510 lines
238 KiB
Plaintext
510 lines
238 KiB
Plaintext
{
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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": [
|
|
"<Figure size 800x500 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"import numpy as np\n",
|
|
"from scipy.stats import uniform # Import scipys uniform\n",
|
|
"import matplotlib.pyplot as plt\n",
|
|
"\n",
|
|
"# Define the distribution parameters to be plotted\n",
|
|
"sigma = 1\n",
|
|
"mu = 0\n",
|
|
"x = np.linspace(-0.5, 1.5, 1000)\n",
|
|
"\n",
|
|
"\n",
|
|
"# plot the distributions\n",
|
|
"fig, ax = plt.subplots(figsize=(8, 5))\n",
|
|
"\n",
|
|
"dist = uniform(mu, sigma)\n",
|
|
"\n",
|
|
"plt.plot(x, dist.pdf(x), c='black', label=r'$\\mu=%i,\\ \\sigma=%i$' % (mu, sigma))\n",
|
|
"\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('Uniform Distribution')\n",
|
|
"\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 2,
|
|
"id": "2431e6fc-1efb-40e1-8865-42b1be95f95e",
|
|
"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": [
|
|
"# 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.uniform(mu, sigma, 3)\n",
|
|
"\n",
|
|
"# Linespace\n",
|
|
"x = np.linspace(-0.5, 2, 1000)\n",
|
|
"\n",
|
|
"# Get uniform from linespace\n",
|
|
"dist = uniform(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, .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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",
|
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"text/plain": [
|
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"<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",
|
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"fig, ax = plt.subplots(figsize=(5,5))\n",
|
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"ax.add_patch(circle)\n",
|
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"ax.plot(np.linspace(0,1), np.zeros(50), color='black')\n",
|
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"ax.text(0.5, 0.05, \"$r = 1$\")\n",
|
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"plt.xlim(-1, 1)\n",
|
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"plt.ylim(-1, 1)\n",
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"\n",
|
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"# 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
|
|
}
|