SLATEC Routines --- DNBFA ---

*DECK DNBFA
      SUBROUTINE DNBFA (ABE, LDA, N, ML, MU, IPVT, INFO)
C***BEGIN PROLOGUE  DNBFA
C***PURPOSE  Factor a band matrix by elimination.
C***LIBRARY   SLATEC
C***CATEGORY  D2A2
C***TYPE      DOUBLE PRECISION (SNBFA-S, DNBFA-D, CNBFA-C)
C***KEYWORDS  BANDED, LINEAR EQUATIONS, MATRIX FACTORIZATION,
C             NONSYMMETRIC
C***AUTHOR  Voorhees, E. A., (LANL)
C***DESCRIPTION
C
C     DNBFA factors a double precision band matrix by elimination.
C
C     DNBFA is usually called by DNBCO, but it can be called
C     directly with a saving in time if RCOND is not needed.
C
C     On Entry
C
C        ABE     DOUBLE PRECISION(LDA, NC)
C                contains the matrix in band storage.  The rows
C                of the original matrix are stored in the rows
C                of ABE and the diagonals of the original matrix
C                are stored in columns 1 through ML+MU+1 of ABE.
C                NC must be .GE. 2*ML+MU+1 .
C                See the comments below for details.
C
C        LDA     INTEGER
C                the leading dimension of the array ABE.
C                LDA must be .GE.  N .
C
C        N       INTEGER
C                the order of the original matrix.
C
C        ML      INTEGER
C                number of diagonals below the main diagonal.
C                0 .LE. ML .LT.  N .
C
C        MU      INTEGER
C                number of diagonals above the main diagonal.
C                0 .LE. MU .LT.  N .
C                More efficient if ML .LE. MU .
C
C     On Return
C
C        ABE     an upper triangular matrix in band storage
C                and the multipliers which were used to obtain it.
C                The factorization can be written  A = L*U  where
C                L is a product of permutation and unit lower
C                triangular matrices and  U  is upper triangular.
C
C        IPVT    INTEGER(N)
C                an integer vector of pivot indices.
C
C        INFO    INTEGER
C                =0  normal value
C                =K  if  U(K,K) .EQ. 0.0 .  This is not an error
C                condition for this subroutine, but it does
C                indicate that DNBSL will divide by zero if
C                called.  Use RCOND in DNBCO for a reliable
C                indication of singularity.
C
C     Band Storage
C
C           If  A  is a band matrix, the following program segment
C           will set up the input.
C
C                   ML = (band width below the diagonal)
C                   MU = (band width above the diagonal)
C                   DO 20 I = 1, N
C                      J1 = MAX(1, I-ML)
C                      J2 = MIN(N, I+MU)
C                      DO 10 J = J1, J2
C                         K = J - I + ML + 1
C                         ABE(I,K) = A(I,J)
C                10    CONTINUE
C                20 CONTINUE
C
C           This uses columns  1  through  ML+MU+1  of ABE .
C           Furthermore,  ML  additional columns are needed in
C           ABE  starting with column  ML+MU+2  for elements
C           generated during the triangularization.  The total
C           number of columns needed in  ABE  is  2*ML+MU+1 .
C
C     Example:  If the original matrix is
C
C           11 12 13  0  0  0
C           21 22 23 24  0  0
C            0 32 33 34 35  0
C            0  0 43 44 45 46
C            0  0  0 54 55 56
C            0  0  0  0 65 66
C
C      then  N = 6, ML = 1, MU = 2, LDA .GE. 5  and ABE should contain
C
C            * 11 12 13  +     , * = not used
C           21 22 23 24  +     , + = used for pivoting
C           32 33 34 35  +
C           43 44 45 46  +
C           54 55 56  *  +
C           65 66  *  *  +
C
C***REFERENCES  J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
C                 Stewart, LINPACK Users' Guide, SIAM, 1979.
C***ROUTINES CALLED  DAXPY, DSCAL, DSWAP, IDAMAX
C***REVISION HISTORY  (YYMMDD)
C   800728  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   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  DNBFA