BEGIN PROLOGUE VCOSQI DATE WRITTEN R

      SUBROUTINE VCOSQI(N,WSAVE)

C***BEGIN PROLOGUE  VCOSQI

C***DATE WRITTEN   860701   (YYMMDD)

C***REVISION DATE  900509   (YYMMDD)

C***CATEGORY NO.  J1A3

C***KEYWORDS  FAST FOURIER TRANSFORM, COSINE TRANSFORM, ODD WAVE

C             NUMBERS, MULTIPLE SEQUENCES

C***AUTHOR  BOISVERT, R. F. (NIST)

C***PURPOSE  Initialize for VCOSQF and VCOSQB.

C***DESCRIPTION

C

C  Subroutine VCOSQI initializes the array WSAVE which is used in

C  both VCOSQF and VCOSQB.  The prime factorization of N together with

C  a tabulation of the trigonometric functions are computed and

C  stored in WSAVE.

C

C  Input Parameter

C

C  N       the length of the array to be transformed.  The method

C          is most efficient when N is a product of small primes.

C

C  Output Parameter

C

C  WSAVE   a work array which must be dimensioned at least 2*N+15.

C          The same work array can be used for both VCOSQF and VCOSQB

C          as long as N remains unchanged.  Different WSAVE arrays

C          are required for different values of N.  The contents of

C          WSAVE must not be changed between calls of VCOSQF or VCOSQB.

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  VRFFTI

C***END PROLOGUE  VCOSQI

      DIMENSION       WSAVE(*)

C***FIRST EXECUTABLE STATEMENT  VCOSQI

      PIH = 0.5*PIMACH(1.0)

      DT = PIH/REAL(N)

      FK = 0.

      DO 101 K=1,N

         FK = FK+1.

         WSAVE(K) = COS(FK*DT)

  101 CONTINUE

      CALL VRFFTI (N,WSAVE(N+1))

      RETURN

      END

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