slaein (l)  Linux Man Pages
slaein: uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
Command to display slaein
manual in Linux: $ man l slaein
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 machinedependent value which is used to perturb
close eigenvalues, and to replace zero pivots.
 SMLNUM (input) REAL

A machinedependent value close to the underflow threshold.
 BIGNUM (input) REAL

A machinedependent 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.
Pages related to slaein
 slaein (3)
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 slaebz (l)  contains the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
 slaed0 (l)  computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
 slaed1 (l)  computes the updated eigensystem of a diagonal matrix after modification by a rankone symmetric matrix
 slaed2 (l)  merges the two sets of eigenvalues together into a single sorted set
 slaed3 (l)  finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
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