# claein.f - Man Page

SRC/claein.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine claein (logical rightv, logical noinit, integer n, complex, dimension( ldh, * ) h, integer ldh, complex w, complex, dimension( * ) v, complex, dimension( ldb, * ) b, integer ldb, real, dimension( * ) rwork, real eps3, real smlnum, integer info)

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

**Purpose:**

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

*V*V is 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*B is COMPLEX array, dimension (LDB,N)

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

*RWORK*RWORK is REAL array, dimension (N)

*EPS3*EPS3 is REAL A small machine-dependent value which is used to perturb close eigenvalues, and to replace zero pivots.

*SMLNUM*SMLNUM is REAL 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 **claein.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page claein(3) is an alias of claein.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK