 
      SUBROUTINE DNBCO(ABE,LDA,N,ML,MU,IPVT,RCOND,Z)
C***BEGIN PROLOGUE  DNBCO
C***DATE WRITTEN   800728   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  D2A2
C***KEYWORDS  BAND,DOUBLE PRECISION,LINEAR EQUATIONS,NONSYMMETRIC
C***AUTHOR  VOORHEES, E., (LANL)
C***PURPOSE  Factors a double precision BAND matrix by Gaussian
C            elimination and estimates the condition of the matrix.
C***DESCRIPTION
C
C     DNBCO factors a double precision band matrix by Gaussian
C     elimination and estimates the condition of the matrix.
C
C     If RCOND is not needed, DNBFA is slightly faster.
C     To solve  A*X = B , follow DNBCO by DNBSL.
C     To compute  INVERSE(A)*C , follow DNBCO by DNBSL.
C     To compute  DETERMINANT(A) , follow DNBCO by DNBDI.
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        RCOND   DOUBLE PRECISION
C                an estimate of the reciprocal condition of  A .
C                For the system  A*X = B , relative perturbations
C                in  A  and  B  of size  EPSILON  may cause
C                relative perturbations in  X  of size  EPSILON/RCOND .
C                If  RCOND  is so small that the logical expression
C                         1.0 + RCOND .EQ. 1.0
C                is true, then  A  may be singular to working
C                precision.  In particular,  RCOND  is zero  if
C                exact singularity is detected or the estimate
C                underflows.
C
C        Z       DOUBLE PRECISION(N)
C                a work vector whose contents are usually unimportant.
C                If  A  is close to a singular matrix, then  Z  is
C                an approximate null vector in the sense that
C                NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
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 = MAX0(1, I-ML)
C                      J2 = MIN0(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     SLATEC.  This version dated 07/28/80 .
C     E. A. Voorhees, Los Alamos Scientific Laboratory
C
C     Subroutines and Functions
C
C     SLATEC DNBFA
C      DDOT,DAXPY,DSCAL,DASUM
C     Fortran  DABS,DMAX1,MAX0,MIN0,DSIGN
C***REFERENCES  SUBROUTINE DNBCO WAS DEVELOPED BY GROUP C-3, LOS ALAMOS
C                 SCIENTIFIC LABORATORY, LOS ALAMOS, NM 87545.
C***ROUTINES CALLED  DASUM,DAXPY,DDOT,DNBFA,DSCAL
C***END PROLOGUE  DNBCO
 
 
