# SLAQTR (3) - Linux Man Pages

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