175 lines
56 KiB
Plaintext
175 lines
56 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "b5867788",
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"metadata": {},
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"outputs": [],
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"source": [
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"import random\n",
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"import time\n",
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"import matplotlib.pyplot as plt\n",
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"import numpy as np"
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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": "ba84224d",
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"metadata": {},
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"outputs": [],
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"source": [
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"class Point:\n",
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" x: float\n",
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" y: float\n",
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"\n",
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" def __init__(self, point: (float, float)):\n",
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" self.x, self.y = point\n",
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"\n",
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"\n",
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"class LinearBounds:\n",
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" lower: float\n",
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" higher: float\n",
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"\n",
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" def __init__(self, lower: float, higher: float):\n",
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" self.lower = lower\n",
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" self.higher = higher\n",
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"\n",
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" def length(self) -> float:\n",
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" return self.higher - self.lower\n",
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"\n",
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" def get_random_value(self) -> float:\n",
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" return random.uniform(self.lower, self.higher)\n",
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"\n",
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"\n",
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"class Bounds:\n",
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" x: LinearBounds\n",
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" y: LinearBounds\n",
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"\n",
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" def __init__(self, x: LinearBounds, y: LinearBounds):\n",
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" self.x = x\n",
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" self.y = y\n",
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"\n",
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" def area(self) -> float:\n",
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" return self.x.length() * self.y.length()\n",
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"\n",
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" def get_random_point(self) -> Point:\n",
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" return Point((self.x.get_random_value(), self.y.get_random_value()))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5c2bd4e3",
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"metadata": {},
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"source": [
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"## Heart function\n",
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"\n",
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"$\\left(x^{2}+y^{2}-1\\right)^{3}=x^{2}y^{3}$"
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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": 3,
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"id": "bdc2240a",
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"metadata": {},
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"outputs": [],
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"source": [
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"def getIsInside(p: Point) -> bool:\n",
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" if (p.x**2 + p.y**2 - 1)**3 <= p.x**2 * p.y**3:\n",
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" return True\n",
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" return False"
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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": 4,
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"id": "d3f58a1f",
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"metadata": {},
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"outputs": [],
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"source": [
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"bounds = Bounds(LinearBounds(-1.25, 1.25), LinearBounds(-1.25, 1.25))"
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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": 5,
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"id": "93672263",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The approximated Integral of the function is: 3.64688\n",
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"And the whole thing took 0.58856 Seconds for 2000 samples\n"
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]
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},
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"fig, axs = plt.subplot_mosaic([['linear-linear']], layout='constrained')\n",
|
|
"ax = axs['linear-linear']\n",
|
|
"ax.set_xscale('linear')\n",
|
|
"ax.set_yscale('linear')\n",
|
|
"ax.set_xlabel('x')\n",
|
|
"ax.set_ylabel('f')\n",
|
|
"ax.set_box_aspect(1)\n",
|
|
"\n",
|
|
"startTime = time.time()\n",
|
|
"pointsInside: int = 0\n",
|
|
"samples: int = 2 * 10**3\n",
|
|
"\n",
|
|
"for i in range(samples):\n",
|
|
" toTestPoint = bounds.get_random_point()\n",
|
|
" if getIsInside(toTestPoint):\n",
|
|
" pointsInside += 1\n",
|
|
" ax.plot(toTestPoint.x, toTestPoint.y, \"ro\")\n",
|
|
"\n",
|
|
"integral = (pointsInside / samples) * bounds.area()\n",
|
|
"print(f\"The approximated Integral of the function is: {integral:.5f}\")\n",
|
|
"\n",
|
|
"print(f\"And the whole thing took {time.time()-startTime:.5f} Seconds for {samples} samples\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "ce2f249e",
|
|
"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": "3.11.4"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|