SLATEC Routines --- QAWC ---
*DECK QAWC
SUBROUTINE QAWC (F, A, B, C, EPSABS, EPSREL, RESULT, ABSERR,
+ NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK)
C***BEGIN PROLOGUE QAWC
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 SINGLE 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 Real version
C
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 Under limit of integration
C
C B - Real
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 - 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 ON RETURN
C RESULT - Real
C Approximation to the integral
C
C ABSERR - Real
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 - Real
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 QAWCE, 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 QAWC