*DECK DQAGI SUBROUTINE DQAGI (F, BOUND, INF, EPSABS, EPSREL, RESULT, ABSERR, + NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK) C***BEGIN PROLOGUE DQAGI C***PURPOSE The routine calculates an approximation result to a given C INTEGRAL I = Integral of F over (BOUND,+INFINITY) C OR I = Integral of F over (-INFINITY,BOUND) C OR I = Integral of F over (-INFINITY,+INFINITY) C Hopefully satisfying following claim for accuracy C ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)). C***LIBRARY SLATEC (QUADPACK) C***CATEGORY H2A3A1, H2A4A1 C***TYPE DOUBLE PRECISION (QAGI-S, DQAGI-D) C***KEYWORDS AUTOMATIC INTEGRATOR, EXTRAPOLATION, GENERAL-PURPOSE, C GLOBALLY ADAPTIVE, INFINITE INTERVALS, QUADPACK, C QUADRATURE, TRANSFORMATION 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 over infinite intervals C Standard fortran subroutine 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 BOUND - Double precision C Finite bound of integration range C (has no meaning if interval is doubly-infinite) C C INF - Integer C indicating the kind of integration range involved C INF = 1 corresponds to (BOUND,+INFINITY), C INF = -1 to (-INFINITY,BOUND), C INF = 2 to (-INFINITY,+INFINITY). 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 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. The C estimates for result and error are less C reliable. It is assumed that the requested C 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 (e.g. SINGULARITY, C DISCONTINUITY within the interval) one C will probably gain from splitting up the C interval at this point and calling the C integrator on the subranges. If possible, C an appropriate special-purpose integrator C should 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 assumed that the requested tolerance C cannot be achieved, and that the returned C RESULT is the best which 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. C = 6 The input is invalid, because C (EPSABS.LE.0 and C EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28)) C or LIMIT.LT.1 or LENIW.LT.LIMIT*4. C RESULT, ABSERR, NEVAL, LAST are set to C zero. Except when LIMIT or LENIW is C invalid, 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 subintervals C in the partition of the given integration interval C (A,B), LIMIT.GE.1. C If LIMIT.LT.1, 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 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 LIMIT, the first C K 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), and C K = LIMIT+1-LAST otherwise 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 the C integral approximations over the subintervals, C WORK(LIMIT*3+1), ..., WORK(LIMIT*3) C contain the error estimates. C C***REFERENCES (NONE) C***ROUTINES CALLED DQAGIE, 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 DQAGI C DOUBLE PRECISION ABSERR,BOUND,EPSABS,EPSREL,F,RESULT,WORK INTEGER IER,INF,IWORK,LAST,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 DQAGI IER = 6 NEVAL = 0 LAST = 0 RESULT = 0.0D+00 ABSERR = 0.0D+00 IF(LIMIT.LT.1.OR.LENW.LT.LIMIT*4) GO TO 10 C C PREPARE CALL FOR DQAGIE. C L1 = LIMIT+1 L2 = LIMIT+L1 L3 = LIMIT+L2 C CALL DQAGIE(F,BOUND,INF,EPSABS,EPSREL,LIMIT,RESULT,ABSERR, 1 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', 'DQAGI', + 'ABNORMAL RETURN', IER, LVL) RETURN END