quadrature-fortran : Adaptive Gaussian Quadrature with Modern Fortran

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.

License

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

Keywords

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