LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ slaein()

subroutine slaein ( logical rightv,
logical noinit,
integer n,
real, dimension( ldh, * ) h,
integer ldh,
real wr,
real wi,
real, dimension( * ) vr,
real, dimension( * ) vi,
real, dimension( ldb, * ) b,
integer ldb,
real, dimension( * ) work,
real eps3,
real smlnum,
real bignum,
integer info )

SLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

Download SLAEIN + dependencies [TGZ] [ZIP] [TXT]

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.
!>
Parameters
[in]RIGHTV
!>          RIGHTV is LOGICAL
!>          = .TRUE. : compute right eigenvector;
!>          = .FALSE.: compute left eigenvector.
!>
[in]NOINIT
!>          NOINIT is LOGICAL
!>          = .TRUE. : no initial vector supplied in (VR,VI).
!>          = .FALSE.: initial vector supplied in (VR,VI).
!>
[in]N
!>          N is INTEGER
!>          The order of the matrix H.  N >= 0.
!>
[in]H
!>          H is REAL array, dimension (LDH,N)
!>          The upper Hessenberg matrix H.
!>
[in]LDH
!>          LDH is INTEGER
!>          The leading dimension of the array H.  LDH >= max(1,N).
!>
[in]WR
!>          WR is REAL
!>
[in]WI
!>          WI is REAL
!>          The real and imaginary parts of the eigenvalue of H whose
!>          corresponding right or left eigenvector is to be computed.
!>
[in,out]VR
!>          VR is REAL array, dimension (N)
!>
[in,out]VI
!>          VI is 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.
!>
[out]B
!>          B is REAL array, dimension (LDB,N)
!>
[in]LDB
!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= N+1.
!>
[out]WORK
!>          WORK is REAL array, dimension (N)
!>
[in]EPS3
!>          EPS3 is REAL
!>          A small machine-dependent value which is used to perturb
!>          close eigenvalues, and to replace zero pivots.
!>
[in]SMLNUM
!>          SMLNUM is REAL
!>          A machine-dependent value close to the underflow threshold.
!>
[in]BIGNUM
!>          BIGNUM is REAL
!>          A machine-dependent value close to the overflow threshold.
!>
[out]INFO
!>          INFO is 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.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.