---
name: "dlaqr1"
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/dlaqr1.f"
---

# dlaqr1(3)

Part of [dlaqr1.f(3)](/dlaqr1.f/3.md).

## NAME

SRC/dlaqr1.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dlaqr1** (n, h, ldh, sr1, si1, sr2, si2, v)\
 **DLAQR1** sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

## Function/Subroutine Documentation

### subroutine dlaqr1 (integer n, double precision, dimension( ldh, \* ) h, integer ldh, double precision sr1, double precision si1, double precision sr2, double precision si2, double precision, dimension( \* ) v)

**DLAQR1** sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and specified shifts.

**Purpose:**

```
!>
!>      Given a 2-by-2 or 3-by-3 matrix H, DLAQR1 sets v to a
!>      scalar multiple of the first column of the product
!>
!>      (*)  K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)
!>
!>      scaling to avoid overflows and most underflows. It
!>      is assumed that either
!>
!>              1) sr1 = sr2 and si1 = -si2
!>          or
!>              2) si1 = si2 = 0.
!>
!>      This is useful for starting double implicit shift bulges
!>      in the QR algorithm.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>              Order of the matrix H. N must be either 2 or 3.
!>
```

*H*

```
!>          H is DOUBLE PRECISION array, dimension (LDH,N)
!>              The 2-by-2 or 3-by-3 matrix H in (*).
!>
```

*LDH*

```
!>          LDH is INTEGER
!>              The leading dimension of H as declared in
!>              the calling procedure.  LDH >= N
!>
```

*SR1*

```
!>          SR1 is DOUBLE PRECISION
!>
```

*SI1*

```
!>          SI1 is DOUBLE PRECISION
!>
```

*SR2*

```
!>          SR2 is DOUBLE PRECISION
!>
```

*SI2*

```
!>          SI2 is DOUBLE PRECISION
!>              The shifts in (*).
!>
```

*V*

```
!>          V is DOUBLE PRECISION array, dimension (N)
!>              A scalar multiple of the first column of the
!>              matrix K in (*).
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

Definition at line **120** of file **dlaqr1.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.