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@paulromano
Created December 18, 2023 21:04
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Notebook demonstrating roundoff error in calculation speed
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "66962f04",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import mpmath"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "4d0479e4",
"metadata": {},
"outputs": [],
"source": [
"c_light = 2.99792458e10\n",
"\n",
"def speed_rel(mass, E, dps=15):\n",
" \"\"\"Relativistic calculation of speed with specified decimal precision\"\"\"\n",
" with mpmath.workdps(dps):\n",
" mass = mpmath.mpf(mass)\n",
" E = mpmath.mpf(E)\n",
" inv_gamma = mass/(E + mass)\n",
" return c_light * mpmath.sqrt(1.0 - inv_gamma*inv_gamma)\n",
"\n",
"def speed_nonrel(mass, E):\n",
" \"\"\"Non-relativistic calculation of speed\"\"\"\n",
" return c_light * np.sqrt(2*E/mass)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "5c486c03",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Error')"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mass_neutron = 939.56542052e6\n",
"energies = np.geomspace(1e-5, 1e3)\n",
"\n",
"speed_rel_15 = np.array([speed_rel(mass_neutron, E, dps=15) for E in energies])\n",
"speed_rel_100 = np.array([speed_rel(mass_neutron, E, dps=100) for E in energies])\n",
"speed_approx = np.array([speed_nonrel(mass_neutron, E) for E in energies])\n",
"\n",
"error_rel_15 = np.abs(speed_rel_15 - speed_rel_100)/speed_rel_100\n",
"error_nonrel = np.abs(speed_approx - speed_rel_100)/speed_rel_100\n",
"plt.loglog(energies, error_rel_15, label='Relativistic, 15 digits')\n",
"plt.loglog(energies, error_nonrel, label='Non-relativistic')\n",
"plt.legend()\n",
"plt.xlabel('Neutron Energy [eV]')\n",
"plt.ylabel('Error')"
]
},
{
"cell_type": "markdown",
"id": "f1b205c1",
"metadata": {},
"source": [
"We see that below an energy of about 1.0 eV, using the non-relativistic formula for speed is more accurate than using the relativistic formula (which starts to suffer from limited precision). Let's do the same calculation for electrons"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "2f3c351e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Error')"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mass_electron = 0.51099895000e6\n",
"\n",
"speed_rel_15 = np.array([speed_rel(mass_electron, E, dps=15) for E in energies])\n",
"speed_rel_100 = np.array([speed_rel(mass_electron, E, dps=100) for E in energies])\n",
"speed_approx = np.array([speed_nonrel(mass_electron, E) for E in energies])\n",
"\n",
"error_rel_15 = np.abs(speed_rel_15 - speed_rel_100)/speed_rel_100\n",
"error_nonrel = np.abs(speed_approx - speed_rel_100)/speed_rel_100\n",
"plt.loglog(energies, error_rel_15, label='Relativistic, 15 digits')\n",
"plt.loglog(energies, error_nonrel, label='Non-relativistic')\n",
"plt.legend()\n",
"plt.xlabel('Electron Energy [eV]')\n",
"plt.ylabel('Error')"
]
},
{
"cell_type": "markdown",
"id": "4c7d22ac",
"metadata": {},
"source": [
"The same conclusion holds: when the energy is about $10^{-9}$ smaller than the rest mass energy of the particle, it makes sense to switch over to the non-relativistic formula."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1bbe6ef9",
"metadata": {},
"outputs": [],
"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": "3.10.6"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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