# slaein.f - Man Page

SRC/slaein.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

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

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

**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.

**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 REAL 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 REAL

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

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

*VI*VI is 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*B is REAL array, dimension (LDB,N)

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

*WORK*WORK 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.

*BIGNUM*BIGNUM is REAL 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 **slaein.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK