SPBFA(3F)

NAME
     SPBFA   - SPBFA factors a real symmetric positive definite matrix stored
     in band form.

     SPBFA is usually called by SPBCO, but it can be called directly with a
     saving in time if  RCOND  is not needed.


SYNOPSYS
      SUBROUTINE SPBFA(ABD,LDA,N,M,INFO)

DESCRIPTION
     On Entry

     ABD REAL(LDA, N)
        the matrix to be factored.  The columns of the upper
        triangle are stored in the columns of ABD and the
        diagonals of the upper triangle are stored in the
        rows of ABD .  See the comments below for details.

     LDA INTEGER
        the leading dimension of the array  ABD .
        LDA must be .GE. M + 1 .

     N INTEGER
        the order of the matrix  A .

     M INTEGER
        the number of diagonals above the main diagonal.
        0 .LE. M .LT. N .  On Return

     ABD an upper triangular matrix  R , stored in band
        form, so that  A = TRANS(R)*R .

     INFO INTEGER
        = 0  for normal return.
        = K  if the leading minor of order  K  is not
        positive definite.  Band Storage
        If  A  is a symmetric positive definite band matrix,
        the following program segment will set up the input.
        M = (band width above diagonal)
        DO 20 J = 1, N
        I1 = MAX0(1, J-M)
        DO 10 I = I1, J
        K = I-J+M+1
        ABD(K,J) = A(I,J)
        10    CONTINUE
        20 CONTINUE LINPACK.  This version dated 08/14/78 .  Cleve Moler,
     University of New Mexico, Argonne National Lab.  Subroutines and
     Functions BLAS SDOT Fortran MAX0,SQRT