---
name: "dlaqtr.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/dlaqtr.f"
---

# dlaqtr.f(3)

## NAME

SRC/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 (logical ltran, logical lreal, integer n, double precision, dimension( ldt, \* ) t, integer ldt, double precision, dimension( \* ) b, double precision w, double precision scale, double precision, dimension( \* ) x, double precision, dimension( \* ) work, integer info)

**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.

Definition at line **163** of file **dlaqtr.f**.

## Author

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