*DECK BNFAC SUBROUTINE BNFAC (W, NROWW, NROW, NBANDL, NBANDU, IFLAG) C***BEGIN PROLOGUE BNFAC C***SUBSIDIARY C***PURPOSE Subsidiary to BINT4 and BINTK C***LIBRARY SLATEC C***TYPE SINGLE PRECISION (BNFAC-S, DBNFAC-D) C***AUTHOR (UNKNOWN) C***DESCRIPTION C C BNFAC is the BANFAC routine from C * A Practical Guide to Splines * by C. de Boor C C Returns in W the lu-factorization (without pivoting) of the banded C matrix A of order NROW with (NBANDL + 1 + NBANDU) bands or diag- C onals in the work array W . C C ***** I N P U T ****** C W.....Work array of size (NROWW,NROW) containing the interesting C part of a banded matrix A , with the diagonals or bands of A C stored in the rows of W , while columns of A correspond to C columns of W . This is the storage mode used in LINPACK and C results in efficient innermost loops. C Explicitly, A has NBANDL bands below the diagonal C + 1 (main) diagonal C + NBANDU bands above the diagonal C and thus, with MIDDLE = NBANDU + 1, C A(I+J,J) is in W(I+MIDDLE,J) for I=-NBANDU,...,NBANDL C J=1,...,NROW . C For example, the interesting entries of A (1,2)-banded matrix C of order 9 would appear in the first 1+1+2 = 4 rows of W C as follows. C 13 24 35 46 57 68 79 C 12 23 34 45 56 67 78 89 C 11 22 33 44 55 66 77 88 99 C 21 32 43 54 65 76 87 98 C C All other entries of W not identified in this way with an en- C try of A are never referenced . C NROWW.....Row dimension of the work array W . C must be .GE. NBANDL + 1 + NBANDU . C NBANDL.....Number of bands of A below the main diagonal C NBANDU.....Number of bands of A above the main diagonal . C C ***** O U T P U T ****** C IFLAG.....Integer indicating success( = 1) or failure ( = 2) . C If IFLAG = 1, then C W.....contains the LU-factorization of A into a unit lower triangu- C lar matrix L and an upper triangular matrix U (both banded) C and stored in customary fashion over the corresponding entries C of A . This makes it possible to solve any particular linear C system A*X = B for X by A C CALL BNSLV ( W, NROWW, NROW, NBANDL, NBANDU, B ) C with the solution X contained in B on return . C If IFLAG = 2, then C one of NROW-1, NBANDL,NBANDU failed to be nonnegative, or else C one of the potential pivots was found to be zero indicating C that A does not have an LU-factorization. This implies that C A is singular in case it is totally positive . C C ***** M E T H O D ****** C Gauss elimination W I T H O U T pivoting is used. The routine is C intended for use with matrices A which do not require row inter- C changes during factorization, especially for the T O T A L L Y C P O S I T I V E matrices which occur in spline calculations. C The routine should not be used for an arbitrary banded matrix. C C***SEE ALSO BINT4, BINTK C***ROUTINES CALLED (NONE) C***REVISION HISTORY (YYMMDD) C 800901 DATE WRITTEN C 890531 Changed all specific intrinsics to generic. (WRB) C 890831 Modified array declarations. (WRB) C 891214 Prologue converted to Version 4.0 format. (BAB) C 900328 Added TYPE section. (WRB) C***END PROLOGUE BNFAC