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lanv2

lanv2: 2x2 Schur factor


subroutine dlanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)
DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. subroutine slanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)
SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

Purpose:

!>
!> DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
!> matrix in standard form:
!>
!>      [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
!>      [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]
!>
!> where either
!> 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
!> 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
!> conjugate eigenvalues.
!>

Parameters

A 

!>          A is DOUBLE PRECISION
!>

B

!>          B is DOUBLE PRECISION
!>

C

!>          C is DOUBLE PRECISION
!>

D

!>          D is DOUBLE PRECISION
!>          On entry, the elements of the input matrix.
!>          On exit, they are overwritten by the elements of the
!>          standardised Schur form.
!>

RT1R

!>          RT1R is DOUBLE PRECISION
!>

RT1I

!>          RT1I is DOUBLE PRECISION
!>

RT2R

!>          RT2R is DOUBLE PRECISION
!>

RT2I

!>          RT2I is DOUBLE PRECISION
!>          The real and imaginary parts of the eigenvalues. If the
!>          eigenvalues are a complex conjugate pair, RT1I > 0.
!>

CS

!>          CS is DOUBLE PRECISION
!>

SN

!>          SN is DOUBLE PRECISION
!>          Parameters of the rotation matrix.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Modified by V. Sima, Research Institute for Informatics, Bucharest,
!>  Romania, to reduce the risk of cancellation errors,
!>  when computing real eigenvalues, and to ensure, if possible, that
!>  abs(RT1R) >= abs(RT2R).
!>

SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

Purpose:

!>
!> SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
!> matrix in standard form:
!>
!>      [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
!>      [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]
!>
!> where either
!> 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
!> 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
!> conjugate eigenvalues.
!>

Parameters

A 

!>          A is REAL
!>

B

!>          B is REAL
!>

C

!>          C is REAL
!>

D

!>          D is REAL
!>          On entry, the elements of the input matrix.
!>          On exit, they are overwritten by the elements of the
!>          standardised Schur form.
!>

RT1R

!>          RT1R is REAL
!>

RT1I

!>          RT1I is REAL
!>

RT2R

!>          RT2R is REAL
!>

RT2I

!>          RT2I is REAL
!>          The real and imaginary parts of the eigenvalues. If the
!>          eigenvalues are a complex conjugate pair, RT1I > 0.
!>

CS

!>          CS is REAL
!>

SN

!>          SN is REAL
!>          Parameters of the rotation matrix.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Modified by V. Sima, Research Institute for Informatics, Bucharest,
!>  Romania, to reduce the risk of cancellation errors,
!>  when computing real eigenvalues, and to ensure, if possible, that
!>  abs(RT1R) >= abs(RT2R).
!>

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