SLATEC Routines --- QAWOE ---
*DECK QAWOE
SUBROUTINE QAWOE (F, A, B, OMEGA, INTEGR, EPSABS, EPSREL, LIMIT,
+ ICALL, MAXP1, RESULT, ABSERR, NEVAL, IER, LAST, ALIST, BLIST,
+ RLIST, ELIST, IORD, NNLOG, MOMCOM, CHEBMO)
C***BEGIN PROLOGUE QAWOE
C***PURPOSE Calculate an approximation to a given definite integral
C I = Integral of F(X)*W(X) over (A,B), where
C W(X) = COS(OMEGA*X)
C or W(X) = SIN(OMEGA*X),
C hopefully satisfying the following claim for accuracy
C ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
C***LIBRARY SLATEC (QUADPACK)
C***CATEGORY H2A2A1
C***TYPE SINGLE PRECISION (QAWOE-S, DQAWOE-D)
C***KEYWORDS AUTOMATIC INTEGRATOR, CLENSHAW-CURTIS METHOD,
C EXTRAPOLATION, GLOBALLY ADAPTIVE,
C INTEGRAND WITH OSCILLATORY COS OR SIN FACTOR, QUADPACK,
C QUADRATURE, SPECIAL-PURPOSE
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 Oscillatory integrals
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 OMEGA - Real
C Parameter in the integrand weight function
C
C INTEGR - Integer
C Indicates which of the WEIGHT functions is to be
C used
C INTEGR = 1 W(X) = COS(OMEGA*X)
C INTEGR = 2 W(X) = SIN(OMEGA*X)
C If INTEGR.NE.1 and INTEGR.NE.2, the routine
C will end with IER = 6.
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 LIMIT - Integer
C Gives an upper bound on the number of subdivisions
C in the partition of (A,B), LIMIT.GE.1.
C
C ICALL - Integer
C If QAWOE is to be used only once, ICALL must
C be set to 1. Assume that during this call, the
C Chebyshev moments (for CLENSHAW-CURTIS integration
C of degree 24) have been computed for intervals of
C lengths (ABS(B-A))*2**(-L), L=0,1,2,...MOMCOM-1.
C If ICALL.GT.1 this means that QAWOE has been
C called twice or more on intervals of the same
C length ABS(B-A). The Chebyshev moments already
C computed are then re-used in subsequent calls.
C If ICALL.LT.1, the routine will end with IER = 6.
C
C MAXP1 - Integer
C Gives an upper bound on the number of Chebyshev
C moments which can be stored, i.e. for the
C intervals of lengths ABS(B-A)*2**(-L),
C L=0,1, ..., MAXP1-2, MAXP1.GE.1.
C If MAXP1.LT.1, 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
C requested 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 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.
C If the position of a local difficulty can
C be determined (e.g. 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 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 due to
C roundoff in the extrapolation table,
C and that the returned result is the
C best which 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 (EPSABS.LE.0 and
C EPSREL.LT.MAX(50*REL.MACH.ACC.,0.5D-28))
C or (INTEGR.NE.1 and INTEGR.NE.2) or
C ICALL.LT.1 or MAXP1.LT.1.
C RESULT, ABSERR, NEVAL, LAST, RLIST(1),
C ELIST(1), IORD(1) and NNLOG(1) are set
C to ZERO. ALIST(1) and BLIST(1) are set
C to A and B respectively.
C
C LAST - Integer
C On return, LAST equals the number of
C subintervals produces in the subdivision
C process, which determines the number of
C significant elements actually in the
C WORK ARRAYS.
C ALIST - Real
C Vector of dimension at least LIMIT, the first
C LAST elements of which are the left
C end points of the subintervals in the partition
C of the given integration range (A,B)
C
C BLIST - Real
C Vector of dimension at least LIMIT, the first
C LAST elements of which are the right
C end points of the subintervals in the partition
C of the given integration range (A,B)
C
C RLIST - Real
C Vector of dimension at least LIMIT, the first
C LAST elements of which are the integral
C approximations on the subintervals
C
C ELIST - Real
C Vector of dimension at least LIMIT, the first
C LAST elements of which are the moduli of the
C absolute error estimates on the subintervals
C
C IORD - Integer
C Vector of dimension at least LIMIT, the first K
C elements of which are pointers to the error
C estimates over the subintervals,
C such that ELIST(IORD(1)), ...,
C ELIST(IORD(K)) form a decreasing sequence, with
C K = LAST if LAST.LE.(LIMIT/2+2), and
C K = LIMIT+1-LAST otherwise.
C
C NNLOG - Integer
C Vector of dimension at least LIMIT, containing the
C subdivision levels of the subintervals, i.e.
C IWORK(I) = L means that the subinterval
C numbered I is of length ABS(B-A)*2**(1-L)
C
C ON ENTRY AND RETURN
C MOMCOM - Integer
C Indicating that the Chebyshev moments
C have been computed for intervals of lengths
C (ABS(B-A))*2**(-L), L=0,1,2, ..., MOMCOM-1,
C MOMCOM.LT.MAXP1
C
C CHEBMO - Real
C Array of dimension (MAXP1,25) containing the
C Chebyshev moments
C
C***REFERENCES (NONE)
C***ROUTINES CALLED QC25F, QELG, QPSRT, R1MACH
C***REVISION HISTORY (YYMMDD)
C 800101 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
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***END PROLOGUE QAWOE