PPVAL(3)

SYNOPSIS
FUNCTION PPVAL (LDC, C, XI, LXI, K, IDERIV, X, INPPV)

NAME
ppval - Calculate the value of the IDERIV-th derivative of the B-spline from the PP-representation.

LIBRARY
SLATEC

CATEGORY
E3, K6

TYPE
SINGLE PRECISION (PPVAL-S, DPPVAL-D)

KEYWORDS
B-SPLINE, DATA FITTING, INTERPOLATION, SPLINES

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Written by Carl de Boor and modified by D. E. Amos Abstract PPVAL is the PPVALU function of the reference. PPVAL calculates (at X) the value of the IDERIV-th derivative of the B-spline from the PP-representation (C,XI,LXI,K). The Taylor expansion about XI(J) for X in the interval XI(J) .LE. X .LT. XI(J+1) is evaluated, J=1,LXI. Right limiting values at X=XI(J) are obtained. PPVAL will extrapolate beyond XI(1) and XI(LXI+1). To obtain left limiting values (left derivatives) at XI(J), replace LXI by J-1 and set X=XI(J),J=2,LXI+1. Description of Arguments Input LDC - leading dimension of C matrix, LDC .GE. K C - matrix of dimension at least (K,LXI) containing right derivatives at break points XI(*). XI - break point vector of length LXI+1 LXI - number of polynomial pieces K - order of B-spline, K .GE. 1 IDERIV - order of the derivative, 0 .LE. IDERIV .LE. K-1 IDERIV=0 gives the B-spline value X - argument, XI(1) .LE. X .LE. XI(LXI+1) INPPV - an initialization parameter which must be set to 1 the first time PPVAL is called. Output INPPV - INPPV contains information for efficient process- ing after the initial call and INPPV must not be changed by the user. Distinct splines require distinct INPPV parameters. PPVAL - value of the IDERIV-th derivative at X Error Conditions Improper input is a fatal error

REFERENCES
Carl de Boor, Package for calculating with B-splines, SIAM Journal on Numerical Analysis 14, 3 (June 1977), pp. 441-472.

ROUTINES CALLED
INTRV, XERMSG

REVISION HISTORY (YYMMDD)
800901 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890831 Modified array declarations. (WRB)
890831 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
920501 Reformatted the REFERENCES section. (WRB)