LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  slagv2 (A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR) 
SLAGV2 computes the Generalized Schur factorization of a real 2by2 matrix pencil (A,B) where B is upper triangular. 
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 2by2 matrix pencil (A,B) where B is upper triangular.
Download SLAGV2 + dependencies [TGZ] [ZIP] [TXT]SLAGV2 computes the Generalized Schur factorization of a real 2by2 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 ``Apart'' 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 ``Bpart'' 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 157 of file slagv2.f.