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SUBROUTINE DP1VLU (L, NDER, X, YFIT, YP, A)
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C***BEGIN PROLOGUE DP1VLU
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C***PURPOSE Use the coefficients generated by DPOLFT to evaluate the
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C polynomial fit of degree L, along with the first NDER of
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C its derivatives, at a specified point.
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C***TYPE DOUBLE PRECISION (PVALUE-S, DP1VLU-D)
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C***KEYWORDS CURVE FITTING, LEAST SQUARES, POLYNOMIAL APPROXIMATION
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C***AUTHOR Shampine, L. F., (SNLA)
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C Davenport, S. M., (SNLA)
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C The subroutine DP1VLU uses the coefficients generated by DPOLFT
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C to evaluate the polynomial fit of degree L , along with the first
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C NDER of its derivatives, at a specified point. Computationally
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C stable recurrence relations are used to perform this task.
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C The parameters for DP1VLU are
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C Input -- ALL TYPE REAL variables are DOUBLE PRECISION
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C L - the degree of polynomial to be evaluated. L may be
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C any non-negative integer which is less than or equal
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C to NDEG , the highest degree polynomial provided
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C NDER - the number of derivatives to be evaluated. NDER
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C may be 0 or any positive value. If NDER is less
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C than 0, it will be treated as 0.
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C X - the argument at which the polynomial and its
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C derivatives are to be evaluated.
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C A - work and output array containing values from last
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C Output -- ALL TYPE REAL variables are DOUBLE PRECISION
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C YFIT - value of the fitting polynomial of degree L at X
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C YP - array containing the first through NDER derivatives
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C of the polynomial of degree L . YP must be
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C dimensioned at least NDER in the calling program.
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C***REFERENCES L. F. Shampine, S. M. Davenport and R. E. Huddleston,
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C Curve fitting by polynomials in one variable, Report
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C SLA-74-0270, Sandia Laboratories, June 1974.
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C***ROUTINES CALLED XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890911 Removed unnecessary intrinsics. (WRB)
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C 891006 Cosmetic changes to prologue. (WRB)
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C 891006 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 900510 Convert XERRWV calls to XERMSG calls. (RWC)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE DP1VLU
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IMPLICIT DOUBLE PRECISION (A-H,O-Z)
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INTEGER I,IC,ILO,IN,INP1,IUP,K1,K1I,K2,K3,K3P1,K3PN,K4,K4P1,K4PN,
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* KC,L,LM1,LP1,MAXORD,N,NDER,NDO,NDP1,NORD
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DOUBLE PRECISION A(*),CC,DIF,VAL,X,YFIT,YP(*)
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CHARACTER*8 XERN1, XERN2
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C***FIRST EXECUTABLE STATEMENT DP1VLU
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IF (L .LT. 0) GO TO 12
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IF (L .GT. NORD) GO TO 11
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IF (NDER .LT. 1) GO TO 2
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2 IF (L .GE. 2) GO TO 4
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VAL = A(K2+1) + (X-A(2))*CC
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IF (NDER .GE. 1) YP(1) = CC
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A(K3P1) = A(KC-1) + DIF*A(K4P1)
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C EVALUATE RECURRENCE RELATIONS FOR FUNCTION VALUE AND DERIVATIVES
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VAL = A(IC) + DIF*A(K3P1) - A(K1I)*A(K4P1)
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IF (NDO .LE. 0) GO TO 8
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6 YP(N) = DIF*A(K3PN) + N*A(K3PN-1) - A(K1I)*A(K4PN)
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C SAVE VALUES NEEDED FOR NEXT EVALUATION OF RECURRENCE RELATIONS
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C NORMAL RETURN OR ABORT DUE TO ERROR
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11 WRITE (XERN1, '(I8)') L
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WRITE (XERN2, '(I8)') NORD
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CALL XERMSG ('SLATEC', 'DP1VLU',
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* 'THE ORDER OF POLYNOMIAL EVALUATION, L = ' // XERN1 //
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* ' REQUESTED EXCEEDS THE HIGHEST ORDER FIT, NORD = ' // XERN2 //
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* ', COMPUTED BY DPOLFT -- EXECUTION TERMINATED.', 8, 2)
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12 CALL XERMSG ('SLATEC', 'DP1VLU',
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+ 'INVALID INPUT PARAMETER. ORDER OF POLYNOMIAL EVALUATION ' //
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+ 'REQUESTED IS NEGATIVE.', 2, 2)
added
removed
Lib/Slatec/slatec/dp1vlu.f
