# Numerical Computation with Python

## Numerical Computation

Usually, the term numerical computation means to use computing machines to solve problems involving numbers. In programming, numerical analysis refers to methods that help in solving science and engineering problems. A numerical method determines a mathematical tool that solves numerical problems. Moreover, a numerical algorithm implements a numerical method with a suitable convergence check in any programming language.

## Use of Numerical Computation in Python

Numerical computation is very crucial for determining the accurate output of a program. With the evolution in programming and its need in life, there is a frequent need to process large amounts of data sets for computational science applications. There is a setback in computation with simple Python for loops as they lead to slow code compared to other languages such as Fortran, C, and C++. Therefore, there is an extension of Python known as the Numerical Python or NumPy. NumPy efficiently allows array computations. There is a fixed size, fix type, multidimensional array type, and various other array options for numerical Python. Moreover, the speed of NumPy operations is very similar to those of Fortran, C, and C++.

## Python Numerical Libraries

One of the critical features for using Python for numerical computations is the numerous libraries and packages. Following are some of the most popular packages and libraries, which prove beneficial for numeric and scientific applications.

- SciPy (Scientific Numeric Library)
- Pandas (Data Analytics Library)
- IPython (Command Shell)
- Numeric (Fundamental Numeric Package)
- Natural Language Toolkit (Library for Mathematical and Text Analysis)

Explanation of some of these libraries is as follows.

### SciPy (Scientific Numeric Library)

SciPy is a free and open-source library for scientific and technical computing. There are various vital modules in SciPy for optimization, Fast Fourier Transform (FFT), image processing, signal processing, and special functions. Moreover, the SciPy package possesses functions and algorithms at the root of Python’s scientific computing capabilities. These algorithms include io, signal, spatial, linas, lib, interpolate, fftpack, integrate, cluster, stats, and many others.

### Pandas (Data Analytics Library)

Pandas is the most important library for data analysis. Pandas supports formats such as CSV, TSV, or an SQL database and converts it to Python data frames to make it similar to tables having rows and columns for statistical formats. The important codes to implement different operations with Pandas after importing the library are following:

- read_filetype() to open a specific file
- DataFrame() to convert a specific Python object
- to_filetype(file) to save a data frame

Moreover, the users can perform functions such as mean(), mode(), max(), min(), std(), corr(), and count() on a data frame.

### IPython (Command Shell)

IPython is a command shell that is helpful for interactive calculation in different programming languages. IPython provides features like self-examination, shell syntax, rich media, tab completion, and history. Moreover, it is a browser-based notebook interface that supports code, text, inline plots, mathematical expressions, interactive data visualization, and Graphical User Interface (GUI) toolkits. It also contributes to parallel and distributed computing. It supports enhanced parallel applications, including task parallelism, customer user-defined prototypes, data parallelism, message cursory using MPI, multiple programs, multiple data parallelism, and single program multiple data parallelism.

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