DQAWS(3)

SYNOPSIS
SUBROUTINE DQAWS (F, A, B, ALFA, BETA, INTEGR, EPSABS, EPSREL, + RESULT, ABSERR, NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK)

NAME
dqaws - 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
DOUBLE PRECISION (QAWS-S, DQAWS-D)

KEYWORDS
ALGEBRAIC-LOGARITHMIC END POINT SINGULARITIES, AUTOMATIC INTEGRATOR, CLENSHAW-CURTIS METHOD, GLOBALLY ADAPTIVE, 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 Double precision version PARAMETERS ON ENTRY F - Double precision 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 - Double precision Lower limit of integration B - Double precision Upper limit of integration, B.GT.A If B.LE.A, the routine will end with IER = 6. ALFA - Double precision Parameter in the integrand function, ALFA.GT.(-1) If ALFA.LE.(-1), the routine will end with IER = 6. BETA - Double precision Parameter in the integrand 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 - Double precision Absolute accuracy requested EPSREL - Double precision 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. ON RETURN RESULT - Double precision Approximation to the integral ABSERR - Double precision 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 IER = 1 Maximum number of subdivisions allowed has been achieved. One can allow more subdivisions by increasing the value of LIMIT (and taking the according dimension adjustments into account). 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 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 or LENW.LT.LIMIT*4. RESULT, ABSERR, NEVAL, LAST are set to zero. Except when LENW or LIMIT is invalid IWORK(1), WORK(LIMIT*2+1) and WORK(LIMIT*3+1) are set to zero, WORK(1) is set to A and WORK(LIMIT+1) to B. DIMENSIONING PARAMETERS LIMIT - Integer Dimensioning parameter for IWORK LIMIT determines the maximum number of subintervals in the partition of the given integration interval (A,B), LIMIT.GE.2. If LIMIT.LT.2, the routine will end with IER = 6. LENW - Integer Dimensioning parameter for WORK LENW must be at least LIMIT*4. If LENW.LT.LIMIT*4, the routine will end with IER = 6. LAST - Integer On return, LAST equals the number of subintervals produced in the subdivision process, which determines the significant number of elements actually in the WORK ARRAYS. WORK ARRAYS IWORK - Integer Vector of dimension LIMIT, the first K elements of which contain pointers to the error estimates over the subintervals, such that WORK(LIMIT*3+IWORK(1)), ..., WORK(LIMIT*3+IWORK(K)) form a decreasing sequence with K = LAST if LAST.LE.(LIMIT/2+2), and K = LIMIT+1-LAST otherwise WORK - Double precision Vector of dimension LENW On return WORK(1), ..., WORK(LAST) contain the left end points of the subintervals in the partition of (A,B), WORK(LIMIT+1), ..., WORK(LIMIT+LAST) contain the right end points, WORK(LIMIT*2+1), ..., WORK(LIMIT*2+LAST) contain the integral approximations over the subintervals, WORK(LIMIT*3+1), ..., WORK(LIMIT*3+LAST) contain the error estimates.

REFERENCES
(NONE)

ROUTINES CALLED
DQAWSE, XERMSG

REVISION HISTORY (YYMMDD)
800101 DATE WRITTEN
890831 Modified array declarations. (WRB)
890831 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)