| lanv2(3) | LAPACK | lanv2(3) |
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 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 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 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 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).
Generated automatically by Doxygen for LAPACK from the source code.
| Thu Aug 7 2025 17:26:25 | Version 3.12.0 |