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112 lines
3.6 KiB
Fortran
112 lines
3.6 KiB
Fortran
*DECK COST
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SUBROUTINE COST (N, X, WSAVE)
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C***BEGIN PROLOGUE COST
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C***PURPOSE Compute the cosine transform of a real, even sequence.
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C***LIBRARY SLATEC (FFTPACK)
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C***CATEGORY J1A3
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C***TYPE SINGLE PRECISION (COST-S)
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C***KEYWORDS COSINE FOURIER TRANSFORM, FFTPACK
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C***AUTHOR Swarztrauber, P. N., (NCAR)
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C***DESCRIPTION
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C
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C Subroutine COST computes the discrete Fourier cosine transform
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C of an even sequence X(I). The transform is defined below at output
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C parameter X.
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C
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C COST is the unnormalized inverse of itself since a call of COST
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C followed by another call of COST will multiply the input sequence
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C X by 2*(N-1). The transform is defined below at output parameter X.
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C
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C The array WSAVE which is used by subroutine COST must be
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C initialized by calling subroutine COSTI(N,WSAVE).
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C
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C Input Parameters
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C
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C N the length of the sequence X. N must be greater than 1.
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C The method is most efficient when N-1 is a product of
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C small primes.
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C
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C X an array which contains the sequence to be transformed
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C
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C WSAVE a work array which must be dimensioned at least 3*N+15
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C in the program that calls COST. The WSAVE array must be
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C initialized by calling subroutine COSTI(N,WSAVE), and a
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C different WSAVE array must be used for each different
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C value of N. This initialization does not have to be
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C repeated so long as N remains unchanged. Thus subsequent
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C transforms can be obtained faster than the first.
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C
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C Output Parameters
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C
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C X For I=1,...,N
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C
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C X(I) = X(1)+(-1)**(I-1)*X(N)
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C
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C + the sum from K=2 to K=N-1
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C
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C 2*X(K)*COS((K-1)*(I-1)*PI/(N-1))
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C
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C A call of COST followed by another call of
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C COST will multiply the sequence X by 2*(N-1).
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C Hence COST is the unnormalized inverse
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C of itself.
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C
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C WSAVE contains initialization calculations which must not be
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C destroyed between calls of COST.
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C
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C***REFERENCES P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
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C Computations (G. Rodrigue, ed.), Academic Press,
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C 1982, pp. 51-83.
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C***ROUTINES CALLED RFFTF
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C***REVISION HISTORY (YYMMDD)
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C 790601 DATE WRITTEN
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C 830401 Modified to use SLATEC library source file format.
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C 860115 Modified by Ron Boisvert to adhere to Fortran 77 by
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C changing dummy array size declarations (1) to (*)
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C 861211 REVISION DATE from Version 3.2
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C 881128 Modified by Dick Valent to meet prologue standards.
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE COST
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DIMENSION X(*), WSAVE(*)
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C***FIRST EXECUTABLE STATEMENT COST
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NM1 = N-1
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NP1 = N+1
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NS2 = N/2
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IF (N-2) 106,101,102
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101 X1H = X(1)+X(2)
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X(2) = X(1)-X(2)
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X(1) = X1H
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RETURN
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102 IF (N .GT. 3) GO TO 103
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X1P3 = X(1)+X(3)
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TX2 = X(2)+X(2)
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X(2) = X(1)-X(3)
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X(1) = X1P3+TX2
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X(3) = X1P3-TX2
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RETURN
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103 C1 = X(1)-X(N)
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X(1) = X(1)+X(N)
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DO 104 K=2,NS2
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KC = NP1-K
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T1 = X(K)+X(KC)
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T2 = X(K)-X(KC)
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C1 = C1+WSAVE(KC)*T2
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T2 = WSAVE(K)*T2
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X(K) = T1-T2
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X(KC) = T1+T2
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104 CONTINUE
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MODN = MOD(N,2)
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IF (MODN .NE. 0) X(NS2+1) = X(NS2+1)+X(NS2+1)
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CALL RFFTF (NM1,X,WSAVE(N+1))
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XIM2 = X(2)
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X(2) = C1
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DO 105 I=4,N,2
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XI = X(I)
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X(I) = X(I-2)-X(I-1)
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X(I-1) = XIM2
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XIM2 = XI
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105 CONTINUE
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IF (MODN .NE. 0) X(N) = XIM2
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106 RETURN
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END
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