1 2 REAL FUNCTION PCHDF(K,X,S,IERR) 3C***BEGIN PROLOGUE PCHDF 4C***REFER TO PCHCE,PCHSP 5C***ROUTINES CALLED XERROR 6C***REVISION DATE 870707 (YYMMDD) 7C***DESCRIPTION 8C 9C PCHDF: PCHIP Finite Difference Formula 10C 11C Uses a divided difference formulation to compute a K-point approx- 12C imation to the derivative at X(K) based on the data in X and S. 13C 14C Called by PCHCE and PCHSP to compute 3- and 4-point boundary 15C derivative approximations. 16C 17C ---------------------------------------------------------------------- 18C 19C On input: 20C K is the order of the desired derivative approximation. 21C K must be at least 3 (error return if not). 22C X contains the K values of the independent variable. 23C X need not be ordered, but the values **MUST** be 24C distinct. (Not checked here.) 25C S contains the associated slope values: 26C S(I) = (F(I+1)-F(I))/(X(I+1)-X(I)), I=1(1)K-1. 27C (Note that S need only be of length K-1.) 28C 29C On return: 30C S will be destroyed. 31C IERR will be set to -1 if K.LT.2 . 32C PCHDF will be set to the desired derivative approximation if 33C IERR=0 or to zero if IERR=-1. 34C 35C ---------------------------------------------------------------------- 36C 37C Reference: Carl de Boor, A Practical Guide to Splines, Springer- 38C Verlag (New York, 1978), pp. 10-16. 39C 40C ---------------------------------------------------------------------- 41C 42C Programmed by: Fred N. Fritsch, FTS 532-4275, (415) 422-4275, 43C Mathematics and Statistics Division, 44C Lawrence Livermore National Laboratory. 45C 46C Change record: 47C 82-08-05 Converted to SLATEC library version. 48C 49C ---------------------------------------------------------------------- 50C 51C Programming notes: 52C 53C To produce a double precision version, simply: 54C a. Change PCHDF to DPCHDF wherever it occurs, 55C b. Change the real declarations to double precision, and 56C c. Change the constant ZERO to double precision. 57C***END PROLOGUE PCHDF 58 59 60