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)