bspvd.f
SUBROUTINE BSPVD (T, K, NDERIV, X, ILEFT, LDVNIK, VNIKX, WORK)
C***BEGIN PROLOGUE BSPVD
C***PURPOSE Calculate the value and all derivatives of order less than
C NDERIV of all basis functions which do not vanish at X.
C***LIBRARY SLATEC
C***CATEGORY E3, K6
C***TYPE SINGLE PRECISION (BSPVD-S, DBSPVD-D)
C***KEYWORDS DIFFERENTIATION OF B-SPLINE, EVALUATION OF B-SPLINE
C***AUTHOR Amos, D. E., (SNLA)
C***DESCRIPTION
C
C Written by Carl de Boor and modified by D. E. Amos
C
C Abstract
C BSPVD is the BSPLVD routine of the reference.
C
C BSPVD calculates the value and all derivatives of order
C less than NDERIV of all basis functions which do not
C (possibly) vanish at X. ILEFT is input such that
C T(ILEFT) .LE. X .LT. T(ILEFT+1). A call to INTRV(T,N+1,X,
C ILO,ILEFT,MFLAG) will produce the proper ILEFT. The output of
C BSPVD is a matrix VNIKX(I,J) of dimension at least (K,NDERIV)
C whose columns contain the K nonzero basis functions and
C their NDERIV-1 right derivatives at X, I=1,K, J=1,NDERIV.
C These basis functions have indices ILEFT-K+I, I=1,K,
C K .LE. ILEFT .LE. N. The nonzero part of the I-th basis
C function lies in (T(I),T(I+K)), I=1,N.
C
C If X=T(ILEFT+1) then VNIKX contains left limiting values
C (left derivatives) at T(ILEFT+1). In particular, ILEFT = N
C produces left limiting values at the right end point
C X=T(N+1). To obtain left limiting values at T(I), I=K+1,N+1,
C set X= next lower distinct knot, call INTRV to get ILEFT,
C set X=T(I), and then call BSPVD.
C
C Description of Arguments
C Input
C T - knot vector of length N+K, where
C N = number of B-spline basis functions
C N = sum of knot multiplicities-K
C K - order of the B-spline, K .GE. 1
C NDERIV - number of derivatives = NDERIV-1,
C 1 .LE. NDERIV .LE. K
C X - argument of basis functions,
C T(K) .LE. X .LE. T(N+1)
C ILEFT - largest integer such that
C T(ILEFT) .LE. X .LT. T(ILEFT+1)
C LDVNIK - leading dimension of matrix VNIKX
C
C Output
C VNIKX - matrix of dimension at least (K,NDERIV) contain-
C ing the nonzero basis functions at X and their
C derivatives columnwise.
C WORK - a work vector of length (K+1)*(K+2)/2
C
C Error Conditions
C Improper input is a fatal error
C
C***REFERENCES Carl de Boor, Package for calculating with B-splines,
C SIAM Journal on Numerical Analysis 14, 3 (June 1977),
C pp. 441-472.
C***ROUTINES CALLED BSPVN, XERMSG
C***REVISION HISTORY (YYMMDD)
C 800901 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
C 900326 Removed duplicate information from DESCRIPTION section.
C (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE BSPVD