{ "cells": [ { "cell_type": "markdown", "id": "ae2e642f", "metadata": {}, "source": [ "## Import Packages" ] }, { "cell_type": "code", "execution_count": 1, "id": "ab9f9d01", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import time\n", "from numba import njit" ] }, { "cell_type": "code", "execution_count": 2, "id": "8d6511c4", "metadata": {}, "outputs": [], "source": [ "# Python Version\n", "import sys \n", "sys.path.append('../../')\n", "import evaLEs.LE as ly\n", "# Python + Numba Version\n", "import evaLEs.numbaLE as nly" ] }, { "cell_type": "markdown", "id": "2bd21048", "metadata": {}, "source": [ "## Definition of Dynamical System with Numba" ] }, { "cell_type": "markdown", "id": "f6edc6b8", "metadata": {}, "source": [ "You can use the @njit decorator for numbaLE" ] }, { "cell_type": "code", "execution_count": 3, "id": "13f3e650", "metadata": {}, "outputs": [], "source": [ "@njit\n", "def ODE(t, val, p):\n", " \"\"\"\n", " Define the increment of the Dyn. Syst. in the scipy.integrate.ode way\n", " \"\"\"\n", " x, y = val\n", " diff = [x*p[0] - y, y*p[1] - x] \n", " return np.array(diff)\n", "\n", "@njit\n", "def J(t, val, p):\n", " \"\"\"\n", " The Jacobian of the system (evaluated by you)\n", " \"\"\"\n", " D = len(val)\n", " J = - np.ones((D,D)) + np.eye(D) * ( p + 1 )\n", " return J" ] }, { "cell_type": "markdown", "id": "45e5164e", "metadata": {}, "source": [ "## Define parameters, temporal interval and initial conditions:" ] }, { "cell_type": "code", "execution_count": 4, "id": "59527169", "metadata": {}, "outputs": [], "source": [ "p = np.array([-0.01, -0.03], dtype=np.float64)\n", "init = np.array([0.1, 0.1], dtype=np.float64)\n", "\n", "ttrans = np.arange(0.0, 100, 0.1, dtype=np.float64)\n", "t = np.arange(0.0, 100, 0.01, dtype=np.float64)" ] }, { "cell_type": "markdown", "id": "015d7def", "metadata": {}, "source": [ "## Evaluate the Lyapunov Spectrum" ] }, { "cell_type": "code", "execution_count": 5, "id": "1e78e82f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Exec Time: 4.918744087219238\n", "The LEs are: [ 0.97663367 -1.01663367]\n" ] } ], "source": [ "start = time.time()\n", "LE, sol = nly.computeLE(ODE, J, init, t, p, ttrans)\n", "print(f'Exec Time: {time.time()-start}')\n", "print(f'The LEs are: {LE[-1]}')" ] }, { "cell_type": "markdown", "id": "be69d364", "metadata": {}, "source": [ "Note that the first execution will be slower than the second: let's try another time!" ] }, { "cell_type": "code", "execution_count": 6, "id": "eae99650", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Exec Time: 0.043151140213012695\n", "The LEs are: [ 0.97663367 -1.01663367]\n" ] } ], "source": [ "start = time.time()\n", "LE, sol = nly.computeLE(ODE, J, init, t, p, ttrans)\n", "print(f'Exec Time: {time.time()-start}')\n", "print(f'The LEs are: {LE[-1]}')" ] }, { "cell_type": "markdown", "id": "de90e7bc", "metadata": {}, "source": [ "You can osserve the convergence of the LEs during the algorithm:" ] }, { "cell_type": "code", "execution_count": 7, "id": "e8d2b57b", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 1080x216 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(1, 2, figsize=(15, 3))\n", "for i, (ax, le) in enumerate(zip(axs.flat, LE.T)):\n", " ax.plot(le)\n", " ax.set_title(f'LE {i}')" ] }, { "cell_type": "markdown", "id": "e0339d42", "metadata": {}, "source": [ "## Definition of Dynamical System just in Python" ] }, { "cell_type": "code", "execution_count": 8, "id": "a66c44eb", "metadata": {}, "outputs": [], "source": [ "def ODE(t, val, p):\n", " \"\"\"\n", " Define the increment of the Dyn. Syst. in the scipy.integrate.ode way\n", " \"\"\"\n", " x = val[0]\n", " y = val[1]\n", " diff = [x*p[0] - y, y*p[1] - x] \n", " return np.array(diff)\n", "\n", "def J(t, val, p):\n", " \"\"\"\n", " The Jacobian of the system (evaluated by you)\n", " \"\"\"\n", " D = len(val)\n", " J = - np.ones((D,D)) + np.eye(D) * ( p + 1 )\n", " return J" ] }, { "cell_type": "markdown", "id": "4295894a", "metadata": {}, "source": [ "## Evaluate the Lyapunov Spectrum" ] }, { "cell_type": "code", "execution_count": 9, "id": "e231e8dc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Exec Time: 1.335341215133667\n", "The LEs are: [ 0.97663367 -1.01663367]\n" ] } ], "source": [ "start = time.time()\n", "LE = ly.computeLE(ODE, J, init, t, p, ttrans)\n", "print(f'Exec Time: {time.time()-start}')\n", "print(f'The LEs are: {LE[-1]}')" ] }, { "cell_type": "code", "execution_count": 10, "id": "2704b66f", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 1080x216 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(1, 2, figsize=(15, 3))\n", "for i, (ax, le) in enumerate(zip(axs.flat, LE.T)):\n", " ax.plot(le)\n", " ax.set_title(f'LE {i}')" ] }, { "cell_type": "markdown", "id": "2eb71186", "metadata": {}, "source": [ "## Advanced Examples" ] }, { "cell_type": "markdown", "id": "ccd80360", "metadata": {}, "source": [ "### Lorenz Attractor\n", "\n", "The Lorenz system is defined as:\n", "\n", "$$\\begin{cases}\n", "\\dot{x} = \\sigma(y-x)\\\\\n", "\\dot{y} = x(\\rho-z)-y\\\\\n", "\\dot{z} = xy-\\beta z\n", "\\end{cases}$$\n", "\n", "We can compute the Lyapunov exponent in case of the famous set of parameters: $(\\sigma, \\rho, \\beta) = (10, 28, 8/3)$ starting from a random initial position." ] }, { "cell_type": "code", "execution_count": 30, "id": "c838fe01", "metadata": {}, "outputs": [], "source": [ "@njit\n", "def Lorenz(_, val, p): # no need of the variable t\n", " \"\"\"\n", " Define the increment of the Dyn. Syst. in the scipy.integrate.ode way\n", " \"\"\"\n", " x, y, z = val\n", " sigma, rho, beta = p\n", " diff = [sigma*(y-x), x*(rho-z)-y,x*y - beta*z] \n", " return np.array(diff)\n", "\n", "@njit\n", "def JLorenz(t, val, p):\n", " \"\"\"\n", " The Jacobian of the system (evaluated by you)\n", " \"\"\"\n", " x, y, z = val\n", " sigma, rho, beta = p\n", " J = [[-sigma, sigma, 0 ], \n", " [rho-z, -1 , -x ],\n", " [y , x , -beta]]\n", " return np.array(J)" ] }, { "cell_type": "code", "execution_count": 31, "id": "b7957482", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Exec Time: 3.9550540447235107\n", "The LEs are: [ 9.07900692e-01 -4.96495991e-03 -1.45694998e+01]\n" ] } ], "source": [ "sigma = 10\n", "rho = 28 \n", "beta = 8/3\n", "p = np.array([sigma, rho, beta], dtype=np.float64)\n", "init = np.random.random(3)\n", "\n", "ttrans = np.arange(0.0, 5000, 0.01, dtype=np.float64)\n", "t = np.arange(0.0, 300, 0.01, dtype=np.float64)\n", "\n", "start = time.time()\n", "LE, s = nly.computeLE(Lorenz, JLorenz, init, t, p,ttrans)\n", "print(f'Exec Time: {time.time()-start}')\n", "print(f'The LEs are: {LE[-1]}')" ] }, { "cell_type": "code", "execution_count": 32, "id": "59067a3d", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 576x576 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot\n", "xs = s[:,0]\n", "ys = s[:,1]\n", "zs = s[:,2]\n", "\n", "ax = plt.figure(figsize = (8, 8)).add_subplot(projection='3d')\n", "\n", "ax.plot(xs, ys, zs, lw=0.4)\n", "ax.set_xlabel(\"X Axis\")\n", "ax.set_ylabel(\"Y Axis\")\n", "ax.set_zlabel(\"Z Axis\")\n", "ax.set_title(\"Lorenz Attractor\")\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 14, "id": "924daeda", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 360x360 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(5, 5))\n", "for i, le in enumerate(LE.T):\n", " ax.plot(t[1:], le, label = f'L.E. ~ {LE[-1,i]:.2f}')\n", "ax.set_ylabel('Lyapunov exponents')\n", "ax.set_xlabel('t')\n", "ax.grid(alpha = 0.5)\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c4bdf204", "metadata": {}, "source": [ "### Quality check of the algorithm\n", "The sum of the Lyapunov exponents must be equal to the sum of the diagonal elements of the jacobian:\n", "\n", "$$Tr(J) = -\\sigma - 1 - \\beta$$" ] }, { "cell_type": "code", "execution_count": 15, "id": "ce73979a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sum of diag. elements = -13.666666666666666\n" ] } ], "source": [ "Tr = - sigma - 1 - beta\n", "print(\"Sum of diag. elements = \", Tr)" ] }, { "cell_type": "code", "execution_count": 16, "id": "f879265d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sum of Lyapunov Exponents = -13.666563901674888\n" ] } ], "source": [ "SumLyap = np.sum(LE[-1, :])\n", "print('Sum of Lyapunov Exponents = ', SumLyap)" ] }, { "cell_type": "markdown", "id": "fc8b9771", "metadata": {}, "source": [ "### Rossler attractor\n", "\n", "\n", "$$\\begin{cases}\n", "\\dot{x} = -y-z\\\\\n", "\\dot{y} = x + ay\\\\\n", "\\dot{z} = b + z(x-c)\n", "\\end{cases}$$\n" ] }, { "cell_type": "code", "execution_count": 44, "id": "1bac3c0d", "metadata": {}, "outputs": [], "source": [ "@njit\n", "def Rossler(_, val, p): # no need for variable t\n", " \"\"\"\n", " Define the increment of the Dyn. Syst. in the scipy.integrate.ode way\n", " \"\"\"\n", " x, y, z = val\n", " a, b, c = p\n", " diff = [- y - z, x + a * y, b + z * (x - c)] \n", " return np.array(diff)\n", "\n", "@njit\n", "def JRossler(_, val, p):\n", " \"\"\"\n", " The Jacobian of the system (evaluated by you)\n", " \"\"\"\n", " x, y, z = val\n", " a, b, c = p\n", " J = [[0. , -1. , -1. ], \n", " [1. , a , 0. ],\n", " [z , 0. , x - c ]]\n", " return np.array(J)" ] }, { "cell_type": "code", "execution_count": 47, "id": "c726d599", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Exec Time: 1.750584363937378\n", "The LEs are: [ 7.07056327e-02 1.18526517e-03 -5.39109601e+00]\n" ] } ], "source": [ "a = 0.2\n", "b = 0.2\n", "c = 5.7\n", "p = np.array([a, b, c], dtype=np.float64)\n", "init = np.random.random(3).astype(np.float64)\n", "\n", "ttrans = np.arange(0.0, 5000, 0.01, dtype=np.float64)\n", "t = np.arange(0.0, 3000, 0.01, dtype=np.float64)\n", "\n", "start = time.time()\n", "LE, s = nly.computeLE(Rossler, JRossler, init, t, p, ttrans)\n", "print(f'Exec Time: {time.time()-start}')\n", "print(f'The LEs are: {LE[-1]}')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.4" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 5 }