|MATLAB Function Reference|
Numerically evaluate integral, adaptive Lobatto quadrature
q = quadl(fun,a,b)
approximates the integral of function
b, to within an error of 10-6 using recursive adaptive Lobatto quadrature.
fun accepts a vector
x and returns a vector
y, the function
fun evaluated at each element of
q = quadl(fun,a,b,tol)
uses an absolute error tolerance of
tol instead of the default, which is
1.0e-6. Larger values of
tol result in fewer function evaluations and faster computation, but less accurate results.
trace shows the values of
[fcnt a b-a q] during the recursion.
provides for additional arguments
p1,p2,... to be passed directly to function
fun(x,p1,p2,...). Pass empty matrices for
trace to use the default values.
[q,fcnt] = quadl(...)
returns the number of function evaluations.
Use array operators
.^ in the definition of
fun so that it can be evaluated with a vector argument.
quad may be more efficient with low accuracies or nonsmooth integrands.
fun can be:
quadl implements a high order method using an adaptive Gauss/Lobatto qudrature rule.
quadl may issue one of the following warnings:
'Minimum step size reached' indicates that the recursive interval subdivision has produced a subinterval whose length is on the order of roundoff error in the length of the original interval. A nonintegrable singularity is possible.
'Maximum function count exceeded' indicates that the integrand has been evaluated more than 10,000 times. A nonintegrable singularity is likely.
'Infinite or Not-a-Number function value encountered' indicates a floating point overflow or division by zero during the evaluation of the integrand in the interior of the interval.
@ (function handle)
 Gander, W. and W. Gautschi, "Adaptive Quadrature - Revisited", BIT, Vol. 40, 2000, pp. 84-101. This document is also available at http:// www.inf.ethz.ch/personal/gander.