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C++ API File Reference

#include <stdlib.h>
#include "lo-math.h"
#include "lo-ieee.h"
#include "oct.h"
#include "parse.h"
#include "ov-fcn-handle.h"
Include dependency graph for


struct  cquad_ival


#define cquad_heapsize   200


void Vinvfx (const double *fx, double *c, const int d)
void downdate (double *c, int n, int d, int *nans, int nnans)
 DEFUN_DLD (quadcc, args, nargout,"-*- texinfo -*-\n\ @deftypefn {Function File} {[@var{int}, @var{err}, @var{nr_points}] =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol})\n\ @deftypefnx {Function File} {[@var{int}, @var{err}, @var{nr_points}] =} quadcc (@var{f}, @var{a}, @var{b}, @var{tol}, @var{sing})\n\ Numerically evaluates an integral using the doubly-adaptive\n\ quadrature described by P. Gonnet in @cite{Increasing the\n\ Reliability of Adaptive Quadrature Using Explicit Interpolants},\n\ ACM Transactions on Mathematical Software, in Press, 2010.\n\ The algorithm uses Clenshaw-Curtis quadrature rules of increasing\n\ degree in each interval and bisects the interval if either the\n\ function does not appear to be smooth or a rule of maximum\n\ degree has been reached. The error estimate is computed from the\n\ L2-norm of the difference between two successive interpolations\n\ of the integrand over the nodes of the respective quadrature rules.\n\ \n\ For example,\n\ \n\ @example\n\ int = quadcc (f, a, b, 1.0e-6);\n\ @end example\n\ \n\ @noindent\n\ computes the integral of a function @var{f} in the interval\n\ [@var{a}, @var{b}] to the relative precision of six\n\ decimal digits.\n\ The integrand @var{f} should accept a vector argument and return a vector\n\ result containing the integrand evaluated at each element of the\n\ argument, for example:\n\ \n\ @example\n\ f = @@(x) x .* sin (1 ./ x) .* sqrt (abs (1 - x));\n\ @end example\n\ \n\ If the integrand has known singularities or discontinuities\n\ in any of its derivatives inside the interval,\n\ as does the above example at x=1, these can be specified in\n\ the additional argument @var{sing} as follows\n\ \n\ @example\n\ int = quadcc (f, a, b, 1.0e-6, [ 1 ]);\n\ @end example\n\ \n\ The two additional output variables @var{err} and @var{nr_points}\n\ return an estimate of the absolute integration error and\n\ the number of points at which the integrand was evaluated\n\ respectively.\n\ If the adaptive integration did not converge, the value of\n\ @var{err} will be larger than the requested tolerance. It is\n\ therefore recommended to verify this value for difficult\n\ integrands.\n\ \n\ If either @var{a} or @var{b} are @code{+/-Inf}, @code{quadcc}\n\ integrates @var{f} by substituting the variable of integration\n\ with @code{x=tan(pi/2*u)}.\n\ \n\ @code{quadcc} is capable of dealing with non-numeric\n\ values of the integrand such as @code{NaN}, @code{Inf}\n\ or @code{-Inf}, as in the above example at x=0.\n\ If the integral diverges and @code{quadcc} detects this, \n\ a warning is issued and @code{Inf} or @code{-Inf} is returned.\n\ \n\ Note that @code{quadcc} is a general purpose quadrature algorithm\n\ and as such may be less efficient for smooth or otherwise\n\ well-behaved integrand than other methods such as\n\ @code{quadgk} or @code{trapz}.\n\ \n\ @seealso{quad, quadv, quadl, quadgk, trapz, dblquad, triplequad}\n\ @end deftypefn")

Define Documentation

#define cquad_heapsize   200

Function Documentation

DEFUN_DLD ( quadcc  ,
args  ,
void downdate ( double *  c,
int  n,
int  d,
int *  nans,
int  nnans 
void Vinvfx ( const double *  fx,
double *  c,
const int  d 
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