PCHFE(3)

SYNOPSIS
SUBROUTINE PCHFE (N, X, F, D, INCFD, SKIP, NE, XE, FE, IERR)

NAME
pchfe - Evaluate a piecewise cubic Hermite function at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for PCHIM or PCHIC.

LIBRARY
SLATEC (PCHIP)

CATEGORY
E3

TYPE
SINGLE PRECISION (PCHFE-S, DPCHFE-D)

KEYWORDS
CUBIC HERMITE EVALUATION, HERMITE INTERPOLATION, PCHIP, PIECEWISE CUBIC EVALUATION

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
PCHFE: Piecewise Cubic Hermite Function Evaluator Evaluates the cubic Hermite function defined by N, X, F, D at the points XE(J), J=1(1)NE. 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, NE, IERR REAL X(N), F(INCFD,N), D(INCFD,N), XE(NE), FE(NE) LOGICAL SKIP CALL PCHFE (N, X, F, D, INCFD, SKIP, NE, XE, FE, IERR) Parameters: 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 normal return. NE -- (input) number of evaluation points. (Error return if NE.LT.1 .) XE -- (input) real array of points at which the function is to be evaluated. NOTES: 1. The evaluation will be most efficient if the elements of XE are increasing relative to X; that is, XE(J) .GE. X(I) implies XE(K) .GE. X(I), all K.GE.J . 2. If any of the XE are outside the interval [X(1),X(N)], values are extrapolated from the nearest extreme cubic, and a warning error is returned. FE -- (output) real array of values of the cubic Hermite function defined by N, X, F, D at the points XE. IERR -- (output) error flag. Normal return: IERR = 0 (no errors). Warning error: IERR.GT.0 means that extrapolation was performed at IERR points. "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 NE.LT.1 . (The FE-array has not been changed 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
CHFEV, XERMSG

REVISION HISTORY (YYMMDD)
811020 DATE WRITTEN
820803 Minor cosmetic changes for release 1.
870707 Minor cosmetic changes to prologue.
890531 Changed all specific intrinsics to generic. (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)