spbt01()

subroutine spbt01	(	character	UPLO,
		integer	N,
		integer	KD,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldafac, * )	AFAC,
		integer	LDAFAC,
		real, dimension( * )	RWORK,
		real	RESID
	)

SPBT01

Purpose:

 SPBT01 reconstructs a symmetric positive definite band matrix A from
 its L*L' or U'*U factorization and computes the residual
    norm( L*L' - A ) / ( N * norm(A) * EPS ) or
    norm( U'*U - A ) / ( N * norm(A) * EPS ),
 where EPS is the machine epsilon, L' is the conjugate transpose of
 L, and U' is the conjugate transpose of U.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	KD	KD is INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
[in]	A	A is REAL array, dimension (LDA,N) The original symmetric band matrix A. If UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. The columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. See SPBTRF for further details.
[in]	LDA	LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).
[in]	AFAC	AFAC is REAL array, dimension (LDAFAC,N) The factored form of the matrix A. AFAC contains the factor L or U from the L*L' or U'*U factorization in band storage format, as computed by SPBTRF.
[in]	LDAFAC	LDAFAC is INTEGER The leading dimension of the array AFAC. LDAFAC >= max(1,KD+1).
[out]	RWORK	RWORK is REAL array, dimension (N)
[out]	RESID	RESID is REAL If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ) If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.