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212 lines
9 KiB
Fortran
212 lines
9 KiB
Fortran
*DECK QAWS
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SUBROUTINE QAWS (F, A, B, ALFA, BETA, INTEGR, EPSABS, EPSREL,
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+ RESULT, ABSERR, NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK)
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C***BEGIN PROLOGUE QAWS
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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*W over (A,B),
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C (where W shows a singular behaviour at the end points
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C see parameter INTEGR).
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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 H2A2A1
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C***TYPE SINGLE PRECISION (QAWS-S, DQAWS-D)
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C***KEYWORDS ALGEBRAIC-LOGARITHMIC END POINT SINGULARITIES,
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C AUTOMATIC INTEGRATOR, CLENSHAW-CURTIS METHOD,
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C GLOBALLY ADAPTIVE, QUADPACK, QUADRATURE, SPECIAL-PURPOSE
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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 Integration of functions having algebraico-logarithmic
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C end point singularities
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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 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, B.GT.A
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C If B.LE.A, the routine will end with IER = 6.
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C
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C ALFA - Real
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C Parameter in the integrand function, ALFA.GT.(-1)
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C If ALFA.LE.(-1), the routine will end with
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C IER = 6.
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C
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C BETA - Real
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C Parameter in the integrand function, BETA.GT.(-1)
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C If BETA.LE.(-1), the routine will end with
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C IER = 6.
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C
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C INTEGR - Integer
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C Indicates which WEIGHT function is to be used
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C = 1 (X-A)**ALFA*(B-X)**BETA
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C = 2 (X-A)**ALFA*(B-X)**BETA*LOG(X-A)
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C = 3 (X-A)**ALFA*(B-X)**BETA*LOG(B-X)
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C = 4 (X-A)**ALFA*(B-X)**BETA*LOG(X-A)*LOG(B-X)
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C If INTEGR.LT.1 or INTEGR.GT.4, the routine
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C will end with IER = 6.
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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 the integral and error
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C are 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
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C subdivisions by increasing the value of
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C LIMIT (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
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C which prevent the requested tolerance from
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C being achieved. In case of a jump
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C discontinuity or a local singularity
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C of algebraico-logarithmic type at one or
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C more interior points of the integration
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C range, one should proceed by splitting up
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C the interval at these points and calling
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C the integrator on the subranges.
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C = 2 The occurrence of roundoff error is
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C detected, which prevents the requested
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C tolerance from being achieved.
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C = 3 Extremely bad integrand behaviour occurs
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C at some points of the integration
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C interval.
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C = 6 The input is invalid, because
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C B.LE.A or ALFA.LE.(-1) or BETA.LE.(-1) or
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C or INTEGR.LT.1 or INTEGR.GT.4 or
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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.2 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 LENW or LIMIT is invalid
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C 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
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C subintervals in the partition of the given
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C integration interval (A,B), LIMIT.GE.2.
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C If LIMIT.LT.2, 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
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C subintervals produced in the subdivision process,
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C which determines the significant number of
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C elements actually in the WORK 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 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 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)
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C contain the integral approximations over
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C 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 QAWSE, 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 QAWS
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C
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REAL A,ABSERR,ALFA,B,BETA,EPSABS,EPSREL,F,RESULT,WORK
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INTEGER IER,INTEGR,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 QAWS
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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.2.OR.LENW.LT.LIMIT*4) GO TO 10
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C
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C PREPARE CALL FOR QAWSE.
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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 QAWSE(F,A,B,ALFA,BETA,INTEGR,EPSABS,EPSREL,LIMIT,RESULT,
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1 ABSERR,NEVAL,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', 'QAWS',
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+ 'ABNORMAL RETURN', IER, LVL)
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RETURN
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END
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