{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "(runtime_param)=\n", "\n", "ODEs with parameters\n", "====================\n", "\n", "The values of numerical constants in heyoka.py can either be specified when constructing an ODE system, or they can be loaded at a later stage when the ODE system is being integrated. The latter type of numerical constant is known as a *parameter*.\n", "\n", "Let's start by importing heyoka.py and NumPy:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import heyoka as hy\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this example, we will be integrating the pendulum ODE:\n", "\n", "$$\n", " \\begin{cases}\n", " x^\\prime = v \\\\\n", " v^\\prime = -g \\sin x\n", " \\end{cases},\n", "$$\n", "\n", "where $g$ is the value of the gravitational acceleration ($9.8\\,\\mathrm{m}/\\mathrm{s}^2$ on Earth). Let's first create the symbolic state variables $x$ and $v$, which represent respectively the pendulum's angle and its time derivative:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "x, v = hy.make_vars(\"x\", \"v\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because we don't want to fix $g$ to a specific numerical value, when writing down the ODE system we will be implementing $g$ as a parameter:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "ode_sys = [(x, v), (v, -hy.par[0] * hy.sin(x))]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The syntax ``par[0]`` means that the actual value of $g$ will be the first value (index 0) loaded from the parameter array when integrating the ODE system.\n", "\n", "Let's now create the integrator object, using as initial conditions $\\left( \\pi/2, 0\\right)$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C++ datatype : double\n", "Tolerance : 2.220446049250313e-16\n", "High accuracy : false\n", "Compact mode : false\n", "Taylor order : 20\n", "Dimension : 2\n", "Time : 0\n", "State : [1.5707963267948966, 0]\n", "Parameters : [0]\n", "\n" ] } ], "source": [ "ta = hy.taylor_adaptive(ode_sys, [np.pi / 2, 0.0])\n", "\n", "print(ta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see from the screen output ``Parameters = ...``, heyoka.py detected that ``ode_sys`` contains one parameter, and set its value to zero. We can change the value of the parameter by directly accessing the parameters array:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C++ datatype : double\n", "Tolerance : 2.220446049250313e-16\n", "High accuracy : false\n", "Compact mode : false\n", "Taylor order : 20\n", "Dimension : 2\n", "Time : 0\n", "State : [1.5707963267948966, 0]\n", "Parameters : [9.8]\n", "\n" ] } ], "source": [ "ta.pars[0] = 9.8\n", "\n", "print(ta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that it is also possible to directly set the value of the parameters on construction via the ``pars`` keyword argument:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C++ datatype : double\n", "Tolerance : 2.220446049250313e-16\n", "High accuracy : false\n", "Compact mode : false\n", "Taylor order : 20\n", "Dimension : 2\n", "Time : 0\n", "State : [1.5707963267948966, 0]\n", "Parameters : [9.8]\n", "\n" ] } ], "source": [ "ta = hy.taylor_adaptive(ode_sys, [np.pi / 2, 0.0], pars=[9.8])\n", "\n", "print(ta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now integrate the ODE system for a few time units:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "t_grid = np.linspace(0, 10, 1000)\n", "e_hist = ta.propagate_grid(t_grid)[5][:, 0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now move to Mars, where the gravitational acceleration on the surface is $3.71\\,\\mathrm{m}/\\mathrm{s}^2$ (instead of good ole Earth's $9.8\\,\\mathrm{m}/\\mathrm{s}^2$):" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Reset time and state.\n", "ta.time = 0\n", "ta.state[:] = [np.pi / 2, 0]\n", "\n", "# Change gravity.\n", "ta.pars[0] = 3.71\n", "\n", "# Integrate again.\n", "m_hist = ta.propagate_grid(t_grid)[5][:, 0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, let's plot the evolution of $x$ in time to show how a pendulum swings more slowly on Mars:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from matplotlib.pylab import plt\n", "\n", "fig = plt.figure(figsize=(9, 6))\n", "\n", "plt.plot(t_grid, e_hist, label=\"Earth\")\n", "plt.plot(t_grid, m_hist, label=\"Mars\")\n", "plt.xlabel(\"Time (s)\")\n", "plt.ylabel(\"x (rad)\")\n", "plt.legend();" ] } ], "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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }