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comparison src/DLD-FUNCTIONS/quadcc.cc @ 12553:7c915d013b9c

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quadcc: Add reference to original paper in docstring.
author Rik <octave@nomad.inbox5.com>
date Thu, 31 Mar 2011 07:13:33 -0700
parents 4ced6b90fffb
children 16cca721117b
comparison
equal deleted inserted replaced
12552:1cfa3d9adf0a 12553:7c915d013b9c
1479 1479
1480 DEFUN_DLD (quadcc, args, nargout, 1480 DEFUN_DLD (quadcc, args, nargout,
1481 "-*- texinfo -*-\n\ 1481 "-*- texinfo -*-\n\
1482 @deftypefn {Function File} {[@var{int}, @var{err}, @var{nr_points}] =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol})\n\ 1482 @deftypefn {Function File} {[@var{int}, @var{err}, @var{nr_points}] =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol})\n\
1483 @deftypefnx {Function File} {[@var{int}, @var{err}, @var{nr_points}] =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing})\n\ 1483 @deftypefnx {Function File} {[@var{int}, @var{err}, @var{nr_points}] =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing})\n\
1484 Numerically evaluates an integral using the doubly-adaptive\n\ 1484 Numerically evaluate an integral using the doubly-adaptive\n\
1485 quadrature described by P. Gonnet in @cite{Increasing the\n\ 1485 Clenshaw-Curtis quadrature described by P. Gonnet in @cite{Increasing the\n\
1486 Reliability of Adaptive Quadrature Using Explicit Interpolants},\n\ 1486 Reliability of Adaptive Quadrature Using Explicit Interpolants}.\n\
1487 ACM Transactions on Mathematical Software, in Press, 2010.\n\
1488 The algorithm uses Clenshaw-Curtis quadrature rules of increasing\n\ 1487 The algorithm uses Clenshaw-Curtis quadrature rules of increasing\n\
1489 degree in each interval and bisects the interval if either the\n\ 1488 degree in each interval and bisects the interval if either the\n\
1490 function does not appear to be smooth or a rule of maximum\n\ 1489 function does not appear to be smooth or a rule of maximum\n\
1491 degree has been reached. The error estimate is computed from the\n\ 1490 degree has been reached. The error estimate is computed from the\n\
1492 L2-norm of the difference between two successive interpolations\n\ 1491 L2-norm of the difference between two successive interpolations\n\
1493 of the integrand over the nodes of the respective quadrature rules.\n\ 1492 of the integrand over the nodes of the respective quadrature rules.\n\
1494 \n\ 1493 \n\
1495 For example,\n\ 1494 For example,\n\
1496 \n\ 1495 \n\
1531 If either @var{a} or @var{b} are @code{+/-Inf}, @code{quadcc}\n\ 1530 If either @var{a} or @var{b} are @code{+/-Inf}, @code{quadcc}\n\
1532 integrates @var{f} by substituting the variable of integration\n\ 1531 integrates @var{f} by substituting the variable of integration\n\
1533 with @code{x=tan(pi/2*u)}.\n\ 1532 with @code{x=tan(pi/2*u)}.\n\
1534 \n\ 1533 \n\
1535 @code{quadcc} is capable of dealing with non-numeric\n\ 1534 @code{quadcc} is capable of dealing with non-numeric\n\
1536 values of the integrand such as @code{NaN}, @code{Inf}\n\ 1535 values of the integrand such as @code{NaN} or @code{Inf}\n\
1537 or @code{-Inf}, as in the above example at x=0.\n\ 1536 , as in the above example at x=0.\n\
1538 If the integral diverges and @code{quadcc} detects this, \n\ 1537 If the integral diverges and @code{quadcc} detects this, \n\
1539 a warning is issued and @code{Inf} or @code{-Inf} is returned.\n\ 1538 a warning is issued and @code{Inf} or @code{-Inf} is returned.\n\
1540 \n\ 1539 \n\
1541 Note that @code{quadcc} is a general purpose quadrature algorithm\n\ 1540 Note that @code{quadcc} is a general purpose quadrature algorithm\n\
1542 and as such may be less efficient for smooth or otherwise\n\ 1541 and as such may be less efficient for smooth or otherwise\n\
1543 well-behaved integrand than other methods such as\n\ 1542 well-behaved integrand than other methods such as\n\
1544 @code{quadgk} or @code{trapz}.\n\ 1543 @code{quadgk} or @code{trapz}.\n\
1545 \n\ 1544 \n\
1545 Reference: P. Gonnet, @cite{Increasing the Reliability of Adaptive\n\
1546 Quadrature Using Explicit Interpolants}, ACM Transactions on\n\
1547 Mathematical Software, Vol. 37, Issue 3, Article No. 3, 2010.\n\
1546 @seealso{quad, quadv, quadl, quadgk, trapz, dblquad, triplequad}\n\ 1548 @seealso{quad, quadv, quadl, quadgk, trapz, dblquad, triplequad}\n\
1547 @end deftypefn") 1549 @end deftypefn")
1548 { 1550 {
1549 1551
1550 /* Some constants that we will need. */ 1552 /* Some constants that we will need. */