vcosqi(3P)

NAME

vcosqi - initialize the array xWSAVE, which is used in both xCOSQF and xCOSQB.

SYNOPSIS

CALL COSQI (N, RWSAVE)

CALL DCOSQI (N, DWSAVE)

CALL VCOSQI (N, RWSAVE)

CALL VDCOSQI (N, DWSAVE)

void cosqi (long int n, float ∗rwsave)

void dcosqi (long int n, double ∗dwsave)

void vcosqi (long int n, float ∗rwsave)

void vdcosqi (long int n, float ∗dwsave)

ARGUMENTS

NLength of the sequence to be transformed. The method is most efficient when N is a product of small
primes.

xWSAVEOn entry, an array with a dimension of at least (3 ∗ N + 15) for scalar subroutines or (2 ∗ N + 15) for
vector subroutines. The same work array can be used for both xCOSQF and xCOSQB as long as N remains unchanged. Different xWSAVE arrays are required for different values of N. This initialization does not have to be repeated between calls to xCOSQF or xCOSQB 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 = 6)
C
      INTEGER       I
      REAL          PI, WSAVE(3 ∗ N + 15), X(N)
C
      EXTERNAL      COSQB, COSQF, COSQI
      INTRINSIC     ACOS, COS
C
C     Initialize array X to a real even quarter-wave sequence, that is,
C     it can be expanded in terms of a cosine series with only odd wave
C     numbers.
C
      PI = ACOS (-1.0)
      DO 100, I=1, N
        X(I) = COS((I - 1) ∗ PI / (2.0 ∗ N))
100 CONTINUE
C
      CALL COSQI (N, WSAVE)
      PRINT 1000
      PRINT 1010, (X(I), I = 1, N)
      CALL COSQF (N, X, WSAVE)
      PRINT 1020
      PRINT 1010, (X(I), I = 1, N)
      CALL COSQB (N, X, WSAVE)
      PRINT 1030
      PRINT 1010, (X(I), I = 1, N)
C
1000 FORMAT(1X, ’Original Sequence: ’)
1010 FORMAT(1X, 100(F7.3, 1X))
1020 FORMAT(1X, ’Transformed Sequence: ’)
1030 FORMAT(1X, ’Recovered Sequence: ’)
      END

SAMPLE OUTPUT

Original Sequence:
   1.000   0.966   0.866   0.707   0.500   0.259
Transformed Sequence:
   6.000   0.000   0.000   0.000   0.000   0.000
Recovered Sequence:
24.000 23.182 20.785 16.971 12.000   6.212