*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