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[jabaws.git] / website / archive / binaries / mac / src / disembl / Tisean_3.0.1 / source_f / slatec / rfftf1.f

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-*DECK RFFTF1
-      SUBROUTINE RFFTF1 (N, C, CH, WA, IFAC)
-C***BEGIN PROLOGUE  RFFTF1
-C***PURPOSE  Compute the forward transform of a real, periodic sequence.
-C***LIBRARY   SLATEC (FFTPACK)
-C***CATEGORY  J1A1
-C***TYPE      SINGLE PRECISION (RFFTF1-S, CFFTF1-C)
-C***KEYWORDS  FFTPACK, FOURIER TRANSFORM
-C***AUTHOR  Swarztrauber, P. N., (NCAR)
-C***DESCRIPTION
-C
-C   Subroutine RFFTF1 computes the Fourier coefficients of a real
-C   periodic sequence (Fourier analysis).  The transform is defined
-C   below at output parameter C.
-C
-C   The arrays WA and IFAC which are used by subroutine RFFTB1 must be
-C   initialized by calling subroutine RFFTI1.
-C
-C   Input Arguments
-C
-C   N       the length of the array R to be transformed.  The method
-C           is most efficient when N is a product of small primes.
-C           N may change so long as different work arrays are provided.
-C
-C   C       a real array of length N which contains the sequence
-C           to be transformed.
-C
-C   CH      a real work array of length at least N.
-C
-C   WA      a real work array which must be dimensioned at least N.
-C
-C   IFAC    an integer work array which must be dimensioned at least 15.
-C
-C           The WA and IFAC arrays must be initialized by calling
-C           subroutine RFFTI1, and different WA and IFAC arrays must be
-C           used for each different value of N.  This initialization
-C           does not have to be repeated so long as N remains unchanged.
-C           Thus subsequent transforms can be obtained faster than the
-C           first.  The same WA and IFAC arrays can be used by RFFTF1
-C           and RFFTB1.
-C
-C   Output Argument
-C
-C   C       C(1) = the sum from I=1 to I=N of R(I)
-C
-C           If N is even set L = N/2; if N is odd set L = (N+1)/2
-C
-C             then for K = 2,...,L
-C
-C                C(2*K-2) = the sum from I = 1 to I = N of
-C
-C                     C(I)*COS((K-1)*(I-1)*2*PI/N)
-C
-C                C(2*K-1) = the sum from I = 1 to I = N of
-C
-C                    -C(I)*SIN((K-1)*(I-1)*2*PI/N)
-C
-C           If N is even
-C
-C                C(N) = the sum from I = 1 to I = N of
-C
-C                     (-1)**(I-1)*C(I)
-C
-C   Notes:  This transform is unnormalized since a call of RFFTF1
-C           followed by a call of RFFTB1 will multiply the input
-C           sequence by N.
-C
-C           WA and IFAC contain initialization calculations which must
-C           not be destroyed between calls of subroutine RFFTF1 or
-C           RFFTB1.
-C
-C***REFERENCES  P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
-C                 Computations (G. Rodrigue, ed.), Academic Press,
-C                 1982, pp. 51-83.
-C***ROUTINES CALLED  RADF2, RADF3, RADF4, RADF5, RADFG
-C***REVISION HISTORY  (YYMMDD)
-C   790601  DATE WRITTEN
-C   830401  Modified to use SLATEC library source file format.
-C   860115  Modified by Ron Boisvert to adhere to Fortran 77 by
-C           changing dummy array size declarations (1) to (*).
-C   881128  Modified by Dick Valent to meet prologue standards.
-C   891214  Prologue converted to Version 4.0 format.  (BAB)
-C   900131  Routine changed from subsidiary to user-callable.  (WRB)
-C   920501  Reformatted the REFERENCES section.  (WRB)
-C***END PROLOGUE  RFFTF1
-      DIMENSION CH(*), C(*), WA(*), IFAC(*)
-C***FIRST EXECUTABLE STATEMENT  RFFTF1
-      NF = IFAC(2)
-      NA = 1
-      L2 = N
-      IW = N
-      DO 111 K1=1,NF
-         KH = NF-K1
-         IP = IFAC(KH+3)
-         L1 = L2/IP
-         IDO = N/L2
-         IDL1 = IDO*L1
-         IW = IW-(IP-1)*IDO
-         NA = 1-NA
-         IF (IP .NE. 4) GO TO 102
-         IX2 = IW+IDO
-         IX3 = IX2+IDO
-         IF (NA .NE. 0) GO TO 101
-         CALL RADF4 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3))
-         GO TO 110
-  101    CALL RADF4 (IDO,L1,CH,C,WA(IW),WA(IX2),WA(IX3))
-         GO TO 110
-  102    IF (IP .NE. 2) GO TO 104
-         IF (NA .NE. 0) GO TO 103
-         CALL RADF2 (IDO,L1,C,CH,WA(IW))
-         GO TO 110
-  103    CALL RADF2 (IDO,L1,CH,C,WA(IW))
-         GO TO 110
-  104    IF (IP .NE. 3) GO TO 106
-         IX2 = IW+IDO
-         IF (NA .NE. 0) GO TO 105
-         CALL RADF3 (IDO,L1,C,CH,WA(IW),WA(IX2))
-         GO TO 110
-  105    CALL RADF3 (IDO,L1,CH,C,WA(IW),WA(IX2))
-         GO TO 110
-  106    IF (IP .NE. 5) GO TO 108
-         IX2 = IW+IDO
-         IX3 = IX2+IDO
-         IX4 = IX3+IDO
-         IF (NA .NE. 0) GO TO 107
-         CALL RADF5 (IDO,L1,C,CH,WA(IW),WA(IX2),WA(IX3),WA(IX4))
-         GO TO 110
-  107    CALL RADF5 (IDO,L1,CH,C,WA(IW),WA(IX2),WA(IX3),WA(IX4))
-         GO TO 110
-  108    IF (IDO .EQ. 1) NA = 1-NA
-         IF (NA .NE. 0) GO TO 109
-         CALL RADFG (IDO,IP,L1,IDL1,C,C,C,CH,CH,WA(IW))
-         NA = 1
-         GO TO 110
-  109    CALL RADFG (IDO,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW))
-         NA = 0
-  110    L2 = L1
-  111 CONTINUE
-      IF (NA .EQ. 1) RETURN
-      DO 112 I=1,N
-         C(I) = CH(I)
-  112 CONTINUE
-      RETURN
-      END