lanv2 - Man Page

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).

Definition at line 126 of file dlanv2.f.

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).

Definition at line 126 of file slanv2.f.