DBSPEV(3)

SYNOPSIS
SUBROUTINE DBSPEV (T, AD, N, K, NDERIV, X, INEV, SVALUE, WORK)

NAME
dbspev - Calculate the value of the spline and its derivatives from the B-representation.

LIBRARY
SLATEC

CATEGORY
E3, K6

TYPE
DOUBLE PRECISION (BSPEV-S, DBSPEV-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 **** a double precision routine **** DBSPEV is the BSPLEV routine of the reference. DBSPEV calculates the value of the spline and its derivatives at X from the B-representation (T,A,N,K) and returns them in SVALUE(I),I=1,NDERIV, T(K) .LE. X .LE. T(N+1). AD(I) can be the B-spline coefficients A(I), I=1,N) if NDERIV=1. Otherwise AD must be computed before hand by a call to DBSPDR (T,A,N,K, NDERIV,AD). If X=T(I),I=K,N), right limiting values are obtained. To compute left derivatives or left limiting values at a knot T(I), replace N by I-1 and set X=T(I), I=K+1,N+1. DBSPEV calls DINTRV, DBSPVN Description of Arguments Input T,AD,X, are double precision T - knot vector of length N+K AD - vector of length (2*N-NDERIV+1)*NDERIV/2 containing the difference table from DBSPDR. N - number of B-spline coefficients N = sum of knot multiplicities-K K - order of the B-spline, K .GE. 1 NDERIV - number of derivatives, 1 .LE. NDERIV .LE. K. NDERIV=1 gives the zero-th derivative = function value X - argument, T(K) .LE. X .LE. T(N+1) INEV - an initialization parameter which must be set to 1 the first time DBSPEV is called. Output SVALUE,WORK are double precision INEV - INEV contains information for efficient process- ing after the initial call and INEV must not be changed by the user. Distinct splines require distinct INEV parameters. SVALUE - vector of length NDERIV containing the spline value in SVALUE(1) and the NDERIV-1 derivatives in the remaining components. WORK - work vector of length 3*K 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
DBSPVN, DINTRV, XERMSG

REVISION HISTORY (YYMMDD)
800901 DATE WRITTEN
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)