# dlaqtr

Langue: en

Version: 319386 (ubuntu - 07/07/09)

Section: 3 (Bibliothèques de fonctions)

# Sommaire

## NAME

DLAQTR - solve the real quasi-triangular system op(T)*p = scale*c, if LREAL = .TRUE

## SYNOPSIS

SUBROUTINE DLAQTR(
LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO )

LOGICAL LREAL, LTRAN

INTEGER INFO, LDT, N

DOUBLE PRECISION SCALE, W

DOUBLE PRECISION B( * ), T( LDT, * ), WORK( * ), X( * )

## PURPOSE

DLAQTR 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', A' denotes the conjugate 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 DTRSNA.

## ARGUMENTS

LTRAN (input) 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)'.
LREAL (input) LOGICAL
On entry, LREAL specifies the input matrix structure: = .FALSE., the input is complex = .TRUE., the input is real
N (input) INTEGER
On entry, N specifies the order of T+i*B. N >= 0.
T (input) DOUBLE PRECISION array, dimension (LDT,N)
On entry, T contains a matrix in Schur canonical form. If LREAL = .FALSE., then the first diagonal block of T mu be 1 by 1.
LDT (input) INTEGER
The leading dimension of the matrix T. LDT >= max(1,N).
B (input) DOUBLE PRECISION array, dimension (N)
On entry, B contains the elements to form the matrix B as described above. If LREAL = .TRUE., B is not referenced.
W (input) DOUBLE PRECISION
On entry, W is the diagonal element of the matrix B. If LREAL = .TRUE., W is not referenced.
SCALE (output) DOUBLE PRECISION
On exit, SCALE is the scale factor.
X (input/output) DOUBLE PRECISION array, dimension (2*N)
On entry, X contains the right hand side of the system. On exit, X is overwritten by the solution.
WORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) 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 DLALN2 to keep nonsingularity. NOTE: In the interests of speed, this routine does not check the inputs for errors.