SINT(3)

SYNOPSIS
SUBROUTINE SINT (N, X, WSAVE)

NAME
sint - Compute the sine transform of a real, odd sequence.

LIBRARY
SLATEC (FFTPACK)

CATEGORY
J1A3

TYPE
SINGLE PRECISION (SINT-S)

KEYWORDS
FFTPACK, FOURIER TRANSFORM

AUTHOR
Swarztrauber, P. N., (NCAR)

DESCRIPTION
Subroutine SINT computes the discrete Fourier sine transform of an odd sequence X(I). The transform is defined below at output parameter X. SINT is the unnormalized inverse of itself since a call of SINT followed by another call of SINT will multiply the input sequence X by 2*(N+1). The array WSAVE which is used by subroutine SINT must be initialized by calling subroutine SINTI(N,WSAVE). Input Parameters N the length of the sequence to be transformed. The method is most efficient when N+1 is the product of small primes. X an array which contains the sequence to be transformed WSAVE a work array with dimension at least INT(3.5*N+16) in the program that calls SINT. The WSAVE array must be initialized by calling subroutine SINTI(N,WSAVE), and a different WSAVE array must be used for each different value of N. This initialization does not have to be repeated so long as N remains unchanged. Thus subsequent transforms can be obtained faster than the first. Output Parameters X For I=1,...,N X(I)= the sum from K=1 to K=N 2*X(K)*SIN(K*I*PI/(N+1)) A call of SINT followed by another call of SINT will multiply the sequence X by 2*(N+1). Hence SINT is the unnormalized inverse of itself. WSAVE contains initialization calculations which must not be destroyed between calls of SINT.

REFERENCES
P. N. Swarztrauber, Vectorizing the FFTs, in Parallel Computations (G. Rodrigue, ed.), Academic Press, 1982, pp. 51-83.

ROUTINES CALLED
RFFTF

REVISION HISTORY (YYMMDD)
790601 DATE WRITTEN
830401 Modified to use SLATEC library source file format.
860115 Modified by Ron Boisvert to adhere to Fortran 77 by (a) changing dummy array size declarations (1) to (*), (b) changing definition of variable SQRT3 by using FORTRAN intrinsic function SQRT instead of a DATA statement.
881128 Modified by Dick Valent to meet prologue standards.
891009 Removed unreferenced statement label. (WRB)
891009 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
920501 Reformatted the REFERENCES section. (WRB)