Library Functions Manual

NAME¶

laqtr - laqtr: quasi-triangular solve

SYNOPSIS¶

Functions¶

subroutine DLAQTR (ltran, lreal, n, t, ldt, b, w, scale, x, work, info)
DLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic. 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.

Detailed Description¶

Function Documentation¶

subroutine DLAQTR (logical ltran, logical lreal, integer n, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) b, double precision w, double precision scale, double precision, dimension( * ) x, double precision, dimension( * ) work, integer info)¶

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

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**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 DTRSNA.
!>

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

!>          T is 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

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

!>          B is 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 is DOUBLE PRECISION
!>          On entry, W is the diagonal element of the matrix B.
!>          If LREAL = .TRUE., W is not referenced.
!>

SCALE

!>          SCALE is DOUBLE PRECISION
!>          On exit, SCALE is the scale factor.
!>

!>          X is 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

!>          WORK is DOUBLE PRECISION 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 DLALN2 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.

Definition at line 163 of file dlaqtr.f.

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.