SLATEC Routines --- DAVINT ---

*DECK DAVINT
      SUBROUTINE DAVINT (X, Y, N, XLO, XUP, ANS, IERR)
C***BEGIN PROLOGUE  DAVINT
C***PURPOSE  Integrate a function tabulated at arbitrarily spaced
C            abscissas using overlapping parabolas.
C***LIBRARY   SLATEC
C***CATEGORY  H2A1B2
C***TYPE      DOUBLE PRECISION (AVINT-S, DAVINT-D)
C***KEYWORDS  INTEGRATION, QUADRATURE, TABULATED DATA
C***AUTHOR  Jones, R. E., (SNLA)
C***DESCRIPTION
C
C     Abstract
C         DAVINT 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.  DAVINT also handles two special cases.
C         If the limits of integration are equal, DAVINT returns a
C         result of zero regardless of the number of tabulated values.
C         If there are only two function values, DAVINT 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    - DOUBLE PRECISION array of abscissas, which must be in
C             increasing order.
C      Y    - DOUBLE PRECISION array of function values. i.e.,
C                Y(I)=FUNC(X(I))
C      N    - The integer number of function values supplied.
C                N .GE. 2 unless XLO = XUP.
C      XLO  - DOUBLE PRECISION lower limit of integration
C      XUP  - DOUBLE PRECISION upper limit of integration.  Must have
C              XLO.LE.XUP
C
C         Output--
C      ANS  - Double Precision 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    DAVINT is documented completely in SC-M-69-335
C    Original program from *Numerical Integration* by Davis & Rabinowitz
C    Adaptation and modifications 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   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  DAVINT