Separating Real and Imaginary Parts of a Function Evaluated in mpmath Python

In this article, we will explore how to separate the real and imaginary parts of a function evaluated in the mpmath Python library. The mpmath library is a high-precision floating-point arithmetic library for Python. It provides support for various mathematical functions, including the MeijerG function.

The MeijerG function is a special function that appears in various areas of mathematics and physics. In this article, we will use the MeijerG function to evaluate an example function and demonstrate how to separate its real and imaginary parts using mpmath and Python.

Introduction to mpmath

The mpmath library provides support for high-precision floating-point arithmetic in Python. It allows you to perform calculations with arbitrary precision, which is useful in various applications such as scientific computing, numerical analysis, and machine learning.

One of the key features of mpmath is its ability to handle complex numbers. Complex numbers are numbers that have both real and imaginary parts. In this article, we will use mpmath to evaluate a function with complex inputs and then separate the real and imaginary parts of the output using Python.

Separating Real and Imaginary Parts

When evaluating a function with complex inputs in mpmath, the output is always a complex number. However, we often want to extract only the real or imaginary part of the result. This can be done using various methods, including numerical differentiation or integration.

In this article, we will use a combination of mpmath and Python to separate the real and imaginary parts of a function evaluated in mpmath. We will demonstrate how to do this for an example function involving the MeijerG function.

The Example Function

Let’s consider an example function that involves the MeijerG function:

from mpmath import *
import numpy as np

# Define the parameters of the function
a = mpf(0.25)
b = mpf(0.25)
z = mpf(0.75)

def q(frequency):
    omega = (((i ** 2) * 2 * math.pi * frequency) / D)  # depends on bh and frequency
    u = ((-j/(math.pi * omega))*meijerg([[1, 3/2], []], [[1, 1], [0.5, 0]], j*omega))
    return np.real(u), np.imag(u)

In this example function, we define the parameters a, b, and z using mpmath. We then define a function q that takes a frequency input and returns the real and imaginary parts of the output.

Evaluating the Function

To evaluate the function q, we can use np.vectorize. This allows us to apply the function q to each element in an array:

T = np.vectorize(q)
print(T(frequency))

This code evaluates the function q for each frequency in the input array and returns the real and imaginary parts of the output as a 2D array.

Separating Real and Imaginary Parts

To separate the real and imaginary parts of the output, we can use numerical methods such as interpolation or extrapolation. In this example, we will simply transpose the 2D array returned by np.vectorize to get the real and imaginary parts:

df = np.array(T(frequency)).T

This code transposes the 2D array to swap the rows and columns, effectively separating the real and imaginary parts of the output.

Creating a DataFrame

To make it easier to work with the data, we can create a pandas DataFrame:

df1 = pd.DataFrame(data=df, columns=['bh', 'frequency','Re', 'Im'])

This code creates a new DataFrame with the real and imaginary parts of the output as columns.

Saving the Data

Finally, we can save the data to a CSV file using pd.to_csv:

df1.to_csv('C:\\Users\\Mohamed Boutchich\\PycharmProjects\\calculations\\T.csv')

This code saves the DataFrame to a CSV file with the specified path.

Conclusion

In this article, we demonstrated how to separate the real and imaginary parts of a function evaluated in mpmath using Python. We used np.vectorize to apply the function to each element in an array and then separated the real and imaginary parts using numerical methods such as interpolation or extrapolation.

We also created a pandas DataFrame to make it easier to work with the data and saved it to a CSV file for further analysis or plotting.

I hope this article has been helpful in explaining how to separate the real and imaginary parts of a function evaluated in mpmath using Python. If you have any questions or comments, please feel free to ask!

Last modified on 2024-01-26