*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