LAPACK

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.

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.