*DECK QAGP
SUBROUTINE QAGP (F, A, B, NPTS2, POINTS, EPSABS, EPSREL, RESULT,
+ ABSERR, NEVAL, IER, LENIW, LENW, LAST, IWORK, WORK)
C***BEGIN PROLOGUE QAGP
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. SINGULARITIES,
C DISCONTINUITIES), are provided by the user.
C***LIBRARY SLATEC (QUADPACK)
C***CATEGORY H2A2A1
C***TYPE SINGLE 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 Real version
C
C PARAMETERS
C ON ENTRY
C F - Real
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 - Real
C Lower limit of integration
C
C B - Real
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 - Real
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 - Real
C Absolute accuracy requested
C EPSREL - Real
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 - Real
C Approximation to the integral
C
C ABSERR - Real
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 - Real
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 QAGPE, 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 QAGP
C
REAL A,ABSERR,B,EPSABS,EPSREL,F,POINTS,RESULT,WORK
INTEGER IER,IWORK,LENIW,LENW,LIMIT,LVL,L1,L2,L3,NEVAL,NPTS2
C
DIMENSION IWORK(*),POINTS(*),WORK(*)
C
EXTERNAL F
C
C CHECK VALIDITY OF LIMIT AND LENW.
C
C***FIRST EXECUTABLE STATEMENT QAGP
IER = 6
NEVAL = 0
LAST = 0
RESULT = 0.0E+00
ABSERR = 0.0E+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 QAGPE.
C
LIMIT = (LENIW-NPTS2)/2
L1 = LIMIT+1
L2 = LIMIT+L1
L3 = LIMIT+L2
L4 = LIMIT+L3
C
CALL QAGPE(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', 'QAGP',
+ 'ABNORMAL RETURN', IER, LVL)
RETURN
END