From 5506b5e6840aa84a17471d10d4be10c9747e739a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Jonathan=20Kr=C3=B6nke?= Date: Thu, 6 Nov 2025 10:33:13 +0100 Subject: [PATCH 01/13] test: add basic test --- pycascades/tests/test_core.py | 25 +++++++++++++++++++++++++ 1 file changed, 25 insertions(+) create mode 100644 pycascades/tests/test_core.py diff --git a/pycascades/tests/test_core.py b/pycascades/tests/test_core.py new file mode 100644 index 0000000..2251f4a --- /dev/null +++ b/pycascades/tests/test_core.py @@ -0,0 +1,25 @@ +import sys +import unittest +import numpy as np +from pycascades import cusp, linear_coupling, tipping_network, evolve + +class TestBasicFunctionality(unittest.TestCase): + def test_simple_system(self): + cusp_element_0 = cusp( a = -4, b = 1, c = 0, x_0 = 0.5 ) + cusp_element_1 = cusp( a = -4, b = 1, c = 0, x_0 = 0.5 ) + coupling_0 = linear_coupling( strength = 0.05 ) + coupling_1 = linear_coupling( strength = 0.2 ) + net = tipping_network() + net.add_element( cusp_element_0 ) + net.add_element( cusp_element_1 ) + net.add_coupling( 0, 1, coupling_1 ) + net.add_coupling( 1, 0, coupling_0 ) + initial_state = [0.1,0.9] + ev = evolve( net, initial_state ) + timestep = 0.01 + t_end = 10 + ev.integrate( timestep , t_end ) + np.set_printoptions(threshold=sys.maxsize) + + self.assertTrue(np.allclose(ev.get_timeseries()[1][-1,:], np.array([0.02725572, 1.00270361]))) + From 28fc684755491813f8e5a1ce5d1b97ecd66ee603 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Jonathan=20Kr=C3=B6nke?= Date: Fri, 7 Nov 2025 11:48:47 +0100 Subject: [PATCH 02/13] refactor: remove redundant evolve code --- pycascades/__init__.py | 5 - pycascades/core/__init__.py | 2 +- pycascades/core/evolve.py | 267 ++++++++++++++++++++++++++-- pycascades/core/evolve_sde.py | 315 ---------------------------------- 4 files changed, 250 insertions(+), 339 deletions(-) delete mode 100644 pycascades/core/evolve_sde.py diff --git a/pycascades/__init__.py b/pycascades/__init__.py index af88f4b..590c099 100644 --- a/pycascades/__init__.py +++ b/pycascades/__init__.py @@ -8,12 +8,7 @@ from . import core, gen, utils, earth_system, amazon from pycascades.core.tipping_element import cusp, hopf, realistic_cusp -from pycascades.core.tipping_element_economic import economic_logistic from pycascades.core.tipping_network import tipping_network -from pycascades.core.tipping_network_economic import tipping_network_economic from pycascades.core.coupling import linear_coupling, cusp_to_hopf, hopf_x_to_cusp, hopf_x_to_hopf, hopf_y_to_cusp, hopf_y_to_hopf -from pycascades.core.coupling_economic import linear_coupling as linear_coupling_economic from pycascades.core.evolve import evolve -from pycascades.core.evolve_sde import evolve as evolve_sde -from pycascades.core.evolve_economic import evolve as evolve_economic from pycascades.utils import plotter diff --git a/pycascades/core/__init__.py b/pycascades/core/__init__.py index 37025f1..2f40e40 100644 --- a/pycascades/core/__init__.py +++ b/pycascades/core/__init__.py @@ -1 +1 @@ -from . import coupling, coupling_economic, evolve_economic, evolve_sde, evolve, tipping_element, tipping_element_economic, tipping_network, tipping_network_economic \ No newline at end of file +from . import coupling, coupling_economic, evolve_economic, evolve, tipping_element, tipping_element_economic, tipping_network, tipping_network_economic diff --git a/pycascades/core/evolve.py b/pycascades/core/evolve.py index f133617..b408e93 100644 --- a/pycascades/core/evolve.py +++ b/pycascades/core/evolve.py @@ -1,14 +1,179 @@ from scipy.integrate import odeint import numpy as np import time +import sdeint +from scipy.stats import levy, cauchy, levy_stable +from numba import jit +import warnings """evolve module""" class NoEquilibrium(Exception): pass + + + +def gen_levy_noise_preproc(alpha, sigma, dt, n = 1): + if not isinstance(alpha, np.ndarray): + if not isinstance(alpha, list): + alpha = [alpha] + alpha = np.array(alpha) + if len(alpha) < n: + alpha = np.repeat(alpha, n//len(alpha) + 1)[:n] + if not isinstance(sigma, np.ndarray): + if not isinstance(sigma, list): + sigma = [sigma] + sigma = np.array(sigma) + if len(sigma) < n: + sigma = np.repeat(sigma, n//len(sigma) + 1)[:n] + return alpha, sigma, dt, n + + + +@jit(nopython = True) +def semi_impl_euler_maruyama_alphastable_sde_nb_loop(n, N, x, xs, t, ts, dt_scaled, coupl, c, L, dt): + for i in range(1,N): + x_new = x.copy() + + transp = (coupl @ x) + + for j in range(n): + if (not np.isnan(x[j])) and (not np.isinf(x[j])): + candidates = np.roots(np.array([dt_scaled[j], 0.0, 1.0 - dt_scaled[j], - x[j] - (c[j] + transp[j]) * dt_scaled[j]]).astype(np.complex128)) + if (np.abs(candidates.imag)<1e-5).sum() == 1: + drift = (candidates[np.abs(candidates.imag)<1e-5][0]).real + else: + best_idx = np.argmin(np.abs(candidates - x[j])) + drift = (candidates[best_idx]).real + else: + drift = x[j] + + x_new[j] = drift + L[j, i] + + # x2 = x1 + (-x2^3 + x2 + c)*dt/taos + + t += dt + ts[i] = t + x = x_new#.copy() + xs[i,:] = x + + return ts, xs + + +def semi_impl_euler_maruyama_alphastable_sde(x0 = [-1.0, -1.0, -1.0], dt = 0.1, cs = [0.0, 0.3, 0.4], taos = [1.0, 1.0, 1.0], t_end = 1000, alphas = [1.5, 1.5, 1.5], sigmas = [0.0, 0.0, 0.1], coupl = np.array([[0.0, 0.1, 0.1], [-0.1, 0.0, 0.2], [0.0, -0.1, 0.0]]), rng = None): + + x0 = np.array(x0, dtype="float").flatten() + taos = np.array(taos, dtype="float").flatten() + cs = np.array(cs, dtype="float").flatten() + alphas = np.array(alphas, dtype="float").flatten() + sigmas = np.array(sigmas, dtype="float").flatten() + coupl = np.array(coupl, dtype="float") + + alphas, sigmas, dt_scaled, n = gen_levy_noise_preproc(alphas, sigmas, dt / (taos + 1e-6), n = len(x0)) + + x = x0.copy() + N = int(t_end // dt) + 1 + xs = np.zeros((N,n)) + xs[0,:] = x + t = 0 + ts = np.zeros(N) + + L = np.zeros((n, N)) + for i in range(n): + if sigmas[i] > 0: + L[i,:] = sigmas[i] * (dt_scaled[i] ** (1/alphas[i])) * levy_stable.rvs(alphas[i], 0.0, size=N, random_state = rng) + + L[np.abs(L) > 1e12] = (np.sign(L) * 1e12)[np.abs(L) > 1e12] + L[np.isinf(L)] = (np.sign(L) * 1e12)[np.isinf(L)] + L[np.isnan(L)] = 0.0 + + ts, xs = semi_impl_euler_maruyama_alphastable_sde_nb_loop(n, N, x, xs, t, ts, dt_scaled, coupl, cs, L, dt) + + return ts, xs, rng + + + +def itoint(f, G, y0, tspan, noise = "normal", levy_alpha = 1.5): + """ Numerically integrate the Ito equation dy = f(y,t)dt + G(y,t)dW + where y is the d-dimensional state vector, f is a vector-valued function, + G is an d x m matrix-valued function giving the noise coefficients and + dW(t) = (dW_1, dW_2, ... dW_m) is a vector of independent Wiener increments + Args: + f: callable(y,t) returning a numpy array of shape (d,) + Vector-valued function to define the deterministic part of the system + G: callable(y,t) returning a numpy array of shape (d,m) + Matrix-valued function to define the noise coefficients of the system + y0: array of shape (d,) giving the initial state vector y(t==0) + tspan (array): The sequence of time points for which to solve for y. + These must be equally spaced, e.g. np.arange(0,10,0.005) + tspan[0] is the intial time corresponding to the initial state y0. + Returns: + y: array, with shape (len(tspan), len(y0)) + With the initial value y0 in the first row + Raises: + SDEValueError + """ + # In future versions we can automatically choose here the most suitable + # Ito algorithm based on properties of the system and noise. + (d, m, f, G, y0, tspan, __, __) = sdeint.integrate._check_args(f, G, y0, tspan, None, None) + N = len(tspan) + h = (tspan[N-1] - tspan[0])/(N - 1) # assuming equal time steps + if noise == "levy": + dW = levy.rvs(0., 1e-11, (N-1, m))+np.random.normal(0., np.sqrt(h), (N-1, m)) + elif noise == "levy_stable": + dW = (h ** (1/levy_alpha)) * levy_stable.rvs(levy_alpha, 0.0, (N-1, m))#+np.random.normal(0., np.sqrt(h), (N-1, m)) + elif noise == "cauchy": + dW = cauchy.rvs(0., 1e-4, (N-1, m)) + else: + dW = None + chosenAlgorithm = sdeint.integrate.itoSRI2 + return chosenAlgorithm(f, G, y0, tspan, dW = dW) + +def get_params_from_es_network(net): + + n_nodes = net.number_of_nodes() + + cs = np.zeros(n_nodes) + taos = np.zeros(n_nodes) + coupl = np.zeros((n_nodes, n_nodes)) + + for i in range(n_nodes): + + node = net.nodes[i] + pars = node["data"].get_par() + taos[i] = 1 / pars["b"] + cs[i] = pars["c"] * taos[i] + + in_idxs = [e[0] for e in list(net.in_edges(i))] + for j in in_idxs: + + if hasattr(net.get_edge_data(j,i)["data"], "_x_0"): + x0 = net.get_edge_data(j,i)["data"]._x_0 + else: + x0 = 0.0 + + d = taos[i] * net.get_edge_data(j,i)["data"]._strength + + coupl[i,j] = d + + cs[i] += -x0 * d + + + return cs, taos, coupl + + class evolve(): def __init__( self, tipping_network, initial_state ): # Initialize solver + + self._all_cusp = all([n == "cusp" for n in tipping_network.get_node_types()]) + self._all_linear_coupl = all([tipping_network.get_edge_data(e[0], e[1])["data"].__class__.__name__ in ["linear_coupling_earth_system", "linear_coupling"] for e in tipping_network.edges]) + + if self._all_cusp and self._all_linear_coupl: + # get c, taos, coupl + self._cs, self._taos, self._coupl = get_params_from_es_network(tipping_network) + + self._net = tipping_network # Initialize state self._times = [] @@ -16,54 +181,120 @@ def __init__( self, tipping_network, initial_state ): self._t = 0 self._x = initial_state - + self.save_state( self._t, self._x ) + + self._rng = None def save_state( self , t, x): """Save current state if save flag is set""" self._times.append( t ) self._states.append( x ) - + def get_timeseries( self ): times = np.array ( self._times ) states = np.array ( self._states ) - return times , states + return [times , states] + + def _integrate_sde( self, t_step, sigma=None, noise = "normal"): + + t_span = [ self._t , self._t + t_step ] + x_init = self._x + + diffusion = lambda x,t: sigma + sol=itoint(self._net.f,diffusion,x_init,t_span, noise = noise) + self._t = t_span[1] - def _integrate( self, t_step ): + self._x = sol[1] + self.save_state(self._t, self._x) + + def _integrate_ode( self, t_step): t_span = [ self._t , self._t + t_step ] x_init = self._x + sol = odeint( self._net.f , x_init, t_span, Dfun=self._net.jac ) + self._t = t_span[1] + self._x = sol[1] + self.save_state(self._t, self._x) + + def _integrate_duffing_sde(self, dt, t_end, alphas, sigmas, rng = None): + + if any(alphas) < 0.1: + warnings.warn("The CMS algorithm for generating levy-stable noise is not reliable for alphas < 0.1. The implementation provided here truncates large noise values above +-1e12 and sets any nans to 0.") + + + x0 = self._x + cs = self._cs + taos = self._taos + coupl = self._coupl - def integrate( self, t_step, t_end ): + ts, xs, rng = semi_impl_euler_maruyama_alphastable_sde(x0 = x0, dt = dt, cs = cs, taos = taos, t_end = t_end, alphas = alphas, sigmas = sigmas, coupl = coupl, rng = rng) + + self._times = ts.tolist() + self._states = xs.tolist() + self._t = self._times[-1] + self._x = self._states[-1] + self._rng = rng + + + def integrate( self, t_step, t_end, sigmas = None , noise = "normal", alphas = None, seed = None): """Manually integrate to t_end""" - while self._times[-1] < t_end: - self._integrate( t_step ) + + if sigmas is None: + while self._times[-1] < t_end: + self._integrate_ode( t_step ) + elif self._all_cusp and self._all_linear_coupl: + if (noise == "normal") and (alphas is None): + alphas = [2.0 for _ in range(len(self._x))] + elif alphas is None: + raise NotImplementedError + + if self._rng is None: + rng = np.random.RandomState(seed) + else: + rng = self._rng + + self._integrate_duffing_sde(t_step, t_end, alphas = alphas, sigmas = sigmas, rng = rng) + else: + while self._times[-1] < t_end: + self._integrate_sde( t_step, sigmas, noise = noise) - def equilibrate( self, tol , t_step, t_break=None ): + def equilibrate( self, tol , t_step, t_break=None,sigma=None ): """Iterate system until it is in equilibrium. After every iteration it is checked if the system is in a stable equilibrium""" t0 = time.process_time() - while not self.is_equilibrium( tol ): - self._integrate( t_step ) - if t_break and (time.process_time() - t0) >= t_break: - raise NoEquilibrium( - "No equilibrium found " \ - "in " + str(t_break) + " seconds." \ - " Increase tolerance or breaktime." - ) + + if sigma is None: + while not self.is_equilibrium( tol ): + self._integrate_ode( t_step,sigma ) + if t_break and (time.process_time() - t0) >= t_break: + raise NoEquilibrium( + "No equilibrium found " \ + "in " + str(t_break) + " seconds." \ + " Increase tolerance or breaktime." + ) + else: + while not self.is_equilibrium( tol ): + self._integrate_sde( t_step,sigma ) + if t_break and (time.process_time() - t0) >= t_break: + raise NoEquilibrium( + "No equilibrium found " \ + "in " + str(t_break) + " seconds." \ + " Increase tolerance or breaktime." + ) def is_equilibrium( self, tol ): """Check if the system is in an equilibrium state, e.g. if the - absolute value of all elements of f_prime is less than tolerance. + absolute value of all elements of f (f is x_dot) is less than tolerance. If True the state can be considered as close to a fixed point""" n = self._net.number_of_nodes() f = self._net.f( self._x, self._t) - fix = np.less( np.abs( f) , tol * np.ones( n )) + fix = np.less( np.abs(f) , tol * np.ones( n )) if fix.all(): return True diff --git a/pycascades/core/evolve_sde.py b/pycascades/core/evolve_sde.py deleted file mode 100644 index b408e93..0000000 --- a/pycascades/core/evolve_sde.py +++ /dev/null @@ -1,315 +0,0 @@ -from scipy.integrate import odeint -import numpy as np -import time -import sdeint -from scipy.stats import levy, cauchy, levy_stable -from numba import jit -import warnings - -"""evolve module""" -class NoEquilibrium(Exception): - pass - - - - -def gen_levy_noise_preproc(alpha, sigma, dt, n = 1): - if not isinstance(alpha, np.ndarray): - if not isinstance(alpha, list): - alpha = [alpha] - alpha = np.array(alpha) - if len(alpha) < n: - alpha = np.repeat(alpha, n//len(alpha) + 1)[:n] - if not isinstance(sigma, np.ndarray): - if not isinstance(sigma, list): - sigma = [sigma] - sigma = np.array(sigma) - if len(sigma) < n: - sigma = np.repeat(sigma, n//len(sigma) + 1)[:n] - return alpha, sigma, dt, n - - - -@jit(nopython = True) -def semi_impl_euler_maruyama_alphastable_sde_nb_loop(n, N, x, xs, t, ts, dt_scaled, coupl, c, L, dt): - for i in range(1,N): - x_new = x.copy() - - transp = (coupl @ x) - - for j in range(n): - if (not np.isnan(x[j])) and (not np.isinf(x[j])): - candidates = np.roots(np.array([dt_scaled[j], 0.0, 1.0 - dt_scaled[j], - x[j] - (c[j] + transp[j]) * dt_scaled[j]]).astype(np.complex128)) - if (np.abs(candidates.imag)<1e-5).sum() == 1: - drift = (candidates[np.abs(candidates.imag)<1e-5][0]).real - else: - best_idx = np.argmin(np.abs(candidates - x[j])) - drift = (candidates[best_idx]).real - else: - drift = x[j] - - x_new[j] = drift + L[j, i] - - # x2 = x1 + (-x2^3 + x2 + c)*dt/taos - - t += dt - ts[i] = t - x = x_new#.copy() - xs[i,:] = x - - return ts, xs - - -def semi_impl_euler_maruyama_alphastable_sde(x0 = [-1.0, -1.0, -1.0], dt = 0.1, cs = [0.0, 0.3, 0.4], taos = [1.0, 1.0, 1.0], t_end = 1000, alphas = [1.5, 1.5, 1.5], sigmas = [0.0, 0.0, 0.1], coupl = np.array([[0.0, 0.1, 0.1], [-0.1, 0.0, 0.2], [0.0, -0.1, 0.0]]), rng = None): - - x0 = np.array(x0, dtype="float").flatten() - taos = np.array(taos, dtype="float").flatten() - cs = np.array(cs, dtype="float").flatten() - alphas = np.array(alphas, dtype="float").flatten() - sigmas = np.array(sigmas, dtype="float").flatten() - coupl = np.array(coupl, dtype="float") - - alphas, sigmas, dt_scaled, n = gen_levy_noise_preproc(alphas, sigmas, dt / (taos + 1e-6), n = len(x0)) - - x = x0.copy() - N = int(t_end // dt) + 1 - xs = np.zeros((N,n)) - xs[0,:] = x - t = 0 - ts = np.zeros(N) - - L = np.zeros((n, N)) - for i in range(n): - if sigmas[i] > 0: - L[i,:] = sigmas[i] * (dt_scaled[i] ** (1/alphas[i])) * levy_stable.rvs(alphas[i], 0.0, size=N, random_state = rng) - - L[np.abs(L) > 1e12] = (np.sign(L) * 1e12)[np.abs(L) > 1e12] - L[np.isinf(L)] = (np.sign(L) * 1e12)[np.isinf(L)] - L[np.isnan(L)] = 0.0 - - ts, xs = semi_impl_euler_maruyama_alphastable_sde_nb_loop(n, N, x, xs, t, ts, dt_scaled, coupl, cs, L, dt) - - return ts, xs, rng - - - -def itoint(f, G, y0, tspan, noise = "normal", levy_alpha = 1.5): - """ Numerically integrate the Ito equation dy = f(y,t)dt + G(y,t)dW - where y is the d-dimensional state vector, f is a vector-valued function, - G is an d x m matrix-valued function giving the noise coefficients and - dW(t) = (dW_1, dW_2, ... dW_m) is a vector of independent Wiener increments - Args: - f: callable(y,t) returning a numpy array of shape (d,) - Vector-valued function to define the deterministic part of the system - G: callable(y,t) returning a numpy array of shape (d,m) - Matrix-valued function to define the noise coefficients of the system - y0: array of shape (d,) giving the initial state vector y(t==0) - tspan (array): The sequence of time points for which to solve for y. - These must be equally spaced, e.g. np.arange(0,10,0.005) - tspan[0] is the intial time corresponding to the initial state y0. - Returns: - y: array, with shape (len(tspan), len(y0)) - With the initial value y0 in the first row - Raises: - SDEValueError - """ - # In future versions we can automatically choose here the most suitable - # Ito algorithm based on properties of the system and noise. - (d, m, f, G, y0, tspan, __, __) = sdeint.integrate._check_args(f, G, y0, tspan, None, None) - N = len(tspan) - h = (tspan[N-1] - tspan[0])/(N - 1) # assuming equal time steps - if noise == "levy": - dW = levy.rvs(0., 1e-11, (N-1, m))+np.random.normal(0., np.sqrt(h), (N-1, m)) - elif noise == "levy_stable": - dW = (h ** (1/levy_alpha)) * levy_stable.rvs(levy_alpha, 0.0, (N-1, m))#+np.random.normal(0., np.sqrt(h), (N-1, m)) - elif noise == "cauchy": - dW = cauchy.rvs(0., 1e-4, (N-1, m)) - else: - dW = None - chosenAlgorithm = sdeint.integrate.itoSRI2 - return chosenAlgorithm(f, G, y0, tspan, dW = dW) - -def get_params_from_es_network(net): - - n_nodes = net.number_of_nodes() - - cs = np.zeros(n_nodes) - taos = np.zeros(n_nodes) - coupl = np.zeros((n_nodes, n_nodes)) - - for i in range(n_nodes): - - node = net.nodes[i] - pars = node["data"].get_par() - taos[i] = 1 / pars["b"] - cs[i] = pars["c"] * taos[i] - - in_idxs = [e[0] for e in list(net.in_edges(i))] - for j in in_idxs: - - if hasattr(net.get_edge_data(j,i)["data"], "_x_0"): - x0 = net.get_edge_data(j,i)["data"]._x_0 - else: - x0 = 0.0 - - d = taos[i] * net.get_edge_data(j,i)["data"]._strength - - coupl[i,j] = d - - cs[i] += -x0 * d - - - return cs, taos, coupl - - -class evolve(): - def __init__( self, tipping_network, initial_state ): - # Initialize solver - - self._all_cusp = all([n == "cusp" for n in tipping_network.get_node_types()]) - self._all_linear_coupl = all([tipping_network.get_edge_data(e[0], e[1])["data"].__class__.__name__ in ["linear_coupling_earth_system", "linear_coupling"] for e in tipping_network.edges]) - - if self._all_cusp and self._all_linear_coupl: - # get c, taos, coupl - self._cs, self._taos, self._coupl = get_params_from_es_network(tipping_network) - - - self._net = tipping_network - # Initialize state - self._times = [] - self._states = [] - - self._t = 0 - self._x = initial_state - - self.save_state( self._t, self._x ) - - self._rng = None - - def save_state( self , t, x): - """Save current state if save flag is set""" - self._times.append( t ) - self._states.append( x ) - - def get_timeseries( self ): - times = np.array ( self._times ) - states = np.array ( self._states ) - return [times , states] - - def _integrate_sde( self, t_step, sigma=None, noise = "normal"): - - t_span = [ self._t , self._t + t_step ] - x_init = self._x - - diffusion = lambda x,t: sigma - sol=itoint(self._net.f,diffusion,x_init,t_span, noise = noise) - self._t = t_span[1] - - self._x = sol[1] - self.save_state(self._t, self._x) - - def _integrate_ode( self, t_step): - - t_span = [ self._t , self._t + t_step ] - x_init = self._x - - sol = odeint( self._net.f , x_init, t_span, Dfun=self._net.jac ) - - self._t = t_span[1] - - self._x = sol[1] - - self.save_state(self._t, self._x) - - def _integrate_duffing_sde(self, dt, t_end, alphas, sigmas, rng = None): - - if any(alphas) < 0.1: - warnings.warn("The CMS algorithm for generating levy-stable noise is not reliable for alphas < 0.1. The implementation provided here truncates large noise values above +-1e12 and sets any nans to 0.") - - - x0 = self._x - cs = self._cs - taos = self._taos - coupl = self._coupl - - ts, xs, rng = semi_impl_euler_maruyama_alphastable_sde(x0 = x0, dt = dt, cs = cs, taos = taos, t_end = t_end, alphas = alphas, sigmas = sigmas, coupl = coupl, rng = rng) - - self._times = ts.tolist() - self._states = xs.tolist() - self._t = self._times[-1] - self._x = self._states[-1] - self._rng = rng - - - def integrate( self, t_step, t_end, sigmas = None , noise = "normal", alphas = None, seed = None): - """Manually integrate to t_end""" - - if sigmas is None: - while self._times[-1] < t_end: - self._integrate_ode( t_step ) - elif self._all_cusp and self._all_linear_coupl: - if (noise == "normal") and (alphas is None): - alphas = [2.0 for _ in range(len(self._x))] - elif alphas is None: - raise NotImplementedError - - if self._rng is None: - rng = np.random.RandomState(seed) - else: - rng = self._rng - - self._integrate_duffing_sde(t_step, t_end, alphas = alphas, sigmas = sigmas, rng = rng) - else: - while self._times[-1] < t_end: - self._integrate_sde( t_step, sigmas, noise = noise) - - def equilibrate( self, tol , t_step, t_break=None,sigma=None ): - """Iterate system until it is in equilibrium. - After every iteration it is checked if the system is in a stable - equilibrium""" - t0 = time.process_time() - - if sigma is None: - while not self.is_equilibrium( tol ): - self._integrate_ode( t_step,sigma ) - if t_break and (time.process_time() - t0) >= t_break: - raise NoEquilibrium( - "No equilibrium found " \ - "in " + str(t_break) + " seconds." \ - " Increase tolerance or breaktime." - ) - else: - while not self.is_equilibrium( tol ): - self._integrate_sde( t_step,sigma ) - if t_break and (time.process_time() - t0) >= t_break: - raise NoEquilibrium( - "No equilibrium found " \ - "in " + str(t_break) + " seconds." \ - " Increase tolerance or breaktime." - ) - - def is_equilibrium( self, tol ): - """Check if the system is in an equilibrium state, e.g. if the - absolute value of all elements of f (f is x_dot) is less than tolerance. - If True the state can be considered as close to a fixed point""" - n = self._net.number_of_nodes() - f = self._net.f( self._x, self._t) - fix = np.less( np.abs(f) , tol * np.ones( n )) - - if fix.all(): - return True - else: - return False - - def is_stable( self ): - """Check stability of current system state by calculating the - eigenvalues of the jacobian (all eigenvalues < 0 => stable).""" - n = self._net.number_of_nodes() - jacobian = self._net.jac( self._x, self._t) - val, vec = np.linalg.eig( jacobian ) - stable = np.less( val, np.zeros( n ) ) - - if stable.all(): - return True - else: - return False From d5f1726303ff058a55b834c44b5b455753ca0dac Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Jonathan=20Kr=C3=B6nke?= Date: Fri, 7 Nov 2025 11:52:29 +0100 Subject: [PATCH 03/13] refactor: move economic code to application directory --- pycascades/core/__init__.py | 2 +- pycascades/economic/README.md | 2 ++ pycascades/{core => economic}/coupling_economic.py | 0 pycascades/{core => economic}/evolve_economic.py | 0 pycascades/{core => economic}/tipping_element_economic.py | 0 pycascades/{core => economic}/tipping_network_economic.py | 0 6 files changed, 3 insertions(+), 1 deletion(-) create mode 100644 pycascades/economic/README.md rename pycascades/{core => economic}/coupling_economic.py (100%) rename pycascades/{core => economic}/evolve_economic.py (100%) rename pycascades/{core => economic}/tipping_element_economic.py (100%) rename pycascades/{core => economic}/tipping_network_economic.py (100%) diff --git a/pycascades/core/__init__.py b/pycascades/core/__init__.py index 2f40e40..59f1908 100644 --- a/pycascades/core/__init__.py +++ b/pycascades/core/__init__.py @@ -1 +1 @@ -from . import coupling, coupling_economic, evolve_economic, evolve, tipping_element, tipping_element_economic, tipping_network, tipping_network_economic +from . import coupling, evolve, tipping_element, tipping_network diff --git a/pycascades/economic/README.md b/pycascades/economic/README.md new file mode 100644 index 0000000..ab6766d --- /dev/null +++ b/pycascades/economic/README.md @@ -0,0 +1,2 @@ +This directory contains old files from economic application that reduntantly defined the core classes. +If this is used in the future it needs to be updated and integrated into pycascades. diff --git a/pycascades/core/coupling_economic.py b/pycascades/economic/coupling_economic.py similarity index 100% rename from pycascades/core/coupling_economic.py rename to pycascades/economic/coupling_economic.py diff --git a/pycascades/core/evolve_economic.py b/pycascades/economic/evolve_economic.py similarity index 100% rename from pycascades/core/evolve_economic.py rename to pycascades/economic/evolve_economic.py diff --git a/pycascades/core/tipping_element_economic.py b/pycascades/economic/tipping_element_economic.py similarity index 100% rename from pycascades/core/tipping_element_economic.py rename to pycascades/economic/tipping_element_economic.py diff --git a/pycascades/core/tipping_network_economic.py b/pycascades/economic/tipping_network_economic.py similarity index 100% rename from pycascades/core/tipping_network_economic.py rename to pycascades/economic/tipping_network_economic.py From 50d7eb93ae6e427485c5f840be09db1bd105b84f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Jonathan=20Kr=C3=B6nke?= Date: Mon, 10 Nov 2025 15:14:54 +0100 Subject: [PATCH 04/13] refactor!: clean evolve module --- pycascades/core/evolve.py | 315 ------------------ pycascades/core/evolve/evolve.py | 94 ++++++ pycascades/core/evolve/itoint.py | 39 +++ ...emi_impl_euler_maruyama_alphastable_sde.py | 140 ++++++++ pycascades/tests/test_core.py | 56 +++- 5 files changed, 311 insertions(+), 333 deletions(-) delete mode 100644 pycascades/core/evolve.py create mode 100644 pycascades/core/evolve/evolve.py create mode 100644 pycascades/core/evolve/itoint.py create mode 100644 pycascades/core/evolve/semi_impl_euler_maruyama_alphastable_sde.py diff --git a/pycascades/core/evolve.py b/pycascades/core/evolve.py deleted file mode 100644 index b408e93..0000000 --- a/pycascades/core/evolve.py +++ /dev/null @@ -1,315 +0,0 @@ -from scipy.integrate import odeint -import numpy as np -import time -import sdeint -from scipy.stats import levy, cauchy, levy_stable -from numba import jit -import warnings - -"""evolve module""" -class NoEquilibrium(Exception): - pass - - - - -def gen_levy_noise_preproc(alpha, sigma, dt, n = 1): - if not isinstance(alpha, np.ndarray): - if not isinstance(alpha, list): - alpha = [alpha] - alpha = np.array(alpha) - if len(alpha) < n: - alpha = np.repeat(alpha, n//len(alpha) + 1)[:n] - if not isinstance(sigma, np.ndarray): - if not isinstance(sigma, list): - sigma = [sigma] - sigma = np.array(sigma) - if len(sigma) < n: - sigma = np.repeat(sigma, n//len(sigma) + 1)[:n] - return alpha, sigma, dt, n - - - -@jit(nopython = True) -def semi_impl_euler_maruyama_alphastable_sde_nb_loop(n, N, x, xs, t, ts, dt_scaled, coupl, c, L, dt): - for i in range(1,N): - x_new = x.copy() - - transp = (coupl @ x) - - for j in range(n): - if (not np.isnan(x[j])) and (not np.isinf(x[j])): - candidates = np.roots(np.array([dt_scaled[j], 0.0, 1.0 - dt_scaled[j], - x[j] - (c[j] + transp[j]) * dt_scaled[j]]).astype(np.complex128)) - if (np.abs(candidates.imag)<1e-5).sum() == 1: - drift = (candidates[np.abs(candidates.imag)<1e-5][0]).real - else: - best_idx = np.argmin(np.abs(candidates - x[j])) - drift = (candidates[best_idx]).real - else: - drift = x[j] - - x_new[j] = drift + L[j, i] - - # x2 = x1 + (-x2^3 + x2 + c)*dt/taos - - t += dt - ts[i] = t - x = x_new#.copy() - xs[i,:] = x - - return ts, xs - - -def semi_impl_euler_maruyama_alphastable_sde(x0 = [-1.0, -1.0, -1.0], dt = 0.1, cs = [0.0, 0.3, 0.4], taos = [1.0, 1.0, 1.0], t_end = 1000, alphas = [1.5, 1.5, 1.5], sigmas = [0.0, 0.0, 0.1], coupl = np.array([[0.0, 0.1, 0.1], [-0.1, 0.0, 0.2], [0.0, -0.1, 0.0]]), rng = None): - - x0 = np.array(x0, dtype="float").flatten() - taos = np.array(taos, dtype="float").flatten() - cs = np.array(cs, dtype="float").flatten() - alphas = np.array(alphas, dtype="float").flatten() - sigmas = np.array(sigmas, dtype="float").flatten() - coupl = np.array(coupl, dtype="float") - - alphas, sigmas, dt_scaled, n = gen_levy_noise_preproc(alphas, sigmas, dt / (taos + 1e-6), n = len(x0)) - - x = x0.copy() - N = int(t_end // dt) + 1 - xs = np.zeros((N,n)) - xs[0,:] = x - t = 0 - ts = np.zeros(N) - - L = np.zeros((n, N)) - for i in range(n): - if sigmas[i] > 0: - L[i,:] = sigmas[i] * (dt_scaled[i] ** (1/alphas[i])) * levy_stable.rvs(alphas[i], 0.0, size=N, random_state = rng) - - L[np.abs(L) > 1e12] = (np.sign(L) * 1e12)[np.abs(L) > 1e12] - L[np.isinf(L)] = (np.sign(L) * 1e12)[np.isinf(L)] - L[np.isnan(L)] = 0.0 - - ts, xs = semi_impl_euler_maruyama_alphastable_sde_nb_loop(n, N, x, xs, t, ts, dt_scaled, coupl, cs, L, dt) - - return ts, xs, rng - - - -def itoint(f, G, y0, tspan, noise = "normal", levy_alpha = 1.5): - """ Numerically integrate the Ito equation dy = f(y,t)dt + G(y,t)dW - where y is the d-dimensional state vector, f is a vector-valued function, - G is an d x m matrix-valued function giving the noise coefficients and - dW(t) = (dW_1, dW_2, ... dW_m) is a vector of independent Wiener increments - Args: - f: callable(y,t) returning a numpy array of shape (d,) - Vector-valued function to define the deterministic part of the system - G: callable(y,t) returning a numpy array of shape (d,m) - Matrix-valued function to define the noise coefficients of the system - y0: array of shape (d,) giving the initial state vector y(t==0) - tspan (array): The sequence of time points for which to solve for y. - These must be equally spaced, e.g. np.arange(0,10,0.005) - tspan[0] is the intial time corresponding to the initial state y0. - Returns: - y: array, with shape (len(tspan), len(y0)) - With the initial value y0 in the first row - Raises: - SDEValueError - """ - # In future versions we can automatically choose here the most suitable - # Ito algorithm based on properties of the system and noise. - (d, m, f, G, y0, tspan, __, __) = sdeint.integrate._check_args(f, G, y0, tspan, None, None) - N = len(tspan) - h = (tspan[N-1] - tspan[0])/(N - 1) # assuming equal time steps - if noise == "levy": - dW = levy.rvs(0., 1e-11, (N-1, m))+np.random.normal(0., np.sqrt(h), (N-1, m)) - elif noise == "levy_stable": - dW = (h ** (1/levy_alpha)) * levy_stable.rvs(levy_alpha, 0.0, (N-1, m))#+np.random.normal(0., np.sqrt(h), (N-1, m)) - elif noise == "cauchy": - dW = cauchy.rvs(0., 1e-4, (N-1, m)) - else: - dW = None - chosenAlgorithm = sdeint.integrate.itoSRI2 - return chosenAlgorithm(f, G, y0, tspan, dW = dW) - -def get_params_from_es_network(net): - - n_nodes = net.number_of_nodes() - - cs = np.zeros(n_nodes) - taos = np.zeros(n_nodes) - coupl = np.zeros((n_nodes, n_nodes)) - - for i in range(n_nodes): - - node = net.nodes[i] - pars = node["data"].get_par() - taos[i] = 1 / pars["b"] - cs[i] = pars["c"] * taos[i] - - in_idxs = [e[0] for e in list(net.in_edges(i))] - for j in in_idxs: - - if hasattr(net.get_edge_data(j,i)["data"], "_x_0"): - x0 = net.get_edge_data(j,i)["data"]._x_0 - else: - x0 = 0.0 - - d = taos[i] * net.get_edge_data(j,i)["data"]._strength - - coupl[i,j] = d - - cs[i] += -x0 * d - - - return cs, taos, coupl - - -class evolve(): - def __init__( self, tipping_network, initial_state ): - # Initialize solver - - self._all_cusp = all([n == "cusp" for n in tipping_network.get_node_types()]) - self._all_linear_coupl = all([tipping_network.get_edge_data(e[0], e[1])["data"].__class__.__name__ in ["linear_coupling_earth_system", "linear_coupling"] for e in tipping_network.edges]) - - if self._all_cusp and self._all_linear_coupl: - # get c, taos, coupl - self._cs, self._taos, self._coupl = get_params_from_es_network(tipping_network) - - - self._net = tipping_network - # Initialize state - self._times = [] - self._states = [] - - self._t = 0 - self._x = initial_state - - self.save_state( self._t, self._x ) - - self._rng = None - - def save_state( self , t, x): - """Save current state if save flag is set""" - self._times.append( t ) - self._states.append( x ) - - def get_timeseries( self ): - times = np.array ( self._times ) - states = np.array ( self._states ) - return [times , states] - - def _integrate_sde( self, t_step, sigma=None, noise = "normal"): - - t_span = [ self._t , self._t + t_step ] - x_init = self._x - - diffusion = lambda x,t: sigma - sol=itoint(self._net.f,diffusion,x_init,t_span, noise = noise) - self._t = t_span[1] - - self._x = sol[1] - self.save_state(self._t, self._x) - - def _integrate_ode( self, t_step): - - t_span = [ self._t , self._t + t_step ] - x_init = self._x - - sol = odeint( self._net.f , x_init, t_span, Dfun=self._net.jac ) - - self._t = t_span[1] - - self._x = sol[1] - - self.save_state(self._t, self._x) - - def _integrate_duffing_sde(self, dt, t_end, alphas, sigmas, rng = None): - - if any(alphas) < 0.1: - warnings.warn("The CMS algorithm for generating levy-stable noise is not reliable for alphas < 0.1. The implementation provided here truncates large noise values above +-1e12 and sets any nans to 0.") - - - x0 = self._x - cs = self._cs - taos = self._taos - coupl = self._coupl - - ts, xs, rng = semi_impl_euler_maruyama_alphastable_sde(x0 = x0, dt = dt, cs = cs, taos = taos, t_end = t_end, alphas = alphas, sigmas = sigmas, coupl = coupl, rng = rng) - - self._times = ts.tolist() - self._states = xs.tolist() - self._t = self._times[-1] - self._x = self._states[-1] - self._rng = rng - - - def integrate( self, t_step, t_end, sigmas = None , noise = "normal", alphas = None, seed = None): - """Manually integrate to t_end""" - - if sigmas is None: - while self._times[-1] < t_end: - self._integrate_ode( t_step ) - elif self._all_cusp and self._all_linear_coupl: - if (noise == "normal") and (alphas is None): - alphas = [2.0 for _ in range(len(self._x))] - elif alphas is None: - raise NotImplementedError - - if self._rng is None: - rng = np.random.RandomState(seed) - else: - rng = self._rng - - self._integrate_duffing_sde(t_step, t_end, alphas = alphas, sigmas = sigmas, rng = rng) - else: - while self._times[-1] < t_end: - self._integrate_sde( t_step, sigmas, noise = noise) - - def equilibrate( self, tol , t_step, t_break=None,sigma=None ): - """Iterate system until it is in equilibrium. - After every iteration it is checked if the system is in a stable - equilibrium""" - t0 = time.process_time() - - if sigma is None: - while not self.is_equilibrium( tol ): - self._integrate_ode( t_step,sigma ) - if t_break and (time.process_time() - t0) >= t_break: - raise NoEquilibrium( - "No equilibrium found " \ - "in " + str(t_break) + " seconds." \ - " Increase tolerance or breaktime." - ) - else: - while not self.is_equilibrium( tol ): - self._integrate_sde( t_step,sigma ) - if t_break and (time.process_time() - t0) >= t_break: - raise NoEquilibrium( - "No equilibrium found " \ - "in " + str(t_break) + " seconds." \ - " Increase tolerance or breaktime." - ) - - def is_equilibrium( self, tol ): - """Check if the system is in an equilibrium state, e.g. if the - absolute value of all elements of f (f is x_dot) is less than tolerance. - If True the state can be considered as close to a fixed point""" - n = self._net.number_of_nodes() - f = self._net.f( self._x, self._t) - fix = np.less( np.abs(f) , tol * np.ones( n )) - - if fix.all(): - return True - else: - return False - - def is_stable( self ): - """Check stability of current system state by calculating the - eigenvalues of the jacobian (all eigenvalues < 0 => stable).""" - n = self._net.number_of_nodes() - jacobian = self._net.jac( self._x, self._t) - val, vec = np.linalg.eig( jacobian ) - stable = np.less( val, np.zeros( n ) ) - - if stable.all(): - return True - else: - return False diff --git a/pycascades/core/evolve/evolve.py b/pycascades/core/evolve/evolve.py new file mode 100644 index 0000000..2f84154 --- /dev/null +++ b/pycascades/core/evolve/evolve.py @@ -0,0 +1,94 @@ +from . import semi_impl_euler_maruyama_alphastable_sde +from . import itoint + +from scipy.integrate import solve_ivp +import numpy as np + + +class NoEquilibrium(Exception): + pass + + +def integrate( + tipping_network, + initial_state, + t_span, + t_step, + backend = "solve_ivp", + **opts +): + match backend: + case "solve_ivp": + sol = solve_ivp( + lambda t, x : tipping_network.f(x, t), + t_span, + initial_state, + t_eval=np.arange(t_span[0], t_span[1], step=t_step), + events=opts.get("events", None) + ) + case "itoint": + for opt in ["sigma", "noise"]: + if opt not in opts: + raise Exception(f'Keyword Argument {opt} missing') + + sol = itoint( + tipping_network.f, + lambda x, t: opts["sigma"], + initial_state, + t_span, + noise = opts["noise"] + ) + case "duffing": + for opt in ["cs", "taos", "alphas", "sigmas", "coupl"]: + if opt not in opts: + raise Exception(f'Keyword Argument {opt} missing') + + sol = semi_impl_euler_maruyama_alphastable_sde( + x0 = t_span[0], + dt = t_step, + cs = opts["cs"], + taos = opts["taos"], + t_end = t_span[1], + alphas = opts["alphas"], + sigmas = opts["sigmas"], + coupl = opts["coupl"], + rng = opts.get("rng", None) + ) + return sol + + +def make_equilibrium_event(network, tol): + def event(t, x): + dxdt = network.f(x, t) + return np.linalg.norm(dxdt) - tol + event.terminal = True + event.direction = 0 + return event + + +def is_equilibrium(f, t, x, tol): + """Check if the system is in an equilibrium state, e.g. if the + absolute value of all elements of f (f is dxdt) is less than tolerance. + If True the state can be considered as close to a fixed point""" + dxdt = f(x, t) + n = len(dxdt) + fix = np.less(np.abs(dxdt), tol * np.ones(n)) + + if fix.all(): + return True + else: + return False + + +def is_stable(jacobian, t, x): + """Check stability of current system state by calculating the + eigenvalues of the jacobian (all eigenvalues < 0 => stable).""" + jac_values = jacobian(x, t) + n = len(jac_values) + val, vec = np.linalg.eig(jac_values) + stable = np.less(val, np.zeros(n)) + + if stable.all(): + return True + else: + return False diff --git a/pycascades/core/evolve/itoint.py b/pycascades/core/evolve/itoint.py new file mode 100644 index 0000000..a34644d --- /dev/null +++ b/pycascades/core/evolve/itoint.py @@ -0,0 +1,39 @@ +import sdeint + + +def itoint(f, G, y0, tspan, noise = "normal", levy_alpha = 1.5): + """ Numerically integrate the Ito equation dy = f(y,t)dt + G(y,t)dW + where y is the d-dimensional state vector, f is a vector-valued function, + G is an d x m matrix-valued function giving the noise coefficients and + dW(t) = (dW_1, dW_2, ... dW_m) is a vector of independent Wiener increments + Args: + f: callable(y,t) returning a numpy array of shape (d,) + Vector-valued function to define the deterministic part of the system + G: callable(y,t) returning a numpy array of shape (d,m) + Matrix-valued function to define the noise coefficients of the system + y0: array of shape (d,) giving the initial state vector y(t==0) + tspan (array): The sequence of time points for which to solve for y. + These must be equally spaced, e.g. np.arange(0,10,0.005) + tspan[0] is the intial time corresponding to the initial state y0. + Returns: + y: array, with shape (len(tspan), len(y0)) + With the initial value y0 in the first row + Raises: + SDEValueError + """ + # In future versions we can automatically choose here the most suitable + # Ito algorithm based on properties of the system and noise. + (d, m, f, G, y0, tspan, __, __) = sdeint.integrate._check_args(f, G, y0, tspan, None, None) + N = len(tspan) + h = (tspan[N-1] - tspan[0]) / (N - 1) # assuming equal time steps + if noise == "levy": + dW = levy.rvs(0., 1e-11, (N-1, m))+np.random.normal(0., np.sqrt(h), (N-1, m)) + elif noise == "levy_stable": + dW = (h ** (1/levy_alpha)) * levy_stable.rvs(levy_alpha, 0.0, (N-1, m))#+np.random.normal(0., np.sqrt(h), (N-1, m)) + elif noise == "cauchy": + dW = cauchy.rvs(0., 1e-4, (N-1, m)) + else: + dW = None + chosenAlgorithm = sdeint.integrate.itoSRI2 + return chosenAlgorithm(f, G, y0, tspan, dW = dW) + diff --git a/pycascades/core/evolve/semi_impl_euler_maruyama_alphastable_sde.py b/pycascades/core/evolve/semi_impl_euler_maruyama_alphastable_sde.py new file mode 100644 index 0000000..fa44559 --- /dev/null +++ b/pycascades/core/evolve/semi_impl_euler_maruyama_alphastable_sde.py @@ -0,0 +1,140 @@ +import numpy as np +from numba import jit +import warnings + + +def gen_levy_noise_preproc(alpha, sigma, dt, n = 1): + if not isinstance(alpha, np.ndarray): + if not isinstance(alpha, list): + alpha = [alpha] + alpha = np.array(alpha) + if len(alpha) < n: + alpha = np.repeat(alpha, n // len(alpha) + 1)[:n] + if not isinstance(sigma, np.ndarray): + if not isinstance(sigma, list): + sigma = [sigma] + sigma = np.array(sigma) + if len(sigma) < n: + sigma = np.repeat(sigma, n // len(sigma) + 1)[:n] + return alpha, sigma, dt, n + + +@jit(nopython = True) +def semi_impl_euler_maruyama_alphastable_sde_nb_loop( + n, N, x, xs, t, ts, dt_scaled, coupl, c, L, dt +): + for i in range(1, N): + x_new = x.copy() + + transp = (coupl @ x) + for j in range(n): + if (not np.isnan(x[j])) and (not np.isinf(x[j])): + candidates = np.roots(np.array( + [ + dt_scaled[j], + 0.0, + 1.0 - dt_scaled[j], + - x[j] - (c[j] + transp[j]) * dt_scaled[j] + ] + ).astype(np.complex128)) + if (np.abs(candidates.imag) < 1e-5).sum() == 1: + drift = (candidates[np.abs(candidates.imag) < 1e-5][0]).real + else: + best_idx = np.argmin(np.abs(candidates - x[j])) + drift = (candidates[best_idx]).real + else: + drift = x[j] + + x_new[j] = drift + L[j, i] + + # x2 = x1 + (-x2^3 + x2 + c)*dt/taos + + t += dt + ts[i] = t + x = x_new # .copy() + xs[i, :] = x + return ts, xs + + +def semi_impl_euler_maruyama_alphastable_sde( + x0 = [-1.0, -1.0, -1.0], + dt = 0.1, + cs = [0.0, 0.3, 0.4], + taos = [1.0, 1.0, 1.0], + t_end = 1000, + alphas = [1.5, 1.5, 1.5], + sigmas = [0.0, 0.0, 0.1], + coupl = np.array([[0.0, 0.1, 0.1], [-0.1, 0.0, 0.2], [0.0, -0.1, 0.0]]), + rng = None +): + if any(alphas) < 0.1: + warnings.warn( + """The CMS algorithm for generating levy-stable noise is not + reliable for alphas < 0.1. The implementation provided here + truncates large noise values above +-1e12 and sets any + nans to 0.""" + ) + + x0 = np.array(x0, dtype="float").flatten() + taos = np.array(taos, dtype="float").flatten() + cs = np.array(cs, dtype="float").flatten() + alphas = np.array(alphas, dtype="float").flatten() + sigmas = np.array(sigmas, dtype="float").flatten() + coupl = np.array(coupl, dtype="float") + + alphas, sigmas, dt_scaled, n = gen_levy_noise_preproc( + alphas, sigmas, dt / (taos + 1e-6), n = len(x0) + ) + + x = x0.copy() + N = int(t_end // dt) + 1 + xs = np.zeros((N, n)) + xs[0, :] = x + t = 0 + ts = np.zeros(N) + + L = np.zeros((n, N)) + for i in range(n): + if sigmas[i] > 0: + L[i,:] = sigmas[i] * (dt_scaled[i] ** (1/alphas[i])) * levy_stable.rvs(alphas[i], 0.0, size=N, random_state = rng) + L[np.abs(L) > 1e12] = (np.sign(L) * 1e12)[np.abs(L) > 1e12] + L[np.isinf(L)] = (np.sign(L) * 1e12)[np.isinf(L)] + L[np.isnan(L)] = 0.0 + + ts, xs = semi_impl_euler_maruyama_alphastable_sde_nb_loop( + n, N, x, xs, t, ts, dt_scaled, coupl, cs, L, dt + ) + return ts, xs, rng + +def get_params_from_es_network(net): + + n_nodes = net.number_of_nodes() + + cs = np.zeros(n_nodes) + taos = np.zeros(n_nodes) + coupl = np.zeros((n_nodes, n_nodes)) + + for i in range(n_nodes): + + node = net.nodes[i] + pars = node["data"].get_par() + taos[i] = 1 / pars["b"] + cs[i] = pars["c"] * taos[i] + + in_idxs = [e[0] for e in list(net.in_edges(i))] + for j in in_idxs: + + if hasattr(net.get_edge_data(j,i)["data"], "_x_0"): + x0 = net.get_edge_data(j,i)["data"]._x_0 + else: + x0 = 0.0 + + d = taos[i] * net.get_edge_data(j,i)["data"]._strength + + coupl[i,j] = d + + cs[i] += -x0 * d + + + return cs, taos, coupl + diff --git a/pycascades/tests/test_core.py b/pycascades/tests/test_core.py index 2251f4a..d3dc96e 100644 --- a/pycascades/tests/test_core.py +++ b/pycascades/tests/test_core.py @@ -1,25 +1,45 @@ -import sys +from pycascades import cusp, linear_coupling, tipping_network +from pycascades.core.evolve.evolve import make_equilibrium_event, integrate + import unittest import numpy as np -from pycascades import cusp, linear_coupling, tipping_network, evolve + class TestBasicFunctionality(unittest.TestCase): - def test_simple_system(self): - cusp_element_0 = cusp( a = -4, b = 1, c = 0, x_0 = 0.5 ) - cusp_element_1 = cusp( a = -4, b = 1, c = 0, x_0 = 0.5 ) - coupling_0 = linear_coupling( strength = 0.05 ) - coupling_1 = linear_coupling( strength = 0.2 ) + def test_evolve(self): + cusp_element_0 = cusp(a = -4, b = 1, c = 0, x_0 = 0.5) + cusp_element_1 = cusp(a = -4, b = 1, c = 0, x_0 = 0.5) + coupling_0 = linear_coupling(strength = 0.05) + coupling_1 = linear_coupling(strength = 0.2) net = tipping_network() - net.add_element( cusp_element_0 ) - net.add_element( cusp_element_1 ) - net.add_coupling( 0, 1, coupling_1 ) - net.add_coupling( 1, 0, coupling_0 ) - initial_state = [0.1,0.9] - ev = evolve( net, initial_state ) - timestep = 0.01 + net.add_element(cusp_element_0) + net.add_element(cusp_element_1) + net.add_coupling(0, 1, coupling_1) + net.add_coupling(1, 0, coupling_0) + initial_state = [0.1, 0.9] t_end = 10 - ev.integrate( timestep , t_end ) - np.set_printoptions(threshold=sys.maxsize) - - self.assertTrue(np.allclose(ev.get_timeseries()[1][-1,:], np.array([0.02725572, 1.00270361]))) + sol = integrate(net, initial_state, [0, t_end], 0.1) + self.assertTrue(np.allclose( + sol.y[:, -1], + np.array([0.02726913, 1.00262741]) + )) + def test_equilibration(self): + cusp_element_0 = cusp(a = -4, b = 1, c = 0, x_0 = 0.5) + cusp_element_1 = cusp(a = -4, b = 1, c = 0, x_0 = 0.5) + coupling_0 = linear_coupling(strength = 0.05) + coupling_1 = linear_coupling(strength = 0.2) + net = tipping_network() + net.add_element(cusp_element_0) + net.add_element(cusp_element_1) + net.add_coupling(0, 1, coupling_1) + net.add_coupling(1, 0, coupling_0) + initial_state = [0.1, 0.9] + t_end = 10 + event = make_equilibrium_event(net, 0.001) + sol = integrate(net, initial_state, [0, t_end], 0.1, events=event) + print(sol.y[:, -1]) + self.assertTrue(np.allclose( + sol.y[:, -1], + np.array([0.02790202, 1.00254695]) + )) From e7af3cd5fb90f97d25247cb5cc2ced647625968d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Jonathan=20Kr=C3=B6nke?= Date: Mon, 17 Nov 2025 15:27:22 +0100 Subject: [PATCH 05/13] refactor!: refactor core tipping network --- pycascades/__init__.py | 4 +- pycascades/amazon/__init__.py | 5 - pycascades/amazon/amazon.py | 151 ------------- pycascades/core/__init__.py | 1 - pycascades/core/coupling.py | 205 +++--------------- pycascades/core/system/system.py | 92 ++++++++ pycascades/core/tipping_element.py | 129 ----------- pycascades/core/tipping_network.py | 99 --------- pycascades/earth_system/__init__.py | 5 - pycascades/earth_system/earth.py | 86 -------- .../earth_system/functions_earth_system.py | 45 ---- pycascades/earth_system/timing.py | 75 ------- .../tipping_network_earth_system.py | 96 -------- pycascades/gen/__init__.py | 1 - pycascades/tests/test_core.py | 55 +++-- 15 files changed, 153 insertions(+), 896 deletions(-) delete mode 100644 pycascades/amazon/__init__.py delete mode 100644 pycascades/amazon/amazon.py create mode 100644 pycascades/core/system/system.py delete mode 100644 pycascades/core/tipping_element.py delete mode 100644 pycascades/core/tipping_network.py delete mode 100644 pycascades/earth_system/__init__.py delete mode 100644 pycascades/earth_system/earth.py delete mode 100644 pycascades/earth_system/functions_earth_system.py delete mode 100644 pycascades/earth_system/timing.py delete mode 100644 pycascades/earth_system/tipping_network_earth_system.py delete mode 100644 pycascades/gen/__init__.py diff --git a/pycascades/__init__.py b/pycascades/__init__.py index 590c099..81e2630 100644 --- a/pycascades/__init__.py +++ b/pycascades/__init__.py @@ -7,8 +7,6 @@ from . import core, gen, utils, earth_system, amazon -from pycascades.core.tipping_element import cusp, hopf, realistic_cusp -from pycascades.core.tipping_network import tipping_network -from pycascades.core.coupling import linear_coupling, cusp_to_hopf, hopf_x_to_cusp, hopf_x_to_hopf, hopf_y_to_cusp, hopf_y_to_hopf +from pycascades.core.coupling import linear_coupling from pycascades.core.evolve import evolve from pycascades.utils import plotter diff --git a/pycascades/amazon/__init__.py b/pycascades/amazon/__init__.py deleted file mode 100644 index 21e5a03..0000000 --- a/pycascades/amazon/__init__.py +++ /dev/null @@ -1,5 +0,0 @@ - - -from . import amazon - -from pycascades.amazon.amazon import generate_network \ No newline at end of file diff --git a/pycascades/amazon/amazon.py b/pycascades/amazon/amazon.py deleted file mode 100644 index a426426..0000000 --- a/pycascades/amazon/amazon.py +++ /dev/null @@ -1,151 +0,0 @@ - - -from pycascades.core.tipping_network import tipping_network -from pycascades.core.tipping_element import cusp -from pycascades.core.coupling import linear_coupling - - -from netCDF4 import Dataset - -import networkx as nx -import numpy as np - - - -def Rain(datasets): - """ - Computation of rainfall values; all datasets are necessary and a potential rain factor - """ - rain = [] - for data in datasets: - net_data = Dataset(data) - #get mean value for rainfall - rain_dataset = net_data.variables["rain"][:] - if len(rain) == 0: - rain = rain_dataset - else: - rain = np.add(rain, rain_dataset) - rain = np.array(rain) - return rain - -def Amazon_CUSPc(a, b, rain_current, rain_critical, rain_mean): - """ - c = c(rainfall) where tipping occurs at sqrt((4*b**3)/(27*a)) - """ - c = np.sqrt((4*np.abs(b)**3) / (27*np.abs(a)))/(rain_critical - rain_mean)*(rain_current - rain_mean) - return c - - - -def Amazon_cpl(a, b, rain_critical, rain_current, rain_mean, delta_rain): - """ - Factor of (1/2) is necessary since delta(state)=2 from -1 to +1 - Factor (-1) is necessary since delta_rain < 0, but the coupling must be positive - """ - - #rain [c, cpl]-values - c = np.sqrt((4*np.abs(b)**3) / (27*np.abs(a)))/(rain_critical - rain_mean)*(rain_current - rain_mean) - cpl = np.sqrt((4*np.abs(b)**3) / (27*np.abs(a)))/(rain_mean - rain_critical)*(1/2)*(-1)*delta_rain - - - if cpl < 0.0: - raise ValueError("Coupling strengths below 0.0 are not allowed") - - return cpl - - - -def Rain_moisture_delta_only(moist_rec_val): - """ - Computation of moisture recycling value for a year - """ - rain_moist = - np.sum(moist_rec_val) - return rain_moist - - -def generate_network(rain_crit, data_eval, no_cpl_dummy): - net = tipping_network() - - #get longitude and latitude values, for that use first network - net_data = Dataset(data_eval[0]) - lon_x = net_data.variables["lon"][:] - lat_y = net_data.variables["lat"][:] - - #rainfall value - rain = Rain(data_eval) - rain_mean = np.nanmean(rain) - - for idx, val in enumerate(lon_x): - #constants that are necessary to set up the tipping network - rain_current = rain[idx] #rainfall in a certain cell - rain_critical = rain_crit #critical rainfall of a certain cell - - a = 1 - b = 1 - element = cusp( a = -1, b = 1, c = Amazon_CUSPc(a, b, rain_current, rain_critical, rain_mean), x_0 = 0) - net.add_element(element) - net.nodes[idx]['pos'] = (val, lat_y[idx]) - - - flows_xy_total = [] - for data in data_eval: - data_file = Dataset(data) - flows_xy_total.append(data_file.variables["network"][:, :]) - flows_xy_total = np.array(flows_xy_total) - - #compute total moisture recycling within a year - flows_xy = Dataset(data_eval[0]).variables["network"][:, :] - it = np.nditer(flows_xy, flags=['multi_index']) - - - couplings = [] - while not it.finished: - if not it.multi_index[0] == it.multi_index[1]: - ########### - #need to get value for each month - monthly = [] - for i in range(0, len(flows_xy_total)): - monthly.append(flows_xy_total[i, it.multi_index[0], it.multi_index[1]]) - - appender = [it.multi_index[1], it.multi_index[0], np.sum(monthly)] - for i in monthly: - appender.append(i) - couplings.append([i for i in appender]) - it.iternext() - - couplings = np.array(couplings) - couplings = np.array(sorted(couplings, key=lambda x: x[2])) - - - #sort out zero values in array - cpl_hist = np.array(couplings).T[2] - start_idx = len(couplings) - np.count_nonzero(cpl_hist)#count length of zeros - couplings = np.array(couplings[start_idx:]) # sort out where couplings are zero - - - - #Resolution dependent coupling limit: Setting where couplings below cpl_limit mm/year are neglected; default value 1.0 mm - cpl_limit = 1.0 # time to compute the new network sensitively depends on the coupling limit; - - for cpl in couplings: - if cpl[2] > cpl_limit: - if no_cpl_dummy == True: - coupling_object = linear_coupling(strength = 0.0) - else: - #get the difference between rainfall in the respective cell after[rain_new] and before[rain_old] tipping - delta_rain = Rain_moisture_delta_only([cpl[i] for i in range(3, len(cpl))]) #delta_rain is a negative number - #current and critical values are required for the rainfall and mcwd - rain_current = rain[int(cpl[1])] - rain_critical = rain_crit - - #Amount of change of MCWD is the coupling strength - coupling_object = linear_coupling(strength = Amazon_cpl(a, b, rain_critical, rain_current, rain_mean, delta_rain)) - net.add_coupling( int(cpl[0]), int(cpl[1]), coupling_object ) #needs to be saved as integer here - - print("Amazon rainforest network generated! Restriction: Only moisture recycling links above {} mm/yr are considered".format(cpl_limit)) - d = net.number_of_edges() / net.number_of_nodes() - average_clustering = nx.average_clustering(net) - #print("Average degree: ", d) - #print("Average clustering: ", average_clustering) - return net - diff --git a/pycascades/core/__init__.py b/pycascades/core/__init__.py index 59f1908..e69de29 100644 --- a/pycascades/core/__init__.py +++ b/pycascades/core/__init__.py @@ -1 +0,0 @@ -from . import coupling, evolve, tipping_element, tipping_network diff --git a/pycascades/core/coupling.py b/pycascades/core/coupling.py index 5578a9a..53db909 100644 --- a/pycascades/core/coupling.py +++ b/pycascades/core/coupling.py @@ -1,193 +1,54 @@ -"""coupling module - -Provides classes for couplings. -Note that a coupling consists of two elements. The active element (called -coupling element here) affects the passive element (called coupled -element here). -""" import math -class coupling: - """Abstract class for coupling of two tipping_elements - Class should not be used but rather be inherited from by concrete coupling - classes.""" - - def __init__(self): - pass - - def dxdt_cpl(self): - """Returns callable for the coupling term of dxdt.""" - return lambda t, x_from , x_to : 0 - - def jac_cpl(self): - """Returns callable for the jacobian coupling matrix element.""" - return lambda t, x_from , x_to : 0 - - def jac_diag(self): - return lambda t, x_from , x_to : 0 - - def projection(self): - return lambda t : 1 - -class linear_coupling(coupling): - """Class for linear coupling - The coupling consists of a factor (strength) and a coupling element. - """ +class linear_coupling(): + sizes = (1, 1) def __init__(self, strength): - """Constructor""" - coupling.__init__(self) - self._strength = strength - - def dxdt_cpl(self): - """Returns callable for the coupling term of dxdt.""" - return lambda t, x_from , x_to : self._strength * x_from - - def jac_cpl(self): - """Returns callable for the jacobian coupling matrix element.""" - return lambda t, x_from , x_to : self._strength - - def jac_diag(self): - return lambda t, x_from , x_to : 0 - - def bif_impact(self): - return lambda t, x_from , x_to : self._strength * x_from - - - -class cusp_to_hopf(coupling): - """Class for coupling """ - - def __init__(self, _from, _to, a_hopf, strength): - coupling.__init__(self, _from, _to) - self._strength = strength - self._a = a_hopf - - def dxdt_cpl(self): - """coupling""" - return lambda t, x_from, r_to : self._a*r_to*self._strength*x_from - - def jac_cpl(self): - """partial derivative of dxdt with respect to x_from""" - return lambda t, x_from, r_to : self._a*r_to*self._strength - - def jac_diag(self): - """partial derivative with respect to r_to""" - return lambda t, x_from, r_to : self._a*self._strength*x_from - - def bif_impact(self): - return lambda t, x_from, r_to : self._strength*x_from - - -class hopf_x_to_cusp(coupling): - """Class for coupling """ - - def __init__(self, _from, _to, b_hopf, strength): - """Constructor""" - coupling.__init__(self, _from, _to) - self._b = b_hopf self._strength = strength - def dxdt_cpl(self): - """coupling""" - return lambda t, r_from, x_to : self._strength*r_from*math.cos(self._b - *t) + def f(self, t, x_from, x_to): + return self._strength * x_from - def jac_cpl(self): - """partial derivative of dxdt with respect to r_from""" - return lambda t, r_from, x_to : self._strength*math.cos(self._b*t) - def jac_diag(self): - """partial derivative with respect to x_to""" - return lambda t, r_from, x_to : 0 +class multiplicative_coupling(): + sizes = (1, 1) - def projection(self): - return lambda t : math.cos(self._b*t) - - def bif_impact(self): - return lambda t, r_from, x_to : self._strength*r_from*math.cos(self._b - *t) - -class hopf_y_to_cusp(coupling): - """Class for coupling """ - - def __init__(self, _from, _to, b_hopf, strength): - """Constructor""" - self._b = b_hopf + def __init__(self, strength): self._strength = strength - def dxdt_cpl(self): - """coupling""" - return lambda t, r_from, x_to : self._strength*r_from*math.sin(self._b - *t) + def f(self, t, x_from, x_to): + return self._strength * x_from * x_to - def jac_cpl(self): - """partial derivative of dxdt with respect to r_from""" - return lambda t, r_from, x_to : self._strength*math.sin(self._b*t) - def jac_diag(self): - """partial derivative with respect to x_to""" - return lambda t, r_from, x_to : 0 +class hopf_to_cusp(): + sizes = (1, 1) - def projection(self): - return lambda t : math.sin(self._b*t) - - def bif_impact(self): - return lambda t, r_from, x_to : self._strength*r_from*math.sin(self._b - *t) - -class hopf_x_to_hopf(coupling): - """Class for coupling """ - def __init__(self, _from, _to, a_to, b_from, strength): - coupling.__init__(self, _from, _to) - self._a_to = a_to - self._b_from = b_from + def __init__(self, strength, frequency, shift): self._strength = strength + self._frequency = frequency + self._shift = shift - def dxdt_cpl(self): - return lambda t, r_from, r_to : self._a_to*r_to*self._strength*r_from*\ - math.cos(self._b_from*t) - - def jac_cpl(self): - return lambda t, r_from, r_to : self._a_to*r_to*self._strength*\ - math.cos(self._b_from*t) + def f(self, t, x_from, x_to): + return ( + self._strength + * x_from + * math.sin(self._frequency * t + self._shift) + ) - def jac_diag(self): - return lambda t, r_from, r_to : self._a_to*self._strength*r_from*\ - math.cos(self._b_from*t) - def projection(self): - return lambda t : math.cos(self._b_from*t) +class hopf_to_hopf(): + sizes = (1, 1) - def bif_impact(self): - return lambda t, r_from, r_to : self._strength*r_from*\ - math.cos(self._b_from*t) - -class hopf_y_to_hopf(coupling): - """Class for coupling """ - - def __init__(self, _from, _to, a_to, b_from, strength): - coupling.__init__(self, _from, _to) - self._a_to = a_to - self._b_from = b_from + def __init__(self, strength, frequency, shift): self._strength = strength - - def dxdt_cpl(self): - return lambda t, r_from, r_to: self._a_to*r_to*self._strength*r_from*\ - math.sin(self._b_from * t) - - def jac_cpl(self): - return lambda t, r_from, r_to: self._a_to*r_to*self._strength*\ - math.sin(self._b_from * t) - - def jac_diag(self): - return lambda t, r_from, r_to: self._a_to*self._strength*r_from*\ - math.sin(self._b_from * t) - - def projection(self): - return lambda t : math.sin(self._b_from * t) - - def bif_impact(self): - return lambda t, r_from, r_to : self._strength*r_from*\ - math.sin(self._b_from*t) + self._frequency = frequency + self._shift = shift + + def f(self, t, x_from, x_to): + return ( + self._strength + * x_to + * x_from + * math.sin(self._frequency * t + self._shift) + ) diff --git a/pycascades/core/system/system.py b/pycascades/core/system/system.py new file mode 100644 index 0000000..415d134 --- /dev/null +++ b/pycascades/core/system/system.py @@ -0,0 +1,92 @@ +from copy import deepcopy + +import numpy as np +import abc + + +class system(metaclass=abc.ABCMeta): + @classmethod + def __subclasshook__(cls, subclass): + return ( + hasattr(subclass, 'size') + and callable(subclass.size) + and hasattr(subclass, 'f') + and callable(subclass.f) + or NotImplemented + ) + + @abc.abstractmethod + def size(self): + raise NotImplementedError + + @abc.abstractmethod + def f(self, x, t): + raise NotImplementedError + + +class network(system): + def __init__(self): + self._elements = [] + self._couplings = [] + + def size(self): + return np.sum([element.size() for element in self._elements]) + + def add_element(self, element): + copy = deepcopy(self) + copy._elements.append(element) + return copy + + def add_coupling(self, from_coupling, to_coupling, coupling): + copy = deepcopy(self) + if ( + self._elements[from_coupling].size() != coupling.sizes[0] + or self._elements[to_coupling].size() != coupling.sizes[1] + ): + raise Exception("Coupling not possible!") + copy._couplings.append((from_coupling, to_coupling, coupling)) + return copy + + def f(self, x, t): + matrix = np.zeros((self.size(), self.size())) + for cpl in self._couplings: + i, j, val = cpl + matrix[i, j] = val.f(t, x[j], x[i]) + diagonal = np.diag( + [element.f(x[idx], t) for idx, element in enumerate(self._elements)] + ) + matrix = matrix + diagonal + return np.add.reduce(matrix, axis=1) + + +class double_fold(system): + def __init__(self, a=-1, b=1, c=0, x_0=0.0): + self._par = {} + self._par['a'] = a + self._par['b'] = b + self._par['c'] = c + self._par['x_0'] = x_0 + + def size(self): + return 1 + + def f(self, x, t): + return np.array( + self._par['a'] * pow(x - self._par['x_0'], 3) + + self._par['b'] * (x - self._par['x_0']) + + self._par['c'] + ) + + +class pitchfork(system): + """Can also be used as polar representation of hopf""" + + def __init__(self, a, c): + self._par['a'] = a + self._par['c'] = c + + def size(self): + return 1 + + def f(self, x, t): + return np.array((self._par['c'] - pow(x, 2)) * x * self._par['a']) diff --git a/pycascades/core/tipping_element.py b/pycascades/core/tipping_element.py deleted file mode 100644 index e73ab56..0000000 --- a/pycascades/core/tipping_element.py +++ /dev/null @@ -1,129 +0,0 @@ -"""tipping_element module - -Provides classes for tipping_element objects -""" -import numpy as np - -class tipping_element: - """Abstract tipping_element class - This class provides the interface for tipping_element classes. - It should not be used but rather inherited from by the concrete - tipping_element classes. - """ - - def __init__(self): - """Constructor""" - self._type = None - self._par = {} - - """dx/dt and jacobian diagonal element of tipping element. - This method should be overwritten from the - concrete tipping_element classes to implement - the special form of the tipping element. - """ - - def get_type(self): - return self._type - - def get_par(self): - return self._par - - def set_par(self, key, val): - self._par[key] = val - - def dxdt_diag(self): - """dx/dt diagonal element of tipping element. - This method should be overwritten from the - concrete tipping_element classes to implement - the special form of the tipping element. - """ - return lambda t, x : 0 - - def jac_diag(self): - """jacobian diagonal element of tipping element. - This method should be overwritten from the - concrete tipping_element classes to implement - the special form of the tipping element. - """ - return lambda t, x : 0 - - def tip_state(self): - return lambda x : 0 - -class cusp(tipping_element): - """Concrete class for cusp-like tipping element""" - def __init__(self, a = -4, b = 1, c = 0, x_0 = 0.5 ): - """Constructor with additional parameters for cusp""" - super().__init__() - self._type = 'cusp' - self._par['a'] = a - self._par['b'] = b - self._par['c'] = c - self._par['x_0'] = x_0 - - def dxdt_diag(self): - """returns callable of dx/dt diagonal element of cusp""" - return lambda t, x : self._par['a'] * pow(x - self._par['x_0'],3) \ - + self._par['b'] * (x - self._par['x_0']) \ - + self._par['c'] - - def jac_diag(self): - """returns callable jacobian diagonal element of cusp.""" - return lambda t, x : 3 * self._par['a'] * pow(x - self._par['x_0'],2) \ - + self._par['b'] - - def tip_state(self): - return lambda x : x > self._par['x_0'] - -class realistic_cusp(cusp): - """Class for cusp-like tipping elements with realistic parameters""" - def __init__(self, timescale, x_tuple, rho_tuple, rho_init ): - b = 1/timescale - x_0 = (x_tuple[0] + x_tuple[1]) / 2 - a = - 4 * b / pow(x_tuple[1] - x_tuple[0], 2) - - self._rho_tuple = rho_tuple - self._tip_width = 2 * np.sqrt(-4 * pow(b, 3) / (27 * a) ) - - super().__init__( a = a, b = b, c = 0, x_0 = x_0) - self._par['rho'] = rho_init - self._update_par() - - def set_par(self, key, val): - if key == 'c': - raise ValueError("c is bounded to the control parameter rho!") - self._par[key] = val - self._update_par() - - def _update_par(self): - rho1 = self._rho_tuple[0] - rho2 = self._rho_tuple[1] - width = self._tip_width - rho = self._par['rho'] - self._par['c'] = width / (rho2 - rho1) * (rho - (rho1 + rho2) / 2) - -class hopf(tipping_element): - """Concrete class for tipping_elements following the dynamics of a - Hopfbifurcation. - Implementation using a representation with polar coordinates: - dr/dt=(bif_par-r^2)*r*a, dphi/dt=b (time-dependence of angle)""" - - def __init__(self, a, c): - """Constructor with additional parameters for (half a) Hopf - element""" - super().__init__() - self._type = 'hopf' - self._par['a'] = a - self._par['c'] = c - - def dxdt_diag(self): - """returns callable of dx/dt diagonal element of Hopf element""" - return lambda t, r: ( self._par['c'] - pow(r,2) ) * r * self._par['a'] - - def jac_diag(self): - """returns callable jacobian diagonal element of Hopf""" - return lambda t, r: self._par['a'] * self._par['c'] - \ - self._par['a'] * 3 * pow(r,2) - - def tip_state(self): - return lambda x: self._par['c'] > 0 diff --git a/pycascades/core/tipping_network.py b/pycascades/core/tipping_network.py deleted file mode 100644 index eaa4215..0000000 --- a/pycascades/core/tipping_network.py +++ /dev/null @@ -1,99 +0,0 @@ -import networkx as nx -import numpy as np -from copy import deepcopy - -class tipping_network(nx.DiGraph): - - def __init__( self, incoming_graph_data=None, **attr): - nx.DiGraph.__init__( self, incoming_graph_data=None, **attr) - - def add_element( self, tipping_element ): - tipping_element = deepcopy(tipping_element) - ind = self.number_of_nodes() - super().add_node( ind, data = tipping_element ) - self.nodes[ind]['lambda_f'] = tipping_element.dxdt_diag() - self.nodes[ind]['lambda_jac'] = tipping_element.jac_diag() - - def add_coupling( self, from_id, to_id, coupling): - coupling = deepcopy(coupling) - super().add_edge( from_id, to_id, data = coupling) - self[from_id][to_id]['lambda_f'] = coupling.dxdt_cpl() - self[from_id][to_id]['lambda_jac'] = coupling.jac_cpl() - self[from_id][to_id]['lambda_jac_diag'] = coupling.jac_diag() - - def set_param( self, node_id, key, val ): - element = self.nodes[node_id]['data'] - element.set_par( key, val) - self.nodes[node_id]['lambda_f'] = self.nodes[node_id]['data'].dxdt_diag() - self.nodes[node_id]['lambda_jac'] = self.nodes[node_id]['data'].jac_diag() - - def get_tip_states( self, x): - tipped = [self.nodes[i]['data'].tip_state()(x[i]) for i in self.nodes()] - return np.array( tipped ) - - def get_node_types( self ): - type_list = [self.nodes[i]['data'].get_type() for i in self.nodes()] - return type_list - - def get_number_tipped( self, x): - return np.count_nonzero( self.get_tip_states( x ) ) - - def f( self, x, t): - f = np.zeros( self.number_of_nodes() ) - for node in self.nodes(data=True): - ind = node[0] - x_comp = x[ind] - f[ind] = node[1]['lambda_f'].__call__( t, x_comp) - for edge in self.edges(data=True): - from_id = edge[0] - to_id = edge[1] - lmd = edge[2]['lambda_f'] - f[to_id] += lmd.__call__( t, x[from_id], x[to_id]) - return f - - def jac(self, x, t): - jac = np.zeros((self.number_of_nodes(), self.number_of_nodes())) - for node in self.nodes(data=True): - ind = node[0] - x_comp = x[ind] - jac[ind,ind] = node[1]['lambda_jac'].__call__( t, x_comp) - for edge in self.edges(data=True): - from_id = edge[0] - to_id = edge[1] - lmd = edge[2]['lambda_jac'] - jac[to_id, from_id] = lmd.__call__( t, x[from_id], x[to_id] ) - lmd_diag = edge[2]['lambda_jac_diag'] - jac[to_id, to_id] += lmd_diag.__call__( t, x[from_id], x[to_id] ) - return jac - - def set_vulnerability(self, node_id, bool_val): - self.nodes[node_id]["vulnerable"] = bool_val - - def get_vulnerability_network(self): - G = nx.Graph() - for node in self.nodes(): - G.add_node(node) - G.nodes[node]["vulnerable"] = self.nodes[node]["vulnerable"] - for edge in self.edges(): - if self.nodes[edge[0]]["vulnerable"] and self.nodes[edge[1]]["vulnerable"]: - G.add_edge(edge[0],edge[1]) - return G - - def get_out_component_size(self, from_id): - out_component_size = -1 - for node in self.nodes(): - if nx.has_path(self, from_id, node): - out_component_size += 1 - return out_component_size - - def compute_impact_matrix(self): - n = self.number_of_nodes() - impact_matrix = [[lambda t, x1, x2: 0 for j in range(n)] for i in range(n)] - for edge in self.edges.data(): - print(edge[2]['data'].bif_impact()) - impact_matrix[edge[1]][edge[0]]=edge[2]['data'].bif_impact() - # if self.get_node_types()[edge[1]]=='cusp': - # impact_matrix[edge[1]][edge[0]]=edge['data'].dxdt_cpl() - # elif self.get_node_types()[edge[1]]=='hopf': - # impact_matrix[edge[1]][edge[0]]=edge['data'] - return impact_matrix diff --git a/pycascades/earth_system/__init__.py b/pycascades/earth_system/__init__.py deleted file mode 100644 index 71e3b67..0000000 --- a/pycascades/earth_system/__init__.py +++ /dev/null @@ -1,5 +0,0 @@ -from . import earth, functions_earth_system, timing, tipping_network_earth_system - -from pycascades.earth_system.earth import Earth_System -from pycascades.earth_system.timing import Timing - diff --git a/pycascades/earth_system/earth.py b/pycascades/earth_system/earth.py deleted file mode 100644 index ecc6d56..0000000 --- a/pycascades/earth_system/earth.py +++ /dev/null @@ -1,86 +0,0 @@ -import numpy as np -# private imports from sys.path -from pycascades.core.coupling import coupling -from pycascades.core.tipping_element import cusp -from pycascades.earth_system.tipping_network_earth_system import tipping_network -from pycascades.earth_system.functions_earth_system import global_functions - -""" -Here the Earth system network is defined after Kriegler et al., 2009 -""" - -class linear_coupling_earth_system(coupling): - - def __init__(self, strength, x_0): - coupling.__init__(self) - self._strength = strength - self._x_0 = x_0 - - def dxdt_cpl(self): - return lambda t, x_from, x_to: self._strength * (x_from - self._x_0) - - def jac_cpl(self): - return lambda t, x_from, x_to: self._strength - - def jac_diag(self): - return lambda t, x_from, x_to: 0 - - def bif_impact(self): - return lambda t, x_from, x_to: self._strength * (x_from - self._x_0) - - -class Earth_System(): - def __init__(self, gis_time, thc_time, wais_time, amaz_time, limits_gis, limits_thc, limits_wais, limits_amaz, - pf_wais_to_gis, pf_thc_to_gis, pf_gis_to_thc, pf_wais_to_thc, pf_gis_to_wais, pf_thc_to_wais, pf_thc_to_amaz): - #timescales - self._gis_time = gis_time - self._thc_time = thc_time - self._wais_time = wais_time - self._amaz_time = amaz_time - - #tipping limits - self._limits_gis = limits_gis - self._limits_thc = limits_thc - self._limits_wais = limits_wais - self._limits_amaz = limits_amaz - - #probability fractions - self._pf_wais_to_gis = pf_wais_to_gis - self._pf_thc_to_gis = pf_thc_to_gis - self._pf_gis_to_thc = pf_gis_to_thc - self._pf_wais_to_thc = pf_wais_to_thc - self._pf_gis_to_wais = pf_gis_to_wais - self._pf_thc_to_wais = pf_thc_to_wais - self._pf_thc_to_amaz = pf_thc_to_amaz - - """ - you must provide this method with a global mean temperature, a coupling strength and - an integer (-1, 0, +1) for the network type that you want to invoke, i.e. kk0, kk1 and kk2 must be -1, 0 or +1 - """ - def earth_network(self, effective_GMT, strength, kk0, kk1): - gis = cusp(a=-1 / self._gis_time, b=1 / self._gis_time, c=(1 / self._gis_time) * global_functions.CUSPc(0., self._limits_gis, effective_GMT), x_0=0.0) - thc = cusp(a=-1 / self._thc_time, b=1 / self._thc_time, c=(1 / self._thc_time) * global_functions.CUSPc(0., self._limits_thc, effective_GMT), x_0=0.0) - wais = cusp(a=-1 / self._wais_time, b=1 / self._wais_time, c=(1 / self._wais_time) * global_functions.CUSPc(0., self._limits_wais, effective_GMT), x_0=0.0) - amaz = cusp(a=-1 / self._amaz_time, b=1 / self._amaz_time, c=(1 / self._amaz_time) * global_functions.CUSPc(0., self._limits_amaz, effective_GMT), x_0=0.0) - - # set up network - net = tipping_network() - net.add_element(gis) - net.add_element(thc) - net.add_element(wais) - net.add_element(amaz) - - - ######################################Set edges to active state##################################### - net.add_coupling(1, 0, linear_coupling_earth_system(strength=-(1 / self._gis_time) * strength * self._pf_thc_to_gis, x_0=-1)) - net.add_coupling(2, 0, linear_coupling_earth_system(strength=(1 / self._gis_time) * strength * self._pf_wais_to_gis, x_0=-1)) - - net.add_coupling(0, 1, linear_coupling_earth_system(strength=(1 / self._thc_time) * strength * self._pf_gis_to_thc, x_0=-1)) - net.add_coupling(2, 1, linear_coupling_earth_system(strength=(1 / self._thc_time) * strength * self._pf_wais_to_thc * kk0, x_0=-1)) - - net.add_coupling(0, 2, linear_coupling_earth_system(strength=(1 / self._wais_time) * strength * self._pf_gis_to_wais, x_0=-1)) - net.add_coupling(1, 2, linear_coupling_earth_system(strength=(1 / self._wais_time) * strength * self._pf_thc_to_wais, x_0=-1)) - - net.add_coupling(1, 3, linear_coupling_earth_system(strength=(1 / self._amaz_time) * strength * self._pf_thc_to_amaz * kk1, x_0=-1)) - - return net diff --git a/pycascades/earth_system/functions_earth_system.py b/pycascades/earth_system/functions_earth_system.py deleted file mode 100644 index 4a2e595..0000000 --- a/pycascades/earth_system/functions_earth_system.py +++ /dev/null @@ -1,45 +0,0 @@ -import numpy as np - -""" -Here all global functions are stored - the functions are up to "choice": Here, linear functions are used -""" - - -class global_functions(): - """ - Linear feedback function to compute feedbacks. Maximal feedback is obtained from 2.0°C onwards. - feedbacks for Arctic summer sea ice, mountain glaciers, GIS and WAIS are proven to be constant also for higher temperatures - feedbacks for Amazon and feedbacks_steffen are computed for a temperature increase of 2.0°C until 2100, see paper - """ - def feedback_function(GMT, fbmax): - # fbmax = maximal feedback - # only returns a value in case GMT is higher than lower boundary of the respective tipping element, otherwise return 0.0 (lower cap), N.B.: No upper cap - if GMT <= 2.0: - y = (fbmax / 2.0) * GMT - return y - elif GMT > 2.0: - return fbmax - else: - raise Exception("GMT negativ: Feedbacks do not work for temperatures smaller 0!") - - # feedbacks of state dependent variables, linear increase of feedbacks between state -1 and +1 for GIS, WAIS, THC, NINO and AMAZ - def state_feedback(state, fbmax): - if state >= -1 and state <= 1: - y = fbmax / 2 * (state + 1) - elif state < -1: - y = 0. - elif state > +1: - y = fbmax - return y - - # c = c(GMT) where tipping occurs at sqrt(4/27) ~ 0.38 - # Linear function through two points maps GMT --> c, where x-values represent GMT and y-values represent CUSP-c values - def CUSPc(x1, x2, x): - # only returns a value in case GMT is higher than lower boundary of the respective tipping element, otherwise return 0.0 (lower cap), N.B.: No upper cap - if x >= x1: - y1 = 0.0 - y2 = np.sqrt(4 / 27) - y = (y2 - y1) / (x2 - x1) * (x - x1) + y1 - return y - else: - return 0.0 \ No newline at end of file diff --git a/pycascades/earth_system/timing.py b/pycascades/earth_system/timing.py deleted file mode 100644 index 6343c4d..0000000 --- a/pycascades/earth_system/timing.py +++ /dev/null @@ -1,75 +0,0 @@ -""" -Timing module: This module computes the conversion factor -between one year in the simulation and one "real" year depending on the tipping time scale of the Amazon rainforest -""" - - -import numpy as np -from pycascades.core.tipping_element import cusp -from pycascades.core.evolve import evolve -from pycascades.earth_system.functions_earth_system import global_functions -from pycascades.earth_system.tipping_network_earth_system import tipping_network - - -class Timing(): - - def __init__(self): - #Timescales - self._gis_realtime = 4900. - self._thc_realtime = 300. - self._wais_realtime = 2400. - self._amaz_realtime = 50. - - - #Compute conversion factor - self._real_timescale = self._gis_realtime #value normed to GIS - self._timescale = self._gis_realtime/self._amaz_realtime #value normed to GIS - self._tip_point_gis = 1.8 # most probable tipping point (see Robinson, 2012) #value normed to GIS - self._c_krit = np.sqrt(4 / 27) - self._GMT_cal = 4.0 #normed temperature - self._epsilon_c = global_functions.CUSPc(0., self._tip_point_gis, self._GMT_cal) - self._c_krit - self._initial_state = [-1.] - self._threshold = 1.0 - - - """ - Time scale, normed to the shortest tipping scale, in years - N.B.: Note that we can only insert a RELATIVE time scale, in principle the time scale is dependent on the GMT, - Here we insert tipping time scales at a temperature around 4°C above pre-industrial, since time scales are shifting during simulation due to structure of CUSP-catastrophe - """ - def timescales(self): - gis_time = self._gis_realtime/self._amaz_realtime - thc_time = self._thc_realtime/self._amaz_realtime - wais_time = self._wais_realtime/self._amaz_realtime - amaz_time = self._amaz_realtime/self._amaz_realtime - return gis_time, thc_time, wais_time, amaz_time - - - """ - Here we insert a conversion factor to get a translation from a.u. to "true" years - """ - def conversion(self): - cusp_deq = cusp(a=-1/self._timescale, b=1/self._timescale, c=self._c_krit/self._timescale, x_0=0.0) - net = tipping_network() - net.add_element(cusp_deq) - cusp_deq._par['c'] = self._c_krit/self._timescale + self._epsilon_c/self._timescale - - timestep = 0.01 - t_end = 5000 - ev = evolve(net, self._initial_state) - ev.integrate(timestep, t_end) - - t_arr = np.array(ev.get_timeseries()[0]) - cusp_deq = np.array(ev.get_timeseries()[1][:, 0]) - - # find point where state crosses threshold - th = cusp_deq > self._threshold - th[1:][th[:-1] & th[1:]] = False - - # conversion factor from arbitrary units to years - conv_fac = self._real_timescale / t_arr[np.nonzero(th)[0][0]] - return conv_fac - - - - diff --git a/pycascades/earth_system/tipping_network_earth_system.py b/pycascades/earth_system/tipping_network_earth_system.py deleted file mode 100644 index 6a5751e..0000000 --- a/pycascades/earth_system/tipping_network_earth_system.py +++ /dev/null @@ -1,96 +0,0 @@ -import networkx as nx -import numpy as np - -class tipping_network(nx.DiGraph): - - def __init__( self, incoming_graph_data=None, **attr): - nx.DiGraph.__init__( self, incoming_graph_data=None, **attr) - - def add_element( self, tipping_element ): - ind = self.number_of_nodes() - super().add_node( ind, data = tipping_element ) - self.nodes[ind]['lambda_f'] = tipping_element.dxdt_diag() - self.nodes[ind]['lambda_jac'] = tipping_element.jac_diag() - - def add_coupling( self, from_id, to_id, coupling): - super().add_edge( from_id, to_id, data = coupling) - self[from_id][to_id]['lambda_f'] = coupling.dxdt_cpl() - self[from_id][to_id]['lambda_jac'] = coupling.jac_cpl() - self[from_id][to_id]['lambda_jac_diag'] = coupling.jac_diag() - - def set_param( self, node_id, key, val ): - element = self.nodes[node_id]['data'] - element.set_par( key, val) - self.nodes[node_id]['lambda_f'] = self.nodes[node_id]['data'].dxdt_diag() - self.nodes[node_id]['lambda_jac'] = self.nodes[node_id]['data'].jac_diag() - - def get_tip_states( self, x): - tipped = [self.nodes[i]['data'].tip_state()(x[i]) for i in self.nodes()] - return np.array( tipped ) - - def get_node_types( self ): - type_list = [self.nodes[i]['data'].get_type() for i in self.nodes()] - return type_list - - def get_number_tipped( self, x): - return np.count_nonzero( self.get_tip_states( x ) ) - - def f( self, x, t): - f = np.zeros( self.number_of_nodes() ) - for node in self.nodes(data=True): - ind = node[0] - x_comp = x[ind] - f[ind] = node[1]['lambda_f'].__call__( t, x_comp) - for edge in self.edges(data=True): - from_id = edge[0] - to_id = edge[1] - lmd = edge[2]['lambda_f'] - f[to_id] += lmd.__call__( t, x[from_id], x[to_id]) - return f - - def jac(self, x, t): - jac = np.zeros((self.number_of_nodes(), self.number_of_nodes())) - for node in self.nodes(data=True): - ind = node[0] - x_comp = x[ind] - jac[ind,ind] = node[1]['lambda_jac'].__call__( t, x_comp) - for edge in self.edges(data=True): - from_id = edge[0] - to_id = edge[1] - lmd = edge[2]['lambda_jac'] - jac[to_id, from_id] = lmd.__call__( t, x[from_id], x[to_id] ) - lmd_diag = edge[2]['lambda_jac_diag'] - jac[to_id, to_id] += lmd_diag.__call__( t, x[from_id], x[to_id] ) - return jac - - def set_vulnerability(self, node_id, bool_val): - self.nodes[node_id]["vulnerable"] = bool_val - - def get_vulnerability_network(self): - G = nx.Graph() - for node in self.nodes(): - G.add_node(node) - G.nodes[node]["vulnerable"] = self.nodes[node]["vulnerable"] - for edge in self.edges(): - if self.nodes[edge[0]]["vulnerable"] and self.nodes[edge[1]]["vulnerable"]: - G.add_edge(edge[0],edge[1]) - return G - - def get_out_component_size(self, from_id): - out_component_size = -1 - for node in self.nodes(): - if nx.has_path(self, from_id, node): - out_component_size += 1 - return out_component_size - - def compute_impact_matrix(self): - n = self.number_of_nodes() - impact_matrix = [[lambda t, x1, x2: 0 for j in range(n)] for i in range(n)] - for edge in self.edges.data(): - print(edge[2]['data'].bif_impact()) - impact_matrix[edge[1]][edge[0]]=edge[2]['data'].bif_impact() - # if self.get_node_types()[edge[1]]=='cusp': - # impact_matrix[edge[1]][edge[0]]=edge['data'].dxdt_cpl() - # elif self.get_node_types()[edge[1]]=='hopf': - # impact_matrix[edge[1]][edge[0]]=edge['data'] - return impact_matrix diff --git a/pycascades/gen/__init__.py b/pycascades/gen/__init__.py deleted file mode 100644 index 7623fdb..0000000 --- a/pycascades/gen/__init__.py +++ /dev/null @@ -1 +0,0 @@ -from . import networks \ No newline at end of file diff --git a/pycascades/tests/test_core.py b/pycascades/tests/test_core.py index d3dc96e..abb1f60 100644 --- a/pycascades/tests/test_core.py +++ b/pycascades/tests/test_core.py @@ -1,45 +1,44 @@ -from pycascades import cusp, linear_coupling, tipping_network +from pycascades.core.coupling import linear_coupling from pycascades.core.evolve.evolve import make_equilibrium_event, integrate +from pycascades.core.system.system import network, double_fold import unittest import numpy as np class TestBasicFunctionality(unittest.TestCase): - def test_evolve(self): - cusp_element_0 = cusp(a = -4, b = 1, c = 0, x_0 = 0.5) - cusp_element_1 = cusp(a = -4, b = 1, c = 0, x_0 = 0.5) - coupling_0 = linear_coupling(strength = 0.05) - coupling_1 = linear_coupling(strength = 0.2) - net = tipping_network() - net.add_element(cusp_element_0) - net.add_element(cusp_element_1) - net.add_coupling(0, 1, coupling_1) - net.add_coupling(1, 0, coupling_0) + def test_equilibration(self): + sys1 = double_fold(a = -4, b = 1, c = 0, x_0 = 0.5) + sys2 = double_fold(a = -4, b = 1, c = 0, x_0 = 0.5) + net = ( + network() + .add_element(sys1) + .add_element(sys2) + .add_coupling(0, 1, linear_coupling(strength=0.05)) + .add_coupling(1, 0, linear_coupling(strength=0.2)) + ) initial_state = [0.1, 0.9] t_end = 10 - sol = integrate(net, initial_state, [0, t_end], 0.1) + event = make_equilibrium_event(net, 0.001) + sol = integrate(net, initial_state, [0, t_end], 0.1, events=event) self.assertTrue(np.allclose( sol.y[:, -1], - np.array([0.02726913, 1.00262741]) + np.array([0.02790202, 1.00254695]) )) - def test_equilibration(self): - cusp_element_0 = cusp(a = -4, b = 1, c = 0, x_0 = 0.5) - cusp_element_1 = cusp(a = -4, b = 1, c = 0, x_0 = 0.5) - coupling_0 = linear_coupling(strength = 0.05) - coupling_1 = linear_coupling(strength = 0.2) - net = tipping_network() - net.add_element(cusp_element_0) - net.add_element(cusp_element_1) - net.add_coupling(0, 1, coupling_1) - net.add_coupling(1, 0, coupling_0) + def test_system(self): + sys1 = double_fold(a = -4, b = 1, c = 0, x_0 = 0.5) + sys2 = double_fold(a = -4, b = 1, c = 0, x_0 = 0.5) + sys = ( + network() + .add_element(sys1) + .add_element(sys2) + .add_coupling(0, 1, linear_coupling(strength=0.05)) + .add_coupling(1, 0, linear_coupling(strength=0.2)) + ) initial_state = [0.1, 0.9] - t_end = 10 - event = make_equilibrium_event(net, 0.001) - sol = integrate(net, initial_state, [0, t_end], 0.1, events=event) - print(sol.y[:, -1]) + sol = integrate(sys, initial_state, [0, 10], 0.1) self.assertTrue(np.allclose( sol.y[:, -1], - np.array([0.02790202, 1.00254695]) + np.array([0.02726913, 1.00262741]) )) From 58a1aff496667eab5c87b35e631d8ca3756de30d Mon Sep 17 00:00:00 2001 From: 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