174 lines
4.3 KiB
Plaintext
174 lines
4.3 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 1,
|
|
"id": "b5867788",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"import random\n",
|
|
"import time\n",
|
|
"import numpy as np\n",
|
|
"\n",
|
|
"from scipy.integrate import quad"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 2,
|
|
"id": "ba84224d",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"class Point:\n",
|
|
" x: float\n",
|
|
" y: float\n",
|
|
"\n",
|
|
" def __init__(self, point: (float, float)):\n",
|
|
" self.x, self.y = point\n",
|
|
"\n",
|
|
"\n",
|
|
"class LinearBounds:\n",
|
|
" lower: float\n",
|
|
" higher: float\n",
|
|
"\n",
|
|
" def __init__(self, lower: float, higher: float):\n",
|
|
" self.lower = lower\n",
|
|
" self.higher = higher\n",
|
|
"\n",
|
|
" def length(self) -> float:\n",
|
|
" return self.higher - self.lower\n",
|
|
"\n",
|
|
" def get_random_value(self) -> float:\n",
|
|
" return random.uniform(self.lower, self.higher)\n",
|
|
"\n",
|
|
"\n",
|
|
"class Bounds:\n",
|
|
" x: LinearBounds\n",
|
|
" y: LinearBounds\n",
|
|
"\n",
|
|
" def __init__(self, x: LinearBounds, y: LinearBounds):\n",
|
|
" self.x = x\n",
|
|
" self.y = y\n",
|
|
"\n",
|
|
" def area(self) -> float:\n",
|
|
" return self.x.length() * self.y.length()\n",
|
|
"\n",
|
|
" def get_random_point(self) -> Point:\n",
|
|
" return Point((self.x.get_random_value(), self.y.get_random_value()))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 3,
|
|
"id": "2120dbad",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def getRealIntegral(f, bounds: LinearBounds) -> float:\n",
|
|
" return quad(f, bounds.lower, bounds.higher)[0]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"id": "bdc2240a",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def getIsInside(f, p: Point) -> bool:\n",
|
|
" y_0: float = f(p.x)\n",
|
|
" if abs(y_0) > abs(p.y) and y_0*p.y >= 0:\n",
|
|
" return True\n",
|
|
"\n",
|
|
" return False"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"id": "d3f58a1f",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def function(x: float) -> float:\n",
|
|
" return x**2-3\n",
|
|
"\n",
|
|
"bounds = Bounds(LinearBounds(-1, 4), LinearBounds(-4, 15))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"id": "93672263",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"The approximated Integral of the function is: 6.67280\n",
|
|
"The real Integral of the function is: 6.66667\n",
|
|
"That's an error of 0.00613 or 0.09200% \n",
|
|
"And the whole thing took 1.37645 Seconds for 1000000 samples\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"startTime = time.time()\n",
|
|
"pointsInside: int = 0\n",
|
|
"samples: int = 10**6\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",
|
|
" else:\n",
|
|
" pointsInside -= 1\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:.5f} or {(error/real_value)*100:.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
|
|
}
|