Adaptive Gaussian Quadrature with Modern Fortran

Status

Brief description

An object-oriented modern Fortran library to integrate functions using adaptive Gaussian quadrature. There are five selectable methods to use:

• Adaptive 6-point Legendre-Gauss
• Adaptive 8-point Legendre-Gauss
• Adaptive 10-point Legendre-Gauss
• Adaptive 12-point Legendre-Gauss
• Adaptive 14-point Legendre-Gauss

The library supports:

1D integration: $$\int_{x_l}^{x_u} f(x) dx$$ 2D integration: $$\int_{y_l}^{y_u} \int_{x_l}^{x_u} f(x,y) dx dy$$ 3D integration: $$\int_{z_l}^{z_u} \int_{y_l}^{y_u} \int_{x_l} ^{x_u} f(x,y,z) dx dy dz$$ 4D integration: $$\int_{q_l}^{q_u} \int_{z_l}^{z_u} \int_{y_l} ^{y_u} \int_{x_l}^{x_u} f(x,y,z,q) dx dy dz dq$$ 5D integration: $$\int_{r_l}^{r_u} \int_{q_l}^{q_u} \int_{z_l} ^{z_u} \int_{y_l}^{y_u} \int_{x_l}^{x_u} f(x, y,z,q,r) dx dy dz dq dr$$ 6D integration: $$\int_{s_l}^{s_u} \int_{r_l}^{r_u} \int_{q_l} ^{q_u} \int_{z_l}^{z_u} \int_{y_l}^{y_u} \int_ {x_l}^{x_u} f(x,y,z,q,r,s) dx dy dz dq dr ds$$

The core code is based on the SLATEC routine DGAUS8 (which is the source of the 8-point routine). Coefficients for the others were obtained from here. The original 1D code has been generalized for multi-dimensional integration.

Compiling

A Fortran Package Manager manifest file is included, so that the library and test cases can be compiled with FPM. For example:

fpm build --profile release
fpm test --profile release

By default, the library is built with double precision (real64) real values. Explicitly specifying the real kind can be done using the following preprocessor flags:

Preprocessor flag	Kind	Number of bytes
REAL32	real(kind=real32)	4
REAL64	real(kind=real64)	8
REAL128	real(kind=real128)	16

For example, to build a single precision version of the library, use:

fpm build --profile release --flag "-DREAL32"

To use quadrature-fortran within your fpm project, add the following to your fpm.toml file:

[dependencies]
quadrature-fortran = { git="https://github.com/jacobwilliams/quadrature-fortran.git" }

or, to use a specific version:

[dependencies]
quadrature-fortran = { git="https://github.com/jacobwilliams/quadrature-fortran.git", tag = "1.0.0" }

Documentation

The API documentation for the current master branch can be found here. This is generated by processing the source files with FORD.

License

The quadrature-fortran source code and related files and documentation are distributed under a permissive free software license (BSD-style).

See also

• quadpack -- Modern Fortran QUADPACK Library for 1D numerical quadrature

Keywords

• adaptive quadrature, automatic integrator, gauss quadrature, numerical integration