zlaein (l) - Linux Manuals

zlaein: uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H

NAME

ZLAEIN - uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H

SYNOPSIS

SUBROUTINE ZLAEIN(
RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3, SMLNUM, INFO )

    
LOGICAL NOINIT, RIGHTV

    
INTEGER INFO, LDB, LDH, N

    
DOUBLE PRECISION EPS3, SMLNUM

    
COMPLEX*16 W

    
DOUBLE PRECISION RWORK( * )

    
COMPLEX*16 B( LDB, * ), H( LDH, * ), V( * )

PURPOSE

ZLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex 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 V
= .FALSE.: initial vector supplied in V.
N (input) INTEGER
The order of the matrix H. N >= 0.
H (input) COMPLEX*16 array, dimension (LDH,N)
The upper Hessenberg matrix H.
LDH (input) INTEGER
The leading dimension of the array H. LDH >= max(1,N).
W (input) COMPLEX*16
The eigenvalue of H whose corresponding right or left eigenvector is to be computed.
V (input/output) COMPLEX*16 array, dimension (N)
On entry, if NOINIT = .FALSE., V must contain a starting vector for inverse iteration; otherwise V need not be set. On exit, V contains the computed eigenvector, 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|.
B (workspace) COMPLEX*16 array, dimension (LDB,N)
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
RWORK (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.
INFO (output) INTEGER
= 0: successful exit
= 1: inverse iteration did not converge; V is set to the last iterate.

Pages related to zlaein

  • zlaein (3)
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  • zlaed7 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
  • zlaed8 (l) - merges the two sets of eigenvalues together into a single sorted set
  • zlaesy (l) - computes the eigendecomposition of a 2-by-2 symmetric matrix ( ( A, B );( B, C ) ) provided the norm of the matrix of eigenvectors is larger than some threshold value
  • zlaev2 (l) - computes the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]
  • zla_gbamv (l) - performs one of the matrix-vector operations y := alpha*abs(A)*abs(x) + beta*abs(y),
  • zla_gbrcond_c (l) - ZLA_GBRCOND_C Compute the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector