simulate a 2d gaussian function and fit it to a 2d gaussian function in python

main.py
import numpy as np
import matplotlib.pyplot as plt

# Define the 2D Gaussian function
def gaussian_2d(x, y, amplitude, x0, y0, sigma_x, sigma_y):
    return amplitude * np.exp(-((x - x0) ** 2 / (2 * sigma_x ** 2) + (y - y0) ** 2 / (2 * sigma_y ** 2)))

# Generate x and y values
x = np.linspace(-10, 10, 100)
y = np.linspace(-10, 10, 100)
x, y = np.meshgrid(x, y)

# Simulate the 2D Gaussian function
amplitude = 1.0
x0 = 0.0
y0 = 0.0
sigma_x = 2.0
sigma_y = 3.0
z = gaussian_2d(x, y, amplitude, x0, y0, sigma_x, sigma_y)

# Add some noise to the simulated data
z += np.random.normal(0, 0.1, size=z.shape)

# Plot the simulated data
plt.imshow(z, cmap='viridis', extent=[-10, 10, -10, 10])
plt.show()
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main.py
from scipy.optimize import curve_fit

# Define the 2D Gaussian function to fit
def gaussian_2d_fit(x, y, amplitude, x0, y0, sigma_x, sigma_y):
    return gaussian_2d(x, y, amplitude, x0, y0, sigma_x, sigma_y)

# Flatten the x, y, and z values for fitting
x_flat = x.flatten()
y_flat = y.flatten()
z_flat = z.flatten()

# Initial guess for the fitting parameters
initial_guess = [amplitude, x0, y0, sigma_x, sigma_y]

# Fit the 2D Gaussian function
popt, pcov = curve_fit(gaussian_2d_fit, (x_flat, y_flat), z_flat, p0=initial_guess)

# Print the fitted parameters
print("Fitted parameters:")
print("Amplitude:", popt[0])
print("x0:", popt[1])
print("y0:", popt[2])
print("sigma_x:", popt[3])
print("sigma_y:", popt[4])

# Plot the fitted function
z_fit = gaussian_2d(x, y, *popt)
plt.imshow(z_fit, cmap='viridis', extent=[-10, 10, -10, 10])
plt.show()
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