233 lines
101 KiB
Plaintext
233 lines
101 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\n",
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"\n",
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"from scipy.integrate import quad"
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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": "code",
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"execution_count": 3,
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"id": "2120dbad",
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"metadata": {},
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"outputs": [],
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"source": [
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"def getRealIntegral(f, bounds: LinearBounds) -> float:\n",
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" return quad(f, bounds.lower, bounds.higher)[0]"
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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": "bdc2240a",
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"metadata": {},
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"outputs": [],
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"source": [
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"def getIsInside(f, p: Point) -> bool:\n",
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" y_0: float = f(p.x)\n",
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" if abs(y_0) > abs(p.y) and y_0*p.y >= 0:\n",
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" return True\n",
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"\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": 5,
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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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"def function(x: float) -> float:\n",
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" return x**2-3\n",
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"\n",
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"bounds = Bounds(LinearBounds(-1, 4), LinearBounds(-4, 15))"
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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": 6,
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"id": "e00e9ced",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[<matplotlib.lines.Line2D at 0xffff78e10310>]"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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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",
|
|
"samples = np.linspace(bounds.x.lower, bounds.x.higher, 10000)\n",
|
|
"ax.plot([bounds.x.lower, bounds.x.higher], [0, 0], \"k\", linewidth=2)\n",
|
|
"ax.plot([0, 0], [bounds.y.lower - 1, bounds.y.higher + 1], \"k\", linewidth=2)\n",
|
|
"\n",
|
|
"ax.plot(samples, function(samples), color=\"blue\", linewidth=3)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"id": "93672263",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"The approximated Integral of the function is: 6.74500\n",
|
|
"The real Integral of the function is: 6.66667\n",
|
|
"That's an error of 0.08 or 1.17500% \n",
|
|
"And the whole thing took 0.52917 Seconds for 1000 samples\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"execution_count": 7,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"startTime = time.time()\n",
|
|
"pointsInside: int = 0\n",
|
|
"samples: int = 10**3\n",
|
|
"\n",
|
|
"for i in range(samples):\n",
|
|
" toTestPoint = bounds.get_random_point()\n",
|
|
" if getIsInside(function, toTestPoint):\n",
|
|
" if toTestPoint.y >= 0:\n",
|
|
" pointsInside += 1\n",
|
|
" ax.plot(toTestPoint.x, toTestPoint.y, \"o\", color=\"limegreen\")\n",
|
|
" else:\n",
|
|
" pointsInside -= 1\n",
|
|
" ax.plot(toTestPoint.x, toTestPoint.y, \"o\", color=\"darkgreen\")\n",
|
|
" else:\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",
|
|
"real_value: float = getRealIntegral(function, bounds.x)\n",
|
|
"print(f\"The real Integral of the function is: {real_value:.5f}\")\n",
|
|
"\n",
|
|
"error: float = abs(real_value-integral)\n",
|
|
"print(f\"That's an error of {error:.2f} or {(error/real_value)*100:.5f}% \")\n",
|
|
"\n",
|
|
"print(f\"And the whole thing took {time.time()-startTime:.5f} Seconds for {samples} samples\")\n",
|
|
"\n",
|
|
"fig"
|
|
]
|
|
},
|
|
{
|
|
"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
|
|
}
|