SLATEC Routines --- PCHIA ---

```*DECK PCHIA
REAL FUNCTION PCHIA (N, X, F, D, INCFD, SKIP, A, B, IERR)
C***BEGIN PROLOGUE  PCHIA
C***PURPOSE  Evaluate the definite integral of a piecewise cubic
C            Hermite function over an arbitrary interval.
C***LIBRARY   SLATEC (PCHIP)
C***CATEGORY  E3, H2A1B2
C***TYPE      SINGLE PRECISION (PCHIA-S, DPCHIA-D)
C***KEYWORDS  CUBIC HERMITE INTERPOLATION, NUMERICAL INTEGRATION, PCHIP,
C***AUTHOR  Fritsch, F. N., (LLNL)
C             Lawrence Livermore National Laboratory
C             P.O. Box 808  (L-316)
C             Livermore, CA  94550
C             FTS 532-4275, (510) 422-4275
C***DESCRIPTION
C
C          PCHIA:  Piecewise Cubic Hermite Integrator, Arbitrary limits
C
C     Evaluates the definite integral of the cubic Hermite function
C     defined by  N, X, F, D  over the interval [A, B].
C
C     To provide compatibility with PCHIM and PCHIC, includes an
C     increment between successive values of the F- and D-arrays.
C
C ----------------------------------------------------------------------
C
C  Calling sequence:
C
C        PARAMETER  (INCFD = ...)
C        INTEGER  N, IERR
C        REAL  X(N), F(INCFD,N), D(INCFD,N), A, B
C        REAL  VALUE, PCHIA
C        LOGICAL  SKIP
C
C        VALUE = PCHIA (N, X, F, D, INCFD, SKIP, A, B, IERR)
C
C   Parameters:
C
C     VALUE -- (output) value of the requested integral.
C
C     N -- (input) number of data points.  (Error return if N.LT.2 .)
C
C     X -- (input) real array of independent variable values.  The
C           elements of X must be strictly increasing:
C                X(I-1) .LT. X(I),  I = 2(1)N.
C           (Error return if not.)
C
C     F -- (input) real array of function values.  F(1+(I-1)*INCFD) is
C           the value corresponding to X(I).
C
C     D -- (input) real array of derivative values.  D(1+(I-1)*INCFD) is
C           the value corresponding to X(I).
C
C     INCFD -- (input) increment between successive values in F and D.
C           (Error return if  INCFD.LT.1 .)
C
C     SKIP -- (input/output) logical variable which should be set to
C           .TRUE. if the user wishes to skip checks for validity of
C           preceding parameters, or to .FALSE. otherwise.
C           This will save time in case these checks have already
C           been performed (say, in PCHIM or PCHIC).
C           SKIP will be set to .TRUE. on return with IERR.GE.0 .
C
C     A,B -- (input) the limits of integration.
C           NOTE:  There is no requirement that [A,B] be contained in
C                  [X(1),X(N)].  However, the resulting integral value
C                  will be highly suspect, if not.
C
C     IERR -- (output) error flag.
C           Normal return:
C              IERR = 0  (no errors).
C           Warning errors:
C              IERR = 1  if  A  is outside the interval [X(1),X(N)].
C              IERR = 2  if  B  is outside the interval [X(1),X(N)].
C              IERR = 3  if both of the above are true.  (Note that this
C                        means that either [A,B] contains data interval
C                        or the intervals do not intersect at all.)
C           "Recoverable" errors:
C              IERR = -1  if N.LT.2 .
C              IERR = -2  if INCFD.LT.1 .
C              IERR = -3  if the X-array is not strictly increasing.
C                (VALUE will be zero in any of these cases.)
C               NOTE:  The above errors are checked in the order listed,
C                   and following arguments have **NOT** been validated.
C              IERR = -4  in case of an error return from PCHID (which
C                         should never occur).
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  CHFIE, PCHID, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   820730  DATE WRITTEN
C   820804  Converted to SLATEC library version.
C   870707  Corrected double precision conversion instructions.
C   870813  Minor cosmetic changes.
C   890411  Added SAVE statements (Vers. 3.2).
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890703  Corrected category record.  (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   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
C   930503  Corrected to set VALUE=0 when IERR.lt.0.  (FNF)
C   930504  Changed CHFIV to CHFIE.  (FNF)
C***END PROLOGUE  PCHIA
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