SLATEC Routines --- DQAWFE ---


*DECK DQAWFE
      SUBROUTINE DQAWFE (F, A, OMEGA, INTEGR, EPSABS, LIMLST, LIMIT,
     +   MAXP1, RESULT, ABSERR, NEVAL, IER, RSLST, ERLST, IERLST, LST,
     +   ALIST, BLIST, RLIST, ELIST, IORD, NNLOG, CHEBMO)
C***BEGIN PROLOGUE  DQAWFE
C***PURPOSE  The routine calculates an approximation result to a
C            given Fourier integral
C            I = Integral of F(X)*W(X) over (A,INFINITY)
C            where W(X)=COS(OMEGA*X) or W(X)=SIN(OMEGA*X),
C            hopefully satisfying following claim for accuracy
C            ABS(I-RESULT).LE.EPSABS.
C***LIBRARY   SLATEC (QUADPACK)
C***CATEGORY  H2A3A1
C***TYPE      DOUBLE PRECISION (QAWFE-S, DQAWFE-D)
C***KEYWORDS  AUTOMATIC INTEGRATOR, CONVERGENCE ACCELERATION,
C             FOURIER INTEGRALS, INTEGRATION BETWEEN ZEROS, QUADPACK,
C             QUADRATURE, SPECIAL-PURPOSE INTEGRAL
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 Fourier integrals
C        Standard fortran subroutine
C        Double precision version
C
C        PARAMETERS
C         ON ENTRY
C            F      - Double precision
C                     Function subprogram defining the integrand
C                     Function F(X). The actual name for F needs to
C                     be declared E X T E R N A L in the driver program.
C
C            A      - Double precision
C                     Lower limit of integration
C
C            OMEGA  - Double precision
C                     Parameter in the WEIGHT function
C
C            INTEGR - Integer
C                     Indicates which WEIGHT function is 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 will
C                     end with IER = 6.
C
C            EPSABS - Double precision
C                     absolute accuracy requested, EPSABS.GT.0
C                     If EPSABS.LE.0, the routine will end with IER = 6.
C
C            LIMLST - Integer
C                     LIMLST gives an upper bound on the number of
C                     cycles, LIMLST.GE.1.
C                     If LIMLST.LT.3, the routine will end with IER = 6.
C
C            LIMIT  - Integer
C                     Gives an upper bound on the number of subintervals
C                     allowed in the partition of each cycle, LIMIT.GE.1
C                     each cycle, LIMIT.GE.1.
C
C            MAXP1  - Integer
C                     Gives an upper bound on the number of
C                     Chebyshev moments which can be stored, I.E.
C                     for the intervals of lengths ABS(B-A)*2**(-L),
C                     L=0,1, ..., MAXP1-2, MAXP1.GE.1
C
C         ON RETURN
C            RESULT - Double precision
C                     Approximation to the integral X
C
C            ABSERR - Double precision
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    - IER = 0 Normal and reliable termination of
C                             the routine. It is assumed that the
C                             requested accuracy has been achieved.
C                     IER.GT.0 Abnormal termination of the routine. The
C                             estimates for integral and error are less
C                             reliable. It is assumed that the requested
C                             accuracy has not been achieved.
C            ERROR MESSAGES
C                    If OMEGA.NE.0
C                     IER = 1 Maximum number of  cycles  allowed
C                             Has been achieved., i.e. of subintervals
C                             (A+(K-1)C,A+KC) where
C                             C = (2*INT(ABS(OMEGA))+1)*PI/ABS(OMEGA),
C                             for K = 1, 2, ..., LST.
C                             One can allow more cycles by increasing
C                             the value of LIMLST (and taking the
C                             according dimension adjustments into
C                             account).
C                             Examine the array IWORK which contains
C                             the error flags on the cycles, in order to
C                             look for eventual local integration
C                             difficulties. If the position of a local
C                             difficulty can be determined (e.g.
C                             SINGULARITY, DISCONTINUITY within the
C                             interval) one will probably gain from
C                             splitting up the interval at this point
C                             and calling appropriate integrators on
C                             the subranges.
C                         = 4 The extrapolation table constructed for
C                             convergence acceleration of the series
C                             formed by the integral contributions over
C                             the cycles, does not converge to within
C                             the requested accuracy. As in the case of
C                             IER = 1, it is advised to examine the
C                             array IWORK which contains the error
C                             flags on the cycles.
C                         = 6 The input is invalid because
C                             (INTEGR.NE.1 AND INTEGR.NE.2) or
C                              EPSABS.LE.0 or LIMLST.LT.3.
C                              RESULT, ABSERR, NEVAL, LST are set
C                              to zero.
C                         = 7 Bad integrand behaviour occurs within one
C                             or more of the cycles. Location and type
C                             of the difficulty involved can be
C                             determined from the vector IERLST. Here
C                             LST is the number of cycles actually
C                             needed (see below).
C                             IERLST(K) = 1 The maximum number of
C                                           subdivisions (= LIMIT) has
C                                           been achieved on the K th
C                                           cycle.
C                                       = 2 Occurrence of roundoff error
C                                           is detected and prevents the
C                                           tolerance imposed on the
C                                           K th cycle, from being
C                                           achieved.
C                                       = 3 Extremely bad integrand
C                                           behaviour occurs at some
C                                           points of the K th cycle.
C                                       = 4 The integration procedure
C                                           over the K th cycle does
C                                           not converge (to within the
C                                           required accuracy) due to
C                                           roundoff in the
C                                           extrapolation procedure
C                                           invoked on this cycle. It
C                                           is assumed that the result
C                                           on this interval is the
C                                           best which can be obtained.
C                                       = 5 The integral over the K th
C                                           cycle is probably divergent
C                                           or slowly convergent. It
C                                           must be noted that
C                                           divergence can occur with
C                                           any other value of
C                                           IERLST(K).
C                    If OMEGA = 0 and INTEGR = 1,
C                    The integral is calculated by means of DQAGIE
C                    and IER = IERLST(1) (with meaning as described
C                    for IERLST(K), K = 1).
C
C            RSLST  - Double precision
C                     Vector of dimension at least LIMLST
C                     RSLST(K) contains the integral contribution
C                     over the interval (A+(K-1)C,A+KC) where
C                     C = (2*INT(ABS(OMEGA))+1)*PI/ABS(OMEGA),
C                     K = 1, 2, ..., LST.
C                     Note that, if OMEGA = 0, RSLST(1) contains
C                     the value of the integral over (A,INFINITY).
C
C            ERLST  - Double precision
C                     Vector of dimension at least LIMLST
C                     ERLST(K) contains the error estimate corresponding
C                     with RSLST(K).
C
C            IERLST - Integer
C                     Vector of dimension at least LIMLST
C                     IERLST(K) contains the error flag corresponding
C                     with RSLST(K). For the meaning of the local error
C                     flags see description of output parameter IER.
C
C            LST    - Integer
C                     Number of subintervals needed for the integration
C                     If OMEGA = 0 then LST is set to 1.
C
C            ALIST, BLIST, RLIST, ELIST - Double precision
C                     vector of dimension at least LIMIT,
C
C            IORD, NNLOG - Integer
C                     Vector of dimension at least LIMIT, providing
C                     space for the quantities needed in the subdivision
C                     process of each cycle
C
C            CHEBMO - Double precision
C                     Array of dimension at least (MAXP1,25), providing
C                     space for the Chebyshev moments needed within the
C                     cycles
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  D1MACH, DQAGIE, DQAWOE, DQELG
C***REVISION HISTORY  (YYMMDD)
C   800101  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   891009  Removed unreferenced variable.  (WRB)
C   891009  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C***END PROLOGUE  DQAWFE