SPBSTF(l)								 )								 SPBSTF(l)

NAME

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

SYNOPSIS

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

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, N

	   REAL 	  AB( LDAB, * )

PURPOSE

       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.

LAPACK version 3.0						   15 June 2000 							 SPBSTF(l)