DPCHFD(3)

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

NAME
dpchfd - Evaluate a piecewise cubic Hermite function and its first derivative at an array of points. May be used by itself for Hermite interpolation, or as an evaluator for DPCHIM or DPCHIC. If only function values are required, use DPCHFE instead.

LIBRARY
SLATEC (PCHIP)

CATEGORY
E3, H1

TYPE
DOUBLE PRECISION (PCHFD-S, DPCHFD-D)

KEYWORDS
CUBIC HERMITE DIFFERENTIATION, 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
DPCHFD: Piecewise Cubic Hermite Function and Derivative evaluator Evaluates the cubic Hermite function defined by N, X, F, D, to- gether with its first derivative, at the points XE(J), J=1(1)NE. If only function values are required, use DPCHFE, instead. To provide compatibility with DPCHIM and DPCHIC, includes an increment between successive values of the F- and D-arrays. ---------------------------------------------------------------------- Calling sequence: PARAMETER (INCFD = ...) INTEGER N, NE, IERR DOUBLE PRECISION X(N), F(INCFD,N), D(INCFD,N), XE(NE), FE(NE), DE(NE) LOGICAL SKIP CALL DPCHFD (N, X, F, D, INCFD, SKIP, NE, XE, FE, DE, IERR) Parameters: N -- (input) number of data points. (Error return if N.LT.2 .) X -- (input) real*8 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*8 array of function values. F(1+(I-1)*INCFD) is the value corresponding to X(I). D -- (input) real*8 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 DPCHIM or DPCHIC). SKIP will be set to .TRUE. on normal return. NE -- (input) number of evaluation points. (Error return if NE.LT.1 .) XE -- (input) real*8 array of points at which the functions are 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*8 array of values of the cubic Hermite function defined by N, X, F, D at the points XE. DE -- (output) real*8 array of values of the first derivative of the same function 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 . (Output arrays have 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. IERR = -5 if an error has occurred in the lower-level routine DCHFDV. NB: this should never happen. Notify the author **IMMEDIATELY** if it does.

REFERENCES
(NONE)

ROUTINES CALLED
DCHFDV, XERMSG

REVISION HISTORY (YYMMDD)
811020 DATE WRITTEN
820803 Minor cosmetic changes for release 1.
870707 Corrected XERROR calls for d.p. name(s).
890206 Corrected XERROR calls.
890531 Changed all specific intrinsics to generic. (WRB)
890831 Modified array declarations. (WRB)
891006 Cosmetic changes to prologue. (WRB)
891006 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)