SLATEC Routines --- DBINT4 ---
*DECK DBINT4
SUBROUTINE DBINT4 (X, Y, NDATA, IBCL, IBCR, FBCL, FBCR, KNTOPT, T,
+ BCOEF, N, K, W)
C***BEGIN PROLOGUE DBINT4
C***PURPOSE Compute the B-representation of a cubic spline
C which interpolates given data.
C***LIBRARY SLATEC
C***CATEGORY E1A
C***TYPE DOUBLE PRECISION (BINT4-S, DBINT4-D)
C***KEYWORDS B-SPLINE, CUBIC SPLINES, DATA FITTING, INTERPOLATION
C***AUTHOR Amos, D. E., (SNLA)
C***DESCRIPTION
C
C Abstract **** a double precision routine ****
C
C DBINT4 computes the B representation (T,BCOEF,N,K) of a
C cubic spline (K=4) which interpolates data (X(I),Y(I)),
C I=1,NDATA. Parameters IBCL, IBCR, FBCL, FBCR allow the
C specification of the spline first or second derivative at
C both X(1) and X(NDATA). When this data is not specified
C by the problem, it is common practice to use a natural
C spline by setting second derivatives at X(1) and X(NDATA)
C to zero (IBCL=IBCR=2,FBCL=FBCR=0.0). The spline is defined
C on T(4) .LE. X .LE. T(N+1) with (ordered) interior knots at
C X(I) values where N=NDATA+2. The knots T(1),T(2),T(3) lie to
C the left of T(4)=X(1) and the knots T(N+2), T(N+3), T(N+4)
C lie to the right of T(N+1)=X(NDATA) in increasing order. If
C no extrapolation outside (X(1),X(NDATA)) is anticipated, the
C knots T(1)=T(2)=T(3)=T(4)=X(1) and T(N+2)=T(N+3)=T(N+4)=
C T(N+1)=X(NDATA) can be specified by KNTOPT=1. KNTOPT=2
C selects a knot placement for T(1), T(2), T(3) to make the
C first 7 knots symmetric about T(4)=X(1) and similarly for
C T(N+2), T(N+3), T(N+4) about T(N+1)=X(NDATA). KNTOPT=3
C allows the user to make his own selection, in increasing
C order, for T(1), T(2), T(3) to the left of X(1) and T(N+2),
C T(N+3), T(N+4) to the right of X(NDATA) in the work array
C W(1) through W(6). In any case, the interpolation on
C T(4) .LE. X .LE. T(N+1) by using function DBVALU is unique
C for given boundary conditions.
C
C Description of Arguments
C
C Input X,Y,FBCL,FBCR,W are double precision
C X - X vector of abscissae of length NDATA, distinct
C and in increasing order
C Y - Y vector of ordinates of length NDATA
C NDATA - number of data points, NDATA .GE. 2
C IBCL - selection parameter for left boundary condition
C IBCL = 1 constrain the first derivative at
C X(1) to FBCL
C = 2 constrain the second derivative at
C X(1) to FBCL
C IBCR - selection parameter for right boundary condition
C IBCR = 1 constrain first derivative at
C X(NDATA) to FBCR
C IBCR = 2 constrain second derivative at
C X(NDATA) to FBCR
C FBCL - left boundary values governed by IBCL
C FBCR - right boundary values governed by IBCR
C KNTOPT - knot selection parameter
C KNTOPT = 1 sets knot multiplicity at T(4) and
C T(N+1) to 4
C = 2 sets a symmetric placement of knots
C about T(4) and T(N+1)
C = 3 sets T(I)=W(I) and T(N+1+I)=W(3+I),I=1,3
C where W(I),I=1,6 is supplied by the user
C W - work array of dimension at least 5*(NDATA+2)
C If KNTOPT=3, then W(1),W(2),W(3) are knot values to
C the left of X(1) and W(4),W(5),W(6) are knot
C values to the right of X(NDATA) in increasing
C order to be supplied by the user
C
C Output T,BCOEF are double precision
C T - knot array of length N+4
C BCOEF - B spline coefficient array of length N
C N - number of coefficients, N=NDATA+2
C K - order of spline, K=4
C
C Error Conditions
C Improper input is a fatal error
C Singular system of equations is a fatal error
C
C***REFERENCES D. E. Amos, Computation with splines and B-splines,
C Report SAND78-1968, Sandia Laboratories, March 1979.
C Carl de Boor, Package for calculating with B-splines,
C SIAM Journal on Numerical Analysis 14, 3 (June 1977),
C pp. 441-472.
C Carl de Boor, A Practical Guide to Splines, Applied
C Mathematics Series 27, Springer-Verlag, New York,
C 1978.
C***ROUTINES CALLED D1MACH, DBNFAC, DBNSLV, DBSPVD, XERMSG
C***REVISION HISTORY (YYMMDD)
C 800901 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890531 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 DBINT4