SLATEC Routines --- AVINT ---

*DECK AVINT
      SUBROUTINE AVINT (X, Y, N, XLO, XUP, ANS, IERR)
C***BEGIN PROLOGUE  AVINT
C***PURPOSE  Integrate a function tabulated at arbitrarily spaced
C            abscissas using overlapping parabolas.
C***LIBRARY   SLATEC
C***CATEGORY  H2A1B2
C***TYPE      SINGLE PRECISION (AVINT-S, DAVINT-D)
C***KEYWORDS  INTEGRATION, QUADRATURE, TABULATED DATA
C***AUTHOR  Jones, R. E., (SNLA)
C***DESCRIPTION
C
C     Abstract
C         AVINT integrates a function tabulated at arbitrarily spaced
C         abscissas.  The limits of integration need not coincide
C         with the tabulated abscissas.
C
C         A method of overlapping parabolas fitted to the data is used
C         provided that there are at least 3 abscissas between the
C         limits of integration.  AVINT also handles two special cases.
C         If the limits of integration are equal, AVINT returns a result
C         of zero regardless of the number of tabulated values.
C         If there are only two function values, AVINT uses the
C         trapezoid rule.
C
C     Description of Parameters
C         The user must dimension all arrays appearing in the call list
C              X(N), Y(N).
C
C         Input--
C         X    - real array of abscissas, which must be in increasing
C                order.
C         Y    - real array of functional values. i.e., Y(I)=FUNC(X(I)).
C         N    - the integer number of function values supplied.
C                N .GE. 2 unless XLO = XUP.
C         XLO  - real lower limit of integration.
C         XUP  - real upper limit of integration.
C                Must have XLO .LE. XUP.
C
C         Output--
C         ANS  - computed approximate value of integral
C         IERR - a status code
C              --normal code
C                =1 means the requested integration was performed.
C              --abnormal codes
C                =2 means XUP was less than XLO.
C                =3 means the number of X(I) between XLO and XUP
C                   (inclusive) was less than 3 and neither of the two
C                   special cases described in the Abstract occurred.
C                   No integration was performed.
C                =4 means the restriction X(I+1) .GT. X(I) was violated.
C                =5 means the number N of function values was .LT. 2.
C                ANS is set to zero if IERR=2,3,4,or 5.
C
C     AVINT is documented completely in SC-M-69-335
C     Original program from "Numerical Integration" by Davis &
C     Rabinowitz.
C     Adaptation and modifications for Sandia Mathematical Program
C     Library by Rondall E. Jones.
C
C***REFERENCES  R. E. Jones, Approximate integrator of functions
C                 tabulated at arbitrarily spaced abscissas,
C                 Report SC-M-69-335, Sandia Laboratories, 1969.
C***ROUTINES CALLED  XERMSG
C***REVISION HISTORY  (YYMMDD)
C   690901  DATE WRITTEN
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   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
C   900326  Removed duplicate information from DESCRIPTION section.
C           (WRB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  AVINT