PCHID(3)

SYNOPSIS
REAL FUNCTION PCHID (N, X, F, D, INCFD, SKIP, IA, IB, IERR)

NAME
pchid - Evaluate the definite integral of a piecewise cubic Hermite function over an interval whose endpoints are data points.

LIBRARY
SLATEC (PCHIP)

CATEGORY
E3, H2A1B2

TYPE
SINGLE PRECISION (PCHID-S, DPCHID-D)

KEYWORDS
CUBIC HERMITE INTERPOLATION, NUMERICAL INTEGRATION, PCHIP, QUADRATURE

AUTHOR
Fritsch, F. N., (LLNL) Lawrence Livermore National Laboratory P.O. Box 808 (L-316) Livermore, CA 94550 FTS 532-4275, (510) 422-4275

DESCRIPTION
PCHID: Piecewise Cubic Hermite Integrator, Data limits Evaluates the definite integral of the cubic Hermite function defined by N, X, F, D over the interval [X(IA), X(IB)]. To provide compatibility with PCHIM and PCHIC, includes an increment between successive values of the F- and D-arrays. ---------------------------------------------------------------------- Calling sequence: PARAMETER (INCFD = ...) INTEGER N, IA, IB, IERR REAL X(N), F(INCFD,N), D(INCFD,N) LOGICAL SKIP VALUE = PCHID (N, X, F, D, INCFD, SKIP, IA, IB, IERR) Parameters: VALUE -- (output) value of the requested integral. N -- (input) number of data points. (Error return if N.LT.2 .) X -- (input) real array of independent variable values. The elements of X must be strictly increasing: X(I-1) .LT. X(I), I = 2(1)N. (Error return if not.) F -- (input) real array of function values. F(1+(I-1)*INCFD) is the value corresponding to X(I). D -- (input) real array of derivative values. D(1+(I-1)*INCFD) is the value corresponding to X(I). INCFD -- (input) increment between successive values in F and D. (Error return if INCFD.LT.1 .) SKIP -- (input/output) logical variable which should be set to preceding parameters, or to .FALSE. otherwise. This will save time in case these checks have already been performed (say, in PCHIM or PCHIC). SKIP will be set to .TRUE. on return with IERR = 0 or -4. IA,IB -- (input) indices in X-array for the limits of integration. both must be in the range [1,N]. (Error return if not.) No restrictions on their relative values. IERR -- (output) error flag. Normal return: IERR = 0 (no errors). "Recoverable" errors: IERR = -1 if N.LT.2 . IERR = -2 if INCFD.LT.1 . IERR = -3 if the X-array is not strictly increasing. IERR = -4 if IA or IB is out of range. (VALUE will be zero in any of these cases.) NOTE: The above errors are checked in the order listed, and following arguments have **NOT** been validated.

REFERENCES
(NONE)

ROUTINES CALLED
XERMSG

REVISION HISTORY (YYMMDD)
820723 DATE WRITTEN
820804 Converted to SLATEC library version.
870813 Minor cosmetic changes.
890411 Added SAVE statements (Vers. 3.2).
890531 Changed all specific intrinsics to generic. (WRB)
890703 Corrected category record. (WRB)
890831 Modified array declarations. (WRB)
890831 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
930504 Corrected to set VALUE=0 when IERR.ne.0. (FNF)