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.