---
name: "zlaein.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/zlaein.f"
---

# zlaein.f(3)

## NAME

SRC/zlaein.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zlaein** (rightv, noinit, n, h, ldh, w, v, b, ldb, rwork, eps3, smlnum, info)\
 **ZLAEIN** computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

## Function/Subroutine Documentation

### subroutine zlaein (logical rightv, logical noinit, integer n, complex\*16, dimension( ldh, \* ) h, integer ldh, complex\*16 w, complex\*16, dimension( \* ) v, complex\*16, dimension( ldb, \* ) b, integer ldb, double precision, dimension( \* ) rwork, double precision eps3, double precision smlnum, integer info)

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

**Purpose:**

```
!>
!> ZLAEIN uses inverse iteration to find a right or left eigenvector
!> corresponding to the eigenvalue W of a complex 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 V
!>          = .FALSE.: initial vector supplied in V.
!>
```

*N*

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

*H*

```
!>          H is COMPLEX*16 array, dimension (LDH,N)
!>          The upper Hessenberg matrix H.
!>
```

*LDH*

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

*W*

```
!>          W is COMPLEX*16
!>          The eigenvalue of H whose corresponding right or left
!>          eigenvector is to be computed.
!>
```

*V*

```
!>          V is COMPLEX*16 array, dimension (N)
!>          On entry, if NOINIT = .FALSE., V must contain a starting
!>          vector for inverse iteration; otherwise V need not be set.
!>          On exit, V contains the computed eigenvector, 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|.
!>
```

*B*

```
!>          B is COMPLEX*16 array, dimension (LDB,N)
!>
```

*LDB*

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

*RWORK*

```
!>          RWORK 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.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          = 1:  inverse iteration did not converge; V is set to the
!>                last iterate.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **147** of file **zlaein.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.