{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The Simple Harmonic Oscillator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we will expand on the harmonic oscillator first shown in the getting started script. I'll walk you through some of the features of desolver and hopefully give a better a sense of how to use the software.\n", "\n", "So let's begin!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we import the libraries we'll need. I import all the matplotlib machinery using the magic command `%matplotlib`, but this is only for notebook/ipython environments.\n", "\n", "Then I import `desolver` and `numpy` for specifying our problem." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Using `autoray` backend\n" ] } ], "source": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt\n", "\n", "import desolver as de\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Specifying the Dynamical System" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's specify the right hand side of our dynamical system. It should be\n", "\n", "$$\n", "\\frac{\\mathrm{d^2}x}{\\mathrm{dt}^2} = -\\frac{k}{m} x\n", "$$\n", "\n", "But desolver only works with first order differential equations, thus we must cast this into a first order system before we can solve it. Thus we obtain the following system\n", "\n", "$$\n", "\\begin{array}{l}\n", "\\frac{\\mathrm{d}x}{\\mathrm{dt}} = v_x \\\\\n", "\\frac{\\mathrm{d}v_x}{\\mathrm{dt}} = -\\frac{k}{m} x\n", "\\end{array}\n", "$$\n", "\n", "which can be specified as a simple matrix equation as\n", "\n", "$$\n", "\\begin{array}{c}\n", "\\frac{\\mathrm{d}y}{\\mathrm{dt}} = \\begin{bmatrix}\n", " 0 & 1 \\\\\n", " -\\frac{k}{m} & 0\n", " \\end{bmatrix} \\cdot \\vec y \\\\\n", "\\vec y = \\begin{bmatrix}x \\\\ v_x\\end{bmatrix}\n", "\\end{array}\n", "$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "@de.rhs_prettifier(\n", " equ_repr=\"[vx, -k*x/m]\",\n", " md_repr=r\"\"\"\n", "$$\n", "\\frac{\\mathrm{d}y}{\\mathrm{dt}} = \\begin{bmatrix}\n", " 0 & 1 \\\\\n", " -\\frac{k}{m} & 0\n", " \\end{bmatrix} \\cdot \\vec y\n", "$$\n", "\"\"\"\n", ")\n", "def rhs(t, state, k, m, **kwargs):\n", " return np.array([[0.0, 1.0], [-k/m, 0.0]])@state" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First thing to notice is that we used the backend to specify the matrix and minimise the use of numpy specific machinery. This isn't necessary if you only use numpy, but by doing this we can make this code run with the pytorch backend with minimal effort.\n", "\n", "Second thing is the use of the decorator `@de.rhs_prettifier`, this is a convenience decorator that allows me to specify a text representation of the differential equations. Convenient if I want to print it" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "$$\n", "\\frac{\\mathrm{d}y}{\\mathrm{dt}} = \\begin{bmatrix}\n", " 0 & 1 \\\\\n", " -\\frac{k}{m} & 0\n", " \\end{bmatrix} \\cdot \\vec y\n", "$$\n", "\n" ] } ], "source": [ "print(rhs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or if I want it to look pretty when it is rendered in the notebook" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "\n", "$$\n", "\\frac{\\mathrm{d}y}{\\mathrm{dt}} = \\begin{bmatrix}\n", " 0 & 1 \\\\\n", " -\\frac{k}{m} & 0\n", " \\end{bmatrix} \\cdot \\vec y\n", "$$\n" ], "text/plain": [ ",\n", "$$\n", "\\frac{\\mathrm{d}y}{\\mathrm{dt}} = \\begin{bmatrix}\n", " 0 & 1 \\\\\n", " -\\frac{k}{m} & 0\n", " \\end{bmatrix} \\cdot \\vec y\n", "$$\n", ",\n", "$$\n", "\\frac{\\mathrm{d}y}{\\mathrm{dt}} = \\begin{bmatrix}\n", " 0 & 1 \\\\\n", " -\\frac{k}{m} & 0\n", " \\end{bmatrix} \\cdot \\vec y\n", "$$\n", ")>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(rhs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's specify the initial conditions as well" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "y_init = np.array([1., 0.])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now we're ready to integrate!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Numerical Integration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are a number of things we must choose before we numerically integrate our system of equations. The first of these is whether or not we want an interpolating spline so that we can compute the state of our system between timesteps. The second is the duration of the numerical integration. And the third is the value of parameters of the system: `k` and `m`. \n", "\n", "Unlike scipy, desolver let's you specify a dictionary of constants that are passed to the `rhs` function and can be modified even after constructing the `OdeSystem` object. This is particularly useful if you want to vary a single constant over multiple integrations without changing any other parameters.\n", "\n", "Now, we'll set the numerical integration to 1 cycle of the oscillator at `k=1` and `m=1` which, when computed from the formula $T=2\\pi\\sqrt{\\frac{k}{m}}$, is exactly $2\\pi$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "a = de.OdeSystem(rhs, y0=y_init, dense_output=True, t=(0, 2*np.pi), dt=0.01, rtol=1e-9, atol=1e-9, constants=dict(k=1.0, m=1.0))" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "a.integrate()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since `k=1` and `m=1` and we integrated for 1 cycle, we expect that the final state of the system is the same as the initial state." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial state = [1. 0.]\n", "final state = [ 1.00000000e+00 -7.77490676e-11]\n", "maximum absolute difference = 2.372387619686833e-09\n" ] } ], "source": [ "print(\"initial state = {}\".format(a[0].y))\n", "print(\"final state = {}\".format(a[-1].y))\n", "print(\"maximum absolute difference = {}\".format(np.max(np.abs(a[-1].y - a[0].y))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wonderful! We see that the final state is almost exactly the same. Furthermore, we see that this is within the tolerances we specified when creating the `OdeSystem` where we set `rtol` and `atol` to `1e-9`.\n", "\n", "To show you that this is not a fluke, we'll change them to `1e-12` and see what happens." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "a.rtol = 1e-12\n", "a.atol = 1e-12\n", "a.reset()\n", "a.integrate()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial state = [1. 0.]\n", "final state = [ 1.00000000e+00 -2.07681095e-14]\n", "maximum absolute difference = 2.4020785360789887e-12\n" ] } ], "source": [ "print(\"initial state = {}\".format(a[0].y))\n", "print(\"final state = {}\".format(a[-1].y))\n", "print(\"maximum absolute difference = {}\".format(np.max(np.abs(a[-1].y - a[0].y))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's very simple to change the tolerances and rerun the system. Furthermore, we can update our constants and see what happens.\n", "\n", "If we quadruple `k`, the spring constant, the period will double, and so after an integration period of $2\\pi$ the system should, yet again, be in a final state that is almost exactly the initial state." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "a.constants['k'] = a.constants['k'] * 4\n", "a.reset()\n", "a.integrate()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial state = [1. 0.]\n", "final state = [ 1.00000000e+00 -8.61394289e-14]\n", "maximum absolute difference = 6.02984329134415e-12\n" ] } ], "source": [ "print(\"initial state = {}\".format(a[0].y))\n", "print(\"final state = {}\".format(a[-1].y))\n", "print(\"maximum absolute difference = {}\".format(np.max(np.abs(a[-1].y - a[0].y))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The final state is again almost the same as the initial state, but now the maximum absolute difference has increasenp. This is due to the fact that the numerical error when using an adaptive runge-kutta method is not a random walk, but a function of the whole numerical procedure. Thus if we double the initial integration time, and set `k=1` again, we'll see that the error is larger." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "a.constants['k'] = 1\n", "a.tf = 4*np.pi\n", "a.reset()\n", "a.integrate()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial state = [1. 0.]\n", "final state = [ 1.0000000e+00 -4.1498055e-14]\n", "maximum absolute difference = 4.810818410305728e-12\n" ] } ], "source": [ "print(\"initial state = {}\".format(a[0].y))\n", "print(\"final state = {}\".format(a[-1].y))\n", "print(\"maximum absolute difference = {}\".format(np.max(np.abs(a[-1].y - a[0].y))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The longer we integrate for, the larger this error will become. Is there anything we can do?\n", "\n", "**YES**\n", "\n", "We can use a symplectic integrator since this is a system with a Hamiltonian $H=\\frac{kx^2}{2} + \\frac{mv_x^2}/2$.\n", "\n", "A symplectic integrator preserves the symplectic two-form $\\mathrm{d}\\vec p \\wedge\\mathrm{d}\\vec q$ where $p$ is the momentum and $q$ is the position such that\n", "\n", "$$\n", "\\begin{array}{l}\n", "\\frac{\\mathrm{d}p}{\\mathrm{dt}} = -\\frac{\\partial H}{\\partial q} \\\\\n", "\\frac{\\mathrm{d}q}{\\mathrm{dt}} = \\frac{\\partial H}{\\partial p}\n", "\\end{array}\n", "$$\n", "\n", "where, in our case, $v_x = \\frac{p}{m}$ and $x = q$.\n", "\n", "Why is this important? I'll leave the detailed theory to [Wikipedia](https://en.wikipedia.org/wiki/Symplectic_integrator) and other sources, but the jist of it is that a symplectic integrator is essentially a geometric transformation in the phase space of the system and thus preserves the differential volume element of a Hamiltonian that is almost, but not quite, the Hamiltonian of the system.\n", "\n", "This is great because it means that, in the best case scenario, the errors in the numerically integrated states are random walks instead of increasing linearly with the integration time. The downside is that a symplectic integrator is not adaptive and thus requires more function evaluations than a Runge-Kutta methonp." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/workspaces/desolver/desolver/utilities/utilities.py:216: RuntimeWarning: An integration was already run, this will not reset the system\n", " warnings.warn(message, category=category)\n" ] } ], "source": [ "a.set_method(\"BABS9O7H\")\n", "a.dt = 0.05\n", "a.tf = 2*np.pi\n", "a.reset()\n", "a.integrate()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial state = [1. 0.]\n", "final state = [ 1.00000000e+00 -8.97658683e-14]\n", "maximum absolute difference = 8.976586834963385e-14\n" ] } ], "source": [ "print(\"initial state = {}\".format(a[0].y))\n", "print(\"final state = {}\".format(a[-1].y))\n", "print(\"maximum absolute difference = {}\".format(np.max(np.abs(a[-1].y - a[0].y))))" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "a.set_method(\"BABS9O7H\")\n", "a.dt = 0.05\n", "a.tf = 8*np.pi\n", "a.integrate()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial state = [1. 0.]\n", "final state = [1.00000000e+00 1.37161116e-13]\n", "maximum absolute difference = 1.3716111579853418e-13\n" ] } ], "source": [ "print(\"initial state = {}\".format(a[0].y))\n", "print(\"final state = {}\".format(a[-1].y))\n", "print(\"maximum absolute difference = {}\".format(np.max(np.abs(a[-1].y - a[0].y))))" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "a.set_method(\"BABS9O7H\")\n", "a.dt = 0.05\n", "a.tf = 32*np.pi\n", "a.integrate()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial state = [1. 0.]\n", "final state = [ 1.00000000e+00 -3.68112485e-12]\n", "maximum absolute difference = 3.681124849386208e-12\n" ] } ], "source": [ "print(\"initial state = {}\".format(a[0].y))\n", "print(\"final state = {}\".format(a[-1].y))\n", "print(\"maximum absolute difference = {}\".format(np.max(np.abs(a[-1].y - a[0].y))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Above, I've run the numerical integration using a step size of $0.05$ for increasing integration periods from one cycle to four cycles to sixteen cycles and, despite that, the error has stayed near the limits of double precision arithmetic. If I further integrate for 1024 cycles, we'll see that the error begins to increase and this is expected because although the errors in each step may be random walks, they have a cumulative effect that is not necessarily a random walk. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "a.set_method(\"BABS9O7H\")\n", "a.dt = 0.05\n", "a.tf = 2*1024*np.pi\n", "a.integrate()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "initial state = [1. 0.]\n", "final state = [1.00000000e+00 1.46386309e-08]\n", "maximum absolute difference = 1.4638630908142547e-08\n" ] } ], "source": [ "print(\"initial state = {}\".format(a[0].y))\n", "print(\"final state = {}\".format(a[-1].y))\n", "print(\"maximum absolute difference = {}\".format(np.max(np.abs(a[-1].y - a[0].y))))" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(14,8))\n", "ax = fig.add_subplot(111)\n", "\n", "displn = ax.plot(a.t, a.y[:, 0], label=\"Oscillator Displacement\", color='C0')\n", "axt = ax.twinx()\n", "velln = axt.plot(a.t, a.y[:, 1], label=\"Oscillator Velocity\", color='red', linestyle='--')\n", "\n", "ax.set_xlabel(\"Time (s)\")\n", "ax.set_ylabel(\"Displacement (m)\")\n", "axt.set_ylabel(\"Velocity (m/s)\")\n", "ax.set_xlim(0, 2*np.pi)\n", "\n", "ax.spines['left'].set_color('C0')\n", "ax.tick_params(axis='y', colors='C0')\n", "ax.yaxis.label.set_color('C0')\n", "\n", "axt.spines['right'].set_color('red')\n", "axt.spines['left'].set_color('C0')\n", "axt.tick_params(axis='y', colors='red')\n", "axt.yaxis.label.set_color('red')\n", "\n", "# added these three lines\n", "lns = displn + velln\n", "labs = [l.get_label() for l in lns]\n", "ax.legend(lns, labs)\n", "\n", "ax.set_title(\"1 Cycle of a Harmonic Oscillator\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Looking at the Hamiltonian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So we've said that a symplectic integrator preserves a perturbed Hamiltonian, we should be able to see this by computing the Hamiltonian at each timestep and looking at how it evolves over the course of a numerical integration.\n", "\n", "Let's first define the Hamiltonian." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "def kinetic_energy(t, state, k, m):\n", " x, vx = state\n", " return m * vx**2 / 2\n", "\n", "def potential_energy(t, state, k, m):\n", " x, vx = state\n", " return k * x**2 / 2\n", "\n", "def hamiltonian(t, state, k, m):\n", " return kinetic_energy(t, state, k, m) + potential_energy(t, state, k, m)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now it's not interesting to just look at the Hamiltonian alone, we'd like to look at **how** the Hamiltonian evolves so we will look at the absolute difference between the Hamiltonian at time $t$ and the initial Hamiltonian.\n", "\n", "To start off, we'll look at the Hamiltonian when we use an adaptive integrator." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "a.reset()\n", "a.method = \"RK45\"\n", "a.rtol = 1e-9\n", "a.atol = 1e-9\n", "a.tf = 4*2*np.pi\n", "a.integrate()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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f9vLLL6e+vj4XXHBBfvd3fzevvfZa2SMBR7Fly5Zs27at1z22trY2TU1N7rFQpZ5++umMGjUqF110Ub761a/m7bffLnsk6PN27dqVJBkxYkSS5Pnnn897773X6/568cUXZ/z48e6vUKIPr9WDHn744YwcOTKf+MQncuedd+bdd98tY7yqNqDsAaheO3bsyIEDB1JXV9freF1dXV566aWSpgI+rKmpKStWrMhFF12UN954I3fddVc+/elPZ+PGjRk6dGjZ4wGHsW3btiQ57D324Dmgelx99dW5/vrrc/7552fz5s354z/+48ybNy9r165N//79yx4P+qSurq7cdttt+c3f/M184hOfSPLB/fWMM87I8OHDe13r/grlOdxaTZLf+Z3fyYQJE1JfX58NGzbkj/7oj7Jp06b88Ic/LHHa6iO4BTjFzZs3r+ffU6ZMSVNTUyZMmJC///u/z5e//OUSJwOA08Ovb18yefLkTJkyJR/72Mfy9NNP5zOf+UyJk0Hf1dLSko0bN3q2A1S5I63V3//93+/59+TJkzNmzJh85jOfyebNm/Oxj32s6DGrlq0SOKKRI0emf//+hzyBc/v27Rk9enRJUwGVDB8+PB//+MfzyiuvlD0KcAQH76PusXBquuCCCzJy5Ej3WijJLbfckh/96Ed56qmnMnbs2J7jo0ePzv79+7Nz585e17u/QjmOtFYPp6mpKUncWz9EcMsRnXHGGbniiiuyevXqnmNdXV1ZvXp1ZsyYUeJkwNHs2bMnmzdvzpgxY8oeBTiC888/P6NHj+51j929e3d+9rOfucfCKeAXv/hF3n77bfdaKFh3d3duueWWPPbYY3nyySdz/vnn9zp/xRVXZODAgb3ur5s2bcprr73m/goFqrRWD+fgw7bdW3uzVQJH1dramgULFmT69Om58sors2zZsnR2dmbRokVljwb8f9/85jczf/78TJgwIa+//nqWLl2a/v3750tf+lLZo0GftmfPnl6NgS1btqS9vT0jRozI+PHjc9ttt+XP//zPM2nSpJx//vn5kz/5k9TX1/d6kj1QjKOt1xEjRuSuu+7K5z//+YwePTqbN2/OH/7hH+bCCy/M3LlzS5wa+p6WlpY88sgj+cd//McMHTq0Z9/a2tranHnmmamtrc2Xv/zltLa2ZsSIERk2bFhuvfXWzJgxI5/85CdLnh76jkprdfPmzXnkkUdyzTXX5JxzzsmGDRty++23Z+bMmZkyZUrJ01eXmu7u7u6yh6C63X///fnOd76Tbdu2Zdq0abnvvvt6KuxA+W688casWbMmb7/9ds4999x86lOfyl/8xV/YFwhK9vTTT2f27NmHHF+wYEFWrFiR7u7uLF26NH/913+dnTt35lOf+lQeeOCBfPzjHy9hWujbjrZev/e97+Xaa6/Nf/3Xf2Xnzp2pr6/PnDlz8md/9meHPGAQOLlqamoOe/xv//Zvs3DhwiTJ3r17841vfCOPPvpo9u3bl7lz5+aBBx6wVQIUqNJa3bp1a37v934vGzduTGdnZ8aNG5frrrsu3/rWtzJs2LCCp61uglsAAAAAgCpjj1sAAAAAgCojuAUAAAAAqDKCWwAAAACAKiO4BQAAAACoMoJbAAAAAIAqI7gFAAAAAKgyglsAAAAAgCojuAUAAAAAqDKCWwAASLJw4cJce+21pX3/TTfdlLvvvvuYrr3xxhvzl3/5lyd5IgAAylTT3d3dXfYQAABwMtXU1Bz1/NKlS3P77benu7s7w4cPL2aoX/Piiy/mqquuyquvvpohQ4ZUvH7jxo2ZOXNmtmzZktra2gImBACgaIJbAABOe9u2bev598qVK7NkyZJs2rSp59iQIUOOKTA9Wb7yla9kwIABWb58+TH/TWNjYxYuXJiWlpaTOBkAAGWxVQIAAKe90aNH97xqa2tTU1PT69iQIUMO2Sph1qxZufXWW3Pbbbfl7LPPTl1dXf7mb/4mnZ2dWbRoUYYOHZoLL7ww//Iv/9LruzZu3Jh58+ZlyJAhqaury0033ZQdO3YccbYDBw7kH/7hHzJ//vxexx944IFMmjQpgwcPTl1dXW644YZe5+fPn5+/+7u/+7//jwMAQFUS3AIAwBF8//vfz8iRI7Nu3brceuut+epXv5ovfOEL+Y3f+I288MILmTNnTm666aa8++67SZKdO3fmqquuymWXXZbnnnsujz/+eLZv357f/u3fPuJ3bNiwIbt27cr06dN7jj333HP52te+lm9/+9vZtGlTHn/88cycObPX31155ZVZt25d9u3bd3J+PAAApRLcAgDAEUydOjXf+ta3MmnSpNx5550ZPHhwRo4cmcWLF2fSpElZsmRJ3n777WzYsCFJcv/99+eyyy7L3XffnYsvvjiXXXZZHnzwwTz11FP57//+78N+x6uvvpr+/ftn1KhRPcdee+21nHXWWfnc5z6XCRMm5LLLLsvXvva1Xn9XX1+f/fv399oGAgCA04fgFgAAjmDKlCk9/+7fv3/OOeecTJ48uedYXV1dkuTNN99M8sFDxp566qmePXOHDBmSiy++OEmyefPmw37Hr371qwwaNKjXA9Q++9nPZsKECbngggty00035eGHH+5p9R505plnJskhxwEAOD0IbgEA4AgGDhzY631NTU2vYwfD1q6uriTJnj17Mn/+/LS3t/d6vfzyy4dsdXDQyJEj8+6772b//v09x4YOHZoXXnghjz76aMaMGZMlS5Zk6tSp2blzZ88177zzTpLk3HPPPSG/FQCA6iK4BQCAE+Tyyy/Pz3/+80ycODEXXnhhr9dZZ5112L+ZNm1akqSjo6PX8QEDBqS5uTn33ntvNmzYkP/5n//Jk08+2XN+48aNGTt2bEaOHHnSfg8AAOUR3AIAwAnS0tKSd955J1/60peyfv36bN68Of/6r/+aRYsW5cCBA4f9m3PPPTeXX355nn322Z5jP/rRj3Lfffelvb09r776ah566KF0dXXloosu6rnmpz/9aebMmXPSfxMAAOUQ3AIAwAlSX1+ff//3f8+BAwcyZ86cTJ48ObfddluGDx+efv2O/J/eX/nKV/Lwww/3vB8+fHh++MMf5qqrrsoll1yS5cuX59FHH82ll16aJNm7d29WrVqVxYsXn/TfBABAOWq6u7u7yx4CAAD6sl/96le56KKLsnLlysyYMaPi9d/73vfy2GOP5YknnihgOgAAyqBxCwAAJTvzzDPz0EMPZceOHcd0/cCBA/NXf/VXJ3kqAADKpHELAAAAAFBlNG4BAAAAAKqM4BYAAAAAoMoIbgEAAAAAqozgFgAAAACgyghuAQAAAACqjOAWAAAAAKDKCG4BAAAAAKqM4BYAAAAAoMoIbgEAAAAAqozgFgAAAACgyvw/KfCsllyNjJAAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(14,8))\n", "ax = fig.add_subplot(111)\n", "\n", "E_H = np.abs(hamiltonian(a.t, a.y.T, **a.constants) - hamiltonian(a.t[0], a.y[0], **a.constants))\n", "\n", "disp_H = ax.plot(a.t, E_H, label=\"Hamiltonian / Total Energy\", color='black')\n", "\n", "ax.set_xlabel(\"Time (s)\")\n", "ax.set_ylabel(\"Hamiltonian (J)\")\n", "\n", "# added these three lines\n", "ax.legend()\n", "ax.set_yscale(\"log\")\n", "\n", "ax.set_title(\"{:.0f} Cycle{} of a Harmonic Oscillator\".format(a.tf/(2*np.pi), \"s\" if a.tf/(2*np.pi) > 1 else \"\"))\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the Hamiltonian starts off correctly, but then, very rapidly, jumps up to an error on the order of $10^{-9}$ which is the same as the tolerance we've set for the numerical integration." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's compare this to a symplectic integrator." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "a.reset()\n", "a.set_method(\"BABS9O7H\")\n", "a.rtol = 1e-9\n", "a.atol = 1e-9\n", "a.dt = 1e-1\n", "a.tf = 4*2*np.pi\n", "a.integrate()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(14,8))\n", "ax = fig.add_subplot(111)\n", "\n", "E_H = np.abs(hamiltonian(a.t, a.y.T, **a.constants) - hamiltonian(a.t[0], a.y[0], **a.constants))\n", "\n", "disp_H = ax.plot(a.t, E_H, label=\"Hamiltonian / Total Energy\", color='C0')\n", "\n", "ax.set_xlabel(\"Time (s)\")\n", "ax.set_ylabel(\"Hamiltonian (J)\")\n", "\n", "# added these three lines\n", "ax.legend()\n", "ax.set_yscale(\"log\")\n", "\n", "ax.set_title(\"{:.0f} Cycle{} of a Harmonic Oscillator\".format(a.tf/(2*np.pi), \"s\" if a.tf/(2*np.pi) > 1 else \"\"))\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Well that's completely different behaviour to the adaptive integrator. We see now that the Hamiltonian oscillates between a maximal error and a minimal one, but remains within $10^{-14}$ of the true Hamiltonian. \n", "This is exactly the behaviour we were expecting. Let's look further long term and compare with the adaptive integrator, we'll decrease the adaptive integration tolerances down to $10^{-12}$ to see if that helps." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(14,8))\n", "ax = fig.add_subplot(111)\n", "\n", "a.tf = 1024*2*np.pi\n", "\n", "a.reset()\n", "a.set_method(\"BABS9O7H\")\n", "a.dt = 1e-1\n", "a.integrate()\n", "\n", "E_H = np.abs(hamiltonian(a.t, a.y.T, **a.constants) - hamiltonian(a.t[0], a.y[0], **a.constants))\n", "\n", "disp_H = ax.plot(a.t, E_H, label=\"BABS9O7H\", color='C0')\n", "\n", "a.reset()\n", "a.set_method(\"RK45\")\n", "a.rtol = 1e-12\n", "a.atol = 1e-12\n", "a.dt = 1e-1\n", "a.integrate()\n", "\n", "E_H = np.abs(hamiltonian(a.t, a.y.T, **a.constants) - hamiltonian(a.t[0], a.y[0], **a.constants))\n", "\n", "disp_H = ax.plot(a.t, E_H, label=\"Runge-Kutta 45\", color='C1')\n", "\n", "a.reset()\n", "a.set_method(\"RK87\")\n", "a.rtol = 1e-12\n", "a.atol = 1e-12\n", "a.dt = 1e-1\n", "a.integrate()\n", "\n", "E_H = np.abs(hamiltonian(a.t, a.y.T, **a.constants) - hamiltonian(a.t[0], a.y[0], **a.constants))\n", "\n", "disp_H = ax.plot(a.t, E_H, label=\"Runge-Kutta 8(7)\", color='C2')\n", "\n", "a.reset()\n", "a.set_method(\"RK108\")\n", "a.rtol = 1e-12\n", "a.atol = 1e-12\n", "a.dt = 1e-1\n", "a.integrate()\n", "\n", "E_H = np.abs(hamiltonian(a.t, a.y.T, **a.constants) - hamiltonian(a.t[0], a.y[0], **a.constants))\n", "\n", "disp_H = ax.plot(a.t, E_H, label=\"Runge-Kutta 10(8)\", color='C3')\n", "\n", "a.reset()\n", "a.set_method(\"RK1412\")\n", "a.rtol = 1e-12\n", "a.atol = 1e-12\n", "a.dt = 1e-1\n", "a.integrate()\n", "\n", "E_H = np.abs(hamiltonian(a.t, a.y.T, **a.constants) - hamiltonian(a.t[0], a.y[0], **a.constants))\n", "\n", "disp_H = ax.plot(a.t, E_H, label=\"Runge-Kutta 14(12)\", color='C4')\n", "\n", "ax.set_xlabel(\"Time (s)\")\n", "ax.set_ylabel(\"Hamiltonian (J)\")\n", "\n", "# added these three lines\n", "ax.legend(loc='lower right')\n", "ax.set_yscale(\"log\")\n", "\n", "ax.set_title(\"{:.0f} Cycle{} of a Harmonic Oscillator\".format(a.tf/(2*np.pi), \"s\" if a.tf/(2*np.pi) > 1 else \"\"))\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's not good, the Hamiltonian error increases consistently with continued integration whereas the 7th order symplectic integrator continues to stay bounded.\n", "\n", "Thus we see that if energy conservation is a concern, then a symplectic integrator should be used. In most cases, the adaptive Runge-Kutta methods are more useful as they generally require fewer function evaluations and give very good results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "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": "3.12.9" } }, "nbformat": 4, "nbformat_minor": 2 }