.TH "dlagv2.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
dlagv2.f \- 
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdlagv2\fP (A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, CSL, SNL, CSR, SNR)"
.br
.RI "\fI\fBDLAGV2\fP computes the Generalized Schur factorization of a real 2-by-2 matrix pencil (A,B) where B is upper triangular\&. \fP"
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dlagv2 (double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( 2 )ALPHAR, double precision, dimension( 2 )ALPHAI, double precision, dimension( 2 )BETA, double precisionCSL, double precisionSNL, double precisionCSR, double precisionSNR)"

.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
\fBDate:\fP
.RS 4
September 2012 
.RE
.PP
\fBContributors: \fP
.RS 4
Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA 
.RE
.PP

.PP
Definition at line 157 of file dlagv2\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.