SLATEC Routines --- DGBFA ---

*DECK DGBFA
      SUBROUTINE DGBFA (ABD, LDA, N, ML, MU, IPVT, INFO)
C***BEGIN PROLOGUE  DGBFA
C***PURPOSE  Factor a band matrix using Gaussian elimination.
C***LIBRARY   SLATEC (LINPACK)
C***CATEGORY  D2A2
C***TYPE      DOUBLE PRECISION (SGBFA-S, DGBFA-D, CGBFA-C)
C***KEYWORDS  BANDED, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION
C***AUTHOR  Moler, C. B., (U. of New Mexico)
C***DESCRIPTION
C
C     DGBFA factors a double precision band matrix by elimination.
C
C     DGBFA is usually called by DGBCO, but it can be called
C     directly with a saving in time if  RCOND  is not needed.
C
C     On Entry
C
C        ABD     DOUBLE PRECISION(LDA, N)
C                contains the matrix in band storage.  The columns
C                of the matrix are stored in the columns of  ABD  and
C                the diagonals of the matrix are stored in rows
C                ML+1 through 2*ML+MU+1 of  ABD .
C                See the comments below for details.
C
C        LDA     INTEGER
C                the leading dimension of the array  ABD .
C                LDA must be .GE. 2*ML + MU + 1 .
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     On Return
C
C        ABD     an upper triangular matrix in band storage and
C                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 DGBSL will divide by zero if
C                     called.  Use  RCOND  in DGBCO 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                   M = ML + MU + 1
C                   DO 20 J = 1, N
C                      I1 = MAX(1, J-MU)
C                      I2 = MIN(N, J+ML)
C                      DO 10 I = I1, I2
C                         K = I - J + M
C                         ABD(K,J) = A(I,J)
C                10    CONTINUE
C                20 CONTINUE
C
C           This uses rows  ML+1  through  2*ML+MU+1  of  ABD .
C           In addition, the first  ML  rows in  ABD  are used for
C           elements generated during the triangularization.
C           The total number of rows needed in  ABD  is  2*ML+MU+1 .
C           The  ML+MU by ML+MU  upper left triangle and the
C           ML by ML  lower right triangle are not referenced.
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, IDAMAX
C***REVISION HISTORY  (YYMMDD)
C   780814  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   900326  Removed duplicate information from DESCRIPTION section.
C           (WRB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  DGBFA