.. highlight:: lua

.. include:: <isogrk1.txt>

Numerical Integration
=====================

This chapter describes routines for performing numerical integration
(quadrature) of a function in one dimension.  There are routines for
adaptive and non-adaptive integration of general functions, with
specialised routines for specific cases.  These include integration over
infinite and semi-infinite ranges, singular integrals, including
logarithmic singularities, computation of Cauchy principal values and
oscillatory integrals.  The library reimplements the algorithms used in
QUADPACK, a numerical integration package written by Piessens,
Doncker-Kapenga, Uberhuber and Kahaner.  Fortran code for QUADPACK is
available on Netlib.

Functions
---------

The function to perform numerical integration if ``integ``.

Here an example::

  myf = function(x) return sin(x)/x end
  x, err = integ {f= myf, points= {1e-6, 12*2*pi}, method='AG.GAUSS31'}
