SLATEC Routines --- DPCHFD ---
*DECK DPCHFD
SUBROUTINE DPCHFD (N, X, F, D, INCFD, SKIP, NE, XE, FE, DE, IERR)
C***BEGIN PROLOGUE DPCHFD
C***PURPOSE Evaluate a piecewise cubic Hermite function and its first
C derivative at an array of points. May be used by itself
C for Hermite interpolation, or as an evaluator for DPCHIM
C or DPCHIC. If only function values are required, use
C DPCHFE instead.
C***LIBRARY SLATEC (PCHIP)
C***CATEGORY E3, H1
C***TYPE DOUBLE PRECISION (PCHFD-S, DPCHFD-D)
C***KEYWORDS CUBIC HERMITE DIFFERENTIATION, CUBIC HERMITE EVALUATION,
C HERMITE INTERPOLATION, PCHIP, 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 DPCHFD: Piecewise Cubic Hermite Function and Derivative
C evaluator
C
C Evaluates the cubic Hermite function defined by N, X, F, D, to-
C gether with its first derivative, at the points XE(J), J=1(1)NE.
C
C If only function values are required, use DPCHFE, instead.
C
C To provide compatibility with DPCHIM and DPCHIC, 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 DOUBLE PRECISION X(N), F(INCFD,N), D(INCFD,N), XE(NE), FE(NE),
C DE(NE)
C LOGICAL SKIP
C
C CALL DPCHFD (N, X, F, D, INCFD, SKIP, NE, XE, FE, DE, IERR)
C
C Parameters:
C
C N -- (input) number of data points. (Error return if N.LT.2 .)
C
C X -- (input) real*8 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*8 array of function values. F(1+(I-1)*INCFD) is
C the value corresponding to X(I).
C
C D -- (input) real*8 array of derivative values. D(1+(I-1)*INCFD)
C is 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 DPCHIM or DPCHIC).
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*8 array of points at which the functions are to
C be evaluated.
C
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*8 array of values of the cubic Hermite
C function defined by N, X, F, D at the points XE.
C
C DE -- (output) real*8 array of values of the first derivative of
C the same function 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 (Output arrays have 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 IERR = -5 if an error has occurred in the lower-level
C routine DCHFDV. NB: this should never happen.
C Notify the author **IMMEDIATELY** if it does.
C
C***REFERENCES (NONE)
C***ROUTINES CALLED DCHFDV, XERMSG
C***REVISION HISTORY (YYMMDD)
C 811020 DATE WRITTEN
C 820803 Minor cosmetic changes for release 1.
C 870707 Corrected XERROR calls for d.p. name(s).
C 890206 Corrected XERROR calls.
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 891006 Cosmetic changes to prologue. (WRB)
C 891006 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 DPCHFD