", + "251 [6.0084112936, -6.9707206595999995, -10.927709... \n", + "252 [2.9795473821, -1.5975323813, -9.6048936178] \n", + "253 [2.9527196396, -1.4346015393, -10.0275127797] \n", + "\n", + " kaplan_yorke_dimension pesin \n", + "0 1.726523 0.432465 \n", + "1 2.871276 1.162954 \n", + "2 0.000000 0.000000 \n", + "3 3.392800 0.346228 \n", + "4 2.403860 0.761033 \n", + ".. ... ... \n", + "249 1.605570 4.727532 \n", + "250 1.205778 0.282331 \n", + "251 1.861950 6.008411 \n", + "252 2.143887 2.979547 \n", + "253 2.151395 2.952720 \n", + "\n", + "[254 rows x 12 columns]" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "df = pd.read_json('/home/vigith/dynadojo/docs/dyna_complexity_data.JSON', orient='records', lines=True)\n", + "df" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.14" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/src/dynadojo/utils/julia_complexity_measures.py b/src/dynadojo/utils/julia_complexity_measures.py new file mode 100644 index 00000000..15a2de8b --- /dev/null +++ b/src/dynadojo/utils/julia_complexity_measures.py @@ -0,0 +1,275 @@ +from juliacall import Main as jl +import importlib +import juliapkg +import numpy as np + +from dynadojo.systems.gilpin_flows import GilpinFlowsSystem + +# ## Neccesary installations, just need to run once +# juliapkg.add("DynamicalSystems", "61744808-ddfa-5f27-97ff-6e42cc95d634") +# juliapkg.resolve() +# juliapkg.status(target=None) + +jl.seval("using DynamicalSystems") + +## FROM CHAOSTOOLS.JL ## + +# Using Self-Defined Python System +def custom_find_lyapunov(rhs, u0, p, timesteps, Δt, max=False): + """ + Compute the Lyapunov spectrum of a customized, self-defined system + Args: + rhs (string): right hand side equations governing system + u0 (array): inital condition + p (array): system parameters in order prescribed by rhs + timesteps (int): the length of trajectory used to calulate Lyapunov exponents + Δt (float): time between timesteps + Returns: + λs (array): Lyapunov spectrum + Example Usage: + >>> def new_lorenz(u, p, t): + >>> σ = p[0] + >>> ρ = p[1] + >>> β = p[2] + >>> du1 = σ * (u[1] - u[0]) + >>> du2 = u[0] * (ρ - u[2]) - u[1] + >>> du3 = u[0] * u[1] - β * u[2] + >>> return jl.SVector[3](du1, du2, du3) + >>> lu0 = [-9.7869288, -15.03852, 20.533978] + >>> lp = [10, 28, 8/3] + >>> print(jl_custom_find_lyapunov(new_lorenz, lu0, lp, 1000, 0.0003002100350058257)) + """ + ds = jl.ContinuousDynamicalSystem(rhs, u0, p) + if max == True: + max_λ = jl.lyapunov(ds, timesteps, Δt = Δt) + return max_λ + return jl.lyapunovspectrum(ds, timesteps, Δt = Δt) + +# Using Gilpin Defined System +def find_lyapunov(system_name, timesteps, u0=None, p=None, Δt=None, max=False): + """ + Given a dynamical system, compute its spectrum of Lyapunov exponents using Julia's DynamicalSystems package + Args: + system_name (string): name of Gilpin class for desired dynamical system + timesteps (int): the length of trajectory used to calulate Lyapunov exponents + u0 (array): inital condition + p (array): system parameters in alphabetical order + Ttr (float): time between timesteps + Returns: + λs (array): Lyapunov spectrum + Note: + Only works for Gilpin flows which have _rhs defined in flows.py + """ + # Creates an instance of Gilpin class, from which to pull attributes/methods + module = importlib.import_module('dysts.flows') + SystemClass = getattr(module, system_name) + system = SystemClass() + + # Defaults to predefined values if not specified + if u0 == None: + u0 = system.ic + if p == None: + p = [] + for key in system.params: + p.append(system.params[key]) + if Δt == None: + Δt = system.dt + + # Wrapper for Gilpin's rhs to work with Julia's rhs + def juliafied_gilpin(u, p, t): + result = system._rhs(*u, t, *p) + return jl.SVector[len(result)](*result) + + # creates a ds class used to calcuate Lyapunov in Julia + ds = jl.ContinuousDynamicalSystem(juliafied_gilpin, u0, p) + + if max == True: + max_λ = jl.lyapunov(ds, timesteps, Δt = Δt) + return max_λ + + λs = jl.lyapunovspectrum(ds, timesteps, Δt = Δt) + return λs + +def local_lyapunov(system_name, n, u0=None, p=None, S = 10): + """ + Given a dynamical system and a number of intial points, compute local exponential growth rate + Args: + system_name (string): name of Gilpin class for desired dynamical system + n (int): number of intial conditions from which to permute + S (optional): number of permutations + Returns: + array: A list of local exponential growth rates + Note: + Only works for Gilpin flows which have _rhs defined in flows.py + """ + if n < 2: + raise ValueError(f"n must be greater than one") + + # Makes n initial conditions + system = GilpinFlowsSystem(latent_dim=3, embed_dim=3, system_name=system_name, seed=1) + x0 = system.make_init_conds(n) + + x0 = jl.SVector[len(x0)](*x0) + + # Creates an instance of Gilpin class, from which to pull attributes/methods + module = importlib.import_module('dysts.flows') + SystemClass = getattr(module, system_name) + system = SystemClass() + + # Defaults to predefined values if not specified + if u0 == None: + u0 = system.ic + if p == None: + p = [] + for key in system.params: + p.append(system.params[key]) + + # Wrapper for Gilpin's rhs to work with Julia's rhs + def juliafied_gilpin(u, p, t): + result = system._rhs(*u, t, *p) + return jl.SVector[len(result)](*result) + + # creates a ds class used to calcuate Lyapunov in Julia + ds = jl.ContinuousDynamicalSystem(juliafied_gilpin, u0, p) + + # calculates local exponential growth rate(s) of perturbations + return jl.local_growth_rates(ds, x0, S = S) + +def naive_lyapunov(x, dt): + """ + Given a trajectory and the dt used to create it, approximate the maximum Lyapunov exponent + by estimating the slope of E(k) + Args: + x (matrix): D x T vector of data points + dt (float): time between each data point + Returns: + float: Maximum Lyapunov exponent + note: + WARNING: kind of broken, a lot of uninformed design choices + """ + # determines how many k points we want to calculate divergence + k_min = 1 + k_max = int(np.floor(len(x) * 0.80)) # recommendation: k_max ≤ length(R) - delay - embedding_dim - 1 + ks = list(range(k_min, k_max, 10)) + # creates E(k), where E is the y-axis and k is the x-axis + E = jl.lyapunov_from_data(jl.StateSpaceSet(x), ks) + E = [e for e in E] + k = [k * dt for k in ks] + # find the slope of the largest linear reigon of E(k) + λ = jl.slopefit(jl.SVector[len(k)](*k), jl.SVector[len(E)](*E), jl.LargestLinearRegion()) + return λ + +## FROM COMPLEXITYMEASURES.JL ## +def perm_en(x, τ = 1, base = 2): + """ + Given a trajectory, compute its permuation entropy + Args: + x (matrix): D x T vector of data points + base (int): log base for caluclating entropy + τ (int): time delay + Returns: + float: Permuation entropy + """ + m = len(x[0]) # dimension of data + x = jl.StateSpaceSet(x) # convert to right data type for julia function, multivariate equivalent + est = jl.OrdinalPatterns(m = m, τ = τ) + return jl.information(jl.Shannon(base), est, x) + +IMPLEMENTATIONS = ["KozachenkoLeonenko", "Kraskov", "Zhu", "ZhuSingh", "Gao", "Goria", "LeonenkoProzantoSavani"] + +def shannon_en(x, implementation = "Kraskov", w = 0, k = 1, base = 2): + """ + Given a trajectory, compute an estimate for Shannon differential information using nearest neighbors + calculated using specified implementation method + Args: + x (matrix): D x T vector of data points + implementation (string): method of implementation + w (int): Theiler window, which determines if temporal neighbors are excluded during neighbor searches + k (int): which specifies k-th nearest neighbor searches method + base (int): log base to evaluate Shannon entropy + Returns: + float: Shannon differential information of a multi-dimensional trajectory + """ + + if implementation not in IMPLEMENTATIONS: + raise ValueError(f"{implementation} is not a valid implementation") + + if implementation == "LeonenkoProzantoSavani": + k = 2 + + if implementation == "KozachenkoLeonenko": + est = jl.KozachenkoLeonenko(w = w) + else: + est = eval(f"jl.{implementation}(jl.Shannon({base}), k = k, w = w)") + + return jl.information(est, jl.StateSpaceSet(x)) + +## FROM FRACTALDIMENSIONS.JL ## + +def generalized_dim(x, molteno = False, q = 1, base = 2, k0 = 10): + """ + Given a trajectory, compute an estimate for the qth order generalized dimension of x + by calculating its histogram-based Rényi entropy + Args: + x (matrix): D x T vector of data points + q (int): 0 is "capacity" or "box-counting" dimension, 1 is the "information" dimension + base (int): log base to evaluate Rényi entropy + molteno (bool): If True, return an estimate of the generalized_dim of X using the molteno algorithm + Returns: + float: qth order generalized dimension of x + """ + if molteno == True: + return jl.molteno_dim(jl.StateSpaceSet(x), k0, q = q, base = base) + else: + return jl.generalized_dim(jl.StateSpaceSet(x), q = q, base = base) + +METHODS = ["grassberger_proccacia", "boxassisted_correlation", "fixedmass_correlation", "takens_best_estimate"] + +def corr_dim(x, method = "grassberger_proccacia"): + """ + Given a trajectory, compute its correlation dimension + Args: + x (matrix): D x T vector of data points + method (string): method of calculating correlation dimension + Returns: + float: Correlation dimension of x + """ + if method not in METHODS: + raise ValueError(f"{method} is not a valid method") + + x = jl.StateSpaceSet(x) + + if method == "takens_best_estimate": + std = np.std(x) + corr_dim = eval(f"jl.{method}_dim(x, {std/4})") + else: + corr_dim = eval(f"jl.{method}_dim(x)") + return corr_dim + +def ky_dim(λs): + """ + Given a Lyapunov spectrum, compute its Kaplan Yorke dimension + Args: + λs (list): Lyapunov spectrum + Returns: + float: Kaplan Yorke dimension + """ + return jl.kaplanyorke_dim(jl.SVector[len(λs)](*λs)) + +# ## TEST DATA ## +# test_data_2d = np.loadtxt("tests/Henon_dim2_seed1_timestep1000_inDist.csv", delimiter=',') +# test_data_3d = np.loadtxt("tests/Lorenz_dim3_seed1_timestep1000_inDist.csv", delimiter=',') +# λs = [0.906, 0, -14.572] +# def new_lorenz(u, p, t): +# σ = p[0] +# ρ = p[1] +# β = p[2] +# du1 = σ * (u[1] - u[0]) +# du2 = u[0] * (ρ - u[2]) - u[1] +# du3 = u[0] * u[1] - β * u[2] +# return jl.SVector[3](du1, du2, du3) +# lu0 = [-9.7869288, -15.03852, 20.533978] +# lp = [10, 28, 8/3] +x = find_lyapunov("Lorenz", 1000) +x = [i for i in x] +print(x) \ No newline at end of file diff --git a/src/dynadojo/utils/juliapkg.json b/src/dynadojo/utils/juliapkg.json new file mode 100644 index 00000000..5b9f1be7 --- /dev/null +++ b/src/dynadojo/utils/juliapkg.json @@ -0,0 +1,8 @@ +{ + "julia": "1", + "packages": { + "DynamicalSystems": { + "uuid": "61744808-ddfa-5f27-97ff-6e42cc95d634" + } + } +} \ No newline at end of file diff --git a/src/dynadojo/utils/old_complexity_measures.py b/src/dynadojo/utils/old_complexity_measures.py new file mode 100644 index 00000000..fc41bef9 --- /dev/null +++ b/src/dynadojo/utils/old_complexity_measures.py @@ -0,0 +1,90 @@ +import neurokit2 +### Multiscale Entropy (Outdated) +#def mse_mv(traj, return_info=False, gilpin=False): +# """ +# Generate an estimate of the multivariate multiscale entropy. The current version +# computes the entropy separately for each channel and then averages. It therefore +# represents an upper-bound on the true multivariate multiscale entropy +# +# Args: +# traj (ndarray): a trajectory of shape (n_timesteps, n_channels) +# +# Returns: +# mmse (float): the multivariate multiscale entropy +# +# TODO: +# Implement algorithm from Ahmed and Mandic PRE 2011 +# """ +# mmse_opts = {"composite": True, "fuzzy": True} +# +# # For univariate data, just calculates once +# if len(traj.shape) == 1: +# mmse, info = neurokit2.entropy_multiscale(traj, dimension=2, **mmse_opts) +# return mmse, info +# +# # traj has shape T by D +# traj = standardize_ts(traj) +# all_mse = list() +# all_info = [] +# +# # Now D by T, where sol_coord is one dimension across all timepoints +# for sol_coord in traj.T: +# all_mse.append( +# neurokit2.entropy_multiscale(sol_coord, dimension=2, **mmse_opts)[0] +# ) +# all_info.append( +# neurokit2.entropy_multiscale(sol_coord, dimension=2, **mmse_opts)[1]["Value"] +# ) +# +# if return_info == True: +# # Additionally returns a dataframe containing all SampEn values across all dimensions and coarse grainings +# return np.sum(all_mse), pd.DataFrame(all_info) +# +# if gilpin == True: +# # If we want to return Gilpin's original version +# return np.median(all_mse) +# +# return np.sum(all_mse) + +### Correlation dimension (Outdated) +#def gp_dim(data, y_data=None, rvals=None, nmax=100): +# """ +# Estimate the Grassberger-Procaccia dimension for a numpy array using the +# empirical correlation integral. +# +# Args: +# data (np.array): T x D, where T is the number of datapoints/timepoints, and D +# is the number of features/dimensions +# y_data (np.array, Optional): A second dataset of shape T2 x D, for +# computing cross-correlation. +# rvals (np.array): A list of radii +# nmax (int): The number of points at which to evaluate the correlation integral +# +# Returns: +# rvals (np.array): The discrete bins at which the correlation integral is +# estimated +# corr_sum (np.array): The estimates of the correlation integral at each bin +# +# """ +# data = np.asarray(data) +# +# # Makes a copy of original data for self correlation +# if y_data is None: +# y_data = data.copy() +# +# if rvals is None: +# std = np.std(data) +# rvals = np.logspace(np.log10(0.1 * std), np.log10(0.5 * std), nmax) +# +# n = len(data) +# +# dists = cdist(data, y_data) +# rvals = dists.ravel() +# +# ## Truncate the distance distribution to the linear scaling range +# std = np.std(data) +# rvals = rvals[rvals > 0] +# rvals = rvals[rvals > np.percentile(rvals, 5)] +# rvals = rvals[rvals < np.percentile(rvals, 50)] +# +# return estimate_powerlaw(rvals) \ No newline at end of file diff --git a/tests/Henon_dim2_seed1_timestep1000_inDist.csv b/tests/Henon_dim2_seed1_timestep1000_inDist.csv new file mode 100644 index 00000000..6c1722f2 --- /dev/null +++ b/tests/Henon_dim2_seed1_timestep1000_inDist.csv @@ -0,0 +1,1000 @@ +-9.674956860381536128e-01,3.589645274107892692e-01 +4.849746390737691426e-02,-2.902487058114460727e-01 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-0,0 +1,128 @@ +import unittest +from parameterized import parameterized +from dynadojo.wrappers import SystemChecker +from dynadojo.systems.gilpin_flows import GilpinFlowsSystem +import numpy as np +import EntropyHub as EH +#from dynadojo.utils.julia_in_python import julia_find_lyapunov +from dynadojo.utils.complexity_measures import multi_en, corr_dim, find_lyapunov_exponents, kaplan_yorke_dimension, pesin + +ALL_FLOWS = [ + "Lorenz", + "Rossler" +] + +ALL_MAPS = [ + "Henon", + "Ikeda" +] + +ALL_CANONCIAL = { + "Lorenz": { + "corr_dim": 2.06, + }, + "Rossler": { + "corr_dim": 2.01, + }, + "Henon": { + "corr_dim": 1.261 + },"Ikeda": { + "corr_dim": 1.7 + } +} + +flows = ALL_FLOWS # To test multiple systems, add them to this list +maps = ALL_MAPS + +# Creates lyapunov spectrum for Lorenz +system = SystemChecker(GilpinFlowsSystem(latent_dim=3, embed_dim=3, system_name="Lorenz", seed=1)) +unwrapped_system = system._system +model = unwrapped_system.system + +model.beta = 8/3 +model.rho = 28 +model.sigma = 10 +timesteps = 2500 +x0 = np.array([[-9.7869288, -15.03852, 20.533978]]) + +lspectrum_calc = find_lyapunov_exponents(unwrapped_system, 1000, x0) + +# Creates lyapunov spectrum for Rossler +system = SystemChecker(GilpinFlowsSystem(latent_dim=3, embed_dim=3, system_name="Rossler", seed=1)) +unwrapped_system = system._system +model = unwrapped_system.system + +model.a = 0.2 +model.b = 0.2 +model.c = 5.7 +timesteps = 1000 +x0 = np.array([[6.5134412, 0.4772013, 0.34164294]]) + +rspectrum_calc = find_lyapunov_exponents(unwrapped_system, 1000, x0) + +class TestCorrDim(unittest.TestCase): + + @parameterized.expand(flows) + def test_corr_dim_flows(self, flows): + data = np.loadtxt(f"tests/{flows}_dim3_seed1_timestep1000_inDist.csv", delimiter=',') + corr_dim_calc = corr_dim(data) + corr_dim_canon = ALL_CANONCIAL[flows]["corr_dim"] + np.testing.assert_allclose(corr_dim_calc, corr_dim_canon, rtol=0.01) + + @parameterized.expand(maps) + def test_corr_dim_maps(self, maps): + data = np.loadtxt(f"tests/{maps}_dim2_seed1_timestep1000_inDist.csv", delimiter=',') + corr_dim_calc = corr_dim(data) + corr_dim_canon = ALL_CANONCIAL[maps]["corr_dim"] + np.testing.assert_allclose(corr_dim_calc, corr_dim_canon, rtol=0.01) + +class TestMultiEn(unittest.TestCase): + + def test_multi_en(self): + data = EH.ExampleData('lorenz') + CI_calc, MSx_calc = multi_en(data, Scales = 5, return_info=True) + CI_canon = 0.04603960 + Msx_canon = [0, 0.00796833, 0.00926765, 0.01193731, 0.01686631] + np.testing.assert_allclose(CI_calc, CI_canon, rtol=0.1) + np.testing.assert_allclose(MSx_calc, Msx_canon, rtol=0.1) +""" These tests will seldom work, since the middle lypaunov exponent of a 3d flow +in canon will always be exactly zero, and the calculation will be close but never +exactly zero. + +class TestLyapunov(unittest.TestCase): + + def test_lorenz(self): + spectrum_canon = [0.906, 0, -14.572] +# spectrum_julia = julia_find_lyapunov("Lorenz", timesteps=timesteps, u0=[-9.7869288, -15.03852, 20.533978], p=[8/3, 28, 10]) + + #np.testing.assert_allclose(lspectrum_calc, spectrum_julia, rtol=0.05) + np.testing.assert_allclose(lspectrum_calc, spectrum_canon, rtol=0.05) + + def test_rossler(self): + spectrum_canon = [0.0714, 0, -5.3943] +# spectrum_julia = julia_find_lyapunov("Rossler", timesteps=timesteps, u0=[6.5134412, 0.4772013, 0.34164294], p=[0.2, 0.2, 5.7]) + + #np.testing.assert_allclose(rspectrum_calc, spectrum_julia, rtol=0.05) + np.testing.assert_allclose(rspectrum_calc, spectrum_canon, rtol=0.05) +""" +class TestKYDim(unittest.TestCase): + + def test_lorenz(self): + ky_dim_calc = kaplan_yorke_dimension(lspectrum_calc) + ky_dim_canon = 2.075158758095728 + np.testing.assert_allclose(ky_dim_calc, ky_dim_canon, rtol=0.01) + + def test_rossler(self): + ky_dim_calc = kaplan_yorke_dimension(rspectrum_calc) + ky_dim_canon = 2.0146095059018845 + np.testing.assert_allclose(ky_dim_calc, ky_dim_canon, rtol=0.01) + +class TestPesinEn(unittest.TestCase): + + def test_lorenz(self): + pesin_calc = pesin(lspectrum_calc) + np.testing.assert_(pesin_calc >= 0) + + def test_rossler(self): + pesin_calc = pesin(rspectrum_calc) + np.testing.assert_(pesin_calc >= 0) \ No newline at end of file