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# dlaqtr.f(3) [centos man page]

```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 (logicalLTRAN, logicalLREAL, integerN, double precision, dimension( ldt, * )T, integerLDT, double precision, dimension( * )B,
double precisionW, double precisionSCALE, double precision, dimension( * )X, double precision, dimension( * )WORK, integerINFO)
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

NAG Ltd.

Date:
September 2012

Definition at line 165 of file dlaqtr.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       dlaqtr.f(3)```

## Check Out this Related Man Page

```slaqtr.f(3)							      LAPACK							       slaqtr.f(3)

NAME
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

NAG Ltd.

Date:
September 2012

Definition at line 165 of file slaqtr.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       slaqtr.f(3)```