slaqtr()

subroutine slaqtr	(	logical	ltran,
		logical	lreal,
		integer	n,
		real, dimension( ldt, * )	t,
		integer	ldt,
		real, dimension( * )	b,
		real	w,
		real	scale,
		real, dimension( * )	x,
		real, dimension( * )	work,
		integer	info )

SLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic.

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Purpose:

!>
!> SLAQTR solves the real quasi-triangular system
!>
!>              op(T)*p = scale*c,               if LREAL = .TRUE.
!>
!> or the complex quasi-triangular systems
!>
!>            op(T + iB)*(p+iq) = scale*(c+id),  if LREAL = .FALSE.
!>
!> in real arithmetic, where T is upper quasi-triangular.
!> If LREAL = .FALSE., then the first diagonal block of T must be
!> 1 by 1, B is the specially structured matrix
!>
!>                B = [ b(1) b(2) ... b(n) ]
!>                    [       w            ]
!>                    [           w        ]
!>                    [              .     ]
!>                    [                 w  ]
!>
!> op(A) = A or A**T, A**T denotes the transpose of
!> matrix A.
!>
!> On input, X = [ c ].  On output, X = [ p ].
!>               [ d ]                  [ q ]
!>
!> This subroutine is designed for the condition number estimation
!> in routine STRSNA.
!> 

Parameters

[in]	LTRAN	!> LTRAN is LOGICAL !> On entry, LTRAN specifies the option of conjugate transpose: !> = .FALSE., op(T+i*B) = T+i*B, !> = .TRUE., op(T+i*B) = (T+i*B)**T. !>
[in]	LREAL	!> LREAL is LOGICAL !> On entry, LREAL specifies the input matrix structure: !> = .FALSE., the input is complex !> = .TRUE., the input is real !>
[in]	N	!> N is INTEGER !> On entry, N specifies the order of T+i*B. N >= 0. !>
[in]	T	!> T is REAL array, dimension (LDT,N) !> On entry, T contains a matrix in Schur canonical form. !> If LREAL = .FALSE., then the first diagonal block of T must !> be 1 by 1. !>
[in]	LDT	!> LDT is INTEGER !> The leading dimension of the matrix T. LDT >= max(1,N). !>
[in]	B	!> B is REAL array, dimension (N) !> On entry, B contains the elements to form the matrix !> B as described above. !> If LREAL = .TRUE., B is not referenced. !>
[in]	W	!> W is REAL !> On entry, W is the diagonal element of the matrix B. !> If LREAL = .TRUE., W is not referenced. !>
[out]	SCALE	!> SCALE is REAL !> On exit, SCALE is the scale factor. !>
[in,out]	X	!> X is REAL array, dimension (2*N) !> On entry, X contains the right hand side of the system. !> On exit, X is overwritten by the solution. !>
[out]	WORK	!> WORK is REAL array, dimension (N) !>
[out]	INFO	!> INFO is INTEGER !> On exit, INFO is set to !> 0: successful exit. !> 1: the some diagonal 1 by 1 block has been perturbed by !> a small number SMIN to keep nonsingularity. !> 2: the some diagonal 2 by 2 block has been perturbed by !> a small number in SLALN2 to keep nonsingularity. !> NOTE: In the interests of speed, this routine does not !> check the inputs for errors. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.