added jupyter nb

MonteCarlo Function.ipynb

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+{
+ "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
+}

out/output11.json

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+{"x":[10000000000,20000000000,50000000000],"y":[[1.1070528943500009,1.107091172850001,1.107024459450001,1.107134587650001,1.107118888850001,1.1070673763500007,1.107102086350001,1.107087578350001,1.1070208383000009,1.1070149558000009],[1.107116142600001,1.107052413675001,1.1070808953750009,1.107057258775001,1.1070388527250008,1.1071355902750009,1.1070987538000008,1.1070910386250008,1.107089875775001,1.107066415325001],[1.107083811470001,1.107081873690001,1.107115097660001,1.1070899834800008,1.107081929590001,1.1070892114100008,1.107080606320001,1.1070829237000008,1.107084684160001,1.1070922865600008]]}

out/output12.json

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+{"x":[100000000000,200000000000,500000000000],"y":[[1.107080884000001],[1.107080584805001],[1.107089721517001]]}