sla_gbrcond()

real function sla_gbrcond	(	character	trans,
		integer	n,
		integer	kl,
		integer	ku,
		real, dimension( ldab, * )	ab,
		integer	ldab,
		real, dimension( ldafb, * )	afb,
		integer	ldafb,
		integer, dimension( * )	ipiv,
		integer	cmode,
		real, dimension( * )	c,
		integer	info,
		real, dimension( * )	work,
		integer, dimension( * )	iwork )

SLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

Download SLA_GBRCOND + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!>    SLA_GBRCOND Estimates the Skeel condition number of  op(A) * op2(C)
!>    where op2 is determined by CMODE as follows
!>    CMODE =  1    op2(C) = C
!>    CMODE =  0    op2(C) = I
!>    CMODE = -1    op2(C) = inv(C)
!>    The Skeel condition number  cond(A) = norminf( |inv(A)||A| )
!>    is computed by computing scaling factors R such that
!>    diag(R)*A*op2(C) is row equilibrated and computing the standard
!>    infinity-norm condition number.
!> 

Parameters

[in]	TRANS	!> TRANS is CHARACTER*1 !> Specifies the form of the system of equations: !> = 'N': A * X = B (No transpose) !> = 'T': A**T * X = B (Transpose) !> = 'C': A**H * X = B (Conjugate Transpose = Transpose) !>
[in]	N	!> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !>
[in]	KL	!> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !>
[in]	KU	!> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !>
[in]	AB	!> AB is REAL array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !>
[in]	AFB	!> AFB is REAL array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by SGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1. !>
[in]	LDAFB	!> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. !>
[in]	IPIV	!> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by SGBTRF; row i of the matrix was interchanged !> with row IPIV(i). !>
[in]	CMODE	!> CMODE is INTEGER !> Determines op2(C) in the formula op(A) * op2(C) as follows: !> CMODE = 1 op2(C) = C !> CMODE = 0 op2(C) = I !> CMODE = -1 op2(C) = inv(C) !>
[in]	C	!> C is REAL array, dimension (N) !> The vector C in the formula op(A) * op2(C). !>
[out]	INFO	!> INFO is INTEGER !> = 0: Successful exit. !> i > 0: The ith argument is invalid. !>
[out]	WORK	!> WORK is REAL array, dimension (5*N). !> Workspace. !>
[out]	IWORK	!> IWORK is INTEGER array, dimension (N). !> Workspace. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.