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Created January 28, 2019 10:21
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# What is $L_p$ norm?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\forall x \\in \\mathbb{R}^n ~~ \\forall p \\in \\mathbb{R} ~~s.t.~~p\\geq 1$\n",
"$$ \\| x\\|_p = \\left( \\sum_{i=1}^n |x_i|^p \\right)^{1/p} $$\n",
"i.e.\n",
" $$ \\| x\\|_p = \\left( |x_1|^p + |x_2|^p + \\cdots + |x_n|^p \\right)^{1/p} $$\n",
"\n",
"and if $p=\\infty$\n",
"$$ \\| x\\|_\\infty = \\max\\left\\{ |x_1| + |x_2| + \\cdots + |x_n| \\right\\} $$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def lp(x, p=1):\n",
" x = np.abs(x)\n",
" return np.sum((x**p))**(1./p)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p = [1, 2, 4, 6, 8, 10]\n",
"plt.figure(figsize=(8, 8))\n",
"for i in range(len(p)):\n",
" plt.subplot(2, 3, i+1)\n",
" for j in range(500):\n",
" x = np.array([np.random.rand()*2-1, np.random.rand()*2-1])\n",
" if lp(x, p[i]) < 1:\n",
" plt.scatter(x[0], x[1], s=5, c='r')\n",
" plt.title('L_{}-norm'.format(p[i]))\n",
" plt.axis([-1.5, 1.5, -1.5, 1.5])\n",
" plt.tight_layout()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.6.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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