*DECK QAWS SUBROUTINE QAWS (F, A, B, ALFA, BETA, INTEGR, EPSABS, EPSREL, + RESULT, ABSERR, NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK) C***BEGIN PROLOGUE QAWS 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 (QAWS-S, DQAWS-D) C***KEYWORDS ALGEBRAIC-LOGARITHMIC END POINT SINGULARITIES, C AUTOMATIC INTEGRATOR, CLENSHAW-CURTIS METHOD, C GLOBALLY ADAPTIVE, QUADPACK, 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 integrand 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 integrand 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 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 IER = 1 Maximum number of subdivisions allowed C has been achieved. One can allow more C subdivisions by increasing the value of C LIMIT (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 which prevent the requested tolerance from C being achieved. In case of a jump C discontinuity or a local singularity C of algebraico-logarithmic type at one or C more interior points of the integration C range, one should proceed by splitting up C the interval at these points and calling C the integrator on the 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 or 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 or LENW.LT.LIMIT*4. C RESULT, ABSERR, NEVAL, LAST are set to C zero. Except when LENW or LIMIT is invalid C 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 C subintervals in the partition of the given C integration interval (A,B), LIMIT.GE.2. C If LIMIT.LT.2, 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 C with IER = 6. C C LAST - Integer C On return, LAST equals the number of C subintervals produced in the subdivision process, C which determines the significant number of C elements actually in the WORK ARRAYS. C C WORK ARRAYS C IWORK - Integer C Vector of dimension 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 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) C contain the integral approximations over C the subintervals, C WORK(LIMIT*3+1), ..., WORK(LIMIT*3+LAST) C contain the error estimates. C C***REFERENCES (NONE) C***ROUTINES CALLED QAWSE, 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 QAWS C REAL A,ABSERR,ALFA,B,BETA,EPSABS,EPSREL,F,RESULT,WORK INTEGER IER,INTEGR,IWORK,LENW,LIMIT,LVL,L1,L2,L3,NEVAL C DIMENSION IWORK(*),WORK(*) C EXTERNAL F C C CHECK VALIDITY OF LIMIT AND LENW. C C***FIRST EXECUTABLE STATEMENT QAWS IER = 6 NEVAL = 0 LAST = 0 RESULT = 0.0E+00 ABSERR = 0.0E+00 IF(LIMIT.LT.2.OR.LENW.LT.LIMIT*4) GO TO 10 C C PREPARE CALL FOR QAWSE. C L1 = LIMIT+1 L2 = LIMIT+L1 L3 = LIMIT+L2 C CALL QAWSE(F,A,B,ALFA,BETA,INTEGR,EPSABS,EPSREL,LIMIT,RESULT, 1 ABSERR,NEVAL,IER,WORK(1),WORK(L1),WORK(L2),WORK(L3),IWORK,LAST) C C CALL ERROR HANDLER IF NECESSARY. C LVL = 0 10 IF(IER.EQ.6) LVL = 1 IF (IER .NE. 0) CALL XERMSG ('SLATEC', 'QAWS', + 'ABNORMAL RETURN', IER, LVL) RETURN END