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104 lines
3.8 KiB
Fortran
104 lines
3.8 KiB
Fortran
*DECK DPPVAL
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DOUBLE PRECISION FUNCTION DPPVAL (LDC, C, XI, LXI, K, IDERIV, X,
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+ INPPV)
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C***BEGIN PROLOGUE DPPVAL
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C***PURPOSE Calculate the value of the IDERIV-th derivative of the
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C B-spline from the PP-representation.
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C***LIBRARY SLATEC
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C***CATEGORY E3, K6
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C***TYPE DOUBLE PRECISION (PPVAL-S, DPPVAL-D)
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C***KEYWORDS B-SPLINE, DATA FITTING, INTERPOLATION, SPLINES
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C***AUTHOR Amos, D. E., (SNLA)
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C***DESCRIPTION
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C
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C Written by Carl de Boor and modified by D. E. Amos
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C
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C Abstract **** a double precision routine ****
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C DPPVAL is the PPVALU function of the reference.
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C
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C DPPVAL calculates (at X) the value of the IDERIV-th
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C derivative of the B-spline from the PP-representation
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C (C,XI,LXI,K). The Taylor expansion about XI(J) for X in
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C the interval XI(J) .LE. X .LT. XI(J+1) is evaluated, J=1,LXI.
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C Right limiting values at X=XI(J) are obtained. DPPVAL will
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C extrapolate beyond XI(1) and XI(LXI+1).
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C
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C To obtain left limiting values (left derivatives) at XI(J)
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C replace LXI by J-1 and set X=XI(J),J=2,LXI+1.
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C
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C Description of Arguments
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C
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C Input C,XI,X are double precision
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C LDC - leading dimension of C matrix, LDC .GE. K
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C C - matrix of dimension at least (K,LXI) containing
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C right derivatives at break points XI(*).
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C XI - break point vector of length LXI+1
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C LXI - number of polynomial pieces
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C K - order of B-spline, K .GE. 1
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C IDERIV - order of the derivative, 0 .LE. IDERIV .LE. K-1
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C IDERIV=0 gives the B-spline value
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C X - argument, XI(1) .LE. X .LE. XI(LXI+1)
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C INPPV - an initialization parameter which must be set
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C to 1 the first time DPPVAL is called.
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C
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C Output DPPVAL is double precision
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C INPPV - INPPV contains information for efficient process-
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C ing after the initial call and INPPV must not
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C be changed by the user. Distinct splines require
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C distinct INPPV parameters.
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C DPPVAL - value of the IDERIV-th derivative at X
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C
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C Error Conditions
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C Improper input is a fatal error
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C
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C***REFERENCES Carl de Boor, Package for calculating with B-splines,
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C SIAM Journal on Numerical Analysis 14, 3 (June 1977),
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C pp. 441-472.
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C***ROUTINES CALLED DINTRV, XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 800901 DATE WRITTEN
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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 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE DPPVAL
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C
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INTEGER I, IDERIV, INPPV, J, K, LDC, LXI, NDUMMY, KK
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DOUBLE PRECISION C, DX, X, XI
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DIMENSION XI(*), C(LDC,*)
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C***FIRST EXECUTABLE STATEMENT DPPVAL
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DPPVAL = 0.0D0
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IF(K.LT.1) GO TO 90
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IF(LDC.LT.K) GO TO 80
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IF(LXI.LT.1) GO TO 85
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IF(IDERIV.LT.0 .OR. IDERIV.GE.K) GO TO 95
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I = K - IDERIV
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KK = I
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CALL DINTRV(XI, LXI, X, INPPV, I, NDUMMY)
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DX = X - XI(I)
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J = K
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10 DPPVAL = (DPPVAL/KK)*DX + C(J,I)
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J = J - 1
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KK = KK - 1
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IF (KK.GT.0) GO TO 10
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RETURN
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C
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C
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80 CONTINUE
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CALL XERMSG ('SLATEC', 'DPPVAL', 'LDC DOES NOT SATISFY LDC.GE.K',
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+ 2, 1)
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RETURN
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85 CONTINUE
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CALL XERMSG ('SLATEC', 'DPPVAL', 'LXI DOES NOT SATISFY LXI.GE.1',
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+ 2, 1)
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RETURN
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90 CONTINUE
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CALL XERMSG ('SLATEC', 'DPPVAL', 'K DOES NOT SATISFY K.GE.1', 2,
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+ 1)
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RETURN
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95 CONTINUE
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CALL XERMSG ('SLATEC', 'DPPVAL',
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+ 'IDERIV DOES NOT SATISFY 0.LE.IDERIV.LT.K', 2, 1)
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RETURN
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END
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