2.3.5 SINQI/SINQF/SINQB

1.
Function
Performs sine transformation only on odd wavenumber components: SINQI initializes; SINQF performs forward sine transformation; and SINQB performs inverse sine transformation.
2.
Definition
Forward transformation is defined as follows:


Inverse transformation is defined as follows:


3.
Call
CALL SINQI(N,WSAVE)
CALL SINQF(N,R,WSAVE)
CALL SINQB(N,R,WSAVE)
4.
Explanation of Parameters
N (I) Length of data to process.
WSAVE (R) Working array. Must have length of at least 3 N+15.
R (R) Floating-point array to process. It is both the input and output parameter. (See above definition.)
5.
Notes
(a)
This transformation does not involve normalization. in other words, when SINQF and SINQB are called successively, then the value of the original value multiplied by a factor of 4N is returned.