# A single-domain implementation of the Voigt/complex error function by vectorized interpolation

## TL;DR

This paper introduces a fast, vectorized interpolation method for computing the Voigt/complex error function over a specific domain, significantly outperforming existing C/C++ implementations, with a practical MATLAB code provided.

## Contribution

The paper presents a novel vectorized interpolation approach for rapid Voigt/complex error function computation over a single domain, optimized for spectroscopic applications.

## Key findings

- Algorithm is 8 times faster in certain domains.
- Algorithm is 3 times faster in larger domains.
- MATLAB implementation demonstrates practical efficiency.

## Abstract

In this work we show how to perform a rapid computation of the Voigt/complex error over a single domain by vectorized interpolation. This approach enables us to cover the entire set of the parameters $x,y \in \mathbb{R}$ required for the HITRAN-based spectroscopic applications. The computational test reveals that within domains $x\in\left[0,15\right]\cap y\in\left[10^{-8},15\right]$ and $x\in\left[0,50000\right]\cap y\geq 10^{-8}$ our algorithmic implementation is faster in computation by factors of about $8$ and $3$, respectively, as compared to the fastest known C/C++ code for the Voigt/complex error function. A rapid MATLAB code is presented.