sinqf(3P)

NAME

sinqf - compute the Fourier coefficients in a sine series representation with only odd wave numbers. The xSINQ operations are unnormalized inverses of themselves, so a call to xSINQF followed by a call to xSINQB will multiply the input sequence by 4 ∗ N. The VxSINQ operations are normalized, so a call of VxSINQF followed by a call of VxSINQB will return the original sequence.

SYNOPSIS

CALL SINQF (N, RX, RWSAVE)

CALL DSINQF (N, DX, DWSAVE)

CALL VSINQF (M, N, RX, RXT, MDIMX, RWSAVE)

CALL VDSINQF (M, N, DX, DXT, MDIMX, DWSAVE)

void sinqf (long int n, float ∗sx, float ∗wsave)

void dsinqf (long int n, double ∗dx, double ∗wsave)

void vsinqf(long int m, long int n, float ∗sx, long int
mdimx, float ∗wsave)

void vdsinqf(long int m, long int n, double ∗dx, long int
mdimx, double ∗wsave)

ARGUMENTS

M(For vector operations only.)
The number of sequences to be transformed. M >= 0.

NLength of the sequence to be transformed. These subroutines are most efficient when N is a product of
small primes. N >= 0.

xXOn entry, an array of length N containing the sequence to be
transformed. For VxSINQF, a real two-dimensional array with dimensions of (MDIMX x N) whose rows contain the sequences to be transformed. On exit, the quarter-wave sine transform 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.

xWSAVEOn entry, an array with dimension of at least (3 ∗ N + 15) for
scalar subroutines or (2 ∗ N + 15) for vector subroutines, initialized by xSINQI or VxSINQI.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           M, N
      PARAMETER        (M = 4)
      PARAMETER        (N = 6)
C
      INTEGER           I, J
      REAL              PI, WSAVE(N + 15), X(M, N+1), XT(M, N + 1)
C
      EXTERNAL          VSINQB, VSINQF, VSINQI
      INTRINSIC         ACOS, SIN
C
C     Initialize the array to m real odd quarter-wave sequence,
C     that is, they can be expanded in terms of a cosine series
C     with only odd wave numbers.
C
      PI = ACOS (-1.0)
      DO 110, J=1, M
        DO 100, I=1, N
          X(J,I) = 40.0 ∗ J ∗ SIN (I ∗ PI / (2.0 ∗ N))
100   CONTINUE
110 CONTINUE
C
      CALL VSINQI (N, WSAVE)
      PRINT 1000
      DO 120, J=1, M
        PRINT 1010, J, (X(J, I), I = 1, N)
120 CONTINUE
      CALL VSINQF (M, N, X, XT, M, WSAVE)
      PRINT 1000
      DO 130, J=1, M
        PRINT 1010, J, (X(J, I), I = 1, N)
130 CONTINUE
      CALL VSINQB (M, N, X, XT, M, WSAVE)
      PRINT 1000
      DO 140, J=1, M
        PRINT 1010, J, (X(J, I), I = 1, N)
140 CONTINUE
C
1000 FORMAT (1X, ’Original Sequence: ’)
1010 FORMAT (1X, ’Sequence’, I2, ’: ’, 100(F5.1, 1X))
1020 FORMAT (1X, ’Transformed Sequence: ’)
1030 FORMAT (1X, ’Recovered Sequence: ’)
C
      END

SAMPLE OUTPUT

Original Sequence:
Sequence 1:   10.4 20.0 28.3 34.6 38.6 40.0
Sequence 2:   20.7 40.0 56.6 69.3 77.3 80.0
Sequence 3:   31.1 60.0 84.9 103.9 115.9 120.0
Sequence 4:   41.4 80.0 113.1 138.6 154.5 160.0
Original Sequence:
Sequence 1:   49.0   0.0   0.0   0.0   0.0   0.0
Sequence 2:   98.0   0.0   0.0   0.0   0.0   0.0
Sequence 3: 147.0   0.0   0.0   0.0   0.0   0.0
Sequence 4: 196.0   0.0   0.0   0.0   0.0   0.0
Original Sequence:
Sequence 1:   10.4 20.0 28.3 34.6 38.6 40.0
Sequence 2:   20.7 40.0 56.6 69.3 77.3 80.0
Sequence 3:   31.1 60.0 84.9 103.9 115.9 120.0
Sequence 4:   41.4 80.0 113.1 138.6 154.5 160.0