C
C          * * * * * * * * * * * * * * * * * * * * * * * * * *
C          *                                                 *
C          * SUBROUTINE VSCOSQ(F,L,M,N,FT,C1,C2,C3,C4,WSAVE) *
C          *                                                 *
C          * * * * * * * * * * * * * * * * * * * * * * * * * *
C
C
C                           * * * * * * * *
C                           *   PURPOSE   *
C                           * * * * * * * *
C
C
C     A VECTORIZED SUBROUTINE TO COMPUTE THE STAGGERED GRID COSINE
C     QUARTER-WAVE ANALYSIS AND SYNTHESIS
C
C       V_HAT(J) = SQRT(2/M)*SUM(L=1,M)[ V(L)*COS((L-.5)*(J-.5)*PI/M) ]
C
C                  (J=1,...,M)
C
C     FOR L*N VECTORS.
C
C
C                    * * * * * * * * * * * * * * *
C                    *   PARAMETER DESCRIPTION   *
C                    * * * * * * * * * * * * * * *
C
C
C     INPUT PARAMETERS
C
C     F      A REAL THREE-DIMENSIONAL ARRAY OF SIZE L X M X N THAT
C            CONTAINS THE L*N VECTORS OF LENGTH M TO BE TRANSFORMED.
C            SPECIFICALLY, FOR EACH I=1,...,L AND K=1,...,N THE VECTOR
C            TO BE TRANSFORMED IS STORED AS F(I,J,K), J=1,...,M.
C
C     L,M,N  NON-NEGATIVE INTEGERS THAT SPECIFY THE NUMBER AND LENGTH OF
C            THE VECTORS TO BE TRANSFORMED.  THERE IS NO RESTRICTION ON
C            M, THE LENGTH OF THE TRANSFORM.
C
C     FT     A WORK ARRAY OF SIZE L*M*N THAT MUST BE PROVIDED BY THE
C            USER.
C
C     C1,C2, FOUR ONE-DIMENSIONAL REAL WORK ARRAYS THAT CONTAIN CERTAIN
C     C3,C4  TRIGONOMETRIC VALUES COMPUTED IN THE SUBROUTINE VSCSQI.
C
C     WORK   A REAL ONE-DIMENSIONAL WORK ARRAY OF SIZE M+15 THAT
C            CONTAINS CERTAIN INTERMEDIATE QUANTITIES USED BY SUBROUTINE
C            VRFFTB, A VECTORIZED REAL PERIODIC FAST FOURIER TRANSFORM
C            ROUTINE.
C
C
C     OUTPUT PARAMETER
C
C     F      CONTAINS THE L*N TRANSFORMS OF THE INPUT VECTORS STORED IN
C            PERMUTED ORDER.  SPECIFICALLY, THE TRANSFORM OF THE INPUT
C            VECTOR F(I,J,K), J=,1,...,M, IS STORED, ON OUTPUT, AS
C            F(I,K,J), J=1,...,M.
C
C
C
C              * * * * * * * * * * * * * * * * * * * * *
C              *                                       *
C              *         PROGRAM SPECIFICATIONS        *
C              *                                       *
C              * * * * * * * * * * * * * * * * * * * * *
C
C
C
C     DIMENSION OF    F(L,M,N), FT(L*M*N), C1(M), C2(M), C3(M), C4(M),
C     ARGUMENTS       WSAVE(N+15)
C
C     LATEST          AUGUST 1, 1985
C     REVISION
C
C     SUBPROGRAMS     VSRFTI, VSCOSI, VSCSQI, VSRFTF, VSRFTB, VSCOSF,
C     REQUIRED        VSCOSB, VSCOSQ, VSSINF, VSSINB, VSSINQ, PIMACH,
C                     VRFFTPK (PACKAGE)
C
C     SPECIAL         NONE
C     CONDITIONS
C
C     COMMON          NONE
C     BLOCKS
C
C     I/O             NONE
C
C     PRECISION       SINGLE
C
C     SPECIALIST      ROLAND SWEET
C
C     LANGUAGE        FORTRAN
C
C     HISTORY         WRITTEN BY LINDA LINDGREN AND ROLAND SWEET AT THE
C                     NATIONAL BUREAU OF STANDARDS (BOULDER).
C
C     ALGORITHM       SEE "FAST FOURIER TRANSFORMS ON A STAGGERED GRID"
C                     BY ROLAND A. SWEET (TO APPEAR)
C
C     PORTABILITY     AMERICAN NATIONAL STANDARDS INSTITUTE FORTRAN 77.
C                     THE ONLY MACHINE DEPENDENT CONSTANT IS LOCATED IN
C                     THE FUNCTION PIMACH.
C
C     REQUIRED        COS,SIN
C     RESIDENT
C     ROUTINES
C