NAME
cosqb - synthesize a Fourier sequence from its representa-
tion in terms of a cosine series with odd wave numbers. The
xCOSQ operations are unnormalized inverses of themselves, so
a call to xCOSQF followed by a call to xCOSQB will multiply
the input sequence by 4 * N. The VxCOSQ operations are nor-
malized, so a call of VxCOSQF followed by a call of VxCOSQB
will return the original sequence.
SYNOPSIS
SUBROUTINE COSQB (N, RX, RWSAVE)
SUBROUTINE DCOSQB (N, DX, DWSAVE)
SUBROUTINE VCOSQB (M, N, RX, RXT, MDIMX, RWSAVE)
SUBROUTINE VDCOSQB (M, N, DX, DXT, MDIMX, DWSAVE)
#include <sunperf.h>
void cosqb (int n, float *sx, float *wsave) ;
void dcosqb (int n, double *dx, double *wsave) ;
void vcosqb(int m, int n, float *sx, int mdimx, float
*wsave)
void vdcosqb(int m, int n, double *dx, int mdimx, double
*wsave)
ARGUMENTS
M (For vector operations only.)
The number of sequences to be transformed. M >=
0.
N Length of the sequence to be transformed. These
subroutines are most efficient when N is a product
of small primes. N >= 0.
xX On entry, an array of length N containing the
sequence to be transformed. For VxCOSQB, a real
two-dimensional array with dimensions of (MDIMX x
N) whose rows contain the sequences to be
transformed. On exit, the quarter-wave cosine
synthesis of the input.
xXT (For vector operations only.)
A real two-dimensional work array with dimensions
of (MDIMX x N).
MDIMX (For vector operations only.)
Leading dimension of the arrays xX and xXT as
specified in a dimension or type statement. MDIMX
>= M.
xWSAVE On entry, an array with dimension of at least (3 *
N + 15) for scalar subroutines or (2 * N + 15) for
vector subroutines, initialized by xCOSQI or
VxCOSQI.
SAMPLE PROGRAM
PROGRAM TEST
IMPLICIT NONE
C
INTEGER M, N
PARAMETER (M = 1)
PARAMETER (N = 6)
C
INTEGER I
REAL PI, WSAVE(N + 15), X(M, N), XT(M, N)
C
EXTERNAL VCOSQB, VCOSQF, VCOSQI
INTRINSIC ACOS, COS
C
C Initialize the first row of the array to a real even
C quarter-wave sequence, that is, it can be expanded in
C terms of a cosine series with only only odd wave numbers.
C
PI = ACOS (-1.0)
DO 100, I=1, N
X(M,I) = 40.0 * COS ((I - 1) * PI / (2.0 * N))
100 CONTINUE
C
PRINT 1000
PRINT 1010, (X(M, I), I = 1, N)
CALL VCOSQI (N, WSAVE)
CALL VCOSQF (M, N, X, XT, M, WSAVE)
PRINT 1020
PRINT 1010, (X(M, I), I = 1, N)
CALL VCOSQB (M, N, X, XT, M, WSAVE)
PRINT 1030
PRINT 1010, (X(M, 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: ')
C
END
SAMPLE OUTPUT
Original Sequence:
40.0 38.6 34.6 28.3 20.0 10.4
Transformed Sequence:
49.0 0.0 0.0 0.0 0.0 0.0
Recovered Sequence:
40.0 38.6 34.6 28.3 20.0 10.4
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