{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial A12 – Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1__ How does logging behave when you rerun the script without restarting the kernel? What happens if you delete the log-file before you rerun?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*If you rerun your script, the new logging messages are append to the log file*\n", "*If you delete the log-file in between, the result is the same. The logger remenbers\n", "everything written to the log file before and the teh log file is complete restored*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__2__ Play around with the `datefmt` keyword when configuring the logger to omit displaying year and months." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```python\n", "logging.basicConfig(\n", " filename=\"file\",\n", " datefmt='%d-%I:%M:%S %p',\n", " )\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__3__ Below you find a script that propagates a particle in a harmonic potential numerically (using the euler integrator). You do not need to know about details of the scientific background yet. Just note so much: The script monitors the total energy of the particle at every propagation step. Whenever the change in energy is larger than 0.3, the velocity should be rescaled (multiplied) by a factor of 0.9. This part is not yet included in the script below. If this happens a message should be written to a log file, stating the old and the new speed. Your task is it, to setup a logger and insert a logging statement at the right position in the code." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "run_control": { "marked": true } }, "outputs": [], "source": [ "import logging\n", "\n", "fname = \"ea8/log.log\"\n", "logging.basicConfig(\n", " filename=fname,\n", " filemode=\"w\",\n", " datefmt=\"%H:%M:%S\",\n", " level=logging.WARNING,\n", " )\n", "\n", "\n", "def force(x):\n", " \"\"\"Compute the instantaneous force acting on the particle\n", " \n", " Args:\n", " x: Current position\n", " x0 (global): Position of the minimum of the potential\n", " k (global): Force constant\n", " \"\"\"\n", " \n", " return -k * (x - x0)\n", "\n", "\n", "def e_pot(x):\n", " \"\"\"Compute the potential energy of the particle\n", " \n", " Args:\n", " x: Current position\n", " x0 (global): Position of the minimum of the potential\n", " k (global): Force constant\n", " \"\"\"\n", "\n", " return 0.5 * k * (x - x0)**2\n", "\n", "\n", "def e_kin(v):\n", " \"\"\"Compute the kinetic energy of the particle\n", " \n", " Args:\n", " v: Particle velocity\n", " m (global): Particle mass\n", " \"\"\"\n", "\n", " return 0.5 * m * v**2\n", "\n", "\n", "def propagate(x, v):\n", " \"\"\"Compute the position of the particle one timestep further\n", " \n", " Args:\n", " x: Current position\n", " v: Current velocity\n", " dt (global): Propagation timestep\n", " m (global): Particle mass\n", " \n", " Returns:\n", " New position and velocity\n", " \"\"\"\n", " \n", " x_new = x + v*dt + force(x)/(2*m) * dt**2\n", " v_new = v + force(x)/m * dt\n", "\n", " return x_new, v_new\n", "\n", "\n", "# Preparing lists to store the computed trajectories\n", "x_t = [] # Position\n", "v_t = [] # Velocity\n", "e_t = [] # Energy\n", "\n", "# Particle/Simulation parameters\n", "x0 = 0 # Position of the potential minimum\n", "k = 1. # Force constant\n", "m = 1. # Particle mass\n", "\n", "dt = 1e-1 # Simulation timestep\n", "T = 1000 # Total number of steps\n", "scale_factor = 0.9\n", "# Rescaling factor to counter energy conservation problems\n", "\n", "x = 1 # starting position\n", "v = -2 # starting velocity\n", "\n", "# Put them in the output lists \n", "x_t.append(x)\n", "v_t.append(v)\n", "e_t.append(e_pot(x) + e_kin(v))\n", "\n", "# Simulate\n", "for i in range(T):\n", " # Update position and velocity\n", " x, v = propagate(x, v)\n", " x_t.append(x)\n", " v_t.append(v)\n", " \n", " # Update total energy\n", " e_t.append(e_pot(x) + e_kin(v)) \n", " \n", " if (e_t[-1] - e_t[-2]) > 0.3:\n", " logging.warning(\n", " 'Energy not conserved!'\n", " f'Rescaling velocity from {v_t[-1]} to {v_t[-1] * scale_factor}'\n", " )\n", "\n", " v *= scale_factor" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING:root:Energy not conserved!Rescaling velocity from -7.952943460471916 to -7.157649114424725\n", "WARNING:root:Energy not conserved!Rescaling velocity from 7.818357041905684 to 7.036521337715116\n", "WARNING:root:Energy not conserved!Rescaling velocity from 7.937734070995736 to 7.143960663896163\n", "WARNING:root:Energy not conserved!Rescaling velocity from -7.991841670210238 to -7.192657503189214\n", "WARNING:root:Energy not conserved!Rescaling velocity from 7.831076595508824 to 7.047968935957941\n", "WARNING:root:Energy not conserved!Rescaling velocity from 7.945001174756476 to 7.150501057280829\n", "WARNING:root:Energy not conserved!Rescaling velocity from -8.02546516176625 to -7.222918645589626\n", "WARNING:root:Energy not conserved!Rescaling velocity from 7.8738492791246015 to 7.0864643512121415\n", "WARNING:root:Energy not conserved!Rescaling velocity from 7.9490910738210205 to 7.154181966438919\n", "WARNING:root:Energy not conserved!Rescaling velocity from -8.06551535987205 to -7.258963823884845\n" ] } ], "source": [ "# Print the first 10 lines of the log file\n", "with open(fname) as f:\n", " for line in f.readlines()[:10]:\n", " print(line, end=\"\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__4__ Plot the result of the simulation as velocity vs. position." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$v$')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "plt.plot(x_t, v_t)\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$v$\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.10" }, "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": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }