MATLAB: Does QUADL in MATLAB 7.2 (R2006a) not work as well as QUAD8

areaintegrationMATLABnumericalquadvolume

I am performing an integration that executes well in older versions of MATLAB using QUAD8. When I execute it with QUADL, it is much slower and gives the following warning regarding a singularity:

 Warning: Maximum function count exceeded; singularity likely.
 > In quadl at 98

and then returns incorrect results.

Best Answer

This result is most likely due to the default absolute error tolerance used for the QUADL function. Try setting a larger tolerance using the tol input to the QUADL function.

If QUADL is still returning incorrect results and if the values in your integrand have a large difference in magnitude, try renormalizing the values so that they are similar. Having values with such a large difference in magnitude in your integrand may cause an accumulation of roundoff errors in the QUADL algorithm.

Related Solutions

MATLAB: Do I receive a “Singularity likely” warning when I use the QUAD function in MATLAB for a function that does not have a singularity

This warning will occur when the default absolute error tolerance of 1.0e-6 is too small to evaluate the integral in fewer function evaluations than the default 10000.

To work around this issue, specify a larger absolute tolerance as the fourth input argument to the QUAD function. For example, the following command specifies an absolute tolerance of 1:

quad(@exp,0,30,1)

and returns the expected result:

 ans =
   1.0686e+013

MATLAB: Quadl with vector bounds

One option is to use ARRAYFUN

>> arrayfun(@(b)integral(@(x)x.*sin(x),0,b,'abstol',1e-5,'reltol',1e-5),0:3)
ans =
         0    0.3012    1.7416    3.1111

If you don't have R2012a, use QUADGK. Though they offer faster results at lower accuracy in some cases (like my example above), QUAD and QUADL are obsolete. I think the most efficient approach might be to sort the vector b, integrate each subinterval, use cumsum to compute the individual integrals, and then unsort it.

function q = vint(f,a,b,atol,rtol)
[bsorted,idx] = sort(b);
avector = [a,bsorted(1:end-1)];
qsub = arrayfun( ...
    @(a,b)integral(f,a,b,'AbsTol',atol,'RelTol',rtol), ...
    avector,bsorted);
qsorted = cumsum(qsub);
q(idx) = qsorted;

But do note that quadgk and integral control the overall error, and doing subintegrations and adding may yield a lower accuracy result than either code would have given in one shot. -- Mike

Best Answer

Related Solutions

MATLAB: Do I receive a “Singularity likely” warning when I use the QUAD function in MATLAB for a function that does not have a singularity

MATLAB: Quadl with vector bounds

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