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236 lines
10 KiB
Fortran
236 lines
10 KiB
Fortran
*DECK QAWO
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SUBROUTINE QAWO (F, A, B, OMEGA, INTEGR, EPSABS, EPSREL, RESULT,
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+ ABSERR, NEVAL, IER, LENIW, MAXP1, LENW, LAST, IWORK, WORK)
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C***BEGIN PROLOGUE QAWO
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C***PURPOSE Calculate an approximation to a given definite integral
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C I = Integral of F(X)*W(X) over (A,B), where
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C W(X) = COS(OMEGA*X)
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C or W(X) = SIN(OMEGA*X),
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C hopefully satisfying the 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 (QAWO-S, DQAWO-D)
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C***KEYWORDS AUTOMATIC INTEGRATOR, CLENSHAW-CURTIS METHOD,
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C EXTRAPOLATION, GLOBALLY ADAPTIVE,
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C INTEGRAND WITH OSCILLATORY COS OR SIN FACTOR, QUADPACK,
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C 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 Computation of oscillatory integrals
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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 function
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C 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 OMEGA - Real
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C Parameter in the integrand weight function
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C
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C INTEGR - Integer
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C Indicates which of the weight functions is used
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C INTEGR = 1 W(X) = COS(OMEGA*X)
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C INTEGR = 2 W(X) = SIN(OMEGA*X)
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C If INTEGR.NE.1.AND.INTEGR.NE.2, the routine will
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C 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 and
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C 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(= LENIW/2). One can
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C allow more subdivisions by increasing the
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C value of LENIW (and taking the according
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C dimension adjustments into account).
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C However, if this yields no improvement it
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C is advised to analyze the integrand in
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C order to determine the integration
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C difficulties. If the position of a local
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C difficulty can be determined (e.g.
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C SINGULARITY, DISCONTINUITY within the
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C interval) one will probably gain from
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C splitting up the interval at this point
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C and calling the integrator on the
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C subranges. If possible, an appropriate
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C special-purpose integrator should be used
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C which is designed for handling the type of
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C difficulty involved.
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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 The error may be under-estimated.
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C = 3 Extremely bad integrand behaviour occurs
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C at some interior points of the
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C integration 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 achieved
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C due to roundoff in the extrapolation
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C table, 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 (INTEGR.NE.1 AND INTEGR.NE.2),
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C or LENIW.LT.2 OR MAXP1.LT.1 or
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C LENW.LT.LENIW*2+MAXP1*25.
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C RESULT, ABSERR, NEVAL, LAST are set to
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C zero. Except when LENIW, MAXP1 or LENW are
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C invalid, WORK(LIMIT*2+1), WORK(LIMIT*3+1),
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C IWORK(1), IWORK(LIMIT+1) are set to zero,
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C WORK(1) is set to A and WORK(LIMIT+1) to
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C B.
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C
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C DIMENSIONING PARAMETERS
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C LENIW - Integer
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C Dimensioning parameter for IWORK.
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C LENIW/2 equals the maximum number of subintervals
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C allowed in the partition of the given integration
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C interval (A,B), LENIW.GE.2.
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C If LENIW.LT.2, the routine will end with IER = 6.
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C
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C MAXP1 - Integer
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C Gives an upper bound on the number of Chebyshev
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C moments which can be stored, i.e. for the
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C intervals of lengths ABS(B-A)*2**(-L),
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C L=0,1, ..., MAXP1-2, MAXP1.GE.1
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C If MAXP1.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 LENIW*2+MAXP1*25.
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C If LENW.LT.(LENIW*2+MAXP1*25), the routine will
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C end 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, which
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C determines the number of significant elements
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C 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 at least LENIW
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C on return, the first K elements of which contain
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C pointers to the error estimates over the
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C subintervals, 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 LIMIT = LENW/2 , and K = LAST
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C if LAST.LE.(LIMIT/2+2), and K = LIMIT+1-LAST
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C otherwise.
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C Furthermore, IWORK(LIMIT+1), ..., IWORK(LIMIT+
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C LAST) indicate the subdivision levels of the
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C subintervals, such that IWORK(LIMIT+I) = L means
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C that the subinterval numbered I is of length
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C ABS(B-A)*2**(1-L).
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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
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C 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 WORK(LIMIT*4+1), ..., WORK(LIMIT*4+MAXP1*25)
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C Provide space for storing the Chebyshev moments.
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C Note that LIMIT = LENW/2.
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED QAWOE, 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 QAWO
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C
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REAL A,ABSERR,B,EPSABS,EPSREL,F,OMEGA,RESULT
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INTEGER IER,INTEGR,LENIW,LVL,L1,L2,L3,L4,MAXP1,MOMCOM,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 LENIW, MAXP1 AND LENW.
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C
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C***FIRST EXECUTABLE STATEMENT QAWO
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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(LENIW.LT.2.OR.MAXP1.LT.1.OR.LENW.LT.(LENIW*2+MAXP1*25))
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1 GO TO 10
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C
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C PREPARE CALL FOR QAWOE
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C
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LIMIT = LENIW/2
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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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L4 = LIMIT+L3
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CALL QAWOE(F,A,B,OMEGA,INTEGR,EPSABS,EPSREL,LIMIT,1,MAXP1,RESULT,
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1 ABSERR,NEVAL,IER,LAST,WORK(1),WORK(L1),WORK(L2),WORK(L3),
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2 IWORK(1),IWORK(L1),MOMCOM,WORK(L4))
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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', 'QAWO',
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+ 'ABNORMAL RETURN', IER, LVL)
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RETURN
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END
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