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

# slaein(3lapack)

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

## NAME

SLAEIN - uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H

## SYNOPSIS

- SUBROUTINE SLAEIN(

  RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO )

- LOGICAL

  NOINIT, RIGHTV

- INTEGER

  INFO, LDB, LDH, N

- REAL

  BIGNUM, EPS3, SMLNUM, WI, WR

- REAL

  B( LDB, \* ), H( LDH, \* ), VI( \* ), VR( \* ), WORK( \* )

## PURPOSE

SLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real 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 (VR,VI).\
   \= .FALSE.: initial vector supplied in (VR,VI).

- N (input) INTEGER

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

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

  The upper Hessenberg matrix H.

- LDH (input) INTEGER

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

- WR (input) REAL

  WI      (input) REAL The real and imaginary parts of the eigenvalue of H whose corresponding right or left eigenvector is to be computed.

- VR (input/output) REAL array, dimension (N)

  VI      (input/output) REAL 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 (workspace) REAL array, dimension (LDB,N)

  - LDB (input) INTEGER

  The leading dimension of the array B.  LDB \>= N+1.

- WORK (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.

- BIGNUM (input) REAL

  A machine-dependent value close to the overflow threshold.

- INFO (output) 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.