SLATEC Routines --- PCHFE ---
*DECK PCHFE
SUBROUTINE PCHFE (N, X, F, D, INCFD, SKIP, NE, XE, FE, IERR)
C***BEGIN PROLOGUE PCHFE
C***PURPOSE Evaluate a piecewise cubic Hermite function at an array of
C points. May be used by itself for Hermite interpolation,
C or as an evaluator for PCHIM or PCHIC.
C***LIBRARY SLATEC (PCHIP)
C***CATEGORY E3
C***TYPE SINGLE PRECISION (PCHFE-S, DPCHFE-D)
C***KEYWORDS CUBIC HERMITE EVALUATION, HERMITE INTERPOLATION, PCHIP,
C PIECEWISE CUBIC EVALUATION
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 PCHFE: Piecewise Cubic Hermite Function Evaluator
C
C Evaluates the cubic Hermite function defined by N, X, F, D at
C the points XE(J), J=1(1)NE.
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, NE, IERR
C REAL X(N), F(INCFD,N), D(INCFD,N), XE(NE), FE(NE)
C LOGICAL SKIP
C
C CALL PCHFE (N, X, F, D, INCFD, SKIP, NE, XE, FE, IERR)
C
C Parameters:
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 normal return.
C
C NE -- (input) number of evaluation points. (Error return if
C NE.LT.1 .)
C
C XE -- (input) real array of points at which the function is to be
C evaluated.
C
C NOTES:
C 1. The evaluation will be most efficient if the elements
C of XE are increasing relative to X;
C that is, XE(J) .GE. X(I)
C implies XE(K) .GE. X(I), all K.GE.J .
C 2. If any of the XE are outside the interval [X(1),X(N)],
C values are extrapolated from the nearest extreme cubic,
C and a warning error is returned.
C
C FE -- (output) real array of values of the cubic Hermite function
C defined by N, X, F, D at the points XE.
C
C IERR -- (output) error flag.
C Normal return:
C IERR = 0 (no errors).
C Warning error:
C IERR.GT.0 means that extrapolation was performed at
C IERR points.
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 IERR = -4 if NE.LT.1 .
C (The FE-array has not been changed 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
C***REFERENCES (NONE)
C***ROUTINES CALLED CHFEV, XERMSG
C***REVISION HISTORY (YYMMDD)
C 811020 DATE WRITTEN
C 820803 Minor cosmetic changes for release 1.
C 870707 Minor cosmetic changes to prologue.
C 890531 Changed all specific intrinsics to generic. (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***END PROLOGUE PCHFE