!DECK PCHDF REAL FUNCTION PCHDF (K, X, S, IERR) !***BEGIN PROLOGUE PCHDF !***SUBSIDIARY !***PURPOSE Computes divided differences for PCHCE and PCHSP !***LIBRARY SLATEC (PCHIP) !***TYPE SINGLE PRECISION (PCHDF-S, DPCHDF-D) !***AUTHOR Fritsch, F. N., (LLNL) !***DESCRIPTION ! ! PCHDF: PCHIP Finite Difference Formula ! ! Uses a divided difference formulation to compute a K-point approx- ! imation to the derivative at X(K) based on the data in X and S. ! ! Called by PCHCE and PCHSP to compute 3- and 4-point boundary ! derivative approximations. ! ! ---------------------------------------------------------------------- ! ! On input: ! K is the order of the desired derivative approximation. ! K must be at least 3 (error return if not). ! X contains the K values of the independent variable. ! X need not be ordered, but the values **MUST** be ! distinct. (Not checked here.) ! S contains the associated slope values: ! S(I) = (F(I+1)-F(I))/(X(I+1)-X(I)), I=1(1)K-1. ! (Note that S need only be of length K-1.) ! ! On return: ! S will be destroyed. ! IERR will be set to -1 if K.LT.2 . ! PCHDF will be set to the desired derivative approximation if ! IERR=0 or to zero if IERR=-1. ! ! ---------------------------------------------------------------------- ! !***SEE ALSO PCHCE, PCHSP !***REFERENCES Carl de Boor, A Practical Guide to Splines, Springer- ! Verlag, New York, 1978, pp. 10-16. !***ROUTINES CALLED XERMSG !***REVISION HISTORY (YYMMDD) ! 820503 DATE WRITTEN ! 820805 Converted to SLATEC library version. ! 870813 Minor cosmetic changes. ! 890411 Added SAVE statements (Vers. 3.2). ! 890411 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) ! 900328 Added TYPE section. (WRB) ! 910408 Updated AUTHOR and DATE WRITTEN sections in prologue. (WRB) ! 920429 Revised format and order of references. (WRB,FNF) ! 930503 Improved purpose. (FNF) !***END PROLOGUE PCHDF ! !**End ! ! DECLARE ARGUMENTS. ! INTEGER :: K, IERR REAL :: X(K), S(K) ! ! DECLARE LOCAL VARIABLES. ! INTEGER :: I, J REAL :: VALUE, ZERO SAVE ZERO DATA ZERO /0./ ! ! CHECK FOR LEGAL VALUE OF K. ! !***FIRST EXECUTABLE STATEMENT PCHDF IF (K .LT. 3) GO TO 5001 ! ! COMPUTE COEFFICIENTS OF INTERPOLATING POLYNOMIAL. ! DO J = 2, K-1 DO I = 1, K-J S(I) = (S(I+1)-S(I))/(X(I+J)-X(I)) END DO END DO ! ! EVALUATE DERIVATIVE AT X(K). ! VALUE = S(1) DO I = 2, K-1 VALUE = S(I) + VALUE*(X(K)-X(I)) END DO ! ! NORMAL RETURN. ! IERR = 0 PCHDF = VALUE RETURN ! ! ERROR RETURN. ! 5001 CONTINUE ! K.LT.3 RETURN. IERR = -1 CALL XERMSG ('SLATEC', 'PCHDF', 'K LESS THAN THREE', IERR, 1) PCHDF = ZERO RETURN !------------- LAST LINE OF PCHDF FOLLOWS ------------------------------ END FUNCTION PCHDF