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man pages->IRIX man pages -> complib/slaqtr (3)
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### Contents

```
SLAQTR(3F)							    SLAQTR(3F)

```

### NAME[Toc][Back]

```     SLAQTR - solve the	real quasi-triangular system   op(T)*p = scale*c, if
LREAL = .TRUE
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SLAQTR(	LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO )

LOGICAL	LREAL, LTRAN

INTEGER	INFO, LDT, N

REAL		SCALE, W

REAL		B( * ),	T( LDT,	* ), WORK( * ),	X( * )
```

### PURPOSE[Toc][Back]

```     SLAQTR solves the real quasi-triangular system

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', A' denotes the conjugate 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.

```

### ARGUMENTS[Toc][Back]

```     LTRAN   (input) 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)'.

LREAL   (input) LOGICAL
On	entry, LREAL specifies the input matrix	structure:  = .FALSE.,
the input is complex = .TRUE.,	the input is real

Page 1

SLAQTR(3F)							    SLAQTR(3F)

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

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

B	     (input) 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	     (input) REAL
On	entry, W is the	diagonal element of the	matrix B.  If LREAL =
.TRUE., W is not referenced.

SCALE   (output) REAL
On	exit, SCALE is the scale factor.

X	     (input/output) 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    (workspace) REAL array, dimension (N)

INFO    (output) 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.
SLAQTR(3F)							    SLAQTR(3F)

```

### NAME[Toc][Back]

```     SLAQTR - solve the	real quasi-triangular system   op(T)*p = scale*c, if
LREAL = .TRUE
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SLAQTR(	LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO )

LOGICAL	LREAL, LTRAN

INTEGER	INFO, LDT, N

REAL		SCALE, W

REAL		B( * ),	T( LDT,	* ), WORK( * ),	X( * )
```

### PURPOSE[Toc][Back]

```     SLAQTR solves the real quasi-triangular system

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', A' denotes the conjugate 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.

```

### ARGUMENTS[Toc][Back]

```     LTRAN   (input) 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)'.

LREAL   (input) LOGICAL
On	entry, LREAL specifies the input matrix	structure:  = .FALSE.,
the input is complex = .TRUE.,	the input is real

Page 1

SLAQTR(3F)							    SLAQTR(3F)

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

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

B	     (input) 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	     (input) REAL
On	entry, W is the	diagonal element of the	matrix B.  If LREAL =
.TRUE., W is not referenced.

SCALE   (output) REAL
On	exit, SCALE is the scale factor.

X	     (input/output) 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    (workspace) REAL array, dimension (N)

INFO    (output) 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.

PPPPaaaaggggeeee 2222```
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