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LAPACK version 3.0
spbstf(3)

PURPOSE
  SPBSTF - compute a split Cholesky factorization of a real symmetric
  positive definite band matrix A

SYNTAX
  SUBROUTINE SPBSTF( UPLO, N, KD, AB, LDAB, INFO )

      CHARACTER	     UPLO

      INTEGER	     INFO, KD, LDAB, N

      REAL	     AB( LDAB, * )

DESCRIPTION
  SPBSTF computes a split Cholesky factorization of a real symmetric positive
  definite band matrix A.  This routine is designed to be used in conjunction
  with SSBGST.

  The factorization has the form  A = S**T*S  where S is a band matrix of the
  same bandwidth as A and the following structure:

    S = ( U    )
	( M  L )

  where U is upper triangular of order m = (n+kd)/2, and L is lower
  triangular of order n-m.

ARGUMENTS
  UPLO	  (input) CHARACTER*1
	  = 'U':  Upper triangle of A is stored;
	  = 'L':  Lower triangle of A is stored.

  N	  (input) INTEGER
	  The order of the matrix A.  N >= 0.

  KD	  (input) INTEGER
	  The number of superdiagonals of the matrix A if UPLO = 'U', or the
	  number of subdiagonals if UPLO = 'L'.	 KD >= 0.

  AB	  (input/output) REAL array, dimension (LDAB,N)
	  On entry, the upper or lower triangle of the symmetric band matrix
	  A, stored in the first kd+1 rows of the array.  The j-th column of
	  A is stored in the j-th column of the array AB as follows: if UPLO
	  = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO =
	  'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

	  On exit, if INFO = 0, the factor S from the split Cholesky
	  factorization A = S**T*S. See Further Details.  LDAB	  (input)
	  INTEGER The leading dimension of the array AB.  LDAB >= KD+1.

  INFO	  (output) INTEGER
	  = 0: successful exit
	  < 0: if INFO = -i, the i-th argument had an illegal value
	  > 0: if INFO = i, the factorization could not be completed, because
	  the updated element a(i,i) was negative; the matrix A is not
	  positive definite.

FURTHER DETAILS
  The band storage scheme is illustrated by the following example, when N =
  7, KD = 2:

  S = ( s11  s12  s13			  )
      (	     s22  s23  s24		  )
      (		  s33  s34		  )
      (		       s44		  )
      (		  s53  s54  s55		  )
      (		       s64  s65	 s66	  )
      (			    s75	 s76  s77 )

  If UPLO = 'U', the array AB holds:

  on entry:			     on exit:

   *	*   a13	 a24  a35  a46	a57   *	   *   s13  s24	 s53  s64  s75
   *   a12  a23	 a34  a45  a56	a67   *	  s12  s23  s34	 s54  s65  s76 a11
  a22  a33  a44	 a55  a66  a77	s11  s22  s33  s44  s55	 s66  s77

  If UPLO = 'L', the array AB holds:

  on entry:			     on exit:

  a11  a22  a33	 a44  a55  a66	a77  s11  s22  s33  s44	 s55  s66  s77 a21
  a32  a43  a54	 a65  a76   *	s12  s23  s34  s54  s65	 s76   * a31  a42
  a53  a64  a64	  *    *   s13	s24  s53  s64  s75   *	  *

  Array elements marked * are not used by the routine.