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@afrozhie
Created April 4, 2024 06:31
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ipynb for issues 9 session 9
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{
"cells": [
{
"cell_type": "markdown",
"id": "94dbde77-f517-4f0d-898f-9fa3097c48f2",
"metadata": {},
"source": [
"#### Resume Session 9\n",
"#### Firman Andrian\n",
"#### 21181094"
]
},
{
"cell_type": "markdown",
"id": "c8c70b92-5ae1-45bf-8409-a5962b598af6",
"metadata": {},
"source": [
"## Monte Carlo Integration\n",
"### Monte Carlo method\n",
"- It is statistical method of understanding complex physical or \n",
"mathematical systems.\n",
"- It is using randomly generated numbers as input into those \n",
"systems to generate a range of solutions."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "6fbceb08-4cb6-431b-9a4e-8ed2f89f44c2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"5 7 3 2 6 2 6 4 8 5 7 3 7 8 5 2 4 7 2 6 5 4 4 4 4 3 6 7 7 7 6 4 3 4 8 4 2 2 7 4 7 6 3 6 7 5 6 3 5 4 7 3 3 4 5 5 4 4 5 3 3 4 2 6 6 7 2 6 6 4 6 2 3 6 7 2 2 4 5 6 7 2 8 5 7 8 6 6 5 6 8 2 4 5 4 7 8 6 8 5 \n",
"\n",
"\n",
"100\n"
]
}
],
"source": [
"\n",
"##### Random numbers\n",
"import random as rnd\n",
"import matplotlib.pyplot as plt\n",
"N = 100\n",
"a = 2\n",
"b = 8\n",
"x = []\n",
"for i in range(N):\n",
" j = rnd.randint(a, b)\n",
" x.append(j)\n",
" print(j, end=' ')\n",
"print('\\n\\n')\n",
"\n",
"print(len(x))"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "df7daa33-6457-4124-81c4-c555f3a91cbc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 400x300 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"##### Linear function\n",
"def f(x):\n",
" y = 3*(x-2) +4\n",
" return y\n",
"\n",
"y = [f(i) for i in x]\n",
"\n",
"plt.figure(figsize=(4, 3))\n",
"plt.plot(x, y)\n",
"plt.xticks(range(a, b + 2))\n",
"plt.yticks(range(0, 26,4))\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"plt.title(\"Monte Carlo Simulation of Linear Function\")\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "cd6ed69b-5013-4b1b-b70c-910e197965ae",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"##### Quadratic function\n",
"import numpy as np\n",
"\n",
"def quadratic(x, a, b, c):\n",
" return a * x**2 + b * x + c\n",
"\n",
"a = 2 # Coefficient of x^2\n",
"b = 3 # Coefficient of x\n",
"c = 1 # Constant term\n",
"\n",
"x_min = -5\n",
"x_max = 5\n",
"num_samples = 10000 # Number of random samples\n",
"\n",
"x_values = np.random.uniform(low=x_min, high=x_max, size=num_samples)\n",
"y_values = quadratic(x_values, a, b, c)\n",
"\n",
"theoretical_x = np.linspace(x_min, x_max, 100) # 100 points for smooth curve\n",
"theoretical_y = quadratic(theoretical_x, a, b, c)\n",
"\n",
"plt.scatter(x_values, y_values, alpha=0.5, label=\"Simulated Points\")\n",
"plt.plot(theoretical_x, theoretical_y, label=\"Theoretical Curve\")\n",
"plt.xlabel(\"X-Values\")\n",
"plt.ylabel(\"Y-Values\")\n",
"plt.title(\"Monte Carlo Simulation of a Quadratic Function\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "332e4973-32b7-4741-9240-1d6ea29532d8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated integral: 2.4703209811358388e-05\n",
"Analytical solution (optional): 0.25\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"##### Cubic function\n",
"def cubic_function(x):\n",
" return x**3\n",
"\n",
"a = 0\n",
"b = 1\n",
"iterations = 10000\n",
"\n",
"x_samples = np.random.uniform(a, b, iterations)\n",
"y_samples = cubic_function(x_samples)\n",
"area_rectangle = (b - a) * (b - a)\n",
"\n",
"estimated_integral = (area_rectangle * np.mean(y_samples)) / iterations\n",
"analytical_solution = (b**4 - a**4) / 4\n",
"\n",
"print(\"Estimated integral:\", estimated_integral)\n",
"print(\"Analytical solution (optional):\", analytical_solution)\n",
"\n",
"plt.plot(np.linspace(a, b, 100), cubic_function(np.linspace(a, b, 100)), label=\"Cubic Function\")\n",
"plt.scatter(x_samples, y_samples, alpha=0.3, label=\"Random Samples\")\n",
"plt.xlabel(\"X\")\n",
"plt.ylabel(\"Y\")\n",
"plt.title(\"Monte Carlo Integration of Cubic Function\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "639a67da-cf74-4618-bdce-fe45de625c05",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated integral of sin^2(x) from 0 to 3.141592653589793 using 10000 samples: 1.5726460131481619\n",
"Analytical solution: 0.0\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"##### Sine squared function\n",
"\n",
"def f(x):\n",
" return np.sin(x)**2\n",
"\n",
"a = 0\n",
"b = np.pi\n",
"N = 10000\n",
"\n",
"x = np.random.uniform(a, b, size=N)\n",
"y = f(x)\n",
"\n",
"integral_estimate = (b - a) * np.mean(y)\n",
"print(\"Estimated integral of sin^2(x) from\", a, \"to\", b, \"using\", N, \"samples:\", integral_estimate)\n",
"analytical_integral = (1 - np.cos(2*b)) / 2 - (1 - np.cos(2*a)) / 2\n",
"print(\"Analytical solution:\", analytical_integral)\n",
"\n",
"x_axis = np.linspace(a, b, 1000)\n",
"plt.plot(x_axis, f(x_axis), label=\"sin^2(x)\")\n",
"plt.axhline(y=integral_estimate, color='r', linestyle='--', label=\"Estimated Integral Area\")\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"f(x)\")\n",
"plt.title(\"Monte Carlo Integration of sin^2(x)\")\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "3329f28b-dbde-446e-9fc1-93424365ff71",
"metadata": {},
"source": [
"### The Fast Fourier Transform (FFT) \n",
"is a powerful algorithm used to analyze signals in the frequency domain. It efficiently calculates the Discrete Fourier Transform (DFT) of a signal, which decomposes the signal into its constituent frequencies and their amplitudes. In Python, the scipy.fftpack library provides functions for performing FFT calculations.\n",
"\n",
"##### Here's a breakdown of Fast Fourier Transform in Python\n",
"- Takes a signal (represented as a list or NumPy array) in the time domain (e.g., voltage vs. time).\n",
"- Decomposes it into its frequency components (sine and cosine waves) and their strengths (amplitudes).\n",
"- Helps understand the frequency content of the signal.\n",
"\n",
"##### Importance:\n",
"- Used in various applications like:\n",
"- Signal processing (filtering noise, analyzing audio/images)\n",
"- Data compression (removing redundant information)\n",
"- Solving differential equations"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "80ce0fef-1b07-412c-b083-98be6598f410",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.fftpack import fft, fftshift\n",
"\n",
"t = np.linspace(0, 1, 1000) # Time samples\n",
"f = 2 # Frequency of the signal\n",
"y = np.sin(2*np.pi*f*t) # Generate the sine wave\n",
"\n",
"fft_data = fft(y)\n",
"fft_abs = np.abs(fft_data)\n",
"freqs = np.fft.fftfreq(len(y)) * f # Calculate frequencies\n",
"fft_shifted = fftshift(fft_abs)\n",
"freqs_shifted = fftshift(freqs)\n",
"\n",
"plt.subplot(2, 1, 1)\n",
"plt.plot(t, y)\n",
"plt.xlabel(\"Time (s)\")\n",
"plt.ylabel(\"Signal\")\n",
"plt.title(\"Original Signal\")\n",
"\n",
"plt.subplot(2, 1, 2)\n",
"plt.plot(freqs_shifted, fft_shifted)\n",
"plt.xlabel(\"Frequency (Hz)\")\n",
"plt.ylabel(\"Magnitude\")\n",
"plt.title(\"Magnitude of the FFT\")\n",
"plt.xlim(-f, f) # Set frequency axis limits\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "51c0f9e5-2385-4ae7-bd66-3cd545abae39",
"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": "3.11.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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