.TH "SRC/zlaesy.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/zlaesy.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzlaesy\fP (a, b, c, rt1, rt2, evscal, cs1, sn1)"
.br
.RI "\fBZLAESY\fP computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zlaesy (complex*16 a, complex*16 b, complex*16 c, complex*16 rt1, complex*16 rt2, complex*16 evscal, complex*16 cs1, complex*16 sn1)"

.PP
\fBZLAESY\fP computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix
!>    ( ( A, B );( B, C ) )
!> provided the norm of the matrix of eigenvectors is larger than
!> some threshold value\&.
!>
!> RT1 is the eigenvalue of larger absolute value, and RT2 of
!> smaller absolute value\&.  If the eigenvectors are computed, then
!> on return ( CS1, SN1 ) is the unit eigenvector for RT1, hence
!>
!> [  CS1     SN1   ] \&. [ A  B ] \&. [ CS1    -SN1   ] = [ RT1  0  ]
!> [ -SN1     CS1   ]   [ B  C ]   [ SN1     CS1   ]   [  0  RT2 ]
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16
!>          The ( 1, 1 ) element of input matrix\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is COMPLEX*16
!>          The ( 1, 2 ) element of input matrix\&.  The ( 2, 1 ) element
!>          is also given by B, since the 2-by-2 matrix is symmetric\&.
!> 
.fi
.PP
.br
\fIC\fP 
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.nf
!>          C is COMPLEX*16
!>          The ( 2, 2 ) element of input matrix\&.
!> 
.fi
.PP
.br
\fIRT1\fP 
.PP
.nf
!>          RT1 is COMPLEX*16
!>          The eigenvalue of larger modulus\&.
!> 
.fi
.PP
.br
\fIRT2\fP 
.PP
.nf
!>          RT2 is COMPLEX*16
!>          The eigenvalue of smaller modulus\&.
!> 
.fi
.PP
.br
\fIEVSCAL\fP 
.PP
.nf
!>          EVSCAL is COMPLEX*16
!>          The complex value by which the eigenvector matrix was scaled
!>          to make it orthonormal\&.  If EVSCAL is zero, the eigenvectors
!>          were not computed\&.  This means one of two things:  the 2-by-2
!>          matrix could not be diagonalized, or the norm of the matrix
!>          of eigenvectors before scaling was larger than the threshold
!>          value THRESH (set below)\&.
!> 
.fi
.PP
.br
\fICS1\fP 
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.nf
!>          CS1 is COMPLEX*16
!> 
.fi
.PP
.br
\fISN1\fP 
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.nf
!>          SN1 is COMPLEX*16
!>          If EVSCAL \&.NE\&. 0,  ( CS1, SN1 ) is the unit right eigenvector
!>          for RT1\&.
!> 
.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

.PP
Definition at line \fB114\fP of file \fBzlaesy\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.