SLATEC Routines --- QAWOE ---

```*DECK QAWOE
SUBROUTINE QAWOE (F, A, B, OMEGA, INTEGR, EPSABS, EPSREL, LIMIT,
+   ICALL, MAXP1, RESULT, ABSERR, NEVAL, IER, LAST, ALIST, BLIST,
+   RLIST, ELIST, IORD, NNLOG, MOMCOM, CHEBMO)
C***BEGIN PROLOGUE  QAWOE
C***PURPOSE  Calculate an approximation to a given definite integral
C               I = Integral of F(X)*W(X) over (A,B), where
C                  W(X) = COS(OMEGA*X)
C               or W(X) = SIN(OMEGA*X),
C            hopefully satisfying the following claim for accuracy
C               ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
C***CATEGORY  H2A2A1
C***TYPE      SINGLE PRECISION (QAWOE-S, DQAWOE-D)
C***KEYWORDS  AUTOMATIC INTEGRATOR, CLENSHAW-CURTIS METHOD,
C             INTEGRAND WITH OSCILLATORY COS OR SIN FACTOR, QUADPACK,
C***AUTHOR  Piessens, Robert
C             Applied Mathematics and Programming Division
C             K. U. Leuven
C           de Doncker, Elise
C             Applied Mathematics and Programming Division
C             K. U. Leuven
C***DESCRIPTION
C
C        Computation of Oscillatory integrals
C        Standard fortran subroutine
C        Real version
C
C        PARAMETERS
C         ON ENTRY
C            F      - Real
C                     Function subprogram defining the integrand
C                     function F(X). The actual name for F needs to be
C                     declared E X T E R N A L in the driver program.
C
C            A      - Real
C                     Lower limit of integration
C
C            B      - Real
C                     Upper limit of integration
C
C            OMEGA  - Real
C                     Parameter in the integrand weight function
C
C            INTEGR - Integer
C                     Indicates which of the WEIGHT functions is to be
C                     used
C                     INTEGR = 1      W(X) = COS(OMEGA*X)
C                     INTEGR = 2      W(X) = SIN(OMEGA*X)
C                     If INTEGR.NE.1 and INTEGR.NE.2, the routine
C                     will end with IER = 6.
C
C            EPSABS - Real
C                     Absolute accuracy requested
C            EPSREL - Real
C                     Relative accuracy requested
C                     If  EPSABS.LE.0
C                     and EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28),
C                     the routine will end with IER = 6.
C
C            LIMIT  - Integer
C                     Gives an upper bound on the number of subdivisions
C                     in the partition of (A,B), LIMIT.GE.1.
C
C            ICALL  - Integer
C                     If QAWOE is to be used only once, ICALL must
C                     be set to 1.  Assume that during this call, the
C                     Chebyshev moments (for CLENSHAW-CURTIS integration
C                     of degree 24) have been computed for intervals of
C                     lengths (ABS(B-A))*2**(-L), L=0,1,2,...MOMCOM-1.
C                     If ICALL.GT.1 this means that QAWOE has been
C                     called twice or more on intervals of the same
C                     length ABS(B-A). The Chebyshev moments already
C                     computed are then re-used in subsequent calls.
C                     If ICALL.LT.1, the routine will end with IER = 6.
C
C            MAXP1  - Integer
C                     Gives an upper bound on the number of Chebyshev
C                     moments which can be stored, i.e. for the
C                     intervals of lengths ABS(B-A)*2**(-L),
C                     L=0,1, ..., MAXP1-2, MAXP1.GE.1.
C                     If MAXP1.LT.1, the routine will end with IER = 6.
C
C         ON RETURN
C            RESULT - Real
C                     Approximation to the integral
C
C            ABSERR - Real
C                     Estimate of the modulus of the absolute error,
C                     which should equal or exceed ABS(I-RESULT)
C
C            NEVAL  - Integer
C                     Number of integrand evaluations
C
C            IER    - Integer
C                     IER = 0 Normal and reliable termination of the
C                             routine. It is assumed that the
C                             requested accuracy has been achieved.
C                   - IER.GT.0 Abnormal termination of the routine.
C                             The estimates for integral and error are
C                             less reliable. It is assumed that the
C                             requested accuracy has not been achieved.
C            ERROR MESSAGES
C                     IER = 1 Maximum number of subdivisions allowed
C                             has been achieved. One can allow more
C                             subdivisions by increasing the value of
C                             LIMIT (and taking according dimension
C                             adjustments into account). However, if
C                             this yields no improvement it is advised
C                             to analyze the integrand, in order to
C                             determine the integration difficulties.
C                             If the position of a local difficulty can
C                             be determined (e.g. SINGULARITY,
C                             DISCONTINUITY within the interval) one
C                             will probably gain from splitting up the
C                             interval at this point and calling the
C                             integrator on the subranges. If possible,
C                             an appropriate special-purpose integrator
C                             should be used which is designed for
C                             handling the type of difficulty involved.
C                         = 2 The occurrence of roundoff error is
C                             detected, which prevents the requested
C                             tolerance from being achieved.
C                             The error may be under-estimated.
C                         = 3 Extremely bad integrand behaviour occurs
C                             at some points of the integration
C                             interval.
C                         = 4 The algorithm does not converge.
C                             Roundoff error is detected in the
C                             extrapolation table.
C                             It is presumed that the requested
C                             tolerance cannot be achieved due to
C                             roundoff in the extrapolation table,
C                             and that the returned result is the
C                             best which can be obtained.
C                         = 5 The integral is probably divergent, or
C                             slowly convergent. It must be noted that
C                             divergence can occur with any other value
C                             of IER.GT.0.
C                         = 6 The input is invalid, because
C                             (EPSABS.LE.0 and
C                              EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28))
C                             or (INTEGR.NE.1 and INTEGR.NE.2) or
C                             ICALL.LT.1 or MAXP1.LT.1.
C                             RESULT, ABSERR, NEVAL, LAST, RLIST(1),
C                             ELIST(1), IORD(1) and NNLOG(1) are set
C                             to ZERO. ALIST(1) and BLIST(1) are set
C                             to A and B respectively.
C
C            LAST  -  Integer
C                     On return, LAST equals the number of
C                     subintervals produces in the subdivision
C                     process, which determines the number of
C                     significant elements actually in the
C                     WORK ARRAYS.
C            ALIST  - Real
C                     Vector of dimension at least LIMIT, the first
C                      LAST  elements of which are the left
C                     end points of the subintervals in the partition
C                     of the given integration range (A,B)
C
C            BLIST  - Real
C                     Vector of dimension at least LIMIT, the first
C                      LAST  elements of which are the right
C                     end points of the subintervals in the partition
C                     of the given integration range (A,B)
C
C            RLIST  - Real
C                     Vector of dimension at least LIMIT, the first
C                      LAST  elements of which are the integral
C                     approximations on the subintervals
C
C            ELIST  - Real
C                     Vector of dimension at least LIMIT, the first
C                      LAST  elements of which are the moduli of the
C                     absolute error estimates on the subintervals
C
C            IORD   - Integer
C                     Vector of dimension at least LIMIT, the first K
C                     elements of which are pointers to the error
C                     estimates over the subintervals,
C                     such that ELIST(IORD(1)), ...,
C                     ELIST(IORD(K)) form a decreasing sequence, with
C                     K = LAST if LAST.LE.(LIMIT/2+2), and
C                     K = LIMIT+1-LAST otherwise.
C
C            NNLOG  - Integer
C                     Vector of dimension at least LIMIT, containing the
C                     subdivision levels of the subintervals, i.e.
C                     IWORK(I) = L means that the subinterval
C                     numbered I is of length ABS(B-A)*2**(1-L)
C
C         ON ENTRY AND RETURN
C            MOMCOM - Integer
C                     Indicating that the Chebyshev moments
C                     have been computed for intervals of lengths
C                     (ABS(B-A))*2**(-L), L=0,1,2, ..., MOMCOM-1,
C                     MOMCOM.LT.MAXP1
C
C            CHEBMO - Real
C                     Array of dimension (MAXP1,25) containing the
C                     Chebyshev moments
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  QC25F, QELG, QPSRT, R1MACH
C***REVISION HISTORY  (YYMMDD)
C   800101  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   890831  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C***END PROLOGUE  QAWOE
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