*DECK QAWSE SUBROUTINE QAWSE (F, A, B, ALFA, BETA, INTEGR, EPSABS, EPSREL, + LIMIT, RESULT, ABSERR, NEVAL, IER, ALIST, BLIST, RLIST, ELIST, + IORD, LAST) C***BEGIN PROLOGUE QAWSE C***PURPOSE The routine calculates an approximation result to a given C definite integral I = Integral of F*W over (A,B), C (where W shows a singular behaviour at the end points, C see parameter INTEGR). C Hopefully satisfying following claim for accuracy C ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)). C***LIBRARY SLATEC (QUADPACK) C***CATEGORY H2A2A1 C***TYPE SINGLE PRECISION (QAWSE-S, DQAWSE-D) C***KEYWORDS ALGEBRAIC-LOGARITHMIC END POINT SINGULARITIES, C AUTOMATIC INTEGRATOR, CLENSHAW-CURTIS METHOD, 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 Integration of functions having algebraico-logarithmic C end point singularities 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, B.GT.A C If B.LE.A, the routine will end with IER = 6. C C ALFA - Real C Parameter in the WEIGHT function, ALFA.GT.(-1) C If ALFA.LE.(-1), the routine will end with C IER = 6. C C BETA - Real C Parameter in the WEIGHT function, BETA.GT.(-1) C If BETA.LE.(-1), the routine will end with C IER = 6. C C INTEGR - Integer C Indicates which WEIGHT function is to be used C = 1 (X-A)**ALFA*(B-X)**BETA C = 2 (X-A)**ALFA*(B-X)**BETA*LOG(X-A) C = 3 (X-A)**ALFA*(B-X)**BETA*LOG(B-X) C = 4 (X-A)**ALFA*(B-X)**BETA*LOG(X-A)*LOG(B-X) C If INTEGR.LT.1 or INTEGR.GT.4, the routine C will end with 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.2 C If LIMIT.LT.2, 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 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 the integral and error C are less reliable. It is assumed that the C requested accuracy has not been achieved. C ERROR MESSAGES C = 1 Maximum number of subdivisions allowed C has been achieved. One can allow more C subdivisions by increasing the value of C LIMIT. However, if this yields no C improvement, it is advised to analyze the C integrand in order to determine the C integration difficulties which prevent the C requested tolerance from being achieved. C In case of a jump DISCONTINUITY or a local C SINGULARITY of algebraico-logarithmic type C at one or more interior points of the C integration range, one should proceed by C splitting up the interval at these C points and calling the integrator on the C subranges. C = 2 The occurrence of roundoff error is C detected, 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 B.LE.A or ALFA.LE.(-1) or BETA.LE.(-1), or C INTEGR.LT.1 or INTEGR.GT.4, or C (EPSABS.LE.0 and C EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28), C or LIMIT.LT.2. 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 at least LIMIT, the first C LAST elements of which are the moduli of the C absolute error estimates on the subintervals C C IORD - Integer C Vector of dimension at least LIMIT, the first K C 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 QC25S, QMOMO, 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 QAWSE