slaqtr.f man page

slaqtr.f —

Synopsis

Functions/Subroutines

subroutine slaqtr (LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO)
SLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic.

Function/Subroutine Documentation

subroutine slaqtr (logicalLTRAN, logicalLREAL, integerN, real, dimension( ldt, * )T, integerLDT, real, dimension( * )B, realW, realSCALE, real, dimension( * )X, real, dimension( * )WORK, integerINFO)

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

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:

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.

LREAL

LREAL is LOGICAL
On entry, LREAL specifies the input matrix structure:
   = .FALSE.,    the input is complex
   = .TRUE.,     the input is real

N

N is INTEGER
On entry, N specifies the order of T+i*B. N >= 0.

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.

LDT

LDT is INTEGER
The leading dimension of the matrix T. LDT >= max(1,N).

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.

W

W is REAL
On entry, W is the diagonal element of the matrix B.
If LREAL = .TRUE., W is not referenced.

SCALE

SCALE is REAL
On exit, SCALE is the scale factor.

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.

WORK

WORK is REAL array, dimension (N)

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.

Date:

September 2012

Definition at line 165 of file slaqtr.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

slaqtr(3) is an alias of slaqtr.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK