LAPACK

NAME¶

lagv2 - lagv2: 2x2 generalized Schur factor

SYNOPSIS¶

Functions¶

subroutine dlagv2 (a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr, snr)
DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular. subroutine slagv2 (a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr, snr)
SLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.

Detailed Description¶

Function Documentation¶

subroutine dlagv2 (double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( 2 ) alphar, double precision, dimension( 2 ) alphai, double precision, dimension( 2 ) beta, double precision csl, double precision snl, double precision csr, double precision snr)¶

DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular.

Purpose:



 DLAGV2 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



          A is DOUBLE PRECISION 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.

LDA



          LDA is INTEGER


          THe leading dimension of the array A.  LDA >= 2.



          B is DOUBLE PRECISION 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.

LDB



          LDB is INTEGER


          THe leading dimension of the array B.  LDB >= 2.

ALPHAR



          ALPHAR is DOUBLE PRECISION array, dimension (2)

ALPHAI



          ALPHAI is DOUBLE PRECISION array, dimension (2)

BETA



          BETA is DOUBLE PRECISION 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.

CSL



          CSL is DOUBLE PRECISION


          The cosine of the left rotation matrix.

SNL



          SNL is DOUBLE PRECISION


          The sine of the left rotation matrix.

CSR



          CSR is DOUBLE PRECISION


          The cosine of the right rotation matrix.

SNR



          SNR is DOUBLE PRECISION


          The sine of the right rotation matrix.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

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.