quadvgk

G7-K15 adaptive quadrature on vector-valued functions

Description

Adaptation of quadgk for use on vector valued functions (i.e. the integral of many functions).

The input function should return a matrix of size (NF, NX) where NF is the number of integrals to calculate and NX is the number of points across each function.

This routine is as efficient as quadgk on a single function, more efficient on calculating multiple functions across the same span (provided they require similar sampling).

Consider the following problem:
E(x, L) = int(z = 0..L, fft(E(kx).*exp(i*kx.^2*z/2k)));

quadvgk allows E(kx) to be evaluated once only for every z position, thus significantly improving performance.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
quad_M;quadl_M

• MATLAB release: MATLAB 7.5 (R2007b)

[Andreas]

 

[Andreas]

This one worked like a charm for a couple of integrals where quadv failed (and iterating over quadgk was too slow).

The file doesn't work if you follow the example though. It should be something like:

Example:
 Y = @(x,n) 1./(bsxfun(@plus,(1:n)',x));
 Qv = quadvgk(@(x) Y(x,10), [0;1], 10)

[Andreas]

Sometimes it becomes really slow (and even though it only occurs on occasion, there many, many occasions in my m-files makes it an issue). Any idea anyone?

[Dezhao]

Hey Andreas, this is what I am searching for.
I runned your package with 'bsxfun'. When the vector is small (or the number of n in your example) it is OK. However when the vector is huge(let's say n>>100) the program ran out of memory. Is there a way to fix it?

[Dezhao]

Hey Andreas, I solved my previous problem. However, I found the quadvgk is lower than using loops.
To make it work I used bsxfun and repmat. I think it is bsxfun and repmat that spent a lot of time. What's your opinion?