Visible to Intel only — GUID: GUID-D08C7156-5EF8-416C-8AD7-BE14DC308282
Visible to Intel only — GUID: GUID-D08C7156-5EF8-416C-8AD7-BE14DC308282
?lagv2
Computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.
call slagv2( a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr, snr )
call dlagv2( a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr, snr )
- mkl.fi
The routine computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. The routine computes orthogonal (rotation) matrices given by csl, snl and csr, snr such that:
1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0 types), then
![Equation](/content/dam/docs/us/en/developer-reference-fortran/2023-1/C1A637C6-6558-4762-933B-77DB7EE29F2D-low.gif)
![Equation](/content/dam/docs/us/en/developer-reference-fortran/2023-1/C41A2E70-5F79-491E-847B-44EA19EA570B-low.gif)
2) if the pencil (A,B) has a pair of complex conjugate eigenvalues, then
![Equation](/content/dam/docs/us/en/developer-reference-fortran/2023-1/6362179C-167E-41B0-9E96-3D4782DD9DF1-low.jpg)
![Equation](/content/dam/docs/us/en/developer-reference-fortran/2023-1/0B907CB6-ED92-4AAA-B7C1-CD4CFF88AD3F-low.jpg)
where b11≥b22>0.
- a, b
-
REAL for slagv2
DOUBLE PRECISION for dlagv2
Arrays:
a(lda,2) contains the 2-by-2 matrix A;
b(ldb,2) contains the upper triangular 2-by-2 matrix B.
- lda
-
INTEGER. The leading dimension of the array a;
lda≥ 2.
- ldb
-
INTEGER. The leading dimension of the array b;
ldb≥ 2.
- a
-
On exit, a is overwritten by the "A-part" of the generalized Schur form.
- b
-
On exit, b is overwritten by the "B-part" of the generalized Schur form.
- alphar, alphai, beta
-
REAL for slagv2
DOUBLE PRECISION for dlagv2.
Arrays, dimension (2) each.
(alphar(k) + i*alphai(k))/beta(k) are the eigenvalues of the pencil (A,B), k=1,2 and i = sqrt(-1).
Note that beta(k) may be zero.
- csl, snl
-
REAL for slagv2
DOUBLE PRECISION for dlagv2
The cosine and sine of the left rotation matrix, respectively.
- csr, snr
-
REAL for slagv2
DOUBLE PRECISION for dlagv2
The cosine and sine of the right rotation matrix, respectively.