# dqawc.f

          SUBROUTINE DQAWC (F, A, B, C, EPSABS, EPSREL, RESULT, ABSERR,
         +   NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK)
    C***BEGIN PROLOGUE  DQAWC
    C***PURPOSE  The routine calculates an approximation result to a
    C            Cauchy principal value I = INTEGRAL of F*W over (A,B)
    C            (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
    C            following claim for accuracy
    C            ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).
    C***LIBRARY   SLATEC (QUADPACK)
    C***CATEGORY  H2A2A1, J4
    C***TYPE      DOUBLE PRECISION (QAWC-S, DQAWC-D)
    C***KEYWORDS  AUTOMATIC INTEGRATOR, CAUCHY PRINCIPAL VALUE,
    C             CLENSHAW-CURTIS METHOD, GLOBALLY ADAPTIVE, QUADPACK,
    C             QUADRATURE, SPECIAL-PURPOSE
    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 a Cauchy principal value
    C        Standard fortran subroutine
    C        Double precision version
    C
    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 be
    C                     declared E X T E R N A L in the driver program.
    C
    C            A      - Double precision
    C                     Under limit of integration
    C
    C            B      - Double precision
    C                     Upper limit of integration
    C
    C            C      - Parameter in the weight function, C.NE.A, C.NE.B.
    C                     If C = A or C = B, the routine will end with
    C                     IER = 6 .
    C
    C            EPSABS - Double precision
    C                     Absolute accuracy requested
    C            EPSREL - Double precision
    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         ON RETURN
    C            RESULT - Double precision
    C                     Approximation to the integral
    C
    C            ABSERR - Double precision
    C                     Estimate or 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 requested
    C                             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 sub-
    C                             divisions by increasing the value of LIMIT
    C                             (and taking the 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
    C                             can 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
    C                             appropriate integrators on the subranges.
    C                         = 2 The occurrence of roundoff error is detec-
    C                             ted, which prevents the requested
    C                             tolerance from being achieved.
    C                         = 3 Extremely bad integrand behaviour occurs
    C                             at some points of the integration
    C                             interval.
    C                         = 6 The input is invalid, because
    C                             C = A or C = B or
    C                             (EPSABS.LE.0 and
    C                              EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28))
    C                             or LIMIT.LT.1 or LENW.LT.LIMIT*4.
    C                             RESULT, ABSERR, NEVAL, LAST are set to
    C                             zero.  Except when LENW or LIMIT is
    C                             invalid, IWORK(1), WORK(LIMIT*2+1) and
    C                             WORK(LIMIT*3+1) are set to zero, WORK(1)
    C                             is set to A and WORK(LIMIT+1) to B.
    C
    C         DIMENSIONING PARAMETERS
    C            LIMIT - Integer
    C                    Dimensioning parameter for IWORK
    C                    LIMIT determines the maximum number of subintervals
    C                    in the partition of the given integration interval
    C                    (A,B), LIMIT.GE.1.
    C                    If LIMIT.LT.1, the routine will end with IER = 6.
    C
    C           LENW   - Integer
    C                    Dimensioning parameter for WORK
    C                    LENW must be at least LIMIT*4.
    C                    If LENW.LT.LIMIT*4, the routine will end with
    C                    IER = 6.
    C
    C            LAST  - Integer
    C                    On return, LAST equals the number of subintervals
    C                    produced in the subdivision process, which
    C                    determines the number of significant elements
    C                    actually in the WORK ARRAYS.
    C
    C         WORK ARRAYS
    C            IWORK - Integer
    C                    Vector of dimension at least LIMIT, the first K
    C                    elements of which contain pointers
    C                    to the error estimates over the subintervals,
    C                    such that WORK(LIMIT*3+IWORK(1)), ... ,
    C                    WORK(LIMIT*3+IWORK(K)) form a decreasing
    C                    sequence, with K = LAST if LAST.LE.(LIMIT/2+2),
    C                    and K = LIMIT+1-LAST otherwise
    C
    C            WORK  - Double precision
    C                    Vector of dimension at least LENW
    C                    On return
    C                    WORK(1), ..., WORK(LAST) contain the left
    C                     end points of the subintervals in the
    C                     partition of (A,B),
    C                    WORK(LIMIT+1), ..., WORK(LIMIT+LAST) contain
    C                     the right end points,
    C                    WORK(LIMIT*2+1), ..., WORK(LIMIT*2+LAST) contain
    C                     the integral approximations over the subintervals,
    C                    WORK(LIMIT*3+1), ..., WORK(LIMIT*3+LAST)
    C                     contain the error estimates.
    C
    C***REFERENCES  (NONE)
    C***ROUTINES CALLED  DQAWCE, XERMSG
    C***REVISION HISTORY  (YYMMDD)
    C   800101  DATE WRITTEN
    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   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
    C***END PROLOGUE  DQAWC