*DECK DPCHDF DOUBLE PRECISION FUNCTION DPCHDF (K, X, S, IERR) C***BEGIN PROLOGUE DPCHDF C***SUBSIDIARY C***PURPOSE Computes divided differences for DPCHCE and DPCHSP C***LIBRARY SLATEC (PCHIP) C***TYPE DOUBLE PRECISION (PCHDF-S, DPCHDF-D) C***AUTHOR Fritsch, F. N., (LLNL) C***DESCRIPTION C C DPCHDF: DPCHIP 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 DPCHCE and DPCHSP 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 DPCHDF will be set to the desired derivative approximation if C IERR=0 or to zero if IERR=-1. C C ---------------------------------------------------------------------- C C***SEE ALSO DPCHCE, DPCHSP 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 870707 Corrected XERROR calls for d.p. name(s). C 870813 Minor cosmetic changes. C 890206 Corrected XERROR calls. 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 DPCHDF C C**End C C DECLARE ARGUMENTS. C INTEGER K, IERR DOUBLE PRECISION X(K), S(K) C C DECLARE LOCAL VARIABLES. C INTEGER I, J DOUBLE PRECISION VALUE, ZERO SAVE ZERO DATA ZERO /0.D0/ C C CHECK FOR LEGAL VALUE OF K. C C***FIRST EXECUTABLE STATEMENT DPCHDF IF (K .LT. 3) GO TO 5001 C C COMPUTE COEFFICIENTS OF INTERPOLATING POLYNOMIAL. C DO 10 J = 2, K-1 DO 9 I = 1, K-J S(I) = (S(I+1)-S(I))/(X(I+J)-X(I)) 9 CONTINUE 10 CONTINUE C C EVALUATE DERIVATIVE AT X(K). C VALUE = S(1) DO 20 I = 2, K-1 VALUE = S(I) + VALUE*(X(K)-X(I)) 20 CONTINUE C C NORMAL RETURN. C IERR = 0 DPCHDF = VALUE RETURN C C ERROR RETURN. C 5001 CONTINUE C K.LT.3 RETURN. IERR = -1 CALL XERMSG ('SLATEC', 'DPCHDF', 'K LESS THAN THREE', IERR, 1) DPCHDF = ZERO RETURN C------------- LAST LINE OF DPCHDF FOLLOWS ----------------------------- END