---
name: "dlaein.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/dlaein.f"
---

# dlaein.f(3)

## NAME

SRC/dlaein.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dlaein** (rightv, noinit, n, h, ldh, wr, wi, vr, vi, b, ldb, work, eps3, smlnum, bignum, info)\
 **DLAEIN** computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

## Function/Subroutine Documentation

### subroutine dlaein (logical rightv, logical noinit, integer n, double precision, dimension( ldh, \* ) h, integer ldh, double precision wr, double precision wi, double precision, dimension( \* ) vr, double precision, dimension( \* ) vi, double precision, dimension( ldb, \* ) b, integer ldb, double precision, dimension( \* ) work, double precision eps3, double precision smlnum, double precision bignum, integer info)

**DLAEIN** computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

**Purpose:**

```
!>
!> DLAEIN uses inverse iteration to find a right or left eigenvector
!> corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg
!> matrix H.
!>
```

**Parameters**

*RIGHTV*

```
!>          RIGHTV is LOGICAL
!>          = .TRUE. : compute right eigenvector;
!>          = .FALSE.: compute left eigenvector.
!>
```

*NOINIT*

```
!>          NOINIT is LOGICAL
!>          = .TRUE. : no initial vector supplied in (VR,VI).
!>          = .FALSE.: initial vector supplied in (VR,VI).
!>
```

*N*

```
!>          N is INTEGER
!>          The order of the matrix H.  N >= 0.
!>
```

*H*

```
!>          H is DOUBLE PRECISION array, dimension (LDH,N)
!>          The upper Hessenberg matrix H.
!>
```

*LDH*

```
!>          LDH is INTEGER
!>          The leading dimension of the array H.  LDH >= max(1,N).
!>
```

*WR*

```
!>          WR is DOUBLE PRECISION
!>
```

*WI*

```
!>          WI is DOUBLE PRECISION
!>          The real and imaginary parts of the eigenvalue of H whose
!>          corresponding right or left eigenvector is to be computed.
!>
```

*VR*

```
!>          VR is DOUBLE PRECISION array, dimension (N)
!>
```

*VI*

```
!>          VI is DOUBLE PRECISION array, dimension (N)
!>          On entry, if NOINIT = .FALSE. and WI = 0.0, VR must contain
!>          a real starting vector for inverse iteration using the real
!>          eigenvalue WR; if NOINIT = .FALSE. and WI.ne.0.0, VR and VI
!>          must contain the real and imaginary parts of a complex
!>          starting vector for inverse iteration using the complex
!>          eigenvalue (WR,WI); otherwise VR and VI need not be set.
!>          On exit, if WI = 0.0 (real eigenvalue), VR contains the
!>          computed real eigenvector; if WI.ne.0.0 (complex eigenvalue),
!>          VR and VI contain the real and imaginary parts of the
!>          computed complex eigenvector. The eigenvector is normalized
!>          so that the component of largest magnitude has magnitude 1;
!>          here the magnitude of a complex number (x,y) is taken to be
!>          |x| + |y|.
!>          VI is not referenced if WI = 0.0.
!>
```

*B*

```
!>          B is DOUBLE PRECISION array, dimension (LDB,N)
!>
```

*LDB*

```
!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= N+1.
!>
```

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (N)
!>
```

*EPS3*

```
!>          EPS3 is DOUBLE PRECISION
!>          A small machine-dependent value which is used to perturb
!>          close eigenvalues, and to replace zero pivots.
!>
```

*SMLNUM*

```
!>          SMLNUM is DOUBLE PRECISION
!>          A machine-dependent value close to the underflow threshold.
!>
```

*BIGNUM*

```
!>          BIGNUM is DOUBLE PRECISION
!>          A machine-dependent value close to the overflow threshold.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          = 1:  inverse iteration did not converge; VR is set to the
!>                last iterate, and so is VI if WI.ne.0.0.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **170** of file **dlaein.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.