SLATEC Routines --- DQAWCE ---
*DECK DQAWCE
SUBROUTINE DQAWCE (F, A, B, C, EPSABS, EPSREL, LIMIT, RESULT,
+ ABSERR, NEVAL, IER, ALIST, BLIST, RLIST, ELIST, IORD, LAST)
C***BEGIN PROLOGUE DQAWCE
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(EPSABS,EPSREL*ABS(I))
C***LIBRARY SLATEC (QUADPACK)
C***CATEGORY H2A2A1, J4
C***TYPE DOUBLE PRECISION (QAWCE-S, DQAWCE-D)
C***KEYWORDS AUTOMATIC INTEGRATOR, CAUCHY PRINCIPAL VALUE,
C CLENSHAW-CURTIS METHOD, QUADPACK, QUADRATURE,
C 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 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 Lower limit of integration
C
C B - Double precision
C Upper limit of integration
C
C C - Double precision
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 LIMIT - Integer
C Gives an upper bound on the number of subintervals
C in the partition of (A,B), LIMIT.GE.1
C
C ON RETURN
C RESULT - Double precision
C Approximation to the integral
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 - 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
C LIMIT. However, if this yields no
C improvement it is advised to analyze the
C the integrand, in order to determine the
C the integration difficulties. If the
C position of a local difficulty can be
C 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
C occurs at some interior points of
C the integration 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.
C RESULT, ABSERR, NEVAL, RLIST(1), ELIST(1),
C IORD(1) and LAST are set to zero. ALIST(1)
C and BLIST(1) are set to A and B
C respectively.
C
C ALIST - Double precision
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 - Double precision
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 - Double precision
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 - Double precision
C Vector of dimension LIMIT, the first LAST
C elements of which are the moduli of the absolute
C 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, so that
C ELIST(IORD(1)), ..., ELIST(IORD(K)) with K = LAST
C If LAST.LE.(LIMIT/2+2), and K = LIMIT+1-LAST
C otherwise, form a decreasing sequence
C
C LAST - Integer
C Number of subintervals actually produced in
C the subdivision process
C
C***REFERENCES (NONE)
C***ROUTINES CALLED D1MACH, DQC25C, DQPSRT
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 DQAWCE