Re: 2d Gaussian Quadrature

From: Peter Simon (petersamsimon2_at_hotmail.com)
Date: 09/13/04

  • Next message: GreyCloud: "Re: Bruce digest, volume 2453261" 
    Date: 13 Sep 2004 09:03:28 -0700

    "Confused Scientist" <Confused.Scientist@gmail.com> wrote in message news:<ci2h8s$ead@odak26.prod.google.com>...
    > Does anyone have a simple 2d Gaussian Quadrature code written up that
    > they can share? I'd prefer FORTRAN 77. The region is smooth and
    > well-behaved.
    Many years ago I wrote a Fortran 77 routine to integrate a
    complex-valued function of two real variables. It is an adaptation of
    the well-known code QUANC8 from the text Computer Methods for
    Mathematical Computations by Forsythe, Malcolm, and Moler, generalized
    to two dimensions using the recommendations given in the paper by
    Fritsch, Kahaner, and Lyness, Double Integration Using One Dimensional
    Adaptive Quadrature Routines: A Software Interface Problem, ACM Trans.
    Math. Software, vol 7, no. 1, March 1981, pp. 46-75. The advantages
    of an adaptive routine over a single application of a gaussian
    quadrature formula are that 1) the function is automatically sampled
    more frequently in regions where it varies more rapidly, hopefully
    achieving the user-specified accuracy bound with the minimum possible
    number of function evaluations, and 2) an estimate of the error in the
    computed value of the integral is provided.

    More recently I converted this routine to Fortran 90 and also created
    a Fortran 90 version for pure real integrands. These are bundled in
    the module dblint.f90

    I have made these routines available on my website at
    http://www.vcnet.com/cdblin.f and http://www.vcnet.com/dblint.f90 If
    you would like to try out my Fortran 77 routine cdblin.f but your
    integrand is pure real you could simply code it up as a complex
    function having zero imaginary part. Then, if you find that cdblin
    works well for your problem you could easily convert it to a version
    that expects a real integrand, to avoid the inefficiency of performing
    unneeded complex calculations. Or you could bite the bullet and use
    the Fortran 90 version. I have tested these routines on a number of
    smooth and singular (but integrable) integrands, and have found them
    to be robust and accurate.

    >
    > Also, does anyone know of a text (that a chemist could understand)
    > about methods for performing/coding multiple integrations...
    > Thanks in advance!

    When I was working on this problem I found the book by Davis, Methods
    of Numerical Integration, useful.

    Hope this helps,

    Peter Simon

  • Next message: GreyCloud: "Re: Bruce digest, volume 2453261"