The R Project SVN R

      subroutine dpbfa(abd,lda,n,m,info)

      implicit none
      integer lda,n,m,info
      double precision abd(lda,n)
c
c     dpbfa factors a double precision symmetric positive definite
c     matrix stored in band form.
c
c     dpbfa is usually called by dpbco, 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        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
c    info    integer
c        = 0  for normal return.
c        = k  if the leading minor of order  k  is not
c             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     linpack.  this version dated 08/14/78 .
c     cleve moler, university of new mexico, argonne national lab.
c
c     subroutines and functions
c
c     blas ddot
c     fortran max0,sqrt
c
c     internal variables
c
      double precision ddot,t
      double precision s
      integer ik,j,jk,k,mu
c     begin block with ...exits to 40
c
c
     do 30 j = 1, n
        info = j
        s = 0.0e0
        ik = m + 1
        jk = max0(j-m,1)
        mu = max0(m+2-j,1)
        if (m .lt. mu) go to 20
        do 10 k = mu, m

           t = abd(k,j) - ddot(k-mu,abd(ik,jk),1,abd(mu,j),1)
           t = t/abd(m+1,jk)
           abd(k,j) = t
           s = s + t*t
           ik = ik - 1
           jk = jk + 1
   10       continue
   20       continue

        s = abd(m+1,j) - s
c     ......exit
        if (s .le. 0.0e0) go to 40

        abd(m+1,j) = sqrt(s)

   30    continue
     info = 0
   40 continue
      return
      end