*DECK SINT SUBROUTINE SINT (N, X, WSAVE) C***BEGIN PROLOGUE SINT C***PURPOSE Compute the sine transform of a real, odd sequence. C***LIBRARY SLATEC (FFTPACK) C***CATEGORY J1A3 C***TYPE SINGLE PRECISION (SINT-S) C***KEYWORDS FFTPACK, FOURIER TRANSFORM C***AUTHOR Swarztrauber, P. N., (NCAR) C***DESCRIPTION C C Subroutine SINT computes the discrete Fourier sine transform C of an odd sequence X(I). The transform is defined below at C output parameter X. C C SINT is the unnormalized inverse of itself since a call of SINT C followed by another call of SINT will multiply the input sequence C X by 2*(N+1). C C The array WSAVE which is used by subroutine SINT must be C initialized by calling subroutine SINTI(N,WSAVE). C C Input Parameters C C N the length of the sequence to be transformed. The method C is most efficient when N+1 is the product of small primes. C C X an array which contains the sequence to be transformed C C C WSAVE a work array with dimension at least INT(3.5*N+16) C in the program that calls SINT. The WSAVE array must be C initialized by calling subroutine SINTI(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)= the sum from K=1 to K=N C C 2*X(K)*SIN(K*I*PI/(N+1)) C C A call of SINT followed by another call of C SINT will multiply the sequence X by 2*(N+1). C Hence SINT is the unnormalized inverse C of itself. C C WSAVE contains initialization calculations which must not be C destroyed between calls of SINT. 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 (a) changing dummy array size declarations (1) to (*), C (b) changing definition of variable SQRT3 by using C FORTRAN intrinsic function SQRT instead of a DATA C statement. C 881128 Modified by Dick Valent to meet prologue standards. C 891009 Removed unreferenced statement label. (WRB) C 891009 REVISION DATE from Version 3.2 C 891214 Prologue converted to Version 4.0 format. (BAB) C 920501 Reformatted the REFERENCES section. (WRB) C***END PROLOGUE SINT DIMENSION X(*), WSAVE(*) C***FIRST EXECUTABLE STATEMENT SINT SQRT3 = SQRT(3.) IF (N-2) 101,102,103 101 X(1) = X(1)+X(1) RETURN 102 XH = SQRT3*(X(1)+X(2)) X(2) = SQRT3*(X(1)-X(2)) X(1) = XH RETURN 103 NP1 = N+1 NS2 = N/2 WSAVE(1) = 0. KW = NP1 DO 104 K=1,NS2 KW = KW+1 KC = NP1-K T1 = X(K)-X(KC) T2 = WSAVE(KW)*(X(K)+X(KC)) WSAVE(K+1) = T1+T2 WSAVE(KC+1) = T2-T1 104 CONTINUE MODN = MOD(N,2) IF (MODN .NE. 0) WSAVE(NS2+2) = 4.*X(NS2+1) NF = NP1+NS2+1 CALL RFFTF (NP1,WSAVE,WSAVE(NF)) X(1) = .5*WSAVE(1) DO 105 I=3,N,2 X(I-1) = -WSAVE(I) X(I) = X(I-2)+WSAVE(I-1) 105 CONTINUE IF (MODN .NE. 0) RETURN X(N) = -WSAVE(N+1) RETURN END