SUBROUTINE VSINQB(M,N,X,XT,MDIMX,WSAVE)
C***BEGIN PROLOGUE VSINQB
C***DATE WRITTEN 860701 (YYMMDD)
C***REVISION DATE 900509 (YYMMDD)
C***CATEGORY NO. J1A3
C***KEYWORDS FAST FOURIER TRANSFORM, SINE TRANSFORM, ODD WAVE
C NUMBERS, MULTIPLE SEQUENCES
C***AUTHOR BOISVERT, R. F. (NIST)
C***PURPOSE Normalized inverse of VSINQF.
C***DESCRIPTION
C
C Subroutine VSINQB computes the backward fast Fourier sine transform
C of M quarter wave sequences. That is, sine series representations
C with only odd wave numbers. The transform is defined below at output
C parameter X.
C
C The array WSAVE which is used by subroutine VSINQB must be
C initialized by calling subroutine VSINQI(N,WSAVE).
C
C
C Input Parameters
C
C M the number of sequences to be transformed.
C
C N the length of the sequences to be transformed. The method
C is most efficient when N is a product of small primes.
C
C X an array of size at least X(MDIMX,N) which contains the
C the sequences to be transformed. The sequences are stored
C in the ROWS of X. Thus, the Jth sequence is stored in
C X(J,I), I=1,..,N.
C
C XT a work array of size at least XT(MDIMX,N).
C
C MDIMX the first dimension of the array X exactly as it appears in
C the calling program.
C
C WSAVE a work array which must be dimensioned at least 2*N+15
C in the program that calls VSINQB. The WSAVE array must be
C initialized by calling subroutine VSINQI(N,WSAVE), and a
C different WSAVE array must be used for each different
C value of N. This initialization does not have to be
C repeated so long as N remains unchanged.
C
C Output Parameters
C
C X for I=1,...,N and J=1,...,M
C
C X(I)= the sum from K=1 to K=N of
C
C 4*X(K)*SIN((2k-1)*I*PI/(2*N)) /SQRT(4*N)
C
C
C WSAVE contains initialization calculations which must not
C be destroyed between calls of VSINQB or VSINQF.
C
C -----------------------------------------------------------------
C
C NOTE - A call of VSINQF followed immediately by a call of
C of VSINQB will return the original sequences X. Thus,
C VSINQB is the correctly normalized inverse VSINQF.
C
C -----------------------------------------------------------------
C
C VSINQB is a straightforward extension of the subprogram SINQB to
C handle M simultaneous sequences. SINQB was originally developed
C by P. N. Swarztrauber of NCAR.
C
C***REFERENCES P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
C Computations, (G. Rodrigue, ed.), Academic Press, 1982,
C pp. 51-83.
C***ROUTINES CALLED VCOSQB
C***END PROLOGUE VSINQB
DIMENSION X(MDIMX,*), XT(MDIMX,*), WSAVE(*)
C***FIRST EXECUTABLE STATEMENT VSINQB
IF (M .LE. 0) GO TO 900
IF (N .LE. 1) GO TO 900
C
C CASE N .GT. 1
C
C ... PREPROCESSING
C
NS2 = N/2
DO 210 K=2,N,2
DO 210 J=1,M
X(J,K) = -X(J,K)
210 CONTINUE
C
C ... COSINE QUARTER WAVE TRANSFORM
C
CALL VCOSQB (M,N,X,XT,MDIMX,WSAVE)
C
C ... POSTPROCESSING
C
DO 220 K=1,NS2
KC = N-K
DO 220 J=1,M
XHOLD = X(J,K)
X(J,K) = X(J,KC+1)
X(J,KC+1) = XHOLD
220 CONTINUE
C
C EXIT
C
900 CONTINUE
RETURN
END