*DECK COST
SUBROUTINE COST (N, X, WSAVE)
C***BEGIN PROLOGUE COST
C***PURPOSE Compute the cosine transform of a real, even sequence.
C***LIBRARY SLATEC (FFTPACK)
C***CATEGORY J1A3
C***TYPE SINGLE PRECISION (COST-S)
C***KEYWORDS COSINE FOURIER TRANSFORM, FFTPACK
C***AUTHOR Swarztrauber, P. N., (NCAR)
C***DESCRIPTION
C
C Subroutine COST computes the discrete Fourier cosine transform
C of an even sequence X(I). The transform is defined below at output
C parameter X.
C
C COST is the unnormalized inverse of itself since a call of COST
C followed by another call of COST will multiply the input sequence
C X by 2*(N-1). The transform is defined below at output parameter X.
C
C The array WSAVE which is used by subroutine COST must be
C initialized by calling subroutine COSTI(N,WSAVE).
C
C Input Parameters
C
C N the length of the sequence X. N must be greater than 1.
C The method is most efficient when N-1 is a product of
C small primes.
C
C X an array which contains the sequence to be transformed
C
C WSAVE a work array which must be dimensioned at least 3*N+15
C in the program that calls COST. The WSAVE array must be
C initialized by calling subroutine COSTI(N,WSAVE), and a
C different WSAVE array must be used for each different
C value of N. This initialization does not have to be
C repeated so long as N remains unchanged. Thus subsequent
C transforms can be obtained faster than the first.
C
C Output Parameters
C
C X For I=1,...,N
C
C X(I) = X(1)+(-1)**(I-1)*X(N)
C
C + the sum from K=2 to K=N-1
C
C 2*X(K)*COS((K-1)*(I-1)*PI/(N-1))
C
C A call of COST followed by another call of
C COST will multiply the sequence X by 2*(N-1).
C Hence COST is the unnormalized inverse
C of itself.
C
C WSAVE contains initialization calculations which must not be
C destroyed between calls of COST.
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 RFFTF
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 861211 REVISION DATE from Version 3.2
C 881128 Modified by Dick Valent to meet prologue standards.
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE COST
DIMENSION X(*), WSAVE(*)
C***FIRST EXECUTABLE STATEMENT COST
NM1 = N-1
NP1 = N+1
NS2 = N/2
IF (N-2) 106,101,102
101 X1H = X(1)+X(2)
X(2) = X(1)-X(2)
X(1) = X1H
RETURN
102 IF (N .GT. 3) GO TO 103
X1P3 = X(1)+X(3)
TX2 = X(2)+X(2)
X(2) = X(1)-X(3)
X(1) = X1P3+TX2
X(3) = X1P3-TX2
RETURN
103 C1 = X(1)-X(N)
X(1) = X(1)+X(N)
DO 104 K=2,NS2
KC = NP1-K
T1 = X(K)+X(KC)
T2 = X(K)-X(KC)
C1 = C1+WSAVE(KC)*T2
T2 = WSAVE(K)*T2
X(K) = T1-T2
X(KC) = T1+T2
104 CONTINUE
MODN = MOD(N,2)
IF (MODN .NE. 0) X(NS2+1) = X(NS2+1)+X(NS2+1)
CALL RFFTF (NM1,X,WSAVE(N+1))
XIM2 = X(2)
X(2) = C1
DO 105 I=4,N,2
XI = X(I)
X(I) = X(I-2)-X(I-1)
X(I-1) = XIM2
XIM2 = XI
105 CONTINUE
IF (MODN .NE. 0) X(N) = XIM2
106 RETURN
END