dlaein (l) - Linux Manuals
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 machine-dependent value which is used to perturb
close eigenvalues, and to replace zero pivots.
- SMLNUM (input) DOUBLE PRECISION
-
A machine-dependent value close to the underflow threshold.
- BIGNUM (input) DOUBLE PRECISION
-
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.
Pages related to dlaein
- dlaein (3)
- dlae2 (l) - computes the eigenvalues of a 2-by-2 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 rank-one 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
- dlaed4 (l) - subroutine compute the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
- dlaed5 (l) - subroutine compute the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j
- 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