# dlaqtr.f man page

dlaqtr.f —

## Synopsis

### Functions/Subroutines

subroutinedlaqtr(LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK, INFO)DLAQTRsolves 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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 165 of file dlaqtr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

dlaqtr(3) is an alias of dlaqtr.f(3).