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Last active April 4, 2024 06:01
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Monte Carlo Method and Random Numbers
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{
"cells": [
{
"cell_type": "code",
"execution_count": 4,
"id": "46c049d0",
"metadata": {},
"outputs": [],
"source": [
"# Monte Carlo method\n",
"#• It is statistical method of understanding complex physical or mathematical systems.\n",
"#• It is using randomly generated numbers as input into those systems to generate a range of solutions.\n",
"#• The likelihood of a particular solution can be found by dividing the number of times that solution was generated by the total number of trials.\n",
"#• By using larger and larger numbers of trials, the likelihood of the solutions can be determined more and more accurately.\n",
"#• The Monte Carlo method is used in a wide range of subjects, including mathematics, physics, biology, engineering, and finance.\n",
"#• And it is also used in problems in which determining an ana\u0002lytic solution would be too time-consuming.\n",
"\n",
"# Advantages\n",
"#• Simplicity (adapts well to multi-dimensional integrals).\n",
"#• Unbiased and consistent.\n",
"#• Parallel nature: each processor of a computer can be assigned the task of making a random trial (at least processing trials in batches) and thus work on solving an integration in parallel.\n",
"\n",
"# Disadvantages\n",
"#• Slow rate of convergence.\n",
"#• Difficult to evaluate the variance of the function f(x), and hard to know what the error of the approximation is.\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "2c5c3e4b",
"metadata": {},
"outputs": [],
"source": [
"#Random Numbers\n",
"\n",
"#A random number is a number that is selected seemingly at random from a particular distribution. This means that when you select a large set of these numbers, the distribution of the numbers should match the underlying distribution.\n",
"#Almost always, these numbers also need to be independent, meaning that there is no correlation between consecutive numbers.\n",
"\n",
"#Additional Information:\n",
"#Random numbers are used in various applications, including:\n",
"#-Simulation and modeling\n",
"#-Cryptography\n",
"#-Sampling\n",
"#-Testing\n",
"\n",
"#There are various methods for generating random numbers, including:\n",
"#-Physical methods, such as using dice or a random number generator\n",
"#-Computational methods, such as using pseudorandom number generators\n",
"#-it is important to use high-quality random numbers in order to ensure the accuracy and reliability of the results."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "6bbe43d0",
"metadata": {},
"outputs": [],
"source": [
"# Average rectangular area :\n",
"#• By adding up the area of the rectangles andaveraging the sum,the resulting numbergets closer and closerto the actual result ofthe integral.\n",
"#• In fact, the rectangles which are too large compensate for the rectangles which are too small.\n",
"#• So it seems that the empirical mean of f(x) could be a good estimator for the integral.\n",
"#• This idea is formalized with the following formula, which is the Monte Carlo estimator.\n",
"#• It uses random variable X to get random value of rectangle area FN from N attempts."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "9373b2d5",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Define the linear function (y = mx + b)\n",
"def linear_function(x, m, b):\n",
" return m * x + b\n",
"\n",
"# Set the parameters for the linear function\n",
"m = 2 # Slope\n",
"b = 3 # y-intercept\n",
"\n",
"# Define the range of x values for simulation\n",
"x_min = 0\n",
"x_max = 10\n",
"\n",
"# Set the number of random samples\n",
"num_samples = 1000\n",
"\n",
"# Generate random x values within the defined range\n",
"x = np.random.uniform(low=x_min, high=x_max, size=num_samples)\n",
"\n",
"# Calculate the corresponding y values using the linear function\n",
"y = linear_function(x, m, b)\n",
"\n",
"# Plot the actual linear function\n",
"plt.plot(x, linear_function(x, m, b), label=\"Actual Function\")\n",
"\n",
"# Plot the simulated points\n",
"plt.scatter(x, y, label=\"Simulated Points\")\n",
"\n",
"# Add labels and title\n",
"plt.xlabel(\"X\")\n",
"plt.ylabel(\"Y\")\n",
"plt.title(\"Monte Carlo Simulation of Linear Function\")\n",
"plt.legend()\n",
"\n",
"# Show the plot\n",
"plt.grid(True)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "5dad1438",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Define the quadratic function\n",
"def quadratic(x, a, b, c):\n",
" return a * x**2 + b * x + c\n",
"\n",
"# Set the parameters of the quadratic function\n",
"a = 2 # Coefficient of x^2\n",
"b = 3 # Coefficient of x\n",
"c = 1 # Constant term\n",
"\n",
"# Define the range of x-values for simulation\n",
"x_min = -5\n",
"x_max = 5\n",
"num_samples = 10000 # Number of random samples\n",
"\n",
"# Generate random x-values within the defined range\n",
"x_values = np.random.uniform(low=x_min, high=x_max, size=num_samples)\n",
"\n",
"# Calculate the corresponding y-values using the quadratic function\n",
"y_values = quadratic(x_values, a, b, c)\n",
"\n",
"# Generate a theoretical curve for the quadratic function\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",
"# Plot the results\n",
"plt.scatter(x_values, y_values, alpha=0.5, label=\"Simulated Points\")\n",
"plt.plot(theoretical_x, theoretical_y, label=\"Theoretical Curve\")\n",
"\n",
"# Set labels and title for the plot\n",
"plt.xlabel(\"X-Values\")\n",
"plt.ylabel(\"Y-Values\")\n",
"plt.title(\"Monte Carlo Simulation of a Quadratic Function\")\n",
"plt.legend()\n",
"\n",
"# Show the plot\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "3da23721",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated integral: 2.4794790749132826e-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": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Define the cubic function\n",
"def cubic_function(x):\n",
" return x**3\n",
"\n",
"# Integration limits (a and b)\n",
"a = 0\n",
"b = 1\n",
"\n",
"# Number of random samples (iterations)\n",
"iterations = 10000\n",
"\n",
"# Generate random samples within the integration limits\n",
"x_samples = np.random.uniform(a, b, iterations)\n",
"\n",
"# Calculate the function values at the random samples\n",
"y_samples = cubic_function(x_samples)\n",
"\n",
"# Area of a rectangle under the curve = base * height\n",
"area_rectangle = (b - a) * (b - a)\n",
"\n",
"# Estimate of the integral using Monte Carlo method\n",
"estimated_integral = (area_rectangle * np.mean(y_samples)) / iterations\n",
"\n",
"# Analytical solution for comparison (optional)\n",
"analytical_solution = (b**4 - a**4) / 4\n",
"\n",
"# Print the estimated integral and analytical solution (if available)\n",
"print(\"Estimated integral:\", estimated_integral)\n",
"print(\"Analytical solution (optional):\", analytical_solution)\n",
"\n",
"# Plot the function and the random samples\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()\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "09ef840a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated integral of sin^2(x) from 0 to 3.141592653589793 using 10000 samples: 1.579392497026159\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": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Define the function to integrate (sine squared)\n",
"def f(x):\n",
" return np.sin(x)**2\n",
"\n",
"# Set the integration limits\n",
"a = 0\n",
"b = np.pi\n",
"\n",
"# Number of samples for Monte Carlo simulation (adjust for desired accuracy)\n",
"N = 10000\n",
"\n",
"# Generate random samples within the integration limits\n",
"x = np.random.uniform(a, b, size=N)\n",
"\n",
"# Calculate the function values at the random samples\n",
"y = f(x)\n",
"\n",
"# Estimate the integral using the Monte Carlo method\n",
"integral_estimate = (b - a) * np.mean(y)\n",
"\n",
"# Print the estimated integral value\n",
"print(\"Estimated integral of sin^2(x) from\", a, \"to\", b, \"using\", N, \"samples:\", integral_estimate)\n",
"\n",
"# Analytical solution for comparison (optional)\n",
"analytical_integral = (1 - np.cos(2*b)) / 2 - (1 - np.cos(2*a)) / 2\n",
"print(\"Analytical solution:\", analytical_integral)\n",
"\n",
"# Plot the function and the estimated integral area (optional)\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": "code",
"execution_count": 10,
"id": "fdd7b7c6",
"metadata": {},
"outputs": [],
"source": [
"#The Fast Fourier Transform (FFT) 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",
"\n",
"#What it Does:\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": 11,
"id": "ad4cdb2e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.fftpack import fft, fftshift\n",
"\n",
"# Define a sample signal\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",
"# Perform FFT\n",
"fft_data = fft(y)\n",
"\n",
"# Calculate absolute values and frequencies\n",
"fft_abs = np.abs(fft_data)\n",
"freqs = np.fft.fftfreq(len(y)) * f # Calculate frequencies\n",
"\n",
"# Shift zero-frequency component to the center\n",
"fft_shifted = fftshift(fft_abs)\n",
"freqs_shifted = fftshift(freqs)\n",
"\n",
"# Plot the original signal and its FFT magnitude\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()\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9b89bb33",
"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
}
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