BVALU(3)

SYNOPSIS
FUNCTION BVALU (T, A, N, K, IDERIV, X, INBV, WORK)

NAME
bvalu - Evaluate the B-representation of a B-spline at X for the function value or any of its derivatives.

LIBRARY
SLATEC

CATEGORY
E3, K6

TYPE
SINGLE PRECISION (BVALU-S, DBVALU-D)

KEYWORDS
DIFFERENTIATION OF B-SPLINE, EVALUATION OF B-SPLINE

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Written by Carl de Boor and modified by D. E. Amos Abstract BVALU is the BVALUE function of the reference. BVALU evaluates the B-representation (T,A,N,K) of a B-spline at X for the function value on IDERIV = 0 or any of its derivatives on IDERIV = 1,2,...,K-1. Right limiting values (right derivatives) are returned except at the right end point X=T(N+1) where left limiting values are computed. The spline is defined on T(K) .LE. X .LE. T(N+1). BVALU returns a fatal error message when X is outside of this interval. 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. BVALU calls INTRV Description of Arguments Input T - knot vector of length N+K A - B-spline coefficient vector of length N N - number of B-spline coefficients N = sum of knot multiplicities-K K - order of the B-spline, K .GE. 1 IDERIV - order of the derivative, 0 .LE. IDERIV .LE. K-1 IDERIV=0 returns the B-spline value X - argument, T(K) .LE. X .LE. T(N+1) INBV - an initialization parameter which must be set to 1 the first time BVALU is called. Output INBV - INBV contains information for efficient process- ing after the initial call and INBV must not be changed by the user. Distinct splines require distinct INBV parameters. WORK - work vector of length 3*K. BVALU - value of the IDERIV-th derivative at X Error Conditions An 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)
890531 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)
900326 Removed duplicate information from DESCRIPTION section. (WRB)
920501 Reformatted the REFERENCES section. (WRB)