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@yunisangadji
Created April 22, 2024 01:57
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "b51da827",
"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 analytic 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."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "726cee8e",
"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": 3,
"id": "de46345f",
"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": 4,
"id": "8fb12706",
"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": 5,
"id": "730996d5",
"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": 6,
"id": "5e536f72",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated integral: 2.5261510682484894e-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()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "df67af21",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated integral of sin^2(x) from 0 to 3.141592653589793 using 10000 samples: 1.5743234939856285\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": 8,
"id": "56d69fff",
"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": 9,
"id": "7f74f326",
"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()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bcddaa96",
"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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