10.21 expandEven() and expandOdd()

Prototypes		Header File(s)
`template <class T>`
`RWMathVec<T>`	`expandEven(const RWMathVec<T>&)`	`<rw/math/mathvec.h>`
`RWMathVec<T>`	`expandOdd(const RWMathVec<T>&)`	`<rw/math/mathvec.h>`

10.21.1 Description

Given a real sequence V(n), n=0, ..., 2N points long, it is an even sequence if:

V(n) = V(-n) = V(2N-n),

and an odd sequence if:

V(n) = - V(-n) = - V(2N-n).

Note that for a sequence to be odd, V(0) = V(N) = 0. Given the lower half of an even sequence, that is, V(n), n=0, ..., N, expandEven() expands it out to the entire sequence V(n), n=0, ..., 2N. Given the lower half of an odd sequence, that is, V(n), n=1, ..., N-1, expandOdd() expands it out to the entire sequence V(n), n=0, ..., 2N.