```DPBTRF(l)		LAPACK routine (version	1.1)		    DPBTRF(l)

NAME
DPBTRF - compute the Cholesky	factorization of a real	symmetric positive
definite band	matrix A

SYNOPSIS

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

CHARACTER	     UPLO

INTEGER	     INFO, KD, LDAB, N

DOUBLE	     PRECISION AB( LDAB, * )

PURPOSE
DPBTRF computes the Cholesky factorization of	a real symmetric positive
definite band	matrix A.

The factorization has	the form
A = U**T *	U,  if UPLO = 'U', or
A = L  * L**T,  if	UPLO = 'L',
where	U is an	upper triangular matrix	and L is lower triangular.

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) 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 triangular factor U	or L from the Chole-
sky factorization A =	U**T*U or A = L*L**T of	the band matrix	A, in
the same storage format as A.

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 leading minor of order	i is not positive
definite, and	the factorization could	not be completed.

FURTHER	DETAILS
The band storage scheme is illustrated by the	following example, when	N =
6, KD	= 2, and UPLO =	'U':

On entry:			  On exit:

*	   *   a13  a24	 a35  a46      *    *	u13  u24  u35  u46
*	  a12  a23  a34	 a45  a56      *   u12	u23  u34  u45  u56
a11  a22  a33  a44	 a55  a66     u11  u22	u33  u44  u55  u66

Similarly, if	UPLO = 'L' the format of A is as follows:

On entry:			  On exit:

a11  a22  a33  a44	 a55  a66     l11  l22	l33  l44  l55  l66
a21  a32  a43  a54	 a65   *      l21  l32	l43  l54  l65	*
a31  a42  a53  a64	  *    *      l31  l42	l53  l64   *	*

Array	elements marked	* are not used by the routine.

Contributed by
Peter	Mayes and Giuseppe Radicati, IBM ECSEC,	Rome, March 23,	1989

```

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