*DECK DQAGS
SUBROUTINE DQAGS (F, A, B, EPSABS, EPSREL, RESULT, ABSERR, NEVAL,
+ IER, LIMIT, LENW, LAST, IWORK, WORK)
C***BEGIN PROLOGUE DQAGS
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 ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
C***LIBRARY SLATEC (QUADPACK)
C***CATEGORY H2A1A1
C***TYPE DOUBLE PRECISION (QAGS-S, DQAGS-D)
C***KEYWORDS AUTOMATIC INTEGRATOR, END POINT SINGULARITIES,
C EXTRAPOLATION, GENERAL-PURPOSE, GLOBALLY ADAPTIVE,
C QUADPACK, QUADRATURE
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
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 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 sub-
C divisions by increasing the value of LIMIT
C (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 detec-
C ted, which prevents the requested
C tolerance from being achieved.
C The error may be under-estimated.
C = 3 Extremely bad integrand behaviour
C occurs 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. It is presumed that
C the requested tolerance cannot be
C achieved, and that the returned result is
C 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 LENW.LT.LIMIT*4.
C RESULT, ABSERR, NEVAL, LAST are set to
C zero. Except when LIMIT or LENW 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, determines the
C number of significant elements actually in the WORK
C Arrays.
C
C WORK ARRAYS
C IWORK - Integer
C Vector of dimension at least 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 - 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 error estimates.
C
C***REFERENCES (NONE)
C***ROUTINES CALLED DQAGSE, 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 DQAGS
C
C
DOUBLE PRECISION A,ABSERR,B,EPSABS,EPSREL,F,RESULT,WORK
INTEGER IER,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 DQAGS
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 DQAGSE.
C
L1 = LIMIT+1
L2 = LIMIT+L1
L3 = LIMIT+L2
C
CALL DQAGSE(F,A,B,EPSABS,EPSREL,LIMIT,RESULT,ABSERR,NEVAL,
1 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', 'DQAGS',
+ 'ABNORMAL RETURN', IER, LVL)
RETURN
END