Numerical evaluation of integrals in Mata

[Charles Vellutini]

Dear all,

Is there a Mata equivalent to Stata's -integ-? Alternatively, which combination of Mata commands and functions do you think could be used to numerically evaluate integrals of one-argument functions?

Thanks in advance,
Charles

[P Van Kerm]

Ben Jann's -moremata- bundle of Mata functions includes a -mm_integrate()- function which might be your friend here.

ssc describe moremata

Philippe

[Charles Vellutini]

Many thanks Philippe. Seems to be just what I need.

[Charles Vellutini]

In fact -mm_integrate()- needs a closed-form function, whereas -integ- works by interpolating individual (x,y) points. So to use -mm_integrate()- when you start with individual points, it seems that you need to construct the function first.

[Maarten Buis]

One option would be to use the official Matat function spline3() for interpolation. I don't think you can feed the cubic spline returned by that function to mm_integrate(). However, a cubic spline is just a series of cubic functions, so the integrations should not be hard. You would need to look up how exactly the spline returned by spline3() is parameterised, but all that is doable.

[Charles Vellutini]

Thanks Maarten! Yes, I think that could work. Alternatively, it does not seem that hard to code numerical approximations of one-dimensional integrals directly in Mata. See for example http://en.wikipedia.org/wiki/Numerical_integration. The affine method is straightforward - I did it, seems to work ok. Simson's methods are more involved and I haven't tried them. Maybe your suggestion to use -spline3()- is a better one. I will experiment further and report what I found.