*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