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rifazn/Assignment 3 Part B - Area estimation using Monte Carlo method.ipynb

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Assignment 3 Part B for Simulation & Modeling Lab (UIU)
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Assignment 3 Part B - Area estimation using Monte Carlo method.ipynb
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"# CSI 424, Simulation & Modeling Lab, Sec: B\n",
"\n",
"# Assignment 3 (Part B)\n",
"\n",
"## Using Monte Carlo simulation, find the area of the shaded region\n",
"\n",
"## By: Rifaz Nahiyan (011 152 054)"
],
"cell_type": "markdown",
"metadata": {}
},
{
"source": [
"from matplotlib import pyplot as plt\n",
"from pprint import pprint\n",
"import numpy as np\n",
"import random\n",
"import math"
],
"cell_type": "code",
"metadata": {},
"execution_count": 1,
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"source": [
"# Class definitions to make creating the shapes, checking whether any arbitrary\n",
"# point (x,y) exists in the shape, and plotting the shape on a graph easier.\n",
"\n",
"class Rectangle:\n",
" \"\"\"\n",
" Creates a Rectangle object anchored at `origin`. The rest of the\n",
" coodinates are derived from the `width` and `height` parameters.\n",
"\n",
" Provides the usage of `in` keyword to check whether an arbitrary point\n",
" (x, y) lies within a Rectangle instance.\n",
"\n",
" Also provides methods for calculating the area, and plotting the rectangle\n",
" instance on a graph.\n",
" \"\"\"\n",
"\n",
" def __init__(self, origin: tuple, width, height):\n",
" self.origin = origin\n",
" self.width = width\n",
" self.height = height\n",
"\n",
" def get_area(self):\n",
" return round(abs(self.width * self.height), 5)\n",
"\n",
" def plot_axes(self, ax, **kwargs):\n",
" \"\"\"\n",
" Plot the rectangle instance on a given Axes.\n",
"\n",
" Parameters\n",
" ----------\n",
" ax: a matplotlib subplot axes on which to draw the graph.\n",
" kwargs: These args are passed straight to the Axes instance.\n",
" \"\"\"\n",
" x = self.origin[0]\n",
" y = self.origin[1]\n",
" w, h = (self.width, self.height)\n",
" return ax.plot([x, x+w, x+w, x, x], [y, y, y+h, y+h, y], **kwargs)\n",
" \n",
" def __contains__(self, point):\n",
" \"\"\"\n",
" Check whether `point` is within the Rectangle instance.\n",
"\n",
" Example\n",
" -------\n",
"\n",
" r = Rectangle((0, 0), 5, 5)\n",
" (0, 1) in r # True\n",
" (0, 6) in r # False\n",
" (-1, 2) in r # False\n",
" \"\"\"\n",
" px, py = point\n",
" x1, x2 = self.origin[0], self.origin[0] + self.width\n",
" y1, y2 = self.origin[1], self.origin[1] + self.height\n",
"\n",
" return x1 <= px <= x2 and y1 <= py <= y2\n",
"\n",
"\n",
"class Triangle:\n",
" \"\"\"\n",
" Create a triangle anchored at origin. The `origin` and `width` together make the base.\n",
" The height of the tri-angle is always added at 90 degrees on the origin's x + width.\n",
"\n",
" This will also draw the triangle on the matplotlib axes provided\n",
"\n",
" Parameters\n",
" ----------\n",
" origin : (float, float)\n",
" A tuple containing x and y coordinates.\n",
" width : float\n",
" Width of the tri-angle. The origin x coordinate and the width make the \"base\" of the triangle.\n",
" height : float\n",
" The x-coordinate of height is origin[0] + width.\n",
" \n",
" \"\"\"\n",
"\n",
" def __init__(self, origin: tuple, width: float, height: float):\n",
" self.origin = origin\n",
" self.width = width\n",
" self.height = height\n",
" self.x = [origin[0], origin[0]+width, origin[0]+width]\n",
" self.y = [origin[1], origin[1], origin[1] + height]\n",
" \n",
" def get_area(self):\n",
" return round(0.5 * abs(self.width * self.height), 5)\n",
"\n",
" def plot_axes(self, ax: plt.axes, **kwargs):\n",
" \"\"\"\n",
" Draw the triangle on the ax provided.\n",
" \"\"\"\n",
" x = self.x + [self.x[0]]\n",
" y = self.y + [self.y[0]]\n",
"\n",
" return ax.plot(x, y, **kwargs)\n",
" \n",
"\n",
" def __contains__(self, point: (float, float)):\n",
" \"\"\"\n",
" Return True if a certain `point` is within this Triangle instance.\n",
"\n",
" Example\n",
" -------\n",
" tr = Triangle((0, 0), width=5, height=5, ax)\n",
" point1 = (5, 4)\n",
" point2 = (7, 7)\n",
" \n",
" point1 in tr # True\n",
" point2 in tr # False\n",
" \"\"\"\n",
"\n",
" px, py = point\n",
"\n",
" # Triangle coordinates for origin and hypotenuse\n",
" tx1, tx3 = self.x[0], self.x[2]\n",
" ty1, ty3 = self.y[0], self.y[2]\n",
" \n",
" # See if point lies within the domain (x-axis) of the triangle\n",
" if tx1 <= px <= tx3 or tx3 <= px <= tx1:\n",
" # We now use eqn of hypotenuse to find height of triangle at px\n",
" m = (ty3 - ty1) / (tx3 - tx1) # Gradient\n",
" m = round(m, 3)\n",
" y = m * (px-tx1) + ty1\n",
"\n",
" return py <= y\n",
" return False\n",
"\n",
"class SemiCircle:\n",
" def __init__(self, origin: tuple, radius: float):\n",
" self.origin = origin\n",
" self.theta = np.linspace(0, np.pi, 100) # theta = 0 to pi radians for semi-circle\n",
" self.theta = np.around(self.theta, 5)\n",
" self.radius = radius\n",
" x = radius*np.cos(self.theta)\n",
" y = radius*np.sin(self.theta)\n",
" self.x = np.around(x, 5) + origin[0]\n",
" self.y = np.around(y, 5) + origin[1]\n",
" \n",
" def get_area(self):\n",
" return round(0.5 * abs(np.pi * self.radius**2), 5)\n",
" \n",
" def print_coords(self):\n",
" pprint(list(zip(self.theta, self.x, self.y)))\n",
"\n",
" def plot_axes(self, ax: 'Axes', **kwargs):\n",
" \"\"\"\n",
" Draw the semi-circle on the ax provided.\n",
" \"\"\"\n",
" artist = ax.plot(self.x, self.y, **kwargs)\n",
" return artist\n",
" \n",
" def __contains__(self, point: tuple):\n",
" \"\"\"\n",
" Use the `in` keyword to check whether a given point is within the circle.\n",
"\n",
" Example\n",
" -------\n",
" c = Circle((0,0), 5, None)\n",
" (0, 1) in c # True\n",
" (0, 10) in c # False\n",
" \"\"\"\n",
" cx, cy = self.origin\n",
" px, py = point\n",
" if py >= cy: # Since semi-circle, point must be above or on origin\n",
" distance_from_origin = math.sqrt( (px - cx)**2 + (py - cy)**2 )\n",
" if distance_from_origin <= self.radius:\n",
" return True\n",
" return False"
],
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"source": [
"def plot_the_shapes(ax, shapes):\n",
" for obj in shapes:\n",
" obj.plot_axes(ax, c='blue')\n"
]
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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"# Constants\n",
"N = [100, 1000, 10000]\n",
"LOWERX, UPPERX = 0.0, 4.0\n",
"LOWERY, UPPERY = 0.0, 2.0\n",
"random.seed(1)\n",
"\n",
"# Create the different regions\n",
"triangle1 = Triangle(origin=(0, 0), width=1, height=1)\n",
"triangle2 = Triangle(origin=(4, 0), width=-1, height=1)\n",
"rectangle = Rectangle(origin=(1, 0), width=2, height=1)\n",
"circle = SemiCircle(origin=(2, 1), radius=1)\n",
"\n",
"objects = (triangle1, triangle2, circle, rectangle)\n",
"\n",
"# Matplot figure and axes\n",
"fig, axs = plt.subplots(1, len(N))\n",
"fig.suptitle('Area estimation using Monte Carlo Method')\n",
"fig.set_size_inches((10,5))\n",
"\n",
"# Plot the initial shape on all axes\n",
"for i in range(len(N)):\n",
" ax = axs[i]\n",
" ax.set_aspect('equal')\n",
" ax.set_title(f'N={N[i]}')\n",
" plot_the_shapes(ax, objects)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"tags": []
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"(N= 100) Shaded Area \t Estimated: 4.4 \t Actual: 4.5708\n(N= 1000) Shaded Area \t Estimated: 4.48 \t Actual: 4.5708\n(N=10000) Shaded Area \t Estimated: 4.6152 \t Actual: 4.5708\n"
]
}
],
"source": [
"# Simulate\n",
"total_area = UPPERX * UPPERY\n",
"actual_shaded_area = sum([obj.get_area() for obj in objects])\n",
"estimated_area = 0\n",
"\n",
"for i in range(len(N)):\n",
" epoch = N[i]\n",
" hit_points = []\n",
" missed_points = []\n",
" for _ in range(epoch):\n",
" rx = round(random.uniform(LOWERX, UPPERX), 5)\n",
" ry = round(random.uniform(LOWERY, UPPERY), 5)\n",
" rpoint = (rx, ry)\n",
"\n",
" for obj in objects:\n",
" if rpoint in obj:\n",
" # random point lies within the shaded region\n",
" hit_points.append(rpoint)\n",
" break\n",
" else:\n",
" # the random point does not lie in the shaded region\n",
" missed_points.append(rpoint)\n",
" \n",
" estimated_area = round((len(hit_points) * total_area) / epoch, 5)\n",
" print(f'(N={epoch:>5}) Shaded Area \\t Estimated: {estimated_area} \\t Actual: {actual_shaded_area}')\n",
" hits = np.array(hit_points)\n",
" misses = np.array(missed_points)\n",
" ax = axs[i]\n",
" ax.scatter(hits[:, 0], hits[:, 1], c='g', marker='.')\n",
" ax.scatter(misses[:, 0], misses[:, 1], c='r', marker='.')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<Figure size 720x360 with 3 Axes>"
],
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