From 6b06be4a6bcf77512ee97931a870c57cddbf02a0 Mon Sep 17 00:00:00 2001 From: Yael-II <154762804+Yael-II@users.noreply.github.com> Date: Sun, 19 Jan 2025 17:31:02 +0100 Subject: [PATCH] update --- Source/{main_yael.py => TODEL_main_yael.py} | 4 +- ...oincare_test.py => TODEL_poincare_test.py} | 0 Source/energies.py | 18 +++- Source/initial_conditions.py | 66 ++++++++++-- Source/integrator.py | 33 ++++-- Source/plot_area.py | 78 ++++++++++++++ Source/plot_poincare_sections.py | 4 + Source/plot_poincare_sections_zoom.py | 101 ++++++++++++++++++ Source/poincare_sections.py | 26 ++++- Source/potentials.py | 31 ++++-- Source/test_evolution.py | 2 + Source/test_initial_E.py | 2 + Source/test_potentials.py | 4 + area.pdf | Bin 9980 -> 279374 bytes evolution.png | Bin 0 -> 286156 bytes initial_E.png | Bin 0 -> 147833 bytes mu.pdf | Bin 46179 -> 626063 bytes pcs_linear.pdf | Bin 0 -> 1041673 bytes pcs_parallel.pdf | Bin 0 -> 1042410 bytes pcs_zoom_1_linear.pdf | Bin 0 -> 619599 bytes pcs_zoom_1_parallel.pdf | Bin 0 -> 620382 bytes pcs_zoom_2_linear.pdf | Bin 0 -> 630536 bytes pcs_zoom_2_parallel.pdf | Bin 0 -> 630944 bytes pcs_zoom_3_linear.pdf | Bin 0 -> 488037 bytes pcs_zoom_3_parallel.pdf | Bin 0 -> 488013 bytes pot_hh.png | Bin 0 -> 118413 bytes pot_kepler.png | Bin 0 -> 59247 bytes 27 files changed, 337 insertions(+), 32 deletions(-) rename Source/{main_yael.py => TODEL_main_yael.py} (98%) rename Source/{poincare_test.py => TODEL_poincare_test.py} (100%) create mode 100644 Source/plot_area.py create mode 100644 Source/plot_poincare_sections_zoom.py create mode 100644 evolution.png create mode 100644 initial_E.png create mode 100644 pcs_linear.pdf create mode 100644 pcs_parallel.pdf create mode 100644 pcs_zoom_1_linear.pdf create mode 100644 pcs_zoom_1_parallel.pdf create mode 100644 pcs_zoom_2_linear.pdf create mode 100644 pcs_zoom_2_parallel.pdf create mode 100644 pcs_zoom_3_linear.pdf create mode 100644 pcs_zoom_3_parallel.pdf create mode 100644 pot_hh.png create mode 100644 pot_kepler.png diff --git a/Source/main_yael.py b/Source/TODEL_main_yael.py similarity index 98% rename from Source/main_yael.py rename to Source/TODEL_main_yael.py index d233716..82f551d 100644 --- a/Source/main_yael.py +++ b/Source/TODEL_main_yael.py @@ -98,7 +98,7 @@ ax.set_xlabel("energy E") ax.set_ylabel("quantity mu") fig.tight_layout() -fig.savefig("mu") +# fig.savefig("mu") fig, ax = plt.subplots(1) ax.scatter(all_E, A, color="C0", s=5, marker="o", label="Data") @@ -106,7 +106,7 @@ ax.set_xlabel("energy E") ax.set_ylabel("area A") ax.legend() fig.tight_layout() -fig.savefig("area") +# fig.savefig("area") plt.show() diff --git a/Source/poincare_test.py b/Source/TODEL_poincare_test.py similarity index 100% rename from Source/poincare_test.py rename to Source/TODEL_poincare_test.py diff --git a/Source/energies.py b/Source/energies.py index d3cffee..354d923 100644 --- a/Source/energies.py +++ b/Source/energies.py @@ -1,9 +1,23 @@ +#!/usr/bin/env python +""" +Energies + +Compute energies (kinetic or total) + +@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student) +@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique + de Strasbourg, UMR 7550, F-67000 Strasbourg, France +@ Date: 2024-12-13 +""" + import numpy as np def kinetic(W: np.ndarray) -> np.ndarray: """Computes the kinetic energy. - :param W: Phase-space vectors - :returns T: Kinetic energy + @param + - W: Phase-space vectors + @returns + - T: Kinetic energy """ U = W[1,0] V = W[1,1] diff --git a/Source/initial_conditions.py b/Source/initial_conditions.py index 2ae0cd8..4f48950 100644 --- a/Source/initial_conditions.py +++ b/Source/initial_conditions.py @@ -1,3 +1,15 @@ +#!/usr/bin/env python +""" +Initial Conditions + +Generate initial conditions depending on different criteria + +@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student) +@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique + de Strasbourg, UMR 7550, F-67000 Strasbourg, France +@ Date: 2024-11-29 +""" + import numpy as np import matplotlib.pyplot as plt POS_MIN = -1 @@ -12,12 +24,14 @@ def mesh_grid(N: int = N_PART, ymin: float = POS_MIN, ymax: float = POS_MAX) -> np.ndarray: """Generates a set of regularly sampled particles with no velocity - :param N: number of particles - :parma xmin: Minimum value for position x - :param xmax: Maximum value for position x - :param ymin: Minimum value for position y - :param ymax: Maximum value for position y - :returns W: Phase-space vector + @ params: + - N: number of particles + - xmin: minimum value for position x + - xmax: maximum value for position x + - ymin: minimum value for position y + - ymax: maximum value for position y + @ returns: + - W: phase-space vector """ X = np.linspace(xmin, xmax, N) Y = np.linspace(ymin, ymax, N) @@ -30,10 +44,14 @@ def one_part(x0: float = 0, v0: float = 0) -> np.ndarray: """Generates a particle at position (x0, y0) with velocities (u0,v0) - :param x0: Initial position x - :param y0: Initial position y - :param u0: Initial velocity u - :param v0: Initial velocity v + @ params: + - N: number of particles + - x0: initial position x + - y0: initial position y + - u0: initial velocity u + - v0: initial velocity v + @ returns: + - W: phase-space vector """ X = x0 Y = y0 @@ -48,6 +66,18 @@ def n_energy_part(potential, xmax: float = +1, ymin: float = -0.5, ymax: float = +1): + """Generates N particles with an energy E in a potential. + @ params: + - potential: gravitational potential + - N: number of particles + - E: total energy + - xmin: minimum value for position x + - xmax: maximum value for position x + - ymin: minimum value for position y + - ymax: maximum value for position y + @ returns: + - W: an array of all the positions and velocities. + """ X = [] Y = [] POT = [] @@ -81,6 +111,22 @@ def n_energy_2part(potential, xmax: float = +1, ymin: float = -0.5, ymax: float = +1): + """Generate a sample of 2N particles with the energy E in a potential in + two sets: one "normal" set (see n_energy_part), and a slightly shifted set + with a separation sep. + @ params: + - potential: gravitational potential + - N: number of particles + - E: total energy + - sep: the separation between the two sets + - xmin: minimum value for position x + - xmax: maximum value for position x + - ymin: minimum value for position y + - ymax: maximum value for position y + @ returns: + - (W1, W2): the two arrays of all the positions and velocities for + each set. + """ W_1 = n_energy_part(potential, N, E) W_2 = np.zeros_like(W_1) alpha = np.random.uniform(0, 2*np.pi, N) diff --git a/Source/integrator.py b/Source/integrator.py index 527d6da..ceb765a 100644 --- a/Source/integrator.py +++ b/Source/integrator.py @@ -1,7 +1,18 @@ +#!/usr/bin/env python +""" +Integrator + +Integrate differential equations. + +@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student) +@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique + de Strasbourg, UMR 7550, F-67000 Strasbourg, France +@ Date: 2024-11-29 +""" import numpy as np def euler(x0, y0, h, n, func): # FIXME cannot be used with vectors - """ + """DEPRECIATED - DO NOT USE Euler method adapted for state vector [[x, y], [u, v]] :param x0: initial time value :param y0: initial state vector [[x, y], [u, v]] @@ -25,7 +36,7 @@ def euler(x0, y0, h, n, func): # FIXME cannot be used with vectors # Updated RK2 integrator def rk2(x0, y0, h, n, func): # FIXME cannot be used with vectors - """ + """ DEPRECIATED - DO NOT USE RK2 method adapted for state vector [[x, y], [u, v]] :param x0: initial time value :param y0: initial state vector [[x, y], [u, v]] @@ -54,14 +65,15 @@ def rk4(t0: float, h: float, n: int, func): - """ - RK4 method adapted for state vector [[x, y], [u, v]] - :param x0: initial time value - :param y0: initial state vector [[x, y], [u, v]] - :param h: step size (time step) - :param n: number of steps - :param func: RHS of differential equation - :returns: x array, solution array + """RK4 method adapted for state vector [[x, y], [u, v]] + @ params + - x0: initial time value + - y0: initial state vector [[x, y], [u, v]] + - h: step size (time step) + - n: number of steps + - func: RHS of differential equation + @returns: + - t, W: time and state (solution) arrays, """ time = np.zeros(n) W = np.zeros((n,) + np.shape(W0)) @@ -84,4 +96,5 @@ def rk4(t0: float, def integrator_type(x0, y0, h, n, func, int_type): + """DEPRECIATED - DO NOT USE""" return int_type(x0, y0, h, n, func) diff --git a/Source/plot_area.py b/Source/plot_area.py new file mode 100644 index 0000000..e942745 --- /dev/null +++ b/Source/plot_area.py @@ -0,0 +1,78 @@ +#!/usr/bin/env python +""" +Plot: Area + +Plots areas + +@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student) +@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique + de Strasbourg, UMR 7550, F-67000 Strasbourg, France +@ Date: 2024-11-29 +""" +import os +import numpy as np +import matplotlib.pyplot as plt + +if "YII_1" in plt.style.available: plt.style.use("YII_1") + +OUT_DIR = "./Output/" +FILENAME_PREFIX = "phase_separation_" +EXTENSION = ".csv" + +def plot_area(filelist: list, mu_c = 1e-4) -> int: + """ + Plot all the Poincaré sections in the file list. + @params: + - filelist: the list of files in the output directory, with the format + "poincare_sections_{linear, parallel}_[1/E].csv" + - title: title of the figure + @returns: + - 0. + """ + orderlist = np.argsort([(int(file + .replace(FILENAME_PREFIX, "") + .replace(EXTENSION, ""))) + for file in filelist]) + filelist = np.array(filelist)[orderlist] + N = len(filelist) + E = np.linspace(1/100, 1/6, N) + mu = [] + for filename in filelist: + with open(OUT_DIR + filename) as file: + data = file.readlines() + data = [np.float64(d.replace("\n", "")) for d in data] + mu.append(data) + mu = np.array(mu) + + fig, ax = plt.subplots(1) + ax.scatter([], [], s=1, color="k", label="Data") + for i in range(len(mu)): + Y = mu[i] + ax.scatter([E[i]]*len(Y), Y, s=1, color="k", alpha=0.1) + ax.scatter(E, np.mean(mu, axis=1), s=5, + color="C1", marker="o", label="Mean") + ax.scatter(E, np.median(mu, axis=1), s=5, + color="C3", marker="s", label="Median") + ax.plot(E, [mu_c]*len(E), + color="C5", label="Critical value $\\mu_\\mathrm{{c}}$") + ax.text(0.01, 1e-5, "Regular", va="bottom", ha="left", color="C5") + ax.text(0.01, 1e-3, "Chaotic", va="top", ha="left", color="C5") + ax.set_xlabel("Energy $E$") + ax.set_ylabel("Phase-space squared distance $\\mu$") + ax.set_yscale("log") + ax.legend() + fig.savefig("mu.pdf") + + fig, ax = plt.subplots(1) + N_reg = np.count_nonzero(mu < mu_c, axis=1) + N = np.shape(mu)[1] + Area = N_reg / N + ax.scatter(E, Area, s=5, color="C0") + ax.set_xlabel("Energy $E$") + ax.set_ylabel("Area $N_\\mathrm{{reg}}/N_\\mathrm{{part}}$") + fig.savefig("area.pdf") + return 0 + +filelist = [f for f in os.listdir(OUT_DIR) if FILENAME_PREFIX in f] +plot_area(filelist) +plt.show() diff --git a/Source/plot_poincare_sections.py b/Source/plot_poincare_sections.py index fb60c09..f74b9cc 100644 --- a/Source/plot_poincare_sections.py +++ b/Source/plot_poincare_sections.py @@ -61,6 +61,10 @@ def plot_poincare_sections(filelist: list, title:str = "") -> int: while i < N: i += 1 axs[i].axis('off') + if "linear" in title: kind = "linear" + elif "parallel" in title: kind = "parallel" + else: kind = "error" + fig.savefig("pcs_{}.pdf".format(kind)) return 0 print("\033[32m" + "[P]arallel or [L]inear algorithm result, or [B]oth?" diff --git a/Source/plot_poincare_sections_zoom.py b/Source/plot_poincare_sections_zoom.py new file mode 100644 index 0000000..a338fd4 --- /dev/null +++ b/Source/plot_poincare_sections_zoom.py @@ -0,0 +1,101 @@ +#!/usr/bin/env python +""" +Plot: Poincaré Sections (Linear and Parallel) + +Plots the Poincaré sections for different energies, computed either with linear +or parallel algorithms. + +@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student) +@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique + de Strasbourg, UMR 7550, F-67000 Strasbourg, France +@ Date: 2024-11-29 +""" +import os +import numpy as np +import matplotlib.pyplot as plt + +if "YII_1" in plt.style.available: plt.style.use("YII_1") + +OUT_DIR = "./Output/" +FILENAME_PREFIX = "poincare_sections_" +EXTENSION = ".csv" + +def plot_poincare_sections(filelist: list, title:str = "") -> int: + """ + Plot all the Poincaré sections in the file list. + @params: + - filelist: the list of files in the output directory, with the format + "poincare_sections_{linear, parallel}_[1/E].csv" + - title: title of the figure + @returns: + - 0. + """ + orderlist = np.argsort([(int(file + .replace(FILENAME_PREFIX, "") + .replace(EXTENSION, "") + .replace("linear_", "") + .replace("parallel_", ""))) + for file in filelist]) + filelist = np.array(filelist)[orderlist] + N = len(filelist) + #fig, axs = plt.subplot_mosaic("ABC\nDEF") + fig1, axs1 = plt.subplot_mosaic("AB") + fig2, axs2 = plt.subplot_mosaic("CD") + fig3, axs3 = plt.subplot_mosaic("EF") + + axs = list(axs1.values()) + list(axs2.values()) + list(axs3.values()) + fig1.suptitle(title) + fig2.suptitle(title) + fig3.suptitle(title) + for i in range(N): + ax = axs[i] + filename = filelist[i] + inv_E = (filename + .replace(FILENAME_PREFIX, "") + .replace(EXTENSION, "") + .replace("linear_", "") + .replace("parallel_", "")) + data = np.loadtxt(OUT_DIR + filename) + y_section = data[0] + v_section = data[1] + ax.scatter(y_section, v_section, + s=.1, color="C3", marker=",", alpha=0.5, + label="$E = 1/{}$".format(inv_E)) + ax.set_xlabel("$y$") + ax.set_ylabel("$v$") + ax.legend(loc="upper right") + while i < N: + i += 1 + axs[i].axis('off') + if "linear" in title: kind = "linear" + elif "parallel" in title: kind = "parallel" + else: kind = "error" + fig1.savefig("pcs_zoom_1_{}.pdf".format(kind)) + fig2.savefig("pcs_zoom_2_{}.pdf".format(kind)) + fig3.savefig("pcs_zoom_3_{}.pdf".format(kind)) + return 0 + +print("\033[32m" + + "[P]arallel or [L]inear algorithm result, or [B]oth?" + + "\033[0m") +answer = input("\033[32m" + "> " + "\033[0m").upper() + +if answer == "P": + FILENAME_PREFIX += "parallel_" +elif answer == "L": + FILENAME_PREFIX += "linear_" + +filelist = [fname for fname in os.listdir(OUT_DIR) if FILENAME_PREFIX in fname] + +if answer in ["L", "B"]: + filelist_linear = [fname for fname in filelist if "linear_" in fname] + plot_poincare_sections(filelist_linear, + title=("Poincaré Sections " + "(results from the linear algorithm)")) +if answer in ["P", "B"]: + filelist_parallel = [fname for fname in filelist if "parallel_" in fname] + plot_poincare_sections(filelist_parallel, + title=("Poincaré Sections " + "(results from the parallel algorithm)")) + +plt.show() diff --git a/Source/poincare_sections.py b/Source/poincare_sections.py index 85828f0..1ec7d07 100644 --- a/Source/poincare_sections.py +++ b/Source/poincare_sections.py @@ -1,5 +1,27 @@ +#!/usr/bin/env python +""" +Poincaré Sections + +Computes the Poincaré Sections + +@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student) +@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique + de Strasbourg, UMR 7550, F-67000 Strasbourg, France +@ Date: 2024-11-29 +""" + import numpy as np def pcs_find(pos_x, pos_y, vel_x, vel_y): + """Find Poincaré sections (PCS; x = 0) + @ params: + - pos_x: position along the x axis + - pos_y: position along the y axis + - pos_x: velocity along the x axis + - pos_y: velocity along the y axis + @ returns: (tuple) + - pcs_pos_y: position of the points in the PCS along the y axis + - pcs_vel_y: velocity of the points in the PCS along the y axis + """ if np.ndim(pos_x) == 1: pos_x = np.array([pos_x]) pos_y = np.array([pos_y]) @@ -25,8 +47,10 @@ def pcs_find(pos_x, pos_y, vel_x, vel_y): pcs_vel_y.append(v0) i += 1 return pcs_pos_y, pcs_vel_y + def pcs_find_legacy(pos_x, pos_y, vel_x, vel_y): - """Depreciated legacy function that should not be used + """DEPRECIATED - DO NOT USE + Depreciated legacy function that should not be used """ if np.ndim(pos_x) == 1: pos_x = np.array([pos_x]) diff --git a/Source/potentials.py b/Source/potentials.py index 282a9e4..d81d996 100644 --- a/Source/potentials.py +++ b/Source/potentials.py @@ -1,3 +1,15 @@ +#!/usr/bin/env python +""" +Potentials + +Functions of the different potentials (and their derivatives for the evolution) + +@ Author: Moussouni, Yaël (MSc student) & Bhat, Junaid Ramzan (MSc student) +@ Institution: Université de Strasbourg, CNRS, Observatoire astronomique + de Strasbourg, UMR 7550, F-67000 Strasbourg, France +@ Date: 2024-11-29 +""" + import numpy as np MAX_VAL = 1e3 @@ -11,7 +23,7 @@ def kepler_potential(W_grid: np.ndarray, - W: Phase-space vector - position_only: True if W is np.array([X, Y]) @returns: - - V: computed potential + - computed potential """ if position_only: X = W_grid[0] @@ -29,8 +41,11 @@ def kepler_potential(W_grid: np.ndarray, def hh_potential(W_grid: np.ndarray, position_only=False) -> np.ndarray: """Computes the Hénon-Heiles potential. - :param W: Phase-space vector - :output V: Potential + @params: + - W: Phase-space vector + - position_only: True if W is np.array([X, Y]) + @returns: + - POT: Potential """ if position_only: X = W_grid[0] @@ -48,10 +63,12 @@ def hh_potential(W_grid: np.ndarray, return POT def hh_evolution(t: np.ndarray, W: np.ndarray): - """Computes the evolution from the HH potential - :param t: Time (not used) - :param W: Phase space vector - :returns dot W: Time derivative of the phase space vector + """Computes the evolution from the HH potential derivative + @params + - t: Time (not used) + - W: Phase space vector + &returns + - dot W: Time derivative of the phase space vector """ X = W[0 ,0] Y = W[0, 1] diff --git a/Source/test_evolution.py b/Source/test_evolution.py index 33b88a3..08e9ab5 100644 --- a/Source/test_evolution.py +++ b/Source/test_evolution.py @@ -64,6 +64,8 @@ if __name__ == "__main__": ax.set_ylabel("$y$") ax.set_aspect("equal") + plt.savefig("evolution.png") + plt.show(block=True) diff --git a/Source/test_initial_E.py b/Source/test_initial_E.py index 3c27ed5..9098e51 100644 --- a/Source/test_initial_E.py +++ b/Source/test_initial_E.py @@ -48,6 +48,8 @@ if __name__ == "__main__": ax.set_ylabel("$y$") ax.set_aspect("equal") + fig.savefig("initial_E.png") + plt.show(block=True) diff --git a/Source/test_potentials.py b/Source/test_potentials.py index 84f923c..b205dbc 100644 --- a/Source/test_potentials.py +++ b/Source/test_potentials.py @@ -32,6 +32,8 @@ def kepler(W): ax.set_aspect("equal") ax.set_xlabel("$x$") ax.set_ylabel("$y$") + + fig.savefig("pot_kepler.png") return 0 def hh(W): @@ -46,6 +48,8 @@ def hh(W): ax.set_aspect("equal") ax.set_xlabel("$x$") ax.set_ylabel("$y$") + + fig.savefig("pot_hh.png") return 0 if __name__ == "__main__": diff --git a/area.pdf 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