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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "68e875f0",
"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": "819d2223",
"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"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "47a02832",
"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": "a3afdecd",
"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": "48fd778c",
"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()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "30dc8534",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated integral: 2.513119570361325e-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": "a59ac68c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Estimated integral of sin^2(x) from 0 to 3.141592653589793 using 10000 samples: 1.5749975466591597\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": "d8432960",
"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": "93a38c11",
"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": "3d75ff7c",
"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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