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