Initialize Cosine Even-Wave Transform

Calling Sequence

CALL COSTI	(N, RWSAVE)
CALL DCOSTI	(N, DWSAVE)
CALL VCOSTI	(N, RWSAVE)
CALL VDCOSTI	(N, DWSAVE)
void costi	(int n, float *rwsave)
void dcosti	(int n, double *dwsave)
void vcosti	(int n, float *rwsave)
void vdcosti	(int n, double *dwsave)

Arguments

N	Length of the sequence to be transformed. The method is most efficient when N-1 is a product of small primes. N 2.
xWSAVE	On entry, an array with a dimension of at least (3 × N + 15). Different xWSAVE arrays are required for different values of N. This initialization does not have to be repeated between calls to xCOST as long as N and xWSAVE remain unchanged, thus subsequent transforms can be obtained faster than the first.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER N

PARAMETER (N = 9)

C

INTEGER I

REAL PI, X(N), WSAVE(3 * N + 15)

C

EXTERNAL COST, COSTI

INTRINSIC ACOS, COS

C

C Initialize the array X to an even sequence, that is, it

C can be expanded in terms of a trigonometric series that

C contains only cosine terms.

C

PI = ACOS (-1.0)

DO 100, I=1, N

X(I) = COS ((I - 1.0) * 2.0 * PI / (N - 1.0))

100 CONTINUE

C

CALL COSTI (N, WSAVE)

PRINT 1000

PRINT 1010, (X(I), I = 1, N)

CALL COST (N, X, WSAVE)

PRINT 1020

PRINT 1010, (X(I), I = 1, N)

CALL COST (N, X, WSAVE)

PRINT 1030

PRINT 1010, (X(I), I = 1, N)

C

1000 FORMAT (1X, 'Original Sequence: ')

1010 FORMAT (1X, 100(F5.1, 1X))

1020 FORMAT (1X, 'Transformed Sequence: ')

1030 FORMAT (1X, 'Recovered Sequence: ')

END

Sample Output

Original Sequence:
1.0 0.7 0.0 -0.7 -1.0 -0.7 0.0 0.7 1.0
Transformed Sequence:
0.0 0.0 8.0 0.0 0.0 0.0 0.0 0.0 0.0
Recovered Sequence:
16.0 11.3 0.0 -11.3 -16.0 -11.3 0.0 11.3 16.0