 
      SUBROUTINE SPBCO(ABD,LDA,N,M,RCOND,Z,INFO)
C***BEGIN PROLOGUE  SPBCO
C***DATE WRITTEN   780814   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  D2B2
C***KEYWORDS  BANDED,CONDITION,FACTOR,LINEAR ALGEBRA,LINPACK,MATRIX,
C             POSITIVE DEFINITE
C***AUTHOR  MOLER, C. B., (U. OF NEW MEXICO)
C***PURPOSE  Factors a real SYMMETRIC POSITIVE DEFINITE matrix (band
C            form) and estimates the condition of the matrix.
C***DESCRIPTION
C
C     SPBCO factors a real symmetric positive definite matrix
C     stored in band form and estimates the condition of the matrix.
C
C     If  RCOND  is not needed, SPBFA is slightly faster.
C     To solve  A*X = B , follow SPBCO by SPBSL.
C     To compute  INVERSE(A)*C , follow SPBCO by SPBSL.
C     To compute  DETERMINANT(A) , follow SPBCO by SPBDI.
C
C     On Entry
C
C        ABD     REAL(LDA, N)
C                the matrix to be factored.  The columns of the upper
C                triangle are stored in the columns of ABD and the
C                diagonals of the upper triangle are stored in the
C                rows of ABD .  See the comments below for details.
C
C        LDA     INTEGER
C                the leading dimension of the array  ABD .
C                LDA must be .GE. M + 1 .
C
C        N       INTEGER
C                the order of the matrix  A .
C
C        M       INTEGER
C                the number of diagonals above the main diagonal.
C                0 .LE. M .LT. N .
C
C     On Return
C
C        ABD     an upper triangular matrix  R , stored in band
C                form, so that  A = TRANS(R)*R .
C                If  INFO .NE. 0 , the factorization is not complete.
C
C        RCOND   REAL
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.  If INFO .NE. 0 , RCOND is unchanged.
C
C        Z       REAL(N)
C                a work vector whose contents are usually unimportant.
C                If  A  is singular to working precision, then  Z  is
C                an approximate null vector in the sense that
C                NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
C                If  INFO .NE. 0 , Z  is unchanged.
C
C        INFO    INTEGER
C                = 0  for normal return.
C                = K  signals an error condition.  The leading minor
C                     of order  K  is not positive definite.
C
C     Band Storage
C
C           If  A  is a symmetric positive definite band matrix,
C           the following program segment will set up the input.
C
C                   M = (band width above diagonal)
C                   DO 20 J = 1, N
C                      I1 = MAX0(1, J-M)
C                      DO 10 I = I1, J
C                         K = I-J+M+1
C                         ABD(K,J) = A(I,J)
C                10    CONTINUE
C                20 CONTINUE
C
C           This uses  M + 1  rows of  A , except for the  M by M
C           upper left triangle, which is ignored.
C
C     Example:  If the original matrix is
C
C           11 12 13  0  0  0
C           12 22 23 24  0  0
C           13 23 33 34 35  0
C            0 24 34 44 45 46
C            0  0 35 45 55 56
C            0  0  0 46 56 66
C
C     then  N = 6 , M = 2  and  ABD  should contain
C
C            *  * 13 24 35 46
C            * 12 23 34 45 56
C           11 22 33 44 55 66
C
C     LINPACK.  This version dated 08/14/78 .
C     Cleve Moler, University of New Mexico, Argonne National Lab.
C
C     Subroutines and Functions
C
C     LINPACK SPBFA
C     BLAS SAXPY,SDOT,SSCAL,SASUM
C     Fortran ABS,AMAX1,MAX0,MIN0,REAL,SIGN
C***REFERENCES  DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W.,
C                 *LINPACK USERS  GUIDE*, SIAM, 1979.
C***ROUTINES CALLED  SASUM,SAXPY,SDOT,SPBFA,SSCAL
C***END PROLOGUE  SPBCO
 
 
