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DOUBLE PRECISION FUNCTION DPCHDF (K, X, S, IERR)
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C***BEGIN PROLOGUE DPCHDF
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C***PURPOSE Computes divided differences for DPCHCE and DPCHSP
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C***LIBRARY SLATEC (PCHIP)
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C***TYPE DOUBLE PRECISION (PCHDF-S, DPCHDF-D)
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C***AUTHOR Fritsch, F. N., (LLNL)
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C DPCHDF: DPCHIP Finite Difference Formula
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C Uses a divided difference formulation to compute a K-point approx-
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C imation to the derivative at X(K) based on the data in X and S.
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C Called by DPCHCE and DPCHSP to compute 3- and 4-point boundary
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C derivative approximations.
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C ----------------------------------------------------------------------
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C K is the order of the desired derivative approximation.
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C K must be at least 3 (error return if not).
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C X contains the K values of the independent variable.
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C X need not be ordered, but the values **MUST** be
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C distinct. (Not checked here.)
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C S contains the associated slope values:
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C S(I) = (F(I+1)-F(I))/(X(I+1)-X(I)), I=1(1)K-1.
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C (Note that S need only be of length K-1.)
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C S will be destroyed.
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C IERR will be set to -1 if K.LT.2 .
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C DPCHDF will be set to the desired derivative approximation if
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C IERR=0 or to zero if IERR=-1.
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C ----------------------------------------------------------------------
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C***SEE ALSO DPCHCE, DPCHSP
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C***REFERENCES Carl de Boor, A Practical Guide to Splines, Springer-
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C Verlag, New York, 1978, pp. 10-16.
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C***ROUTINES CALLED XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 820805 Converted to SLATEC library version.
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C 870707 Corrected XERROR calls for d.p. name(s).
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C 870813 Minor cosmetic changes.
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C 890206 Corrected XERROR calls.
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C 890411 Added SAVE statements (Vers. 3.2).
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C 890411 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
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C 900328 Added TYPE section. (WRB)
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C 910408 Updated AUTHOR and DATE WRITTEN sections in prologue. (WRB)
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C 920429 Revised format and order of references. (WRB,FNF)
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C 930503 Improved purpose. (FNF)
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C***END PROLOGUE DPCHDF
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DOUBLE PRECISION X(K), S(K)
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C DECLARE LOCAL VARIABLES.
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DOUBLE PRECISION VALUE, ZERO
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C CHECK FOR LEGAL VALUE OF K.
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C***FIRST EXECUTABLE STATEMENT DPCHDF
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IF (K .LT. 3) GO TO 5001
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C COMPUTE COEFFICIENTS OF INTERPOLATING POLYNOMIAL.
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S(I) = (S(I+1)-S(I))/(X(I+J)-X(I))
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C EVALUATE DERIVATIVE AT X(K).
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VALUE = S(I) + VALUE*(X(K)-X(I))
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CALL XERMSG ('SLATEC', 'DPCHDF', 'K LESS THAN THREE', IERR, 1)
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C------------- LAST LINE OF DPCHDF FOLLOWS -----------------------------
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Lib/Slatec/slatec/dpchdf.f
