How to do exponential and logarithmic curve fitting in Python?

How to do exponential and logarithmic curve fitting in Python?

Exponential and logarithmic curve fitting in Python can be done using the numpy and scipy libraries. Here's how you can fit both types of curves using these libraries:

1. Exponential Curve Fitting:

An exponential function can be represented as y=a×ebx.

import numpy as np from scipy.optimize import curve_fit import matplotlib.pyplot as plt # Define the exponential function def exponential(x, a, b): return a * np.exp(b * x) # Example data x = np.array([0, 1, 2, 3, 4, 5]) y = np.array([1, 2.7, 7.4, 20.1, 54.6, 148.4]) # Assuming y is approximately 1*e^(x) # Curve fitting params, covariance = curve_fit(exponential, x, y) # Predicted values y_fit = exponential(x, *params) # Plotting plt.scatter(x, y, label='Data') plt.plot(x, y_fit, label=f'Fit: a={params[0]:.2f}, b={params[1]:.2f}') plt.legend() plt.show()

2. Logarithmic Curve Fitting:

A logarithmic function can be represented as y=a+b×ln(x).

# Define the logarithmic function def logarithmic(x, a, b): return a + b * np.log(x) # Example data x = np.array([1, 2, 3, 4, 5, 6]) y = np.array([0, 0.7, 1.1, 1.4, 1.6, 1.8]) # Assuming y is approximately 0 + 1*ln(x) # Curve fitting params, covariance = curve_fit(logarithmic, x, y) # Predicted values y_fit = logarithmic(x, *params) # Plotting plt.scatter(x, y, label='Data') plt.plot(x, y_fit, label=f'Fit: a={params[0]:.2f}, b={params[1]:.2f}') plt.legend() plt.show()

For both cases, curve_fit returns the optimal parameters (a and b) for the fit, and the covariance of the parameters. In the plots, you can observe the original data and the curve fit to understand how well the function models the data.

Make sure to handle cases where the logarithm might not be defined (i.e., for x≤0). Adjust your data or model accordingly to avoid this issue.

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