laein(3)

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

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

    H

              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

              W is COMPLEX
              The eigenvalue of H whose corresponding right or left
              eigenvector is to be computed.

    V

              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

              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

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

    H

              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

              WR is DOUBLE PRECISION

    WI

              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

              VR is DOUBLE PRECISION array, dimension (N)

    VI

              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

              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

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

    H

              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

              WR is REAL

    WI

              WI is REAL
              The real and imaginary parts of the eigenvalue of H whose
              corresponding right or left eigenvector is to be computed.

    VR

              VR is REAL array, dimension (N)

    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.

    B

              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, complex*16, dimension( ldh, * ) h, integer ldh, complex*16 w, complex*16, dimension( * ) v, complex*16, 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

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

    H

              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

              W is COMPLEX*16
              The eigenvalue of H whose corresponding right or left
              eigenvector is to be computed.

    V

              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

              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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