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spbtrf.f(3)				      LAPACK				      spbtrf.f(3)

NAME
       spbtrf.f -

SYNOPSIS
   Functions/Subroutines
       subroutine spbtrf (UPLO, N, KD, AB, LDAB, INFO)
	   SPBTRF

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

       Purpose:

	    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.

       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 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

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

       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 = 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.

       Contributors:
	   Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

       Definition at line 143 of file spbtrf.f.

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

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