.TH "lags2" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lags2 \- lags2: 2x2 orthogonal factor, step in tgsja
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclags2\fP (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq)"
.br
.RI "\fBCLAGS2\fP "
.ti -1c
.RI "subroutine \fBdlags2\fP (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq)"
.br
.RI "\fBDLAGS2\fP computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel\&. "
.ti -1c
.RI "subroutine \fBslags2\fP (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq)"
.br
.RI "\fBSLAGS2\fP computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel\&. "
.ti -1c
.RI "subroutine \fBzlags2\fP (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq)"
.br
.RI "\fBZLAGS2\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine clags2 (logical upper, real a1, complex a2, real a3, real b1, complex b2, real b3, real csu, complex snu, real csv, complex snv, real csq, complex snq)"

.PP
\fBCLAGS2\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
 that if ( UPPER ) then

           U**H *A*Q = U**H *( A1 A2 )*Q = ( x  0  )
                             ( 0  A3 )     ( x  x  )
 and
           V**H*B*Q = V**H *( B1 B2 )*Q = ( x  0  )
                            ( 0  B3 )     ( x  x  )

 or if ( \&.NOT\&.UPPER ) then

           U**H *A*Q = U**H *( A1 0  )*Q = ( x  x  )
                             ( A2 A3 )     ( 0  x  )
 and
           V**H *B*Q = V**H *( B1 0  )*Q = ( x  x  )
                             ( B2 B3 )     ( 0  x  )
 where

   U = (   CSU    SNU ), V = (  CSV    SNV ),
       ( -SNU**H  CSU )      ( -SNV**H CSV )

   Q = (   CSQ    SNQ )
       ( -SNQ**H  CSQ )

 The rows of the transformed A and B are parallel\&. Moreover, if the
 input 2-by-2 matrix A is not zero, then the transformed (1,1) entry
 of A is not zero\&. If the input matrices A and B are both not zero,
 then the transformed (2,2) element of B is not zero, except when the
 first rows of input A and B are parallel and the second rows are
 zero\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPPER\fP 
.PP
.nf
          UPPER is LOGICAL
          = \&.TRUE\&.: the input matrices A and B are upper triangular\&.
          = \&.FALSE\&.: the input matrices A and B are lower triangular\&.
.fi
.PP
.br
\fIA1\fP 
.PP
.nf
          A1 is REAL
.fi
.PP
.br
\fIA2\fP 
.PP
.nf
          A2 is COMPLEX
.fi
.PP
.br
\fIA3\fP 
.PP
.nf
          A3 is REAL
          On entry, A1, A2 and A3 are elements of the input 2-by-2
          upper (lower) triangular matrix A\&.
.fi
.PP
.br
\fIB1\fP 
.PP
.nf
          B1 is REAL
.fi
.PP
.br
\fIB2\fP 
.PP
.nf
          B2 is COMPLEX
.fi
.PP
.br
\fIB3\fP 
.PP
.nf
          B3 is REAL
          On entry, B1, B2 and B3 are elements of the input 2-by-2
          upper (lower) triangular matrix B\&.
.fi
.PP
.br
\fICSU\fP 
.PP
.nf
          CSU is REAL
.fi
.PP
.br
\fISNU\fP 
.PP
.nf
          SNU is COMPLEX
          The desired unitary matrix U\&.
.fi
.PP
.br
\fICSV\fP 
.PP
.nf
          CSV is REAL
.fi
.PP
.br
\fISNV\fP 
.PP
.nf
          SNV is COMPLEX
          The desired unitary matrix V\&.
.fi
.PP
.br
\fICSQ\fP 
.PP
.nf
          CSQ is REAL
.fi
.PP
.br
\fISNQ\fP 
.PP
.nf
          SNQ is COMPLEX
          The desired unitary matrix Q\&.
.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

.SS "subroutine dlags2 (logical upper, double precision a1, double precision a2, double precision a3, double precision b1, double precision b2, double precision b3, double precision csu, double precision snu, double precision csv, double precision snv, double precision csq, double precision snq)"

.PP
\fBDLAGS2\fP computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
 that if ( UPPER ) then

           U**T *A*Q = U**T *( A1 A2 )*Q = ( x  0  )
                             ( 0  A3 )     ( x  x  )
 and
           V**T*B*Q = V**T *( B1 B2 )*Q = ( x  0  )
                            ( 0  B3 )     ( x  x  )

 or if ( \&.NOT\&.UPPER ) then

           U**T *A*Q = U**T *( A1 0  )*Q = ( x  x  )
                             ( A2 A3 )     ( 0  x  )
 and
           V**T*B*Q = V**T*( B1 0  )*Q = ( x  x  )
                           ( B2 B3 )     ( 0  x  )

 The rows of the transformed A and B are parallel, where

   U = (  CSU  SNU ), V = (  CSV SNV ), Q = (  CSQ   SNQ )
       ( -SNU  CSU )      ( -SNV CSV )      ( -SNQ   CSQ )

 Z**T denotes the transpose of Z\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPPER\fP 
.PP
.nf
          UPPER is LOGICAL
          = \&.TRUE\&.: the input matrices A and B are upper triangular\&.
          = \&.FALSE\&.: the input matrices A and B are lower triangular\&.
.fi
.PP
.br
\fIA1\fP 
.PP
.nf
          A1 is DOUBLE PRECISION
.fi
.PP
.br
\fIA2\fP 
.PP
.nf
          A2 is DOUBLE PRECISION
.fi
.PP
.br
\fIA3\fP 
.PP
.nf
          A3 is DOUBLE PRECISION
          On entry, A1, A2 and A3 are elements of the input 2-by-2
          upper (lower) triangular matrix A\&.
.fi
.PP
.br
\fIB1\fP 
.PP
.nf
          B1 is DOUBLE PRECISION
.fi
.PP
.br
\fIB2\fP 
.PP
.nf
          B2 is DOUBLE PRECISION
.fi
.PP
.br
\fIB3\fP 
.PP
.nf
          B3 is DOUBLE PRECISION
          On entry, B1, B2 and B3 are elements of the input 2-by-2
          upper (lower) triangular matrix B\&.
.fi
.PP
.br
\fICSU\fP 
.PP
.nf
          CSU is DOUBLE PRECISION
.fi
.PP
.br
\fISNU\fP 
.PP
.nf
          SNU is DOUBLE PRECISION
          The desired orthogonal matrix U\&.
.fi
.PP
.br
\fICSV\fP 
.PP
.nf
          CSV is DOUBLE PRECISION
.fi
.PP
.br
\fISNV\fP 
.PP
.nf
          SNV is DOUBLE PRECISION
          The desired orthogonal matrix V\&.
.fi
.PP
.br
\fICSQ\fP 
.PP
.nf
          CSQ is DOUBLE PRECISION
.fi
.PP
.br
\fISNQ\fP 
.PP
.nf
          SNQ is DOUBLE PRECISION
          The desired orthogonal matrix Q\&.
.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

.SS "subroutine slags2 (logical upper, real a1, real a2, real a3, real b1, real b2, real b3, real csu, real snu, real csv, real snv, real csq, real snq)"

.PP
\fBSLAGS2\fP computes 2-by-2 orthogonal matrices U, V, and Q, and applies them to matrices A and B such that the rows of the transformed A and B are parallel\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
 that if ( UPPER ) then

           U**T *A*Q = U**T *( A1 A2 )*Q = ( x  0  )
                             ( 0  A3 )     ( x  x  )
 and
           V**T*B*Q = V**T *( B1 B2 )*Q = ( x  0  )
                            ( 0  B3 )     ( x  x  )

 or if ( \&.NOT\&.UPPER ) then

           U**T *A*Q = U**T *( A1 0  )*Q = ( x  x  )
                             ( A2 A3 )     ( 0  x  )
 and
           V**T*B*Q = V**T*( B1 0  )*Q = ( x  x  )
                           ( B2 B3 )     ( 0  x  )

 The rows of the transformed A and B are parallel, where

   U = (  CSU  SNU ), V = (  CSV SNV ), Q = (  CSQ   SNQ )
       ( -SNU  CSU )      ( -SNV CSV )      ( -SNQ   CSQ )

 Z**T denotes the transpose of Z\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPPER\fP 
.PP
.nf
          UPPER is LOGICAL
          = \&.TRUE\&.: the input matrices A and B are upper triangular\&.
          = \&.FALSE\&.: the input matrices A and B are lower triangular\&.
.fi
.PP
.br
\fIA1\fP 
.PP
.nf
          A1 is REAL
.fi
.PP
.br
\fIA2\fP 
.PP
.nf
          A2 is REAL
.fi
.PP
.br
\fIA3\fP 
.PP
.nf
          A3 is REAL
          On entry, A1, A2 and A3 are elements of the input 2-by-2
          upper (lower) triangular matrix A\&.
.fi
.PP
.br
\fIB1\fP 
.PP
.nf
          B1 is REAL
.fi
.PP
.br
\fIB2\fP 
.PP
.nf
          B2 is REAL
.fi
.PP
.br
\fIB3\fP 
.PP
.nf
          B3 is REAL
          On entry, B1, B2 and B3 are elements of the input 2-by-2
          upper (lower) triangular matrix B\&.
.fi
.PP
.br
\fICSU\fP 
.PP
.nf
          CSU is REAL
.fi
.PP
.br
\fISNU\fP 
.PP
.nf
          SNU is REAL
          The desired orthogonal matrix U\&.
.fi
.PP
.br
\fICSV\fP 
.PP
.nf
          CSV is REAL
.fi
.PP
.br
\fISNV\fP 
.PP
.nf
          SNV is REAL
          The desired orthogonal matrix V\&.
.fi
.PP
.br
\fICSQ\fP 
.PP
.nf
          CSQ is REAL
.fi
.PP
.br
\fISNQ\fP 
.PP
.nf
          SNQ is REAL
          The desired orthogonal matrix Q\&.
.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

.SS "subroutine zlags2 (logical upper, double precision a1, complex*16 a2, double precision a3, double precision b1, complex*16 b2, double precision b3, double precision csu, complex*16 snu, double precision csv, complex*16 snv, double precision csq, complex*16 snq)"

.PP
\fBZLAGS2\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
 that if ( UPPER ) then

           U**H *A*Q = U**H *( A1 A2 )*Q = ( x  0  )
                             ( 0  A3 )     ( x  x  )
 and
           V**H*B*Q = V**H *( B1 B2 )*Q = ( x  0  )
                            ( 0  B3 )     ( x  x  )

 or if ( \&.NOT\&.UPPER ) then

           U**H *A*Q = U**H *( A1 0  )*Q = ( x  x  )
                             ( A2 A3 )     ( 0  x  )
 and
           V**H *B*Q = V**H *( B1 0  )*Q = ( x  x  )
                             ( B2 B3 )     ( 0  x  )
 where

   U = (   CSU    SNU ), V = (  CSV    SNV ),
       ( -SNU**H  CSU )      ( -SNV**H CSV )

   Q = (   CSQ    SNQ )
       ( -SNQ**H  CSQ )

 The rows of the transformed A and B are parallel\&. Moreover, if the
 input 2-by-2 matrix A is not zero, then the transformed (1,1) entry
 of A is not zero\&. If the input matrices A and B are both not zero,
 then the transformed (2,2) element of B is not zero, except when the
 first rows of input A and B are parallel and the second rows are
 zero\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPPER\fP 
.PP
.nf
          UPPER is LOGICAL
          = \&.TRUE\&.: the input matrices A and B are upper triangular\&.
          = \&.FALSE\&.: the input matrices A and B are lower triangular\&.
.fi
.PP
.br
\fIA1\fP 
.PP
.nf
          A1 is DOUBLE PRECISION
.fi
.PP
.br
\fIA2\fP 
.PP
.nf
          A2 is COMPLEX*16
.fi
.PP
.br
\fIA3\fP 
.PP
.nf
          A3 is DOUBLE PRECISION
          On entry, A1, A2 and A3 are elements of the input 2-by-2
          upper (lower) triangular matrix A\&.
.fi
.PP
.br
\fIB1\fP 
.PP
.nf
          B1 is DOUBLE PRECISION
.fi
.PP
.br
\fIB2\fP 
.PP
.nf
          B2 is COMPLEX*16
.fi
.PP
.br
\fIB3\fP 
.PP
.nf
          B3 is DOUBLE PRECISION
          On entry, B1, B2 and B3 are elements of the input 2-by-2
          upper (lower) triangular matrix B\&.
.fi
.PP
.br
\fICSU\fP 
.PP
.nf
          CSU is DOUBLE PRECISION
.fi
.PP
.br
\fISNU\fP 
.PP
.nf
          SNU is COMPLEX*16
          The desired unitary matrix U\&.
.fi
.PP
.br
\fICSV\fP 
.PP
.nf
          CSV is DOUBLE PRECISION
.fi
.PP
.br
\fISNV\fP 
.PP
.nf
          SNV is COMPLEX*16
          The desired unitary matrix V\&.
.fi
.PP
.br
\fICSQ\fP 
.PP
.nf
          CSQ is DOUBLE PRECISION
.fi
.PP
.br
\fISNQ\fP 
.PP
.nf
          SNQ is COMPLEX*16
          The desired unitary matrix Q\&.
.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

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.