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200 lines
8.5 KiB
Fortran
200 lines
8.5 KiB
Fortran
*DECK QAGS
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SUBROUTINE QAGS (F, A, B, EPSABS, EPSREL, RESULT, ABSERR, NEVAL,
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+ IER, LIMIT, LENW, LAST, IWORK, WORK)
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C***BEGIN PROLOGUE QAGS
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C***PURPOSE The routine calculates an approximation result to a given
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C Definite integral I = Integral of F over (A,B),
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C Hopefully satisfying following claim for accuracy
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C ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
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C***LIBRARY SLATEC (QUADPACK)
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C***CATEGORY H2A1A1
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C***TYPE SINGLE PRECISION (QAGS-S, DQAGS-D)
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C***KEYWORDS AUTOMATIC INTEGRATOR, END POINT SINGULARITIES,
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C EXTRAPOLATION, GENERAL-PURPOSE, GLOBALLY ADAPTIVE,
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C QUADPACK, QUADRATURE
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C***AUTHOR Piessens, Robert
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C Applied Mathematics and Programming Division
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C K. U. Leuven
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C de Doncker, Elise
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C Applied Mathematics and Programming Division
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C K. U. Leuven
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C***DESCRIPTION
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C
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C Computation of a definite integral
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C Standard fortran subroutine
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C Real version
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C
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C
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C PARAMETERS
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C ON ENTRY
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C F - Real
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C Function subprogram defining the integrand
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C Function F(X). The actual name for F needs to be
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C Declared E X T E R N A L in the driver program.
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C
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C A - Real
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C Lower limit of integration
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C
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C B - Real
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C Upper limit of integration
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C
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C EPSABS - Real
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C Absolute accuracy requested
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C EPSREL - Real
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C Relative accuracy requested
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C If EPSABS.LE.0
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C And EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28),
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C The routine will end with IER = 6.
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C
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C ON RETURN
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C RESULT - Real
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C Approximation to the integral
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C
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C ABSERR - Real
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C Estimate of the modulus of the absolute error,
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C which should equal or exceed ABS(I-RESULT)
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C
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C NEVAL - Integer
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C Number of integrand evaluations
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C
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C IER - Integer
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C IER = 0 Normal and reliable termination of the
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C routine. It is assumed that the requested
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C accuracy has been achieved.
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C IER.GT.0 Abnormal termination of the routine
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C The estimates for integral and error are
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C less reliable. It is assumed that the
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C requested accuracy has not been achieved.
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C ERROR MESSAGES
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C IER = 1 Maximum number of subdivisions allowed
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C has been achieved. One can allow more sub-
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C divisions by increasing the value of LIMIT
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C (and taking the according dimension
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C adjustments into account. However, if
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C this yields no improvement it is advised
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C to analyze the integrand in order to
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C determine the integration difficulties. If
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C the position of a local difficulty can be
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C determined (e.g. SINGULARITY,
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C DISCONTINUITY within the interval) one
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C will probably gain from splitting up the
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C interval at this point and calling the
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C integrator on the subranges. If possible,
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C an appropriate special-purpose integrator
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C should be used, which is designed for
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C handling the type of difficulty involved.
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C = 2 The occurrence of roundoff error is detec-
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C ted, which prevents the requested
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C tolerance from being achieved.
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C The error may be under-estimated.
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C = 3 Extremely bad integrand behaviour
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C occurs at some points of the integration
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C interval.
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C = 4 The algorithm does not converge.
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C Roundoff error is detected in the
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C Extrapolation table. It is presumed that
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C the requested tolerance cannot be
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C achieved, and that the returned result is
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C the best which can be obtained.
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C = 5 The integral is probably divergent, or
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C slowly convergent. It must be noted that
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C divergence can occur with any other value
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C of IER.
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C = 6 The input is invalid, because
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C (EPSABS.LE.0 AND
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C EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28)
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C OR LIMIT.LT.1 OR LENW.LT.LIMIT*4.
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C RESULT, ABSERR, NEVAL, LAST are set to
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C zero. Except when LIMIT or LENW is
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C invalid, IWORK(1), WORK(LIMIT*2+1) and
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C WORK(LIMIT*3+1) are set to zero, WORK(1)
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C is set to A and WORK(LIMIT+1) TO B.
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C
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C DIMENSIONING PARAMETERS
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C LIMIT - Integer
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C Dimensioning parameter for IWORK
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C LIMIT determines the maximum number of subintervals
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C in the partition of the given integration interval
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C (A,B), LIMIT.GE.1.
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C IF LIMIT.LT.1, the routine will end with IER = 6.
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C
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C LENW - Integer
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C Dimensioning parameter for WORK
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C LENW must be at least LIMIT*4.
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C If LENW.LT.LIMIT*4, the routine will end
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C with IER = 6.
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C
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C LAST - Integer
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C On return, LAST equals the number of subintervals
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C produced in the subdivision process, determines the
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C number of significant elements actually in the WORK
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C Arrays.
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C
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C WORK ARRAYS
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C IWORK - Integer
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C Vector of dimension at least LIMIT, the first K
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C elements of which contain pointers
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C to the error estimates over the subintervals
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C such that WORK(LIMIT*3+IWORK(1)),... ,
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C WORK(LIMIT*3+IWORK(K)) form a decreasing
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C sequence, with K = LAST IF LAST.LE.(LIMIT/2+2),
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C and K = LIMIT+1-LAST otherwise
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C
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C WORK - Real
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C Vector of dimension at least LENW
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C on return
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C WORK(1), ..., WORK(LAST) contain the left
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C end-points of the subintervals in the
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C partition of (A,B),
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C WORK(LIMIT+1), ..., WORK(LIMIT+LAST) contain
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C the right end-points,
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C WORK(LIMIT*2+1), ..., WORK(LIMIT*2+LAST) contain
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C the integral approximations over the subintervals,
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C WORK(LIMIT*3+1), ..., WORK(LIMIT*3+LAST)
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C contain the error estimates.
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED QAGSE, XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 800101 DATE WRITTEN
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C 890831 Modified array declarations. (WRB)
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C 890831 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
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C***END PROLOGUE QAGS
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C
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C
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REAL A,ABSERR,B,EPSABS,EPSREL,F,RESULT,WORK
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INTEGER IER,IWORK,LENW,LIMIT,LVL,L1,L2,L3,NEVAL
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C
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DIMENSION IWORK(*),WORK(*)
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C
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EXTERNAL F
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C
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C CHECK VALIDITY OF LIMIT AND LENW.
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C
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C***FIRST EXECUTABLE STATEMENT QAGS
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IER = 6
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NEVAL = 0
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LAST = 0
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RESULT = 0.0E+00
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ABSERR = 0.0E+00
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IF(LIMIT.LT.1.OR.LENW.LT.LIMIT*4) GO TO 10
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C
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C PREPARE CALL FOR QAGSE.
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C
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L1 = LIMIT+1
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L2 = LIMIT+L1
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L3 = LIMIT+L2
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C
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CALL QAGSE(F,A,B,EPSABS,EPSREL,LIMIT,RESULT,ABSERR,NEVAL,
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1 IER,WORK(1),WORK(L1),WORK(L2),WORK(L3),IWORK,LAST)
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C
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C CALL ERROR HANDLER IF NECESSARY.
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C
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LVL = 0
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10 IF(IER.EQ.6) LVL = 1
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IF (IER .NE. 0) CALL XERMSG ('SLATEC', 'QAGS',
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+ 'ABNORMAL RETURN', IER, LVL)
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RETURN
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END
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