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   [30]stevengj / [31]cubature Public
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   multi-dimensional adaptive integration (cubature) in C

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stevengj/cubature

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   [60]doc

   [61]doc


   [62].gitignore

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   [64]CITATION.bib

   [65]CITATION.bib


   [66]CMakeLists.txt

   [67]CMakeLists.txt


   [68]COPYING.md

   [69]COPYING.md


   [70]Makefile

   [71]Makefile


   [72]NEWS.md

   [73]NEWS.md


   [74]README.md

   [75]README.md


   [76]clencurt.h

   [77]clencurt.h


   [78]clencurt_gen.c

   [79]clencurt_gen.c


   [80]converged.h

   [81]converged.h


   [82]cubature.h

   [83]cubature.h


   [84]hcubature.c

   [85]hcubature.c


   [86]pcubature.c

   [87]pcubature.c


   [88]test.c

   [89]test.c


   [90]vwrapper.h

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     * [92]README
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Cubature

   This is a simple C package for adaptive multidimensional integration (cubature)
   of vector-valued integrands over hypercubes, written by [94]Steven G. Johnson.
   That is, it computes integrals of the form:

   [95]n-dimensional integral

   (Of course, it can handle scalar integrands as the special case where f is a
   one-dimensional vector: the dimensionalities of f and x are independent.) The
   integrand can be evaluated for an array of points at once to enable easy
   parallelization. The code, which is distributed as free software under the terms
   of the GNU General Public License (v2 or later), implements two algorithms for
   adaptive integration.

   The first, h-adaptive integration (recursively partitioning the integration
   domain into smaller subdomains, applying the same integration rule to each, until
   convergence is achieved), is based on the algorithms described in:
     * A. C. Genz and A. A. Malik, "An adaptive algorithm for numeric integration
       over an N-dimensional rectangular region," J. Comput. Appl. Math. 6 (4),
       295-302 (1980).
     * J. Berntsen, T. O. Espelid, and A. Genz, "An adaptive algorithm for the
       approximate calculation of multiple integrals," ACM Trans. Math. Soft. 17
       (4), 437-451 (1991).

   This algorithm is best suited for a moderate number of dimensions (say, < 7), and
   is superseded for high-dimensional integrals by other methods (e.g. Monte Carlo
   variants or sparse grids).

   (Note that we do not use any of the original DCUHRE code by Genz, which is not
   under a free/open-source license.) Our code is based in part on code borrowed
   from the [96]HIntLib numeric-integration library by Rudolf Schürer and from code
   for Gauss-Kronrod quadrature (for 1d integrals) from the [97]GNU Scientific
   Library, both of which are free software under the GNU GPL. (Another
   free-software multi-dimensional integration library, unrelated to our code here
   but also implementing the Genz-Malik algorithm among other techniques, is
   [98]Cuba.)

   The second, p-adaptive integration (repeatedly doubling the degree of the
   quadrature rules until convergence is achieved), is based on a tensor product of
   [99]Clenshaw-Curtis quadrature rules. This algorithm is often superior to
   h-adaptive integration for [100]smooth integrands in a few (