spbtrf()

subroutine spbtrf	(	character	uplo,
		integer	n,
		integer	kd,
		real, dimension( ldab, * )	ab,
		integer	ldab,
		integer	info )

SPBTRF

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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

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	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. !>
[in,out]	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. !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !>
[out]	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 principal minor of order i !> is not positive, and the factorization could not be !> completed. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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