Numerical integration - Trapz, quad, quadl...
in [Matlab]
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From: John D'Errico on 9 Feb 2010 15:32 "DD C" <dchr0036(a)remove.thisgmail.com> wrote in message <hks23c$8b4$1(a)fred.mathworks.com>... > Hi, > > I am trying to calculate several integrals. It appears that in some cases, trapz provides a result while quad and quadl provides 0. In other cases quad and quadl provides results while trapz returns NaN. > I understand the approximations behind each method but I don't know why one function provides results while the other doesn't. Are there specific cases when quad, quadl, trapz should not be used? or Are there specific cases when they should be used? > I might argue that if you truly do understand the methods involved, then you will also understand their limitations, as well as guidelines where you might use one over another. Trapz is a simple tool that integrates a function represented as a fixed sequence of function evaluations. So you already have a data series here, and you need to know the integral of the function this series is sampled from. Trapz might be applied to data that you have measured, so there might be noise in these measurements. Note that when noise is present, a lower order method (such as trapz) is a good choice, as it will minimize the variance of the estimated integral due to that noise. The quad family of tools are ADAPTIVE methods. They are useful when you have a complete black box of a function to integrate. These tools require the ability to evaluate the function at a programmatically specified set of points, where matlab chooses the specific sequence for these evaluations. Quad and its cousins can be problematic when you have a function with a spike in it. (A spike is a delta function, or something near to that shape.) As such, the quad tools are very distinct from trapz. You will want to use them at different times, based on your goals, on what form your "Function" is in, etc. John |