LAPACK  3.4.0
LAPACK: Linear Algebra PACKage
Functions/Subroutines
slagv2.f File Reference

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Functions/Subroutines

subroutine SLAGV2 (A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR)
 SLAGV2

Function/Subroutine Documentation

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

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Purpose: 

 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.
Parameters:
[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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Contributors:
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 157 of file slagv2.f.

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