dlaein (l)  Linux Man Pages
dlaein: 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 dlaein
manual in Linux: $ man l dlaein
NAME
DLAEIN  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 DLAEIN(

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

LOGICAL
NOINIT, RIGHTV

INTEGER
INFO, LDB, LDH, N

DOUBLE
PRECISION BIGNUM, EPS3, SMLNUM, WI, WR

DOUBLE
PRECISION B( LDB, * ), H( LDH, * ), VI( * ), VR( * ),
WORK( * )
PURPOSE
DLAEIN 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) DOUBLE PRECISION 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) DOUBLE PRECISION

WI (input) DOUBLE PRECISION
The real and imaginary parts of the eigenvalue of H whose
corresponding right or left eigenvector is to be computed.
 VR (input/output) DOUBLE PRECISION array, dimension (N)

VI (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDB,N)

 LDB (input) INTEGER

The leading dimension of the array B. LDB >= N+1.
 WORK (workspace) DOUBLE PRECISION array, dimension (N)

 EPS3 (input) DOUBLE PRECISION

A small machinedependent value which is used to perturb
close eigenvalues, and to replace zero pivots.
 SMLNUM (input) DOUBLE PRECISION

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

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 dlaein
 dlaein (3)
 dlae2 (l)  computes the eigenvalues of a 2by2 symmetric matrix [ A B ] [ B C ]
 dlaebz (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
 dlaed0 (l)  computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
 dlaed1 (l)  computes the updated eigensystem of a diagonal matrix after modification by a rankone symmetric matrix
 dlaed2 (l)  merges the two sets of eigenvalues together into a single sorted set
 dlaed3 (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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 dlaed6 (l)  computes the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho +  +  +  d(1)x d(2)x d(3)x It is assumed that if ORGATI = .true