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rifazn/Assignment 3 Part A - Area (and Pi) estimation using Monte Carlo method.ipynb

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Assignment 3 Part A for Simulation & Modeling Lab (UIU)
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Assignment 3 Part A - Area (and Pi) estimation using Monte Carlo method.ipynb
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"source": [
"# CSI 424, Simulation & Modeling Lab, Sec: B\n",
"\n",
"# Assignment 2 (Part A)\n",
"\n",
"## Using Monte Carlo simulation, find the value of PI and area of the circle using the given circle and square.\n",
"\n",
"## By: Rifaz Nahiyan (011 152 054)"
]
},
{
"cell_type": "code",
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"id": "appropriate-toyota",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import math\n",
"import numpy as np\n",
"import random"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "novel-housing",
"metadata": {},
"outputs": [],
"source": [
"UPPER_X = UPPER_Y = 5\n",
"LOWER_X = LOWER_Y = -5\n",
"AREA_SQUARE = abs(UPPER_X * UPPER_Y) * 4\n",
"RADIUS = 3\n",
"\n",
"random.seed(1)"
]
},
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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"# Draw the inital graph\n",
"\n",
"# We are making 3 axes for doing the simulation 3 times\n",
"fig, axs = plt.subplots(3, 1, sharex=True, sharey=True)\n",
"fig.set_size_inches((10, 12))\n",
"\n",
"def init_plot(ax: 'Axes'):\n",
" \"\"\"\n",
" Draws the red circle and the blue square on the given Axes instance.\n",
" \"\"\"\n",
" square_points = [\n",
" (LOWER_X, LOWER_Y),\n",
" (UPPER_X, LOWER_Y),\n",
" (UPPER_X, UPPER_Y),\n",
" (LOWER_X, UPPER_Y),\n",
" (LOWER_X, LOWER_Y) # Back to start\n",
" ]\n",
" square_points = np.array(square_points)\n",
" ax.plot(square_points[:, 0], square_points[:, 1], c='blue')\n",
"\n",
" # Circle\n",
" cx = np.linspace(-RADIUS, RADIUS, 1000) # Return evenly spaced numbers over a specified interval.\n",
" cy = [math.sqrt(RADIUS**2 - x**2) for x in cx]\n",
"\n",
" ax.grid()\n",
" ax.set_aspect('equal')\n",
" ax.set_ylabel('y-axis')\n",
" ax.plot(cx, cy, c='red')\n",
" ax.plot(cx, [-y for y in cy], c='red')\n",
"\n",
" return ax\n",
"\n",
"for ax in axs:\n",
" init_plot(ax)\n",
"axs[-1].set_xlabel('x-axis')"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "respective-correction",
"metadata": {},
"outputs": [],
"source": [
"def simulate(N: int):\n",
" \"\"\"\n",
" Generate `N` random x,y coordinates within range `UPPER_X` and `UPPER_Y`\n",
" and populate arrays `hit_points` and `missed_points`\n",
" \"\"\"\n",
" def dist(x, y, origin=(0, 0)):\n",
" \"\"\"\n",
" Return distance from origin to point (x,y)\n",
" \"\"\"\n",
" return math.sqrt( (x - origin[0]) ** 2 + (y - origin[1]) ** 2 )\n",
" \n",
" global hit_points\n",
" global missed_points\n",
" \n",
" # Reset the lists before populating them\n",
" hit_points = []\n",
" missed_points = []\n",
" \n",
" # Simulate\n",
" for i in range(N):\n",
" x, y = random.uniform(LOWER_X, UPPER_X), random.uniform(LOWER_Y, UPPER_Y)\n",
"\n",
" if dist(x, y) <= RADIUS:\n",
" hit_points.append( (x,y) )\n",
" else:\n",
"\n",
" missed_points.append( (x,y) )\n",
"\n",
"def plot_simulation(ax: 'An Axes instance'):\n",
" hits = np.array(hit_points)\n",
" misses = np.array(missed_points)\n",
" \n",
" ax.scatter(hits[:, 0], hits[:, 1], c='red')\n",
" ax.scatter(misses[:, 0], misses[:, 1], c='blue')"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "aggressive-india",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"For N=100, Estimated Pi: 3.33333, and Area: 30.0 unit²\nFor N=1000, Estimated Pi: 3.23333, and Area: 29.1 unit²\nFor N=10000, Estimated Pi: 3.10667, and Area: 27.96 unit²\n"
]
}
],
"source": [
"hit_points = []\n",
"missed_points = []\n",
"\n",
"N = [100, 1000, 10000]\n",
"pi_ests = []\n",
"area_ests = []\n",
"\n",
"for i in range(len(N)):\n",
" epoch = N[i]\n",
" # Generate the `hit_points` and `missed_points` array that can be used for pi estimation\n",
" simulate(epoch)\n",
"\n",
" # Use the `hit_points` and `missed_points` array to plot on the graph\n",
" # ### Problem: `plt` is not using the previous graph\n",
" plot_simulation(axs[i])\n",
"\n",
" # Evaluate the value of Pi and the area of the circle\n",
" hits = len(hit_points)\n",
" # π = (hits/N) * (AREA_SQUARE / RADIUS**2)\n",
" est_pi = round(hits / epoch, 5) * round(AREA_SQUARE / RADIUS**2, 5)\n",
"\n",
" area = est_pi * RADIUS**2\n",
"\n",
" pi_ests.append(est_pi)\n",
" area_ests.append(area)\n",
"\n",
" axs[i].text(x=-5, y=4, s=f'est_pi={round(est_pi, 5)}', color='white', backgroundcolor='black')\n",
" print(f'For N={epoch}, Estimated Pi: {round(est_pi, 5)}, and Area: {round(area, 2)} unit²')\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<Figure size 720x864 with 3 Axes>"
],
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