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spbstf.f(3)				      LAPACK				      spbstf.f(3)

NAME
       spbstf.f -

SYNOPSIS
   Functions/Subroutines
       subroutine spbstf (UPLO, N, KD, AB, LDAB, INFO)
	   SPBSTF

Function/Subroutine Documentation
   subroutine spbstf (characterUPLO, integerN, integerKD, real, dimension( ldab, * )AB,
       integerLDAB, integerINFO)
       SPBSTF

       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.

       Parameters:
	   UPLO

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

	   N

		     N is INTEGER
		     The order of the matrix A.  N >= 0.

	   KD

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

	   AB

		     AB is 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

		     LDAB is INTEGER
		     The leading dimension of the array AB.  LDAB >= KD+1.

	   INFO

		     INFO is 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       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.

       Definition at line 153 of file spbstf.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      spbstf.f(3)
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