.TH "lagv2" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lagv2 \- lagv2: 2x2 generalized Schur factor
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdlagv2\fP (a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr, snr)"
.br
.RI "\fBDLAGV2\fP computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular\&. "
.ti -1c
.RI "subroutine \fBslagv2\fP (a, lda, b, ldb, alphar, alphai, beta, csl, snl, csr, snr)"
.br
.RI "\fBSLAGV2\fP computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "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)"

.PP
\fBDLAGV2\fP computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!>
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          THe leading dimension of the array A\&.  LDA >= 2\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          THe leading dimension of the array B\&.  LDB >= 2\&.
!> 
.fi
.PP
.br
\fIALPHAR\fP 
.PP
.nf
!>          ALPHAR is DOUBLE PRECISION array, dimension (2)
!> 
.fi
.PP
.br
\fIALPHAI\fP 
.PP
.nf
!>          ALPHAI is DOUBLE PRECISION array, dimension (2)
!> 
.fi
.PP
.br
\fIBETA\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fICSL\fP 
.PP
.nf
!>          CSL is DOUBLE PRECISION
!>          The cosine of the left rotation matrix\&.
!> 
.fi
.PP
.br
\fISNL\fP 
.PP
.nf
!>          SNL is DOUBLE PRECISION
!>          The sine of the left rotation matrix\&.
!> 
.fi
.PP
.br
\fICSR\fP 
.PP
.nf
!>          CSR is DOUBLE PRECISION
!>          The cosine of the right rotation matrix\&.
!> 
.fi
.PP
.br
\fISNR\fP 
.PP
.nf
!>          SNR is DOUBLE PRECISION
!>          The sine of the right rotation matrix\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA 
.RE
.PP

.PP
Definition at line \fB155\fP of file \fBdlagv2\&.f\fP\&.
.SS "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)"

.PP
\fBSLAGV2\fP computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!>
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          THe leading dimension of the array A\&.  LDA >= 2\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          THe leading dimension of the array B\&.  LDB >= 2\&.
!> 
.fi
.PP
.br
\fIALPHAR\fP 
.PP
.nf
!>          ALPHAR is REAL array, dimension (2)
!> 
.fi
.PP
.br
\fIALPHAI\fP 
.PP
.nf
!>          ALPHAI is REAL array, dimension (2)
!> 
.fi
.PP
.br
\fIBETA\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fICSL\fP 
.PP
.nf
!>          CSL is REAL
!>          The cosine of the left rotation matrix\&.
!> 
.fi
.PP
.br
\fISNL\fP 
.PP
.nf
!>          SNL is REAL
!>          The sine of the left rotation matrix\&.
!> 
.fi
.PP
.br
\fICSR\fP 
.PP
.nf
!>          CSR is REAL
!>          The cosine of the right rotation matrix\&.
!> 
.fi
.PP
.br
\fISNR\fP 
.PP
.nf
!>          SNR is REAL
!>          The sine of the right rotation matrix\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA 
.RE
.PP

.PP
Definition at line \fB155\fP of file \fBslagv2\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.