Computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.
Syntax
call slanv2( a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn )
call dlanv2( a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn )
Include Files
- mkl.fi
Description
The routine computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form:
where either
cc = 0 so that aa and dd are real eigenvalues of the matrix, or
aa = dd and bb*cc < 0, so that aa± sqrt(bb*cc) are complex conjugate eigenvalues.
The routine was adjusted to reduce the risk of cancellation errors, when computing real eigenvalues, and to ensure, if possible, that abs(rt1r) ≥ abs(rt2r).
Input Parameters
- a, b, c, d
REAL for slanv2
DOUBLE PRECISION for dlanv2.
On entry, elements of the input matrix.
Output Parameters
- a, b, c, d
On exit, overwritten by the elements of the standardized Schur form.
- rt1r, rt1i, rt2r, rt2i
REAL for slanv2
DOUBLE PRECISION for dlanv2.
The real and imaginary parts of the eigenvalues.
If the eigenvalues are a complex conjugate pair, rt1i > 0.
- cs, sn
REAL for slanv2
DOUBLE PRECISION for dlanv2.
Parameters of the rotation matrix.