SLATEC Routines --- QAG ---
*DECK QAG
SUBROUTINE QAG (F, A, B, EPSABS, EPSREL, KEY, RESULT, ABSERR,
+ NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK)
C***BEGIN PROLOGUE QAG
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 SINGLE PRECISION (QAG-S, DQAG-D)
C***KEYWORDS AUTOMATIC INTEGRATOR, GAUSS-KRONROD RULES,
C GENERAL-PURPOSE, GLOBALLY ADAPTIVE, INTEGRAND EXAMINATOR,
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 Real version
C
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 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 KEY - Integer
C Key for choice of local integration rule
C A GAUSS-KRONROD PAIR is used with
C 7 - 15 POINTS If KEY.LT.2,
C 10 - 21 POINTS If KEY = 2,
C 15 - 31 POINTS If KEY = 3,
C 20 - 41 POINTS If KEY = 4,
C 25 - 51 POINTS If KEY = 5,
C 30 - 61 POINTS If KEY.GT.5.
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 RESULT 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 yield no improvement it is advised
C to analyze the integrand in order to
C determine the integration difficulties.
C If the position of a local difficulty can
C be determined (I.E. 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 = 3 Extremely bad integrand behaviour occurs
C at some points of the integration
C interval.
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
C to zero.
C EXCEPT when LENW is invalid, IWORK(1),
C WORK(LIMIT*2+1) and WORK(LIMIT*3+1) are
C set to zero, WORK(1) is set to A and
C 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 with
C 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 K
C elements of which contain pointers to the error
C estimates over the subintervals, such that
C WORK(LIMIT*3+IWORK(1)),... , WORK(LIMIT*3+IWORK(K))
C form a decreasing sequence with K = LAST If
C LAST.LE.(LIMIT/2+2), and K = LIMIT+1-LAST otherwise
C
C WORK - Real
C Vector of dimension at least LENW
C on return
C WORK(1), ..., WORK(LAST) contain the left end
C points of the subintervals in the partition of
C (A,B),
C WORK(LIMIT+1), ..., WORK(LIMIT+LAST) contain the
C 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) contain
C the error estimates.
C
C***REFERENCES (NONE)
C***ROUTINES CALLED QAGE, 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 QAG