LMDZ
pchdf.F
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1 *DECK PCHDF
2  REAL FUNCTION pchdf (K, X, S, IERR)
3 C***BEGIN PROLOGUE PCHDF
4 C***SUBSIDIARY
5 C***PURPOSE Computes divided differences for PCHCE and PCHSP
6 C***LIBRARY SLATEC (PCHIP)
7 C***TYPE SINGLE PRECISION (PCHDF-S, DPCHDF-D)
8 C***AUTHOR Fritsch, F. N., (LLNL)
9 C***DESCRIPTION
10 C
11 C PCHDF: PCHIP Finite Difference Formula
12 C
13 C Uses a divided difference formulation to compute a K-point approx-
14 C imation to the derivative at X(K) based on the data in X and S.
15 C
16 C Called by PCHCE and PCHSP to compute 3- and 4-point boundary
17 C derivative approximations.
18 C
19 C ----------------------------------------------------------------------
20 C
21 C On input:
22 C K is the order of the desired derivative approximation.
23 C K must be at least 3 (error return if not).
24 C X contains the K values of the independent variable.
25 C X need not be ordered, but the values **MUST** be
26 C distinct. (Not checked here.)
27 C S contains the associated slope values:
28 C S(I) = (F(I+1)-F(I))/(X(I+1)-X(I)), I=1(1)K-1.
29 C (Note that S need only be of length K-1.)
30 C
31 C On return:
32 C S will be destroyed.
33 C IERR will be set to -1 if K.LT.2 .
34 C PCHDF will be set to the desired derivative approximation if
35 C IERR=0 or to zero if IERR=-1.
36 C
37 C ----------------------------------------------------------------------
38 C
39 C***SEE ALSO PCHCE, PCHSP
40 C***REFERENCES Carl de Boor, A Practical Guide to Splines, Springer-
41 C Verlag, New York, 1978, pp. 10-16.
42 C***ROUTINES CALLED XERMSG
43 C***REVISION HISTORY (YYMMDD)
44 C 820503 DATE WRITTEN
45 C 820805 Converted to SLATEC library version.
46 C 870813 Minor cosmetic changes.
47 C 890411 Added SAVE statements (Vers. 3.2).
48 C 890411 REVISION DATE from Version 3.2
49 C 891214 Prologue converted to Version 4.0 format. (BAB)
50 C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
51 C 900328 Added TYPE section. (WRB)
52 C 910408 Updated AUTHOR and DATE WRITTEN sections in prologue. (WRB)
53 C 920429 Revised format and order of references. (WRB,FNF)
54 C 930503 Improved purpose. (FNF)
55 C***END PROLOGUE PCHDF
56 C
57 C**End
58 C
59 C DECLARE ARGUMENTS.
60 C
61  INTEGER K, IERR
62  REAL X(k), S(k)
63 C
64 C DECLARE LOCAL VARIABLES.
65 C
66  INTEGER I, J
67  REAL VALUE, ZERO
68  SAVE zero
69  DATA zero /0./
70 C
71 C CHECK FOR LEGAL VALUE OF K.
72 C
73 C***FIRST EXECUTABLE STATEMENT PCHDF
74  IF (k .LT. 3) GO TO 5001
75 C
76 C COMPUTE COEFFICIENTS OF INTERPOLATING POLYNOMIAL.
77 C
78  DO 10 j = 2, k-1
79  DO 9 i = 1, k-j
80  s(i) = (s(i+1)-s(i))/(x(i+j)-x(i))
81  9 CONTINUE
82  10 CONTINUE
83 C
84 C EVALUATE DERIVATIVE AT X(K).
85 C
86  VALUE = s(1)
87  DO 20 i = 2, k-1
88  VALUE = s(i) + VALUE*(x(k)-x(i))
89  20 CONTINUE
90 C
91 C NORMAL RETURN.
92 C
93  ierr = 0
94  pchdf = VALUE
95  RETURN
96 C
97 C ERROR RETURN.
98 C
99  5001 CONTINUE
100 C K.LT.3 RETURN.
101  ierr = -1
102  CALL xermsg ('SLATEC', 'PCHDF', 'K LESS THAN THREE', ierr, 1)
103  pchdf = zero
104  RETURN
105 C------------- LAST LINE OF PCHDF FOLLOWS ------------------------------
106  END
pchdf
real function pchdf(K, X, S, IERR)
Definition: pchdf.F:3
xermsg
subroutine xermsg(LIBRAR, SUBROU, MESSG, NERR, LEVEL)
Definition: xermsg.F:3