.TH "lanv2" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lanv2 \- lanv2: 2x2 Schur factor
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdlanv2\fP (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)"
.br
.RI "\fBDLANV2\fP computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form\&. "
.ti -1c
.RI "subroutine \fBslanv2\fP (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)"
.br
.RI "\fBSLANV2\fP computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine dlanv2 (double precision a, double precision b, double precision c, double precision d, double precision rt1r, double precision rt1i, double precision rt2r, double precision rt2i, double precision cs, double precision sn)"

.PP
\fBDLANV2\fP computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
 matrix in standard form:

      [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
      [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]

 where either
 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
 conjugate eigenvalues\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION
          On entry, the elements of the input matrix\&.
          On exit, they are overwritten by the elements of the
          standardised Schur form\&.
.fi
.PP
.br
\fIRT1R\fP 
.PP
.nf
          RT1R is DOUBLE PRECISION
.fi
.PP
.br
\fIRT1I\fP 
.PP
.nf
          RT1I is DOUBLE PRECISION
.fi
.PP
.br
\fIRT2R\fP 
.PP
.nf
          RT2R is DOUBLE PRECISION
.fi
.PP
.br
\fIRT2I\fP 
.PP
.nf
          RT2I is DOUBLE PRECISION
          The real and imaginary parts of the eigenvalues\&. If the
          eigenvalues are a complex conjugate pair, RT1I > 0\&.
.fi
.PP
.br
\fICS\fP 
.PP
.nf
          CS is DOUBLE PRECISION
.fi
.PP
.br
\fISN\fP 
.PP
.nf
          SN is DOUBLE PRECISION
          Parameters of the 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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  Modified by V\&. Sima, Research Institute for Informatics, Bucharest,
  Romania, to reduce the risk of cancellation errors,
  when computing real eigenvalues, and to ensure, if possible, that
  abs(RT1R) >= abs(RT2R)\&.
.fi
.PP
 
.RE
.PP

.SS "subroutine slanv2 (real a, real b, real c, real d, real rt1r, real rt1i, real rt2r, real rt2i, real cs, real sn)"

.PP
\fBSLANV2\fP computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
 matrix in standard form:

      [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
      [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]

 where either
 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
 conjugate eigenvalues\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
          A is REAL
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is REAL
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL
          On entry, the elements of the input matrix\&.
          On exit, they are overwritten by the elements of the
          standardised Schur form\&.
.fi
.PP
.br
\fIRT1R\fP 
.PP
.nf
          RT1R is REAL
.fi
.PP
.br
\fIRT1I\fP 
.PP
.nf
          RT1I is REAL
.fi
.PP
.br
\fIRT2R\fP 
.PP
.nf
          RT2R is REAL
.fi
.PP
.br
\fIRT2I\fP 
.PP
.nf
          RT2I is REAL
          The real and imaginary parts of the eigenvalues\&. If the
          eigenvalues are a complex conjugate pair, RT1I > 0\&.
.fi
.PP
.br
\fICS\fP 
.PP
.nf
          CS is REAL
.fi
.PP
.br
\fISN\fP 
.PP
.nf
          SN is REAL
          Parameters of the 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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  Modified by V\&. Sima, Research Institute for Informatics, Bucharest,
  Romania, to reduce the risk of cancellation errors,
  when computing real eigenvalues, and to ensure, if possible, that
  abs(RT1R) >= abs(RT2R)\&.
.fi
.PP
 
.RE
.PP

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