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NAME
     sinqf - compute the Fourier coefficients in  a  sine  series
     representation with only odd wave numbers.  The xSINQ opera-
     tions are unnormalized inverses of themselves, so a call  to
     xSINQF  followed by a call to xSINQB will multiply the input
     sequence by 4 * N.  The VxSINQ operations are normalized, so
     a  call of VxSINQF followed by a call of VxSINQB will return
     the original sequence.

SYNOPSIS
     SUBROUTINE SINQF (N, RX, RWSAVE)

     SUBROUTINE DSINQF (N, DX, DWSAVE)

     SUBROUTINE VSINQF (M, N, RX, RXT, MDIMX, RWSAVE)

     SUBROUTINE VDSINQF (M, N, DX, DXT, MDIMX, DWSAVE)



     #include <sunperf.h>

     void sinqf (int n, float *sx, float *wsave) ;

     void dsinqf (int n, double *dx, double *wsave) ;

     void vsinqf(int m,  int  n,  float  *sx,  int  mdimx,  float
               *wsave) ;

     void vdsinqf(int m, int n, double  *dx,  int  mdimx,  double
               *wsave) ;

ARGUMENTS
     M         (For vector operations only.)
               The number of sequences to be transformed.   M  >=
               0.

     N         Length of the sequence to be  transformed.   These
               subroutines are most efficient when N is a product
               of small primes.  N >= 0.

     xX        On entry, an array  of  length  N  containing  the
               sequence  to  be transformed.  For VxSINQF, a real
               two-dimensional array with dimensions of (MDIMX  x
               N)   whose   rows  contain  the  sequences  to  be
               transformed.   On  exit,  the  quarter-wave   sine
               transform of the input.

     xXT       (For vector operations only.)
               A real two-dimensional work array with  dimensions
               of (MDIMX x N).

     MDIMX     (For vector operations only.)
               Leading dimension of the  arrays  xX  and  xXT  as
               specified  in a dimension or type statement. MDIMX
               >= M.

     xWSAVE    On entry, an array with dimension of at least   (3
               *  N  + 15) for scalar subroutines or (2 * N + 15)
               for vector subroutines, initialized by  xSINQI  or
               VxSINQI.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           M, N
           PARAMETER        (M = 4)
           PARAMETER        (N = 6)
     C
           INTEGER           I, J
           REAL              PI, WSAVE(N + 15), X(M, N+1), XT(M, N + 1)
     C
           EXTERNAL          VSINQB, VSINQF, VSINQI
           INTRINSIC         ACOS, SIN
     C
     C     Initialize the array to m real odd quarter-wave sequence,
     C     that is, they can be expanded in terms of a cosine series
     C     with only odd wave numbers.
     C
           PI = ACOS (-1.0)
           DO 110, J=1, M
             DO 100, I=1, N
               X(J,I) = 40.0 * J * SIN (I * PI / (2.0 * N))
       100   CONTINUE
       110 CONTINUE
     C
           CALL VSINQI (N, WSAVE)
           PRINT 1000
           DO 120, J=1, M
             PRINT 1010, J, (X(J, I), I = 1, N)
       120 CONTINUE
           CALL VSINQF (M, N, X, XT, M, WSAVE)
           PRINT 1000
           DO 130, J=1, M
             PRINT 1010, J, (X(J, I), I = 1, N)
       130 CONTINUE
           CALL VSINQB (M, N, X, XT, M, WSAVE)
           PRINT 1000
           DO 140, J=1, M
             PRINT 1010, J, (X(J, I), I = 1, N)
       140 CONTINUE
     C
      1000 FORMAT (1X, 'Original Sequence: ')
      1010 FORMAT (1X, 'Sequence', I2, ':  ', 100(F5.1, 1X))
      1020 FORMAT (1X, 'Transformed Sequence: ')
      1030 FORMAT (1X, 'Recovered Sequence: ')
     C
           END

SAMPLE OUTPUT
      Original Sequence:
      Sequence 1:   10.4  20.0  28.3  34.6  38.6  40.0
      Sequence 2:   20.7  40.0  56.6  69.3  77.3  80.0
      Sequence 3:   31.1  60.0  84.9 103.9 115.9 120.0
      Sequence 4:   41.4  80.0 113.1 138.6 154.5 160.0
      Original Sequence:
      Sequence 1:   49.0   0.0   0.0   0.0   0.0   0.0
      Sequence 2:   98.0   0.0   0.0   0.0   0.0   0.0
      Sequence 3:  147.0   0.0   0.0   0.0   0.0   0.0
      Sequence 4:  196.0   0.0   0.0   0.0   0.0   0.0
      Original Sequence:
      Sequence 1:   10.4  20.0  28.3  34.6  38.6  40.0
      Sequence 2:   20.7  40.0  56.6  69.3  77.3  80.0
      Sequence 3:   31.1  60.0  84.9 103.9 115.9 120.0
      Sequence 4:   41.4  80.0 113.1 138.6 154.5 160.0

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