.TH "SRC/slaqtr.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/slaqtr.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBslaqtr\fP (ltran, lreal, n, t, ldt, b, w, scale, x, work, info)"
.br
.RI "\fBSLAQTR\fP solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "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)"

.PP
\fBSLAQTR\fP solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fILTRAN\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILREAL\fP 
.PP
.nf
!>          LREAL is LOGICAL
!>          On entry, LREAL specifies the input matrix structure:
!>             = \&.FALSE\&.,    the input is complex
!>             = \&.TRUE\&.,     the input is real
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          On entry, N specifies the order of T+i*B\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the matrix T\&. LDT >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          W is REAL
!>          On entry, W is the diagonal element of the matrix B\&.
!>          If LREAL = \&.TRUE\&., W is not referenced\&.
!> 
.fi
.PP
.br
\fISCALE\fP 
.PP
.nf
!>          SCALE is REAL
!>          On exit, SCALE is the scale factor\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (N)
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB163\fP of file \fBslaqtr\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.