*DECK QAWCE SUBROUTINE QAWCE (F, A, B, C, EPSABS, EPSREL, LIMIT, RESULT, + ABSERR, NEVAL, IER, ALIST, BLIST, RLIST, ELIST, IORD, LAST) C***BEGIN PROLOGUE QAWCE 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 SINGLE 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 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 C - Real 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 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 - 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 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 - 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 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 QC25C, 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 QAWCE