README.Rmd

---
output: github_document
---

<!-- README.md is generated from README.Rmd. Please edit that file -->

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)
```
# deformula

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Integration of One-Dimensional Functions with Double Exponential Formulas

## Installation

You can install the released version of deformula from [CRAN](https://CRAN.R-project.org) with:

``` r
install.packages("deformula")
```

## Description

The double exponential formula has been proposed by the following:

- H. Takahasi and M. Mori, Double Exponential Formulas for Numerical Integration, Publications of RIMS, Kyoto University, vol. 9 (1974), pg. 721–741.

which is known as the high precision quadrature. The double exponential formula is also called tanh_sinh, sinh_sinh and exp_sinh quadrature such as in Boost C++.

This package only implements tanh_sinh for a finite interval [lower, upper] and exp_sinh for $[0, \infty$.

## Example

The example shows the integral of the function $y = e^{-a x}$ on $[0, \infty)$:

```{r example1}
library(deformula)
f <- function(x, a) exp(-a*x)
deformula.zeroinf(f, a=0.1)
```

The example shows the integral of the function $y = e^{-a x}$ on $[0, 1]$:

```{r example2}
f <- function(x, a) exp(-a*x)
deformula.moneone(f, 0, 1, a=0.1)
```