510 lines
238 KiB
Plaintext
510 lines
238 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "db958d91-e3a0-4c3b-95d9-034a6ec30e8d",
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"metadata": {
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"editable": true,
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"slideshow": {
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"slide_type": ""
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},
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"tags": []
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},
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"source": [
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"# Monte Carlo Simulationen"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "45a2a6a7-7744-493f-becd-ca242a60f3e2",
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"metadata": {
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"editable": true,
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"slideshow": {
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"slide_type": ""
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},
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"tags": []
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},
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"outputs": [
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 800x500 with 1 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"import numpy as np\n",
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"from scipy.stats import uniform # Import scipys uniform\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"# Define the distribution parameters to be plotted\n",
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"sigma = 1\n",
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"mu = 0\n",
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"x = np.linspace(-0.5, 1.5, 1000)\n",
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"\n",
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"\n",
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"# plot the distributions\n",
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"fig, ax = plt.subplots(figsize=(8, 5))\n",
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"\n",
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"dist = uniform(mu, sigma)\n",
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"\n",
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"plt.plot(x, dist.pdf(x), c='black', label=r'$\\mu=%i,\\ \\sigma=%i$' % (mu, sigma))\n",
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"\n",
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"plt.xlim(-0.5, 1.5)\n",
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"plt.ylim(0, 1.2)\n",
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"\n",
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"plt.xlabel('$x$')\n",
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"plt.ylabel(r'$p(x|\\mu, \\sigma)$')\n",
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"plt.title('Uniform Distribution')\n",
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"\n",
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"plt.legend()\n",
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"plt.show()"
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]
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},
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|
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{
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||
|
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"cell_type": "code",
|
||
|
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"execution_count": 2,
|
||
|
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"id": "2431e6fc-1efb-40e1-8865-42b1be95f95e",
|
||
|
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"metadata": {
|
||
|
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"editable": true,
|
||
|
|
"slideshow": {
|
||
|
|
"slide_type": ""
|
||
|
|
},
|
||
|
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"tags": []
|
||
|
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},
|
||
|
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"outputs": [
|
||
|
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{
|
||
|
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"data": {
|
||
|
|
"image/png": "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"text/plain": [
|
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|
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"<Figure size 800x500 with 1 Axes>"
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]
|
||
|
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},
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||
|
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"metadata": {},
|
||
|
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"output_type": "display_data"
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||
|
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}
|
||
|
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],
|
||
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"source": [
|
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|
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"# Parameters\n",
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"mu = 0\n",
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"sigma = 1\n",
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"\n",
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"# Get a 3 random samples\n",
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"rand = np.random.default_rng(5000)\n",
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"uniform_samples = rand.uniform(mu, sigma, 3)\n",
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"\n",
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"# Linespace\n",
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"x = np.linspace(-0.5, 2, 1000)\n",
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"\n",
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"# Get uniform from linespace\n",
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"dist = uniform(mu, sigma)\n",
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"\n",
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|
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"# Plot Uniform\n",
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"fig, ax = plt.subplots(figsize=(8, 5))\n",
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"plt.plot(x, dist.pdf(x), c='black', label=r'$\\mu=%i,\\ \\sigma=%i$' % (mu, sigma))\n",
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"\n",
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|
|
"# Plot samples\n",
|
||
|
|
"step = 0.1\n",
|
||
|
|
"for u in uniform_samples:\n",
|
||
|
|
" u = np.round(u, decimals=2)\n",
|
||
|
|
" plt.axvline(u, color='r')\n",
|
||
|
|
" plt.text(u, .5+step, u, color='g')\n",
|
||
|
|
" step += 0.1\n",
|
||
|
|
"\n",
|
||
|
|
"# Cosmetics\n",
|
||
|
|
"plt.xlim(-0.5, 1.5)\n",
|
||
|
|
"plt.ylim(0, 1.2)\n",
|
||
|
|
"\n",
|
||
|
|
"plt.xlabel('$x$')\n",
|
||
|
|
"plt.ylabel(r'$p(x|\\mu, \\sigma)$')\n",
|
||
|
|
"plt.title('3 Samples from a Uniform Distribution')\n",
|
||
|
|
"\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 3,
|
||
|
|
"id": "91d9bce6-8223-455f-be61-5a932ac73b44",
|
||
|
|
"metadata": {
|
||
|
|
"editable": true,
|
||
|
|
"slideshow": {
|
||
|
|
"slide_type": ""
|
||
|
|
},
|
||
|
|
"tags": []
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 800x500 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# Import scipys norm\n",
|
||
|
|
"from scipy.stats import norm \n",
|
||
|
|
"\n",
|
||
|
|
"#Parameters\n",
|
||
|
|
"mu = 0\n",
|
||
|
|
"sigma = 1\n",
|
||
|
|
"\n",
|
||
|
|
"# Get a 3 random samples\n",
|
||
|
|
"rand = np.random.default_rng(5000)\n",
|
||
|
|
"uniform_samples = rand.normal(mu, sigma, 3)\n",
|
||
|
|
"\n",
|
||
|
|
"# Linespace\n",
|
||
|
|
"x = np.linspace(-4, 4, 1000)\n",
|
||
|
|
"\n",
|
||
|
|
"# Get uniform from linespace\n",
|
||
|
|
"dist = norm(mu, sigma)\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot Uniform\n",
|
||
|
|
"fig, ax = plt.subplots(figsize=(8, 5))\n",
|
||
|
|
"plt.plot(x, dist.pdf(x), c='black', label=r'$\\mu=%i,\\ \\sigma=%i$' % (mu, sigma))\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot samples\n",
|
||
|
|
"step = 0.1\n",
|
||
|
|
"for u in uniform_samples:\n",
|
||
|
|
" u = np.round(u, decimals=2)\n",
|
||
|
|
" plt.axvline(u, color='r')\n",
|
||
|
|
" plt.text(u, .1+step, u, color='g')\n",
|
||
|
|
" step += 0.1\n",
|
||
|
|
"\n",
|
||
|
|
"# Cosmetics\n",
|
||
|
|
"plt.xlim(-4, 4)\n",
|
||
|
|
"plt.ylim(0, .5)\n",
|
||
|
|
"\n",
|
||
|
|
"plt.xlabel('$x$')\n",
|
||
|
|
"plt.ylabel(r'$p(x|\\mu, \\sigma)$')\n",
|
||
|
|
"plt.title('3 Samples from a Normal Distribution')\n",
|
||
|
|
"\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 4,
|
||
|
|
"id": "b9b53ef7-374c-44f3-b1e2-7bf95e77b535",
|
||
|
|
"metadata": {
|
||
|
|
"editable": true,
|
||
|
|
"slideshow": {
|
||
|
|
"slide_type": ""
|
||
|
|
},
|
||
|
|
"tags": []
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 500x500 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"circle = plt.Circle((0, 0), 1, color='black', fill=False)\n",
|
||
|
|
"fig, ax = plt.subplots(figsize=(5,5))\n",
|
||
|
|
"ax.add_patch(circle)\n",
|
||
|
|
"ax.plot(np.linspace(0,1), np.zeros(50), color='black')\n",
|
||
|
|
"ax.text(0.5, 0.05, \"$r = 1$\")\n",
|
||
|
|
"\n",
|
||
|
|
"plt.xlim(-1, 1)\n",
|
||
|
|
"plt.ylim(-1, 1)\n",
|
||
|
|
"\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "8a9aa971-bcc4-49e9-844a-a8e23be0be4d",
|
||
|
|
"metadata": {
|
||
|
|
"editable": true,
|
||
|
|
"slideshow": {
|
||
|
|
"slide_type": ""
|
||
|
|
},
|
||
|
|
"tags": []
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"$$\\frac{A_{circle}}{A_{square}} = \\frac{\\pi}{4}$$\n",
|
||
|
|
"\n",
|
||
|
|
"$$\\pi = 4 \\cdot \\frac{A_{circle}}{A_{square}}$$"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 5,
|
||
|
|
"id": "86b877fd-9713-49a8-bd32-b2b2a4cf6917",
|
||
|
|
"metadata": {
|
||
|
|
"editable": true,
|
||
|
|
"slideshow": {
|
||
|
|
"slide_type": ""
|
||
|
|
},
|
||
|
|
"tags": []
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 500x500 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# Get Uniform x, y samples\n",
|
||
|
|
"rand = np.random.default_rng(42) # Set fixed Value\n",
|
||
|
|
"x_rand = rand.uniform(-1, 1, 100)\n",
|
||
|
|
"y_rand = rand.uniform(-1, 1, 100)\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot \n",
|
||
|
|
"circle = plt.Circle((0, 0), 1, color='black', fill=False)\n",
|
||
|
|
"fig, ax = plt.subplots(figsize=(5,5))\n",
|
||
|
|
"ax.add_patch(circle)\n",
|
||
|
|
"ax.plot(np.linspace(0,1), np.zeros(50), color='black')\n",
|
||
|
|
"ax.text(0.5, 0.05, \"$r = 1$\")\n",
|
||
|
|
"plt.xlim(-1, 1)\n",
|
||
|
|
"plt.ylim(-1, 1)\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot samples as small circles\n",
|
||
|
|
"for x, y in zip(x_rand, y_rand):\n",
|
||
|
|
" c = plt.Circle((x,y), 0.01, color='green')\n",
|
||
|
|
" ax.add_patch(c)\n",
|
||
|
|
"\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "2d6d0132-647a-4f83-82c1-e97e79e68a37",
|
||
|
|
"metadata": {
|
||
|
|
"editable": true,
|
||
|
|
"slideshow": {
|
||
|
|
"slide_type": ""
|
||
|
|
},
|
||
|
|
"tags": []
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Parametrisierte Kreisgleichung: $$x^2+y^2=r,\\quad r=1$$"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 6,
|
||
|
|
"id": "d4416d57-35e6-49c3-8367-592e9814ac7a",
|
||
|
|
"metadata": {
|
||
|
|
"editable": true,
|
||
|
|
"slideshow": {
|
||
|
|
"slide_type": ""
|
||
|
|
},
|
||
|
|
"tags": []
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# reserve two arrays\n",
|
||
|
|
"circle_coords = []\n",
|
||
|
|
"square_coords = []\n",
|
||
|
|
"\n",
|
||
|
|
"for x,y in zip(x_rand, y_rand):\n",
|
||
|
|
" # calculate distance from origin\n",
|
||
|
|
" dist_from_origin = x**2 + y**2\n",
|
||
|
|
"\n",
|
||
|
|
" # if distance smaller or equal than 1, the point is in the circle\n",
|
||
|
|
" if dist_from_origin <= 1:\n",
|
||
|
|
" circle_coords.append((x,y))\n",
|
||
|
|
"\n",
|
||
|
|
" # by definition is every point in the square\n",
|
||
|
|
" square_coords.append((x,y))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 7,
|
||
|
|
"id": "71d3f85c-b85f-488f-8369-c81c5d3d6bf8",
|
||
|
|
"metadata": {
|
||
|
|
"editable": true,
|
||
|
|
"slideshow": {
|
||
|
|
"slide_type": ""
|
||
|
|
},
|
||
|
|
"tags": []
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Pi = 3.12\n",
|
||
|
|
"Difference to real Value 0.02159265358979301\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"pi = 4 * len(circle_coords) / len(square_coords)\n",
|
||
|
|
"print(f\"Pi = {pi}\")\n",
|
||
|
|
"print(f\"Difference to real Value {np.pi - pi}\")"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 8,
|
||
|
|
"id": "31743c3a-4ebe-46ba-a383-0dfdf98d8b37",
|
||
|
|
"metadata": {
|
||
|
|
"editable": true,
|
||
|
|
"slideshow": {
|
||
|
|
"slide_type": ""
|
||
|
|
},
|
||
|
|
"tags": []
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 500x500 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# Plot \n",
|
||
|
|
"circle = plt.Circle((0, 0), 1, color='black', fill=False)\n",
|
||
|
|
"fig, ax = plt.subplots(figsize=(5,5))\n",
|
||
|
|
"ax.add_patch(circle)\n",
|
||
|
|
"ax.plot(np.linspace(0,1), np.zeros(50), color='black')\n",
|
||
|
|
"ax.text(0.5, 0.05, \"$r = 1$\")\n",
|
||
|
|
"plt.xlim(-1, 1)\n",
|
||
|
|
"plt.ylim(-1, 1)\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot samples not in the circle\n",
|
||
|
|
"for coord in square_coords:\n",
|
||
|
|
" c = plt.Circle(coord, 0.01, color='blue')\n",
|
||
|
|
" ax.add_patch(c)\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot samples in the circle\n",
|
||
|
|
"for coord in circle_coords:\n",
|
||
|
|
" c = plt.Circle(coord, 0.01, color='red')\n",
|
||
|
|
" ax.add_patch(c)\n",
|
||
|
|
"\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 9,
|
||
|
|
"id": "bd4c6bab-20dd-4f9c-9966-96b7988f4afa",
|
||
|
|
"metadata": {
|
||
|
|
"editable": true,
|
||
|
|
"slideshow": {
|
||
|
|
"slide_type": ""
|
||
|
|
},
|
||
|
|
"tags": []
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Pi = 3.14178\n",
|
||
|
|
"Difference to real Value -0.00018734641020667908\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# Get Uniform x, y samples\n",
|
||
|
|
"sample_size = 1_000_000\n",
|
||
|
|
"rand = np.random.default_rng(42) # Set fixed Value\n",
|
||
|
|
"x_rand = rand.uniform(-1, 1, sample_size)\n",
|
||
|
|
"y_rand = rand.uniform(-1, 1, sample_size)\n",
|
||
|
|
"\n",
|
||
|
|
"# reserve two arrays\n",
|
||
|
|
"in_circle = 0\n",
|
||
|
|
"in_square = 0\n",
|
||
|
|
"\n",
|
||
|
|
"for x,y in zip(x_rand, y_rand):\n",
|
||
|
|
" # calculate distance from origin\n",
|
||
|
|
" dist_from_origin = x**2 + y**2\n",
|
||
|
|
"\n",
|
||
|
|
" # if distance smaller or equal than 1, the point is in the circle\n",
|
||
|
|
" if dist_from_origin <= 1:\n",
|
||
|
|
" in_circle += 1\n",
|
||
|
|
"\n",
|
||
|
|
" # by definition is every point in the square\n",
|
||
|
|
" in_square += 1\n",
|
||
|
|
"\n",
|
||
|
|
"pi = 4 * in_circle / in_square\n",
|
||
|
|
"print(f\"Pi = {pi}\")\n",
|
||
|
|
"print(f\"Difference to real Value {np.pi - pi}\")"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"id": "618923ef-21b8-4280-abc4-1f1a8a6212a7",
|
||
|
|
"metadata": {
|
||
|
|
"editable": true,
|
||
|
|
"slideshow": {
|
||
|
|
"slide_type": ""
|
||
|
|
},
|
||
|
|
"tags": []
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"import numpy as np\n",
|
||
|
|
"import matplotlib.pyplot as plt\n",
|
||
|
|
"sims = \n",
|
||
|
|
"\n",
|
||
|
|
"excercise_1 = np.random.uniform(,,sims)\n",
|
||
|
|
"excercise_2 = np.random.uniform(,,sims)\n",
|
||
|
|
"\n",
|
||
|
|
"duration = excercise_1 + excercise_2\n",
|
||
|
|
"chance = float(np.round((duration > ).sum()/sims, decimals=2))\n",
|
||
|
|
"\n",
|
||
|
|
"plt.figure(figsize=(5,2.5))\n",
|
||
|
|
"plt.hist(duration, density=True)\n",
|
||
|
|
"plt.axvline(, color='r')\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"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": "3.12.7"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 5
|
||
|
|
}
|