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*DECK PCHFE |
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✗ |
SUBROUTINE PCHFE (N, X, F, D, INCFD, SKIP, NE, XE, FE, IERR) |
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C***BEGIN PROLOGUE PCHFE |
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C***PURPOSE Evaluate a piecewise cubic Hermite function at an array of |
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C points. May be used by itself for Hermite interpolation, |
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C or as an evaluator for PCHIM or PCHIC. |
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C***LIBRARY SLATEC (PCHIP) |
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C***CATEGORY E3 |
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C***TYPE SINGLE PRECISION (PCHFE-S, DPCHFE-D) |
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C***KEYWORDS CUBIC HERMITE EVALUATION, HERMITE INTERPOLATION, PCHIP, |
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C PIECEWISE CUBIC EVALUATION |
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C***AUTHOR Fritsch, F. N., (LLNL) |
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C Lawrence Livermore National Laboratory |
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C P.O. Box 808 (L-316) |
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C Livermore, CA 94550 |
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C FTS 532-4275, (510) 422-4275 |
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C***DESCRIPTION |
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C |
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C PCHFE: Piecewise Cubic Hermite Function Evaluator |
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C |
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C Evaluates the cubic Hermite function defined by N, X, F, D at |
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C the points XE(J), J=1(1)NE. |
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C |
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C To provide compatibility with PCHIM and PCHIC, includes an |
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C increment between successive values of the F- and D-arrays. |
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C |
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C ---------------------------------------------------------------------- |
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C |
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C Calling sequence: |
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C |
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C PARAMETER (INCFD = ...) |
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C INTEGER N, NE, IERR |
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C REAL X(N), F(INCFD,N), D(INCFD,N), XE(NE), FE(NE) |
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C LOGICAL SKIP |
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C |
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C CALL PCHFE (N, X, F, D, INCFD, SKIP, NE, XE, FE, IERR) |
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C |
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C Parameters: |
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C |
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C N -- (input) number of data points. (Error return if N.LT.2 .) |
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C |
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C X -- (input) real array of independent variable values. The |
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C elements of X must be strictly increasing: |
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C X(I-1) .LT. X(I), I = 2(1)N. |
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C (Error return if not.) |
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C |
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C F -- (input) real array of function values. F(1+(I-1)*INCFD) is |
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C the value corresponding to X(I). |
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C |
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C D -- (input) real array of derivative values. D(1+(I-1)*INCFD) is |
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C the value corresponding to X(I). |
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C |
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C INCFD -- (input) increment between successive values in F and D. |
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C (Error return if INCFD.LT.1 .) |
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C |
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C SKIP -- (input/output) logical variable which should be set to |
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C .TRUE. if the user wishes to skip checks for validity of |
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C preceding parameters, or to .FALSE. otherwise. |
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C This will save time in case these checks have already |
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C been performed (say, in PCHIM or PCHIC). |
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C SKIP will be set to .TRUE. on normal return. |
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C |
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C NE -- (input) number of evaluation points. (Error return if |
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C NE.LT.1 .) |
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C |
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C XE -- (input) real array of points at which the function is to be |
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C evaluated. |
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C |
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C NOTES: |
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C 1. The evaluation will be most efficient if the elements |
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C of XE are increasing relative to X; |
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C that is, XE(J) .GE. X(I) |
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C implies XE(K) .GE. X(I), all K.GE.J . |
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C 2. If any of the XE are outside the interval [X(1),X(N)], |
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C values are extrapolated from the nearest extreme cubic, |
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C and a warning error is returned. |
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C |
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C FE -- (output) real array of values of the cubic Hermite function |
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C defined by N, X, F, D at the points XE. |
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C |
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C IERR -- (output) error flag. |
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C Normal return: |
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C IERR = 0 (no errors). |
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C Warning error: |
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C IERR.GT.0 means that extrapolation was performed at |
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C IERR points. |
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C "Recoverable" errors: |
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C IERR = -1 if N.LT.2 . |
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C IERR = -2 if INCFD.LT.1 . |
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C IERR = -3 if the X-array is not strictly increasing. |
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C IERR = -4 if NE.LT.1 . |
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C (The FE-array has not been changed in any of these cases.) |
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C NOTE: The above errors are checked in the order listed, |
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C and following arguments have **NOT** been validated. |
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C |
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C***REFERENCES (NONE) |
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C***ROUTINES CALLED CHFEV, XERMSG |
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C***REVISION HISTORY (YYMMDD) |
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C 811020 DATE WRITTEN |
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C 820803 Minor cosmetic changes for release 1. |
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C 870707 Minor cosmetic changes to prologue. |
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C 890531 Changed all specific intrinsics to generic. (WRB) |
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C 890831 Modified array declarations. (WRB) |
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C 890831 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***END PROLOGUE PCHFE |
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C Programming notes: |
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C |
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C 1. To produce a double precision version, simply: |
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C a. Change PCHFE to DPCHFE, and CHFEV to DCHFEV, wherever they |
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C occur, |
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C b. Change the real declaration to double precision, |
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C |
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C 2. Most of the coding between the call to CHFEV and the end of |
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C the IR-loop could be eliminated if it were permissible to |
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C assume that XE is ordered relative to X. |
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C |
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C 3. CHFEV does not assume that X1 is less than X2. thus, it would |
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C be possible to write a version of PCHFE that assumes a strict- |
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C ly decreasing X-array by simply running the IR-loop backwards |
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C (and reversing the order of appropriate tests). |
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C |
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C 4. The present code has a minor bug, which I have decided is not |
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C worth the effort that would be required to fix it. |
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C If XE contains points in [X(N-1),X(N)], followed by points .LT. |
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C X(N-1), followed by points .GT.X(N), the extrapolation points |
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C will be counted (at least) twice in the total returned in IERR. |
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C |
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C DECLARE ARGUMENTS. |
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C |
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INTEGER N, INCFD, NE, IERR |
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REAL X(*), F(INCFD,*), D(INCFD,*), XE(*), FE(*) |
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LOGICAL SKIP |
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C |
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C DECLARE LOCAL VARIABLES. |
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C |
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INTEGER I, IERC, IR, J, JFIRST, NEXT(2), NJ |
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C |
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C VALIDITY-CHECK ARGUMENTS. |
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C |
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C***FIRST EXECUTABLE STATEMENT PCHFE |
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IF (SKIP) GO TO 5 |
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C |
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IF ( N.LT.2 ) GO TO 5001 |
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IF ( INCFD.LT.1 ) GO TO 5002 |
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DO 1 I = 2, N |
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IF ( X(I).LE.X(I-1) ) GO TO 5003 |
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1 CONTINUE |
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C |
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C FUNCTION DEFINITION IS OK, GO ON. |
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C |
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5 CONTINUE |
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IF ( NE.LT.1 ) GO TO 5004 |
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IERR = 0 |
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SKIP = .TRUE. |
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C |
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C LOOP OVER INTERVALS. ( INTERVAL INDEX IS IL = IR-1 . ) |
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C ( INTERVAL IS X(IL).LE.X.LT.X(IR) . ) |
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JFIRST = 1 |
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IR = 2 |
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10 CONTINUE |
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C |
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C SKIP OUT OF LOOP IF HAVE PROCESSED ALL EVALUATION POINTS. |
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C |
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IF (JFIRST .GT. NE) GO TO 5000 |
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C |
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C LOCATE ALL POINTS IN INTERVAL. |
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C |
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DO 20 J = JFIRST, NE |
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IF (XE(J) .GE. X(IR)) GO TO 30 |
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20 CONTINUE |
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J = NE + 1 |
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GO TO 40 |
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C |
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C HAVE LOCATED FIRST POINT BEYOND INTERVAL. |
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C |
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30 CONTINUE |
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IF (IR .EQ. N) J = NE + 1 |
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C |
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40 CONTINUE |
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NJ = J - JFIRST |
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C |
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C SKIP EVALUATION IF NO POINTS IN INTERVAL. |
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C |
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IF (NJ .EQ. 0) GO TO 50 |
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C |
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C EVALUATE CUBIC AT XE(I), I = JFIRST (1) J-1 . |
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C |
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C ---------------------------------------------------------------- |
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CALL CHFEV (X(IR-1),X(IR), F(1,IR-1),F(1,IR), D(1,IR-1),D(1,IR), |
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* NJ, XE(JFIRST), FE(JFIRST), NEXT, IERC) |
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C ---------------------------------------------------------------- |
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IF (IERC .LT. 0) GO TO 5005 |
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C |
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IF (NEXT(2) .EQ. 0) GO TO 42 |
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C IF (NEXT(2) .GT. 0) THEN |
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C IN THE CURRENT SET OF XE-POINTS, THERE ARE NEXT(2) TO THE |
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C RIGHT OF X(IR). |
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C |
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IF (IR .LT. N) GO TO 41 |
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C IF (IR .EQ. N) THEN |
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C THESE ARE ACTUALLY EXTRAPOLATION POINTS. |
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IERR = IERR + NEXT(2) |
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GO TO 42 |
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41 CONTINUE |
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C ELSE |
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C WE SHOULD NEVER HAVE GOTTEN HERE. |
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GO TO 5005 |
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C ENDIF |
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C ENDIF |
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42 CONTINUE |
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C |
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IF (NEXT(1) .EQ. 0) GO TO 49 |
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C IF (NEXT(1) .GT. 0) THEN |
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C IN THE CURRENT SET OF XE-POINTS, THERE ARE NEXT(1) TO THE |
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C LEFT OF X(IR-1). |
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C |
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IF (IR .GT. 2) GO TO 43 |
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C IF (IR .EQ. 2) THEN |
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C THESE ARE ACTUALLY EXTRAPOLATION POINTS. |
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IERR = IERR + NEXT(1) |
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GO TO 49 |
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43 CONTINUE |
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C ELSE |
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C XE IS NOT ORDERED RELATIVE TO X, SO MUST ADJUST |
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C EVALUATION INTERVAL. |
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C |
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C FIRST, LOCATE FIRST POINT TO LEFT OF X(IR-1). |
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DO 44 I = JFIRST, J-1 |
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IF (XE(I) .LT. X(IR-1)) GO TO 45 |
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44 CONTINUE |
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C NOTE-- CANNOT DROP THROUGH HERE UNLESS THERE IS AN ERROR |
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C IN CHFEV. |
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GO TO 5005 |
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C |
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45 CONTINUE |
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C RESET J. (THIS WILL BE THE NEW JFIRST.) |
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J = I |
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C |
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C NOW FIND OUT HOW FAR TO BACK UP IN THE X-ARRAY. |
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DO 46 I = 1, IR-1 |
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IF (XE(J) .LT. X(I)) GO TO 47 |
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46 CONTINUE |
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C NB-- CAN NEVER DROP THROUGH HERE, SINCE XE(J).LT.X(IR-1). |
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C |
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47 CONTINUE |
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C AT THIS POINT, EITHER XE(J) .LT. X(1) |
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C OR X(I-1) .LE. XE(J) .LT. X(I) . |
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C RESET IR, RECOGNIZING THAT IT WILL BE INCREMENTED BEFORE |
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C CYCLING. |
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IR = MAX(1, I-1) |
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C ENDIF |
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C ENDIF |
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49 CONTINUE |
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C |
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JFIRST = J |
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C |
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C END OF IR-LOOP. |
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C |
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50 CONTINUE |
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IR = IR + 1 |
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IF (IR .LE. N) GO TO 10 |
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C |
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C NORMAL RETURN. |
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C |
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5000 CONTINUE |
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✗ |
RETURN |
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C |
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C ERROR RETURNS. |
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C |
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5001 CONTINUE |
| 273 |
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C N.LT.2 RETURN. |
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IERR = -1 |
| 275 |
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CALL XERMSG ('SLATEC', 'PCHFE', |
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+ 'NUMBER OF DATA POINTS LESS THAN TWO', IERR, 1) |
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✗ |
RETURN |
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C |
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5002 CONTINUE |
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C INCFD.LT.1 RETURN. |
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IERR = -2 |
| 282 |
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CALL XERMSG ('SLATEC', 'PCHFE', 'INCREMENT LESS THAN ONE', IERR, |
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+ 1) |
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RETURN |
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C |
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5003 CONTINUE |
| 287 |
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C X-ARRAY NOT STRICTLY INCREASING. |
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✗ |
IERR = -3 |
| 289 |
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CALL XERMSG ('SLATEC', 'PCHFE', 'X-ARRAY NOT STRICTLY INCREASING' |
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+ , IERR, 1) |
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✗ |
RETURN |
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C |
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5004 CONTINUE |
| 294 |
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C NE.LT.1 RETURN. |
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IERR = -4 |
| 296 |
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CALL XERMSG ('SLATEC', 'PCHFE', |
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+ 'NUMBER OF EVALUATION POINTS LESS THAN ONE', IERR, 1) |
| 298 |
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✗ |
RETURN |
| 299 |
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C |
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5005 CONTINUE |
| 301 |
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C ERROR RETURN FROM CHFEV. |
| 302 |
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C *** THIS CASE SHOULD NEVER OCCUR *** |
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✗ |
IERR = -5 |
| 304 |
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CALL XERMSG ('SLATEC', 'PCHFE', |
| 305 |
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+ 'ERROR RETURN FROM CHFEV -- FATAL', IERR, 2) |
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✗ |
RETURN |
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C------------- LAST LINE OF PCHFE FOLLOWS ------------------------------ |
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END |
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