*DECK PCHDF

C***BEGIN PROLOGUE  PCHDF

C***SUBSIDIARY

C***PURPOSE  Computes divided differences for PCHCE and PCHSP

C***LIBRARY   SLATEC (PCHIP)

C***TYPE      SINGLE PRECISION (PCHDF-S, DPCHDF-D)

C***AUTHOR  Fritsch, F. N., (LLNL)

C***DESCRIPTION

C

C          PCHDF:   PCHIP Finite Difference Formula

C

C     Uses a divided difference formulation to compute a K-point approx-

C     imation to the derivative at X(K) based on the data in X and S.

C

C     Called by  PCHCE  and  PCHSP  to compute 3- and 4-point boundary

C     derivative approximations.

C

C ----------------------------------------------------------------------

C

C     On input:

C        K      is the order of the desired derivative approximation.

C               K must be at least 3 (error return if not).

C        X      contains the K values of the independent variable.

C               X need not be ordered, but the values **MUST** be

C               distinct.  (Not checked here.)

C        S      contains the associated slope values:

C                  S(I) = (F(I+1)-F(I))/(X(I+1)-X(I)), I=1(1)K-1.

C               (Note that S need only be of length K-1.)

C

C     On return:

C        S      will be destroyed.

C        IERR   will be set to -1 if K.LT.2 .

C        PCHDF  will be set to the desired derivative approximation if

C               IERR=0 or to zero if IERR=-1.

C

C ----------------------------------------------------------------------

C

C***SEE ALSO  PCHCE, PCHSP

C***REFERENCES  Carl de Boor, A Practical Guide to Splines, Springer-

C                 Verlag, New York, 1978, pp. 10-16.

C***ROUTINES CALLED  XERMSG

C***REVISION HISTORY  (YYMMDD)

C   820503  DATE WRITTEN

C   820805  Converted to SLATEC library version.

C   870813  Minor cosmetic changes.

C   890411  Added SAVE statements (Vers. 3.2).

C   890411  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   900328  Added TYPE section.  (WRB)

C   910408  Updated AUTHOR and DATE WRITTEN sections in prologue.  (WRB)

C   920429  Revised format and order of references.  (WRB,FNF)

C   930503  Improved purpose.  (FNF)

C***END PROLOGUE  PCHDF

C

C**End

C

C  DECLARE ARGUMENTS.

C

      INTEGER  K, IERR

      REAL  X(K), S(K)

C

C  DECLARE LOCAL VARIABLES.

C

      INTEGER  I, J

      REAL  VALUE, ZERO

      SAVE ZERO

      DATA  ZERO /0./

C

C  CHECK FOR LEGAL VALUE OF K.

C

C***FIRST EXECUTABLE STATEMENT  PCHDF

C

C  COMPUTE COEFFICIENTS OF INTERPOLATING POLYNOMIAL.

C

C

C  EVALUATE DERIVATIVE AT X(K).

C

C

C  NORMAL RETURN.

C

      PCHDF = VALUE

C

C  ERROR RETURN.

C

 5001 CONTINUE

C     K.LT.3 RETURN.

C------------- LAST LINE OF PCHDF FOLLOWS ------------------------------

      END