*DECK DQAGP SUBROUTINE DQAGP (F, A, B, NPTS2, POINTS, EPSABS, EPSREL, RESULT, + ABSERR, NEVAL, IER, LENIW, LENW, LAST, IWORK, WORK) C***BEGIN PROLOGUE DQAGP C***PURPOSE The routine calculates an approximation result to a given C definite integral I = Integral of F over (A,B), C hopefully satisfying following claim for accuracy C break points of the integration interval, where local C difficulties of the integrand may occur (e.g. C SINGULARITIES, DISCONTINUITIES), are provided by the user. C***LIBRARY SLATEC (QUADPACK) C***CATEGORY H2A2A1 C***TYPE DOUBLE PRECISION (QAGP-S, DQAGP-D) C***KEYWORDS AUTOMATIC INTEGRATOR, EXTRAPOLATION, GENERAL-PURPOSE, C GLOBALLY ADAPTIVE, QUADPACK, QUADRATURE, C SINGULARITIES AT USER SPECIFIED POINTS 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 definite integral C Standard fortran subroutine C Double precision version C C PARAMETERS C ON ENTRY C F - Double precision 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 - Double precision C Lower limit of integration C C B - Double precision C Upper limit of integration C C NPTS2 - Integer C Number equal to two more than the number of C user-supplied break points within the integration C range, NPTS.GE.2. C If NPTS2.LT.2, The routine will end with IER = 6. C C POINTS - Double precision C Vector of dimension NPTS2, the first (NPTS2-2) C elements of which are the user provided break C points. If these points do not constitute an C ascending sequence there will be an automatic C sorting. C C EPSABS - Double precision C Absolute accuracy requested C EPSREL - Double precision 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 - Double precision C Approximation to the integral C C ABSERR - Double precision 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 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. If C the position of a local difficulty can be C determined (i.e. SINGULARITY, C DISCONTINUITY within the interval), it C should be supplied to the routine as an C element of the vector points. If necessary C an appropriate special-purpose integrator C must be used, which is designed for C handling the type of difficulty involved. C = 2 The occurrence of roundoff error is C detected, which prevents the requested C tolerance from being achieved. C The error may be under-estimated. C = 3 Extremely bad integrand behaviour occurs C at some points of the integration C interval. C = 4 The algorithm does not converge. C roundoff error is detected in the C extrapolation table. C It is presumed that the requested C tolerance cannot be achieved, and that C the returned RESULT is the best which C can be obtained. C = 5 The integral is probably divergent, or C slowly convergent. it must be noted that C divergence can occur with any other value C of IER.GT.0. C = 6 The input is invalid because C NPTS2.LT.2 or C break points are specified outside C the integration range or C (EPSABS.LE.0 and C EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28)) C RESULT, ABSERR, NEVAL, LAST are set to C zero. Except when LENIW or LENW or NPTS2 C is invalid, IWORK(1), IWORK(LIMIT+1), C WORK(LIMIT*2+1) and WORK(LIMIT*3+1) C are set to zero. C WORK(1) is set to A and WORK(LIMIT+1) C to B (where LIMIT = (LENIW-NPTS2)/2). C C DIMENSIONING PARAMETERS C LENIW - Integer C Dimensioning parameter for IWORK C LENIW determines LIMIT = (LENIW-NPTS2)/2, C which is the maximum number of subintervals in the C partition of the given integration interval (A,B), C LENIW.GE.(3*NPTS2-2). C If LENIW.LT.(3*NPTS2-2), the routine will end with C IER = 6. C C LENW - Integer C Dimensioning parameter for WORK C LENW must be at least LENIW*2-NPTS2. C If LENW.LT.LENIW*2-NPTS2, the routine will end C with IER = 6. C C LAST - Integer C On return, LAST equals the number of subintervals C produced in the subdivision process, which C determines the number of significant elements C actually in the WORK ARRAYS. C C WORK ARRAYS C IWORK - Integer C Vector of dimension at least LENIW. on return, C the first K elements of which contain C pointers to the error estimates over the C subintervals, 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), and C K = LIMIT+1-LAST otherwise C IWORK(LIMIT+1), ...,IWORK(LIMIT+LAST) Contain the C subdivision levels of the subintervals, i.e. C if (AA,BB) is a subinterval of (P1,P2) C where P1 as well as P2 is a user-provided C break point or integration LIMIT, then (AA,BB) has C level L if ABS(BB-AA) = ABS(P2-P1)*2**(-L), C IWORK(LIMIT*2+1), ..., IWORK(LIMIT*2+NPTS2) have C no significance for the user, C note that LIMIT = (LENIW-NPTS2)/2. C C WORK - Double precision C Vector of dimension at least 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) contain C the integral approximations over the subintervals, C WORK(LIMIT*3+1), ..., WORK(LIMIT*3+LAST) C contain the corresponding error estimates, C WORK(LIMIT*4+1), ..., WORK(LIMIT*4+NPTS2) C contain the integration limits and the C break points sorted in an ascending sequence. C note that LIMIT = (LENIW-NPTS2)/2. C C***REFERENCES (NONE) C***ROUTINES CALLED DQAGPE, 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 DQAGP C DOUBLE PRECISION A,ABSERR,B,EPSABS,EPSREL,F,POINTS,RESULT,WORK INTEGER IER,IWORK,LAST,LENIW,LENW,LIMIT,LVL,L1,L2,L3,L4,NEVAL, 1 NPTS2 C DIMENSION IWORK(*),POINTS(*),WORK(*) C EXTERNAL F C C CHECK VALIDITY OF LIMIT AND LENW. C C***FIRST EXECUTABLE STATEMENT DQAGP IER = 6 NEVAL = 0 LAST = 0 RESULT = 0.0D+00 ABSERR = 0.0D+00 IF(LENIW.LT.(3*NPTS2-2).OR.LENW.LT.(LENIW*2-NPTS2).OR.NPTS2.LT.2) 1 GO TO 10 C C PREPARE CALL FOR DQAGPE. C LIMIT = (LENIW-NPTS2)/2 L1 = LIMIT+1 L2 = LIMIT+L1 L3 = LIMIT+L2 L4 = LIMIT+L3 C CALL DQAGPE(F,A,B,NPTS2,POINTS,EPSABS,EPSREL,LIMIT,RESULT,ABSERR, 1 NEVAL,IER,WORK(1),WORK(L1),WORK(L2),WORK(L3),WORK(L4), 2 IWORK(1),IWORK(L1),IWORK(L2),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', 'DQAGP', + 'ABNORMAL RETURN', IER, LVL) RETURN END