DBSPDR(3)

SYNOPSIS
SUBROUTINE DBSPDR (T, A, N, K, NDERIV, AD)

NAME
dbspdr - Use the B-representation to construct a divided difference table preparatory to a (right) derivative calculation.

LIBRARY
SLATEC

CATEGORY
E3, K6

TYPE
DOUBLE PRECISION (BSPDR-S, DBSPDR-D)

KEYWORDS
B-SPLINE, DATA FITTING, DIFFERENTIATION OF SPLINES, INTERPOLATION

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Written by Carl de Boor and modified by D. E. Amos Abstract **** a double precision routine **** DBSPDR is the BSPLDR routine of the reference. DBSPDR uses the B-representation (T,A,N,K) to construct a divided difference table ADIF preparatory to a (right) derivative calculation in DBSPEV. The lower triangular matrix ADIF is stored in vector AD by columns. The arrays are related by ADIF(I,J) = AD(I-J+1 + (2*N-J+2)*(J-1)/2) I = J,N , J=1,NDERIV. Description of Arguments Input T,A are double precision 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 spline, K .GE. 1 NDERIV - number of derivatives, 1 .LE. NDERIV .LE. K. NDERIV=1 gives the zero-th derivative = function value Output AD is double precision AD - table of differences in a vector of length (2*N-NDERIV+1)*NDERIV/2 for input to DBSPEV 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
XERMSG

REVISION HISTORY (YYMMDD)
800901 DATE WRITTEN
890831 Modified array declarations. (WRB)
890911 Removed unnecessary intrinsics. (WRB)
890911 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)