---
name: "claein"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/claein/3lapack"
---

# claein(3lapack)

uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H

## NAME

CLAEIN - uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H

## SYNOPSIS

- SUBROUTINE CLAEIN(

  RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3, SMLNUM, INFO )

- LOGICAL

  NOINIT, RIGHTV

- INTEGER

  INFO, LDB, LDH, N

- REAL

  EPS3, SMLNUM

- COMPLEX

  W

- REAL

  RWORK( \* )

- COMPLEX

  B( LDB, \* ), H( LDH, \* ), V( \* )

## PURPOSE

CLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H.

## ARGUMENTS

- RIGHTV (input) LOGICAL

  \= .TRUE. : compute right eigenvector;\
   \= .FALSE.: compute left eigenvector.

- NOINIT (input) LOGICAL

  \= .TRUE. : no initial vector supplied in V\
   \= .FALSE.: initial vector supplied in V.

- N (input) INTEGER

  The order of the matrix H.  N \>= 0.

- H (input) COMPLEX array, dimension (LDH,N)

  The upper Hessenberg matrix H.

- LDH (input) INTEGER

  The leading dimension of the array H.  LDH \>= max(1,N).

- W (input) COMPLEX

  The eigenvalue of H whose corresponding right or left eigenvector is to be computed.

- V (input/output) COMPLEX 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 (workspace) COMPLEX array, dimension (LDB,N)

  - LDB (input) INTEGER

  The leading dimension of the array B.  LDB \>= max(1,N).

- RWORK (workspace) REAL array, dimension (N)

  - EPS3 (input) REAL

  A small machine-dependent value which is used to perturb close eigenvalues, and to replace zero pivots.

- SMLNUM (input) REAL

  A machine-dependent value close to the underflow threshold.

- INFO (output) INTEGER

  \= 0:  successful exit\
   \= 1:  inverse iteration did not converge; V is set to the last iterate.