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