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dlaqtr.f(3) LAPACK dlaqtr.f(3)

NAME

dlaqtr.f

SYNOPSIS

Functions/Subroutines


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.

Function/Subroutine 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



          N is INTEGER


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

T



          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



          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



          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



          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.

Date:

December 2016

Definition at line 167 of file dlaqtr.f.

Author

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