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Curve fitting is a very effective tool that is widely used in analysis. Curve fitting method studies the relationship between independent variables (also called predictor variables) and dependent variable (called response variable). This method aims to provide the best fit model to fit a certain number of data points.

There are two types of curve fitting:

• Logarithmic Curve Fitting
• Exponential curve fitting

In this tutorial, we will show you how to perform logarithmic curve fitting and exponential curve fitting in Python.

Libraries and modules for logarithmic and exponential curve fitting in Python

Let us discuss the possible libraries and modules that can be used to execute the program.

NumPy library

We will use NumPythe functions from the library as follows.

• array()- This function is used to create an NumPyarray, which is a set of values ​​of the same type with index values ​​in the form of a tuple.
• log()- This function is more like a mathematical operation that helps calculate the natural logarithm of a number that is a part of the input array elements.
• exp()- This function is also a mathematical operation which calculates NumPythe exponential of the elements present in the input array.
• polyfit()- This function helps to fit any data in a polynomial function. It performs least squares on the polynomial fit.

Matplotlib Library

MatplotlibThe library is mainly used for plotting in Python. This library is commonly used to create visualizations in Python. In this tutorial, a module from this library is used, called pyplotmodule.

MatplotlibThe library's MATLAB pyplotmodule is an open source module that helps make Matplotlibthe library work like MATLAB. This module has many functions that help us to create plot areas, create labels on plots, etc.

Logarithmic Curve Fitting

As the name suggests, a logarithmic equation is plotted here. Let’s jump directly to the code where we will do the logarithmic curve fitting in Python.

import numpy as np

x = np.array([5, 10, 15, 20, 25])
y = np.array([3, 6, 9, 12, 15])

log_x = np.log(x)
log_y = np.log(y)

coefficients = np.polyfit(log_x, y, 1)
print(coefficients)

Output:

[ 7.2647162  -9.64806344]

For drawing, follow this procedure.

import matplotlib.pyplot as plt

c = 7.26 * log_x - 9.64
plt.plot(log_x, y, "o")
plt.plot(log_x, c)

Output:

In the above program, we first import the necessary libraries. After that, we create two NumPyarrays as our main data. Then, we calculate the logarithmic values ​​of the elements in both arrays. We use polyfit()the function for the logarithmic values ​​of the xand yarrays. Using polyfit()the function, the coefficient of the logarithmic equation is returned.

• After obtaining the coefficients, we use these coefficients in the logarithmic equation to plot the curve.
• Finally, we draw the graph using the function of the module Matplotlibof the library .pyplotplot()

Exponential curve fitting

As the name suggests, an exponential equation is plotted here. Let’s jump directly to the code where we will do exponential curve fitting in Python.

import numpy as np

a = np.array([6, 12, 18, 24, 30])
b = np.array([4, 8, 12, 16, 20])

log_a = np.log(a)
log_b = np.log(b)

coefficients = np.polyfit(a, log_b, 1)
print(coefficients)

Output:

[0.06520038 1.17018581]

For plotting, here is the code snippet you can follow.

c = np.exp(1.17) * np.exp(0.06 * a)
plt.plot(a, b, "o")
plt.plot(a, c)

Output:

Follow the same process as we did in logarithmic curve fitting. But here, an exponential function is used instead of logarithmic function. So, polyfit()the coefficients returned by the function are passed in the exponential function equation.