dpbstf.f(3)							      LAPACK							       dpbstf.f(3)

NAME

       dpbstf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dpbstf (UPLO, N, KD, AB, LDAB, INFO)
	   DPBSTF

Function/Subroutine Documentation
   subroutine dpbstf (characterUPLO, integerN, integerKD, double precision, dimension( ldab, * )AB, integerLDAB, integerINFO)
       DPBSTF

       Purpose:

	    DPBSTF computes a split Cholesky factorization of a real
	    symmetric positive definite band matrix A.

	    This routine is designed to be used in conjunction with DSBGST.

	    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 DOUBLE PRECISION 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 dpbstf.f.

Author
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Version 3.4.1							  Sun May 26 2013						       dpbstf.f(3)