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NAME
     vdcosqf - compute  the  Fourier  coefficients  in  a  cosine
     series representation with only odd wave numbers.  The xCOSQ
     operations are unnormalized inverses  of  themselves,  so  a
     call  to  xCOSQF  followed by a call to xCOSQB will multiply
     the input sequence by 4 * N.  The VxCOSQ operations are nor-
     malized,  so a call of VxCOSQF followed by a call of VxCOSQB
     will return the original sequence.

SYNOPSIS
     SUBROUTINE COSQF (N, RX, RWSAVE)

     SUBROUTINE DCOSQF (N, DX, RWSAVE)

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

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



     #include <sunperf.h>

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

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

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

     void vdcosqf(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 VxCOSQF, a real
               two-dimensional array with dimensions of (MDIMX  x
               N)   whose   rows  contain  the  sequences  to  be
               transformed.  On  exit,  the  quarter-wave  cosine
               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  xCOSTI  or
               VxCOSTI.

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), XT(M, N)
     C
           EXTERNAL          VCOSQB, VCOSQF, VCOSQI
           INTRINSIC         ACOS, COS
     C
     C     Initialize the array to m real even quarter-wave sequences,
     C     that is, they can be expanded in terms of a cosine series with
     C     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 * COS ((I-1) * PI / 2.0 / N )
       100   CONTINUE
       110 CONTINUE
     C
           CALL VCOSQI (N, WSAVE)
           PRINT 1000
           DO 120, J=1, M
             PRINT 1010, J, (X(J, I), I = 1, N)
       120 CONTINUE
           CALL VCOSQF (M, N, X, XT, M, WSAVE)
           PRINT 1020
           DO 130, J=1, M
             PRINT 1010, J, (X(J, I), I = 1, N)
      130  CONTINUE
           CALL VCOSQB (M, N, X, XT, M, WSAVE)
           PRINT 1030
           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:   40.0  38.6  34.6  28.3  20.0  10.4
      Sequence 2:   80.0  77.3  69.3  56.6  40.0  20.7
      Sequence 3:  120.0 115.9 103.9  84.9  60.0  31.1
      Sequence 4:  160.0 154.5 138.6 113.1  80.0  41.4
      Transformed 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
      Recovered Sequence:
      Sequence 1:   40.0  38.6  34.6  28.3  20.0  10.4
      Sequence 2:   80.0  77.3  69.3  56.6  40.0  20.7
      Sequence 3:  120.0 115.9 103.9  84.9  60.0  31.1
      Sequence 4:  160.0 154.5 138.6 113.1  80.0  41.4

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