Fit a curve to sample data using NumPy and SciPy's curve_fit

NumPy: Integration with SciPy Exercise-6 with Solution

Write a NumPy program to create a set of sample data and fit a curve using SciPy's curve_fit function.

Sample Solution:

Python Code:

# Import necessary libraries
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

# Create a set of sample data using NumPy
np.random.seed(0)  # For reproducibility
x = np.linspace(0, 10, 100)
y = 2.5 * np.sin(1.5 * x) + np.random.normal(size=x.size)

# Define the model function to be fitted
def model_func(x, a, b):
    return a * np.sin(b * x)

# Use SciPy's curve_fit function to fit the model to the data
params, covariance = curve_fit(model_func, x, y)

# Extract the fitted parameters
a_fit, b_fit = params

# Generate y values using the fitted parameters
y_fit = model_func(x, a_fit, b_fit)

# Plot the original data and the fitted curve
plt.scatter(x, y, label='Sample Data')
plt.plot(x, y_fit, label='Fitted Curve', color='red')
plt.legend()
plt.show()

Output:

Explanation:

• Import necessary libraries:
• Import NumPy, SciPy's curve_fit function, and Matplotlib for plotting.
• Create a set of sample data using NumPy:
• Generate x values evenly spaced between 0 and 10, and corresponding y values using a sine function with added noise.
• Define the model function to be fitted:
• Create a sine function model with parameters a and b.
• Use SciPy's curve_fit function to fit the model to the data:
• Fit the model function to the data to determine the best-fit parameters.
• Extract the fitted parameters:
• Retrieve the parameters a and b from the fitting process.
• Generate y values using the fitted parameters:
• Use the fitted parameters to generate the y values.
• Plot the original data and the fitted curve:
• Use Matplotlib to visualize the sample data and the fitted curve.

Python-Numpy Code Editor:

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