d8/d38/dqagi_8f_source.html

       SUBROUTINE dqagi(F,BOUND,INF,EPSABS,EPSREL,RESULT,ABSERR,NEVAL,

      *   IER,LIMIT,LENW,LAST,IWORK,WORK)

 C***BEGIN PROLOGUE  DQAGI

 C***DATE WRITTEN   800101   (YYMMDD)

 C***REVISION DATE  830518   (YYMMDD)

 C***CATEGORY NO.  H2A3A1,H2A4A1

 C***KEYWORDS  AUTOMATIC INTEGRATOR, INFINITE INTERVALS,

 C             GENERAL-PURPOSE, TRANSFORMATION, EXTRAPOLATION,

 C             GLOBALLY ADAPTIVE

 C***AUTHOR  PIESSENS,ROBERT,APPL. MATH. & PROGR. DIV. - K.U.LEUVEN

 C           DE DONCKER,ELISE,APPL. MATH. & PROGR. DIV. -K.U.LEUVEN

 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***DESCRIPTION

 C

 C        INTEGRATION OVER INFINITE INTERVALS

 C        STANDARD FORTRAN SUBROUTINE

 C

 C        PARAMETERS

 C         ON ENTRY

 C            F      - SUBROUTINE F(X,RESULT) 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. EXEPT 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***REFERENCES  (NONE)

 C***ROUTINES CALLED  DQAGIE,XERROR

 C***END PROLOGUE  DQAGI

 C

       DOUBLE PRECISION ABSERR,BOUND,EPSABS,EPSREL,RESULT,WORK

       INTEGER IER,INF,IWORK,LAST,LENW,LIMIT,LVL,L1,L2,L3,NEVAL

 C

       dimension iwork(limit),work(lenw)

 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,

      *  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.GT.0) CALL xerror('ABNORMAL RETURN FROM DQAGI',26,ier,lvl)

       RETURN

       END

dqagi
subroutine dqagi(F, BOUND, INF, EPSABS, EPSREL, RESULT, ABSERR, NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK)
Definition: dqagi.f:3

dqagie
subroutine dqagie(F, BOUND, INF, EPSABS, EPSREL, LIMIT, RESULT, ABSERR, NEVAL, IER, ALIST, BLIST, RLIST, ELIST, IORD, LAST)
Definition: dqagie.f:3

xerror
subroutine xerror(MESSG, NMESSG, NERR, LEVEL)
Definition: xerror.f:2