From bff41fb537840f421d4d641e0d0dc091ef5db18b Mon Sep 17 00:00:00 2001 From: DuncDennis <90915296+DuncDennis@users.noreply.github.com> Date: Fri, 20 Oct 2023 17:18:46 +0200 Subject: [PATCH 1/5] Removed plotly dependence and changed it to matplotlib. --- README.md | 3 +-- pyproject.toml | 3 +-- src/lorenzpy/plot/__init__.py | 1 + src/lorenzpy/plot/plot.py | 39 +++++++++++++++++++++++++++++++ src/lorenzpy/plot/plot_3d.py | 17 -------------- static/gen_attractor_animation.py | 9 ------- 6 files changed, 42 insertions(+), 30 deletions(-) create mode 100644 src/lorenzpy/plot/plot.py delete mode 100644 src/lorenzpy/plot/plot_3d.py diff --git a/README.md b/README.md index 5f5c1bb..28fe734 100644 --- a/README.md +++ b/README.md @@ -22,8 +22,7 @@ $ pip install lorenzpy ``` To install with the additional plotting functionality. -This also installs `plotly` and `matplotlib`. ⚠️ Plotting functionality not in a useful -state. +This also installs `matplotlib`. ⚠️ Plotting functionality not in a useful state. ```bash $ pip install lorenzpy[plot] ``` diff --git a/pyproject.toml b/pyproject.toml index cec70d1..033da02 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -41,7 +41,6 @@ dev = [ "pre-commit==3.1.1", # add version? ] plot = [ - "plotly>=5.11", "matplotlib>=3.5" ] @@ -59,7 +58,7 @@ line-length = 88 files = "src/lorenzpy/" [[tool.mypy.overrides]] -module = ['plotly.*', 'numpy', 'pytest', "scipy.*", "matplotlib.*", "PIL"] # ignore missing imports from the plotly package. +module = ['numpy', 'pytest', "scipy.*", "matplotlib.*", "PIL", "mpl_toolkits.*"] ignore_missing_imports = true [tool.ruff] diff --git a/src/lorenzpy/plot/__init__.py b/src/lorenzpy/plot/__init__.py index d1626c9..d61aac8 100644 --- a/src/lorenzpy/plot/__init__.py +++ b/src/lorenzpy/plot/__init__.py @@ -1 +1,2 @@ """Submodule to plot chaotic dynamics systems.""" +from .plot import create_3d_line_plot diff --git a/src/lorenzpy/plot/plot.py b/src/lorenzpy/plot/plot.py new file mode 100644 index 0000000..a6a1035 --- /dev/null +++ b/src/lorenzpy/plot/plot.py @@ -0,0 +1,39 @@ +"""Plot the data of dynamical systems.""" + +import matplotlib.pyplot as plt +import numpy as np +from mpl_toolkits.mplot3d import Axes3D + + +def create_3d_line_plot(data: np.ndarray, ax: "Axes3D" = None, **kwargs) -> "Axes3D": + """Create a three-dimensional line plot of data. + + Args: + data (np.ndarray): A NumPy array containing 3D data points with shape (n, 3). + ax (Axes3D, optional): A Matplotlib 3D axis to use for plotting. + If not provided, a new 3D plot will be created. + **kwargs: Additional keyword arguments to pass to ax.plot. + + Returns: + Axes3D: The Matplotlib 3D axis used for the plot. + + Example: + >>> data = np.random.rand(100, 3) # Replace this with your own 3D data + >>> create_3d_line_plot(data, color='b', linestyle='--') + >>> plt.show() + """ + if ax is None: + fig = plt.figure() + ax = fig.add_subplot(111, projection="3d") + + x = data[:, 0] + y = data[:, 1] + z = data[:, 2] + + ax.plot(x, y, z, **kwargs) # Use plot for a line plot with kwargs + + ax.set_xlabel("X Axis") + ax.set_ylabel("Y Axis") + ax.set_zlabel("Z Axis") + + return ax diff --git a/src/lorenzpy/plot/plot_3d.py b/src/lorenzpy/plot/plot_3d.py deleted file mode 100644 index 2da2f25..0000000 --- a/src/lorenzpy/plot/plot_3d.py +++ /dev/null @@ -1,17 +0,0 @@ -"""Module to produce three-dimensional plots of time series.""" -import numpy as np -import plotly.graph_objects as go - -DEFAULT_FIGSIZE = (650, 500) - - -def plot_3d(time_series: np.ndarray) -> None: - """Plot simple three-dim time series.""" - fig = go.Figure() - fig.update_layout(height=DEFAULT_FIGSIZE[1], width=DEFAULT_FIGSIZE[0]) - fig.add_trace( - go.Scatter3d( - x=time_series[:, 0], y=time_series[:, 1], z=time_series[:, 2], mode="lines" - ) - ) - fig.show() diff --git a/static/gen_attractor_animation.py b/static/gen_attractor_animation.py index b60e33c..94fb508 100644 --- a/static/gen_attractor_animation.py +++ b/static/gen_attractor_animation.py @@ -18,13 +18,6 @@ "Rucklidge", "Thomas", "WindmiAttractor", - # "DoublePendulum", - # "Lorenz96", - # "Logistic", - # "Henon", - # "SimplestDrivenChaotic", - # "KuramotoSivashinsky", - # "MackeyGlass", ] # create data: @@ -38,9 +31,7 @@ # Plot: plt.style.use("dark_background") fig, axs = plt.subplots(2, 5, figsize=(10, 3), subplot_kw=dict(projection="3d")) -# plt.subplots_adjust(wspace=5) plt.subplots_adjust(hspace=0.5) -# fig.tight_layout() axs = axs.flatten() for i_ax, ax in enumerate(axs): system = systems[i_ax] From 18fafeaaf9697726f0099d26d55806bfc383fd9e Mon Sep 17 00:00:00 2001 From: DuncDennis <90915296+DuncDennis@users.noreply.github.com> Date: Sat, 21 Oct 2023 12:49:20 +0200 Subject: [PATCH 2/5] Added tests and slightly modified mackey_glass. --- src/lorenzpy/simulations/__init__.py | 18 +--------- src/lorenzpy/simulations/others.py | 5 ++- tests/test_simulations.py | 50 ++++++++++++++++++++++++++++ 3 files changed, 53 insertions(+), 20 deletions(-) diff --git a/src/lorenzpy/simulations/__init__.py b/src/lorenzpy/simulations/__init__.py index 5b43bf4..820e510 100644 --- a/src/lorenzpy/simulations/__init__.py +++ b/src/lorenzpy/simulations/__init__.py @@ -28,24 +28,8 @@ >>> data = sims.Lorenz63().simulate(1000) >>> data.shape (1000, 3) - - -TODO - - Probably for each concrete simulation class + public methods. Compare with sklearn - - Find out which functionality is missing. E.g. Raising error when wrong values are - parsed. - - Check where to add proper tests and how to add them efficiently. Fixtures? - Parametrization? - - Implement all the other dynamical systems. - - Check if the names of files and functions make sense? - - Add functionality to add your own dynamical system? As my base-classes are - protected this is maybe not so easy? -> Make ABC public? - - Think about adding NARMA? Maybe I need a random number generator framework. - - Check if I can further reduce code duplication. Maybe regarding solvers. - - Check for proper doc-generation. It seems that the methods of inhereted members - is not implemented yet. See: - https://github.com/mkdocstrings/mkdocstrings/issues/78 """ + from . import solvers from .autonomous_flows import ( Chen, diff --git a/src/lorenzpy/simulations/others.py b/src/lorenzpy/simulations/others.py index 4bbd6cb..c42738f 100644 --- a/src/lorenzpy/simulations/others.py +++ b/src/lorenzpy/simulations/others.py @@ -228,13 +228,12 @@ def simulate( if starting_point.size == self.history_steps + 1: initial_history = starting_point elif starting_point.size == 1: - initial_history = np.repeat(starting_point, self.history_steps) + initial_history = np.repeat(starting_point, self.history_steps + 1) else: raise ValueError("Wrong size of starting point.") traj_w_hist = np.zeros((self.history_steps + time_steps, 1)) - traj_w_hist[: self.history_steps, :] = initial_history[:, np.newaxis] - traj_w_hist[self.history_steps, :] = starting_point + traj_w_hist[: self.history_steps + 1, :] = initial_history[:, np.newaxis] for t in range(1, time_steps + transient): t_shifted = t + self.history_steps diff --git a/tests/test_simulations.py b/tests/test_simulations.py index ae48684..ccd685a 100644 --- a/tests/test_simulations.py +++ b/tests/test_simulations.py @@ -137,6 +137,13 @@ def test_unsupported_solver(): sim_obj.simulate(2) +def test_unsupported_solver_mackey_glass(): + """Test the error raising of an unsupported solver.""" + sim_obj = simulations.MackeyGlass(solver="WRONG_SOLVER") + with pytest.raises(ValueError): + sim_obj.simulate(2) + + def test_custom_solver_as_forward_euler(): """Test a custom solver, which behaves like forward_euler.""" @@ -151,6 +158,20 @@ def custom_solver(flow, dt, x): assert (data_custom == data_forward_euler).all() +def test_custom_solver_as_forward_euler_mackey_glass(): + """Test a custom solver, which behaves like forward_euler for mackey glass.""" + + def custom_solver(flow, dt, x): + # is forward euler + return dt * flow(x) + x + + data_custom = simulations.MackeyGlass(solver=custom_solver).simulate(2) + + data_forward_euler = simulations.MackeyGlass(solver="forward_euler").simulate(2) + + assert (data_custom == data_forward_euler).all() + + def test_simplest_driven_chaotic_time_vs_no_time(): """Test simplest driven chaotic system as an example of a driven system.""" sim_obj = simulations.SimplestDrivenChaotic() @@ -191,3 +212,32 @@ def test_scipy_solvers_lorenz63(solver_method): data_rk4 = simulations.Lorenz63(dt=dt, solver="rk4").simulate(5, starting_point) np.testing.assert_almost_equal(data[-1, 0], data_rk4[-1, 0], decimal=5) + + +def test_long_starting_pnt_mackey_glass(): + """Test the option for long starting_point in mackey_glass.""" + dt = 0.1 + tau = 0.35 + history_steps = int(tau / dt) # 3 + starting_point = np.ones(history_steps + 1) + + data_short_starting_point = simulations.MackeyGlass(dt=dt, tau=tau).simulate( + 10, starting_point=np.array([1]) + ) + + data_long_starting_point = simulations.MackeyGlass(dt=dt, tau=tau).simulate( + 10, starting_point=starting_point + ) + + np.testing.assert_almost_equal(data_short_starting_point, data_long_starting_point) + + +def test_wrong_starting_point_size_mackey_glass(): + """Test ValueError in mackey_glass if long starting pnt is used but wrong shape.""" + dt = 0.1 + tau = 0.35 + starting_point = np.ones(5) # should have length 4 + with pytest.raises(ValueError): + _ = simulations.MackeyGlass(dt=dt, tau=tau).simulate( + 10, starting_point=starting_point + ) From 0017aa8d15b85d037dbf560c4eb20df00ed3ea65 Mon Sep 17 00:00:00 2001 From: DuncDennis <90915296+DuncDennis@users.noreply.github.com> Date: Sat, 21 Oct 2023 15:09:04 +0200 Subject: [PATCH 3/5] Added examples folder and updated project readme. - also added new attractor_animation.gif. --- README.md | 2 + docs/reference.md | 1 + examples/README.md | 8 ++ examples/double_pendulum_lyapunov_spectrum.py | 68 +++++++++++++ ...lyapunov_spectra_of_3d_autonomous_flows.py | 91 ++++++++++++++++++ src/lorenzpy/simulations/autonomous_flows.py | 2 +- static/attractor_animation.gif | Bin 1212275 -> 986014 bytes static/gen_attractor_animation.py | 19 ++-- 8 files changed, 182 insertions(+), 9 deletions(-) create mode 100644 examples/README.md create mode 100644 examples/double_pendulum_lyapunov_spectrum.py create mode 100644 examples/lyapunov_spectra_of_3d_autonomous_flows.py diff --git a/README.md b/README.md index 28fe734..d3ce47a 100644 --- a/README.md +++ b/README.md @@ -58,6 +58,8 @@ lle = lpy.measures.largest_lyapunov_exponent( The calculated largest Lyapunov exponent of *0.9051...* is very close to the literature value of *0.9056*[^SprottChaos]. +For more examples see the [examples folder](examples/README.md). + ## 💫 Supported systems diff --git a/docs/reference.md b/docs/reference.md index bc2a841..095ffc7 100644 --- a/docs/reference.md +++ b/docs/reference.md @@ -3,6 +3,7 @@ ### simulations module: ::: lorenzpy.simulations +::: lorenzpy.simulations.solvers ### measures module: ::: lorenzpy.measures diff --git a/examples/README.md b/examples/README.md new file mode 100644 index 0000000..4a2a57d --- /dev/null +++ b/examples/README.md @@ -0,0 +1,8 @@ +# Examples: + +### Contents +- ``double_pendulum_lyapunov_spectrum.py``: Plot the lyapunov spectrum of the double pendulum. +- ``lyapunov_spectra_of_3d_autonomous_flows.py``: Plot the Lyapunov spectrum of all 3D autonomous dissipative flow systems. + +⚠️ Not many examples here yet, and examples might be flawed. + diff --git a/examples/double_pendulum_lyapunov_spectrum.py b/examples/double_pendulum_lyapunov_spectrum.py new file mode 100644 index 0000000..edd87b6 --- /dev/null +++ b/examples/double_pendulum_lyapunov_spectrum.py @@ -0,0 +1,68 @@ +"""Lyapunov Spectrum of single system.""" + +import matplotlib.pyplot as plt +import numpy as np + +from lorenzpy import measures as meas +from lorenzpy import simulations as sims + +sys_obj = sims.DoublePendulum(dt=0.1) +dt = sys_obj.dt + +# Calculate exponents: +m = 4 +deviation_scale = 1e-10 +steps = 1000 +part_time_steps = 15 +steps_skip = 0 + +iterator_func = sys_obj.iterate +starting_point = sys_obj.get_default_starting_pnt() + +le_spectrum = meas.lyapunov_exponent_spectrum( + iterator_func=iterator_func, + starting_point=starting_point, + deviation_scale=deviation_scale, + steps=steps, + part_time_steps=part_time_steps, + steps_skip=steps_skip, + dt=dt, + m=m, + initial_pert_directions=None, + return_convergence=True, +) + +fig, ax = plt.subplots( + 1, 1, figsize=(6, 6), layout="constrained", sharex=True, sharey=False +) + +# x and y titles: +fig.supxlabel("Number of renormalization steps") +fig.supylabel("Lyapunov exponent convergence") + +x = np.arange(1, steps + 1) +ax.plot( + x, + le_spectrum, + linewidth=1, +) +ax.grid(True) + +final_les = np.round(le_spectrum[-1, :], 4).tolist() +final_les = [str(x) for x in final_les] +le_string = "\n".join(final_les) +le_string = "Final LEs: \n" + le_string +x_position = 0.1 # X-coordinate of the upper-left corner for each subplot +y_position = 0.5 +ax.text( + x_position, + y_position, + le_string, + fontsize=10, + bbox=dict(facecolor="white", edgecolor="black", boxstyle="round"), + verticalalignment="center", + horizontalalignment="left", + transform=ax.transAxes, +) + +plt.show() diff --git a/examples/lyapunov_spectra_of_3d_autonomous_flows.py b/examples/lyapunov_spectra_of_3d_autonomous_flows.py new file mode 100644 index 0000000..019a33f --- /dev/null +++ b/examples/lyapunov_spectra_of_3d_autonomous_flows.py @@ -0,0 +1,91 @@ +"""Calculate and plot the Lyapunov Spectra of all three-dimensional chaotic flows.""" + +import matplotlib.pyplot as plt +import numpy as np + +from lorenzpy import measures as meas +from lorenzpy import simulations as sims + +systems = [ + "Lorenz63", + "Chen", + "ChuaCircuit", + "ComplexButterfly", + "DoubleScroll", + "Halvorsen", + "Roessler", + "Rucklidge", + "Thomas", + "WindmiAttractor", +] + +# Calculate exponents: +m = 3 +deviation_scale = 1e-10 +steps = 1000 +part_time_steps = 15 +steps_skip = 50 + +solver = "rk4" +# solver = sims.solvers.create_scipy_ivp_solver(method="RK45") + +lyap_dict = {} +for i_sys, system in enumerate(systems): + print(system) + sys_obj = getattr(sims, system)(solver=solver) + iterator_func = sys_obj.iterate + starting_point = sys_obj.get_default_starting_pnt() + dt = sys_obj.dt + + lyap_dict[system] = meas.lyapunov_exponent_spectrum( + iterator_func=iterator_func, + starting_point=starting_point, + deviation_scale=deviation_scale, + steps=steps, + part_time_steps=part_time_steps, + steps_skip=steps_skip, + dt=dt, + m=m, + initial_pert_directions=None, + return_convergence=True, + ) + +fig, axs = plt.subplots( + 2, 5, figsize=(15, 8), layout="constrained", sharex=True, sharey=False +) + +# x and y titles: +fig.supxlabel("Number of renormalization steps") +fig.supylabel("Lyapunov exponent convergence") + +axs = axs.flatten() +x = np.arange(1, steps + 1) +for i_ax, ax in enumerate(axs): + system = systems[i_ax] + le_spectrum = lyap_dict[system] + ax.title.set_text(system) + ax.plot( + x, + le_spectrum, + linewidth=1, + ) + ax.grid(True) + + final_les = np.round(le_spectrum[-1, :], 4).tolist() + final_les = [str(x) for x in final_les] + le_string = "\n".join(final_les) + le_string = "Final LEs: \n" + le_string + x_position = 0.1 # X-coordinate of the upper-left corner for each subplot + y_position = 0.5 + ax.text( + x_position, + y_position, + le_string, + fontsize=10, + bbox=dict(facecolor="white", edgecolor="black", boxstyle="round"), + verticalalignment="center", + horizontalalignment="left", + transform=ax.transAxes, + ) + +plt.show() diff --git a/src/lorenzpy/simulations/autonomous_flows.py b/src/lorenzpy/simulations/autonomous_flows.py index 716f659..53b59d3 100644 --- a/src/lorenzpy/simulations/autonomous_flows.py +++ b/src/lorenzpy/simulations/autonomous_flows.py @@ -95,7 +95,7 @@ class ComplexButterfly(_BaseSimFlow): def __init__( self, a: float = 0.55, - dt: float = 0.05, + dt: float = 0.1, solver: 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zS@9Wwa|KXxrOIaDRP8~GI(<9~0xPVMq8BHI*q>qBk54zsvlLBXp{7)&&Eu_>lT6j| zXrRucZnb&som!f&@&Y9e!x=IFbvt1IhdFz_QGl(Vjgd#5Dfaf*LoS050Anf_JGE*8 zjd_MU_Ykzws$boV=#xaFN0q2DeR?CIiRD5AHb48W+L2Aw(tc{hoKH2= z9sG4#4Uvi*)@q4~!8^t?_|&R0#{do*x;pwe_im5!U3~ewWsHKJLf;sC(K?qr7^?m^ D`WcPo diff --git a/static/gen_attractor_animation.py b/static/gen_attractor_animation.py index 94fb508..aaccaa9 100644 --- a/static/gen_attractor_animation.py +++ b/static/gen_attractor_animation.py @@ -21,7 +21,7 @@ ] # create data: -N = 1000 +N = 1500 data_dict = {} for i_sys, system in enumerate(systems): sys_class = sim_class = getattr(sims, system) @@ -37,7 +37,7 @@ system = systems[i_ax] data = data_dict[system] ax.title.set_text(system) - ax.plot(data[:, 0], data[:, 1], data[:, 2], linewidth=0.2, color="white") + ax.plot(data[:, 0], data[:, 1], data[:, 2], linewidth=0.12, color="white") ax.set_xticks([]) # Remove x-axis ticks ax.set_yticks([]) # Remove y-axis ticks ax.set_zticks([]) # Remove y-axis ticks @@ -50,9 +50,9 @@ ax.axis("off") -def update_graph(num): +def update_graph(angle): """Rotate camera angle.""" - azim = num + azim = angle roll = 0 elev = 0 for i_ax, ax in enumerate(axs): @@ -67,9 +67,12 @@ def update_graph(num): for prev_file in previous_files: os.remove(prev_file) -for num in range(0, 360): - update_graph(num) - plt.savefig(f"{frames_dir}/frame_{str(num).zfill(3)}.png", transparent=True, dpi=50) +for num in range(0, 90): + angle = 4 * num + update_graph(angle) + plt.savefig( + f"{frames_dir}/frame_{str(num).zfill(3)}.png", transparent=True, dpi=100 + ) # gif: image_filenames = [ @@ -86,7 +89,7 @@ def update_graph(num): format="GIF", save_all=True, append_images=images[1:], - duration=20, + duration=40, loop=0, transparency=0, disposal=2, From 65f24025cebac337d6c470c07238ca67b20bf547 Mon Sep 17 00:00:00 2001 From: DuncDennis <90915296+DuncDennis@users.noreply.github.com> Date: Sat, 21 Oct 2023 15:18:08 +0200 Subject: [PATCH 4/5] Added v002 entry in changelog. --- CHANGELOG.md | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/CHANGELOG.md b/CHANGELOG.md index 774876b..7b9d72e 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -2,6 +2,15 @@ +### v0.0.2 (21.10.2023) +- Added more Systems. +- Added new Lyapunov spectrum measure. +- Added new simulation backend. +- Added example folder. +- Added static folder to generate animation in readme. +- Changed plotly dependency to matplotlib. +- More smaller improvements... + ### v0.0.1 (16.03.2023) - First release of `lorenzpy` From 64e40fa48df64cb552417094b145fe0007024a0d Mon Sep 17 00:00:00 2001 From: DuncDennis <90915296+DuncDennis@users.noreply.github.com> Date: Sat, 21 Oct 2023 15:20:11 +0200 Subject: [PATCH 5/5] Bump version to 0.0.2. --- pyproject.toml | 2 +- src/lorenzpy/__init__.py | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/pyproject.toml b/pyproject.toml index 033da02..66f0337 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -1,7 +1,7 @@ [project] name = "lorenzpy" readme = "README.md" -version = "0.0.1" +version = "0.0.2" description = "A Python package to simulate and measure chaotic dynamical systems." authors = [ {name = "Dennis Duncan", email = "DuncDennis@gmail.com"}, diff --git a/src/lorenzpy/__init__.py b/src/lorenzpy/__init__.py index 80d29da..ea0578a 100644 --- a/src/lorenzpy/__init__.py +++ b/src/lorenzpy/__init__.py @@ -8,4 +8,4 @@ from . import measures, simulations -__version__ = "0.0.1" +__version__ = "0.0.2"