NAME

laein - laein: eigvec by Hessenberg inverse iteration

SYNOPSIS

Functions

subroutine claein (rightv, noinit, n, h, ldh, w, v, b, ldb, rwork, eps3, smlnum, info)
CLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. subroutine dlaein (rightv, noinit, n, h, ldh, wr, wi, vr, vi, b, ldb, work, eps3, smlnum, bignum, info)
DLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. subroutine slaein (rightv, noinit, n, h, ldh, wr, wi, vr, vi, b, ldb, work, eps3, smlnum, bignum, info)
SLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. subroutine zlaein (rightv, noinit, n, h, ldh, w, v, b, ldb, rwork, eps3, smlnum, info)
ZLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

Detailed Description

Function Documentation

subroutine claein (logical rightv, logical noinit, integer n, complex, dimension( ldh, * ) h, integer ldh, complex w, complex, dimension( * ) v, complex, dimension( ldb, * ) b, integer ldb, real, dimension( * ) rwork, real eps3, real smlnum, integer info)

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

Purpose:



 CLAEIN uses inverse iteration to find a right or left eigenvector


 corresponding to the eigenvalue W of a complex upper Hessenberg


 matrix H.

Parameters

RIGHTV



          RIGHTV is LOGICAL


          = .TRUE. : compute right eigenvector;


          = .FALSE.: compute left eigenvector.

NOINIT



          NOINIT is LOGICAL


          = .TRUE. : no initial vector supplied in V


          = .FALSE.: initial vector supplied in V.



          N is INTEGER


          The order of the matrix H.  N >= 0.



          H is COMPLEX array, dimension (LDH,N)


          The upper Hessenberg matrix H.

LDH



          LDH is INTEGER


          The leading dimension of the array H.  LDH >= max(1,N).



          W is COMPLEX


          The eigenvalue of H whose corresponding right or left


          eigenvector is to be computed.



          V is COMPLEX 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 is COMPLEX array, dimension (LDB,N)

LDB



          LDB is INTEGER


          The leading dimension of the array B.  LDB >= max(1,N).

RWORK



          RWORK is REAL array, dimension (N)

EPS3



          EPS3 is REAL


          A small machine-dependent value which is used to perturb


          close eigenvalues, and to replace zero pivots.

SMLNUM



          SMLNUM is REAL


          A machine-dependent value close to the underflow threshold.

INFO



          INFO is INTEGER


          = 0:  successful exit


          = 1:  inverse iteration did not converge; V is set to the


                last iterate.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 147 of file claein.f.

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

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

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.

Parameters

RIGHTV



          RIGHTV is LOGICAL


          = .TRUE. : compute right eigenvector;


          = .FALSE.: compute left eigenvector.

NOINIT



          NOINIT is LOGICAL


          = .TRUE. : no initial vector supplied in (VR,VI).


          = .FALSE.: initial vector supplied in (VR,VI).



          N is INTEGER


          The order of the matrix H.  N >= 0.



          H is DOUBLE PRECISION array, dimension (LDH,N)


          The upper Hessenberg matrix H.

LDH



          LDH is INTEGER


          The leading dimension of the array H.  LDH >= max(1,N).



          WR is DOUBLE PRECISION



          WI is DOUBLE PRECISION


          The real and imaginary parts of the eigenvalue of H whose


          corresponding right or left eigenvector is to be computed.



          VR is DOUBLE PRECISION array, dimension (N)



          VI is 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 is DOUBLE PRECISION array, dimension (LDB,N)

LDB



          LDB is INTEGER


          The leading dimension of the array B.  LDB >= N+1.

WORK



          WORK is DOUBLE PRECISION array, dimension (N)

EPS3



          EPS3 is DOUBLE PRECISION


          A small machine-dependent value which is used to perturb


          close eigenvalues, and to replace zero pivots.

SMLNUM



          SMLNUM is DOUBLE PRECISION


          A machine-dependent value close to the underflow threshold.

BIGNUM



          BIGNUM is DOUBLE PRECISION


          A machine-dependent value close to the overflow threshold.

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.

Definition at line 170 of file dlaein.f.

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.

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

RIGHTV



          RIGHTV is LOGICAL


          = .TRUE. : compute right eigenvector;


          = .FALSE.: compute left eigenvector.

NOINIT



          NOINIT is LOGICAL


          = .TRUE. : no initial vector supplied in (VR,VI).


          = .FALSE.: initial vector supplied in (VR,VI).



          N is INTEGER


          The order of the matrix H.  N >= 0.



          H is REAL array, dimension (LDH,N)


          The upper Hessenberg matrix H.

LDH



          LDH is INTEGER


          The leading dimension of the array H.  LDH >= max(1,N).



          WR is REAL



          WI is REAL


          The real and imaginary parts of the eigenvalue of H whose


          corresponding right or left eigenvector is to be computed.



          VR is REAL array, dimension (N)



          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.



          B is REAL array, dimension (LDB,N)

LDB



          LDB is INTEGER


          The leading dimension of the array B.  LDB >= N+1.

WORK



          WORK is REAL array, dimension (N)

EPS3



          EPS3 is REAL


          A small machine-dependent value which is used to perturb


          close eigenvalues, and to replace zero pivots.

SMLNUM



          SMLNUM is REAL


          A machine-dependent value close to the underflow threshold.

BIGNUM



          BIGNUM is REAL


          A machine-dependent value close to the overflow threshold.

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.

Definition at line 170 of file slaein.f.

subroutine zlaein (logical rightv, logical noinit, integer n, complex16, dimension( ldh, ) h, integer ldh, complex16 w, complex16, dimension( * ) v, complex16, dimension( ldb, ) b, integer ldb, double precision, dimension( * ) rwork, double precision eps3, double precision smlnum, integer info)

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

Purpose:



 ZLAEIN uses inverse iteration to find a right or left eigenvector


 corresponding to the eigenvalue W of a complex upper Hessenberg


 matrix H.

Parameters

RIGHTV



          RIGHTV is LOGICAL


          = .TRUE. : compute right eigenvector;


          = .FALSE.: compute left eigenvector.

NOINIT



          NOINIT is LOGICAL


          = .TRUE. : no initial vector supplied in V


          = .FALSE.: initial vector supplied in V.



          N is INTEGER


          The order of the matrix H.  N >= 0.



          H is COMPLEX*16 array, dimension (LDH,N)


          The upper Hessenberg matrix H.

LDH



          LDH is INTEGER


          The leading dimension of the array H.  LDH >= max(1,N).



          W is COMPLEX*16


          The eigenvalue of H whose corresponding right or left


          eigenvector is to be computed.



          V is 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 is COMPLEX*16 array, dimension (LDB,N)

LDB



          LDB is INTEGER


          The leading dimension of the array B.  LDB >= max(1,N).

RWORK



          RWORK is DOUBLE PRECISION array, dimension (N)

EPS3



          EPS3 is DOUBLE PRECISION


          A small machine-dependent value which is used to perturb


          close eigenvalues, and to replace zero pivots.

SMLNUM



          SMLNUM is DOUBLE PRECISION


          A machine-dependent value close to the underflow threshold.

INFO



          INFO is INTEGER


          = 0:  successful exit


          = 1:  inverse iteration did not converge; V is set to the


                last iterate.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 147 of file zlaein.f.

Author

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