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SPBTRF(l)					)					SPBTRF(l)

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




	   REAL 	  AB( LDAB, * )

       SPBTRF 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.

       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 sub-
	       diagonals 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 col-
	       umn 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 Cholesky 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.

       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

LAPACK version 3.0			   15 June 2000 				SPBTRF(l)
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