# Quadrature rules
[The online encylopedia of quadrature rules](https://quadraturerules.org) is a reference website that lists a number of quadrature rules.
Quadrature rules are sets of points and weights that are used to approximate integrals. If $\{p_0,\dots,p_{n-1}\}\subset\mathbb{R}^d$ and $\{w_0,\dots,w_{n-1}\}\subset\mathbb{R}$
are the points and weights (repectively) of the quadrature rule for a single integral, then:
$$\int f(x)\,\mathrm{d}x \approx \sum_{i=0}^{n-1}f(p_i)w_i$$
## Website
Before building the online encylopedia of quadrature rules, you must first install qrtools
from the [python](python) directory:
```bash
cd python
python3 -m pip install .
```
The online encylopedia of quadrature rules website can then be built by running:
```bash
cd website
python3 build.py
```
## Libraries
All of the quadrature rules included in the online encylopedia of quadrature rules are included in the quadraturerules library, which is available in the following languages:
| Language | Badges |
| -------------------------------------------------- | ------ |
| [C](https://quadraturerules.org/libraries/c.html) | [](https://github.com/quadraturerules/quadraturerules/actions/workflows/library-c.yml) |
| [C++](https://quadraturerules.org/libraries/cpp.html) | [](https://github.com/quadraturerules/quadraturerules/actions/workflows/library-cpp.yml) |
| [Fortran](https://quadraturerules.org/libraries/fortran90.html) | [](https://github.com/quadraturerules/quadraturerules/actions/workflows/library-fortran90.yml) |
| [FORTRAN 77](https://quadraturerules.org/libraries/fortran77.html) | [](https://github.com/quadraturerules/quadraturerules/actions/workflows/library-fortran77.yml) |
| [Julia](https://quadraturerules.org/libraries/julia.html) | [](https://github.com/quadraturerules/quadraturerules/actions/workflows/library-julia.yml) |
| [Python](https://quadraturerules.org/libraries/python.html) | [](https://github.com/quadraturerules/quadraturerules/actions/workflows/library-python.yml) [](https://pypi.org/project/quadraturerules/) |
| [Rust](https://quadraturerules.org/libraries/rust.html) | [](https://github.com/quadraturerules/quadraturerules/actions/workflows/library-rust.yml) [](https://crates.io/crates/quadraturerules/) [](https://docs.rs/quadraturerules/) |
Before building any of the libraries, you must first install qrtools
from the [python](python) directory:
```bash
cd python
python3 -m pip install .
```
You can then build the libraries using the [build.py](library/build.py) script in the library directory.
For example, to build the python library, you can run:
```bash
cd library
python build.py python
```
and to build the rust library, you can run:
```bash
cd library
python build.py rust
```
## C++ library
The source code of the quadraturerules C++ library can be downloaded from the
[latest release on GitHub](https://github.com/quadraturerules/quadraturerules/releases/latest/).
It can be installed by running:
```bash
wget https://github.com/quadraturerules/quadraturerules/releases/download/v{{VERSION}}/quadraturerules-cpp-v{{VERSION}}.tar.gz
mkdir src
tar -xvf quadraturerules-cpp-v{{VERSION}}.tar.gz -C src
mkdir build
cd build
cmake ../src
make
make install
```
Once the library is installed, you can run the tests by running:
```bash
python src/test/run_tests.py
```
Or you can run individual tests:
```bash
cd src/test/{TEST_NAME}
cmake .
make .
./{TEST_NAME}
```
## Usage
The library's function `single_integral_quadrature` can be used to get the points and weights
of quadrature rules for a single integral. For example the following snippet will create an
order 3 Xiao--Gimbutas rule on a triangle:
```cpp
#include <quadraturerules.h>
using quadraturerules;
auto [points, weights] = single_integral_quadrature(
QuadratureRule::XiaoGimbutas,
Domain::Triangle,
3
);
```
Note that the points returned by the library are represented using
[barycentric coordinates](/barycentric.md).
## Generating the library
The C++ quadraturerules library can be generated from the templates in the online encyclopedia
of quadrature rules GitHub repo. First clone the repo and move into the library directory:
```bash
git clone https://github.com/quadraturerules/quadraturerules.git
cd quadraturerules/library
```
The C++ library can then be generated by running:
```bash
python build.py cpp
```
This will create a directory called cpp.build containing the C++ source code.