SLATEC Routines --- DBNFAC ---

```*DECK DBNFAC
SUBROUTINE DBNFAC (W, NROWW, NROW, NBANDL, NBANDU, IFLAG)
C***BEGIN PROLOGUE  DBNFAC
C***SUBSIDIARY
C***PURPOSE  Subsidiary to DBINT4 and DBINTK
C***LIBRARY   SLATEC
C***TYPE      DOUBLE PRECISION (BNFAC-S, DBNFAC-D)
C***AUTHOR  (UNKNOWN)
C***DESCRIPTION
C
C  DBNFAC is the BANFAC routine from
C        * A Practical Guide to Splines *  by C. de Boor
C
C  DBNFAC is a double precision routine
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  ****** W is double precision
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  ****** W is double precision
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 DBNSLV ( 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