LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
|
subroutine slagv2 | ( | real, dimension( lda, * ) | A, |
integer | LDA, | ||
real, dimension( ldb, * ) | B, | ||
integer | LDB, | ||
real, dimension( 2 ) | ALPHAR, | ||
real, dimension( 2 ) | ALPHAI, | ||
real, dimension( 2 ) | BETA, | ||
real | CSL, | ||
real | SNL, | ||
real | CSR, | ||
real | SNR | ||
) |
SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.
Download SLAGV2 + dependencies [TGZ] [ZIP] [TXT]
SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. This 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 [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ] [ 0 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ] [ b11 b12 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ] [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ], 2) if the pencil (A,B) has a pair of complex conjugate eigenvalues, then [ a11 a12 ] := [ CSL SNL ] [ a11 a12 ] [ CSR -SNR ] [ a21 a22 ] [ -SNL CSL ] [ a21 a22 ] [ SNR CSR ] [ b11 0 ] := [ CSL SNL ] [ b11 b12 ] [ CSR -SNR ] [ 0 b22 ] [ -SNL CSL ] [ 0 b22 ] [ SNR CSR ] where b11 >= b22 > 0.
[in,out] | A | A is REAL array, dimension (LDA, 2) On entry, the 2 x 2 matrix A. On exit, A is overwritten by the ``A-part'' of the generalized Schur form. |
[in] | LDA | LDA is INTEGER THe leading dimension of the array A. LDA >= 2. |
[in,out] | B | B is REAL array, dimension (LDB, 2) On entry, the upper triangular 2 x 2 matrix B. On exit, B is overwritten by the ``B-part'' of the generalized Schur form. |
[in] | LDB | LDB is INTEGER THe leading dimension of the array B. LDB >= 2. |
[out] | ALPHAR | ALPHAR is REAL array, dimension (2) |
[out] | ALPHAI | ALPHAI is REAL array, dimension (2) |
[out] | BETA | BETA is REAL array, dimension (2) (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the pencil (A,B), k=1,2, i = sqrt(-1). Note that BETA(k) may be zero. |
[out] | CSL | CSL is REAL The cosine of the left rotation matrix. |
[out] | SNL | SNL is REAL The sine of the left rotation matrix. |
[out] | CSR | CSR is REAL The cosine of the right rotation matrix. |
[out] | SNR | SNR is REAL The sine of the right rotation matrix. |
Definition at line 159 of file slagv2.f.