QAWSE(3)

SYNOPSIS
SUBROUTINE QAWSE (F, A, B, ALFA, BETA, INTEGR, EPSABS, EPSREL, + LIMIT, RESULT, ABSERR, NEVAL, IER, ALIST, BLIST, RLIST, ELIST, + IORD, LAST)

NAME
qawse - The routine calculates an approximation result to a given definite integral I = Integral of F*W over (A,B), (where W shows a singular behaviour at the end points, see parameter INTEGR). Hopefully satisfying following claim for accuracy ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).

LIBRARY
SLATEC (QUADPACK)

CATEGORY
H2A2A1

TYPE
SINGLE PRECISION (QAWSE-S, DQAWSE-D)

KEYWORDS
ALGEBRAIC-LOGARITHMIC END POINT SINGULARITIES, AUTOMATIC INTEGRATOR, CLENSHAW-CURTIS METHOD, QUADPACK, QUADRATURE, SPECIAL-PURPOSE

AUTHOR
Piessens, Robert Applied Mathematics and Programming Division K. U. Leuven de Doncker, Elise Applied Mathematics and Programming Division K. U. Leuven

DESCRIPTION
Integration of functions having algebraico-logarithmic end point singularities Standard fortran subroutine Real version PARAMETERS ON ENTRY F - Real Function subprogram defining the integrand function F(X). The actual name for F needs to be declared E X T E R N A L in the driver program. A - Real Lower limit of integration B - Real Upper limit of integration, B.GT.A If B.LE.A, the routine will end with IER = 6. ALFA - Real Parameter in the WEIGHT function, ALFA.GT.(-1) If ALFA.LE.(-1), the routine will end with IER = 6. BETA - Real Parameter in the WEIGHT function, BETA.GT.(-1) If BETA.LE.(-1), the routine will end with IER = 6. INTEGR - Integer Indicates which WEIGHT function is to be used = 1 (X-A)**ALFA*(B-X)**BETA = 2 (X-A)**ALFA*(B-X)**BETA*LOG(X-A) = 3 (X-A)**ALFA*(B-X)**BETA*LOG(B-X) = 4 (X-A)**ALFA*(B-X)**BETA*LOG(X-A)*LOG(B-X) If INTEGR.LT.1 or INTEGR.GT.4, the routine will end with IER = 6. EPSABS - Real Absolute accuracy requested EPSREL - Real Relative accuracy requested If EPSABS.LE.0 and EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28), the routine will end with IER = 6. LIMIT - Integer Gives an upper bound on the number of subintervals in the partition of (A,B), LIMIT.GE.2 If LIMIT.LT.2, the routine will end with IER = 6. ON RETURN RESULT - Real Approximation to the integral ABSERR - Real Estimate of the modulus of the absolute error, which should equal or exceed ABS(I-RESULT) NEVAL - Integer Number of integrand evaluations IER - Integer IER = 0 Normal and reliable termination of the routine. It is assumed that the requested accuracy has been achieved. IER.GT.0 Abnormal termination of the routine the estimates for the integral and error are less reliable. It is assumed that the requested accuracy has not been achieved. ERROR MESSAGES = 1 Maximum number of subdivisions allowed has been achieved. One can allow more subdivisions by increasing the value of LIMIT. However, if this yields no improvement, it is advised to analyze the integrand in order to determine the integration difficulties which prevent the requested tolerance from being achieved. In case of a jump DISCONTINUITY or a local SINGULARITY of algebraico-logarithmic type at one or more interior points of the integration range, one should proceed by splitting up the interval at these points and calling the integrator on the subranges. = 2 The occurrence of roundoff error is detected, which prevents the requested tolerance from being achieved. = 3 Extremely bad integrand behaviour occurs at some points of the integration interval. = 6 The input is invalid, because B.LE.A or ALFA.LE.(-1) or BETA.LE.(-1), or INTEGR.LT.1 or INTEGR.GT.4, or (EPSABS.LE.0 and EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28), or LIMIT.LT.2. RESULT, ABSERR, NEVAL, RLIST(1), ELIST(1), IORD(1) and LAST are set to zero. ALIST(1) and BLIST(1) are set to A and B respectively. ALIST - Real Vector of dimension at least LIMIT, the first LAST elements of which are the left end points of the subintervals in the partition of the given integration range (A,B) BLIST - Real Vector of dimension at least LIMIT, the first LAST elements of which are the right end points of the subintervals in the partition of the given integration range (A,B) RLIST - Real Vector of dimension at least LIMIT, the first LAST elements of which are the integral approximations on the subintervals ELIST - Real Vector of dimension at least LIMIT, the first LAST elements of which are the moduli of the absolute error estimates on the subintervals IORD - Integer Vector of dimension at least LIMIT, the first K of which are pointers to the error estimates over the subintervals, so that ELIST(IORD(1)), ..., ELIST(IORD(K)) with K = LAST If LAST.LE.(LIMIT/2+2), and K = LIMIT+1-LAST otherwise form a decreasing sequence LAST - Integer Number of subintervals actually produced in the subdivision process

REFERENCES
(NONE)

ROUTINES CALLED
QC25S, QMOMO, QPSRT, R1MACH

REVISION HISTORY (YYMMDD)
800101 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890831 Modified array declarations. (WRB)
890831 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)