DBSPPP(3)

SYNOPSIS
SUBROUTINE DBSPPP (T, A, N, K, LDC, C, XI, LXI, WORK)

NAME
dbsppp - Convert the B-representation of a B-spline to the piecewise polynomial (PP) form.

LIBRARY
SLATEC

CATEGORY
E3, K6

TYPE
DOUBLE PRECISION (BSPPP-S, DBSPPP-D)

KEYWORDS
B-SPLINE, PIECEWISE POLYNOMIAL

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Written by Carl de Boor and modified by D. E. Amos Abstract **** a double precision routine **** DBSPPP is the BSPLPP routine of the reference. DBSPPP converts the B-representation (T,A,N,K) to the piecewise polynomial (PP) form (C,XI,LXI,K) for use with DPPVAL. Here XI(*), the break point array of length LXI, is the knot array T(*) with multiplicities removed. The columns of the matrix C(I,J) contain the right Taylor derivatives for the polynomial expansion about XI(J) for the intervals XI(J) .LE. X .LE. XI(J+1), I=1,K, J=1,LXI. Function DPPVAL makes this evaluation at a specified point X in XI(1) .LE. X .LE. XI(LXI+1) 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 B-spline, K .GE. 1 LDC - leading dimension of C, LDC .GE. K Output C,XI,WORK are double precision 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 break points, LXI .LE. N-K+1 WORK - work vector of length K*(N+3) 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
DBSPDR, DBSPEV, 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)