.TH "SRC/slaev2.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/slaev2.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBslaev2\fP (a, b, c, rt1, rt2, cs1, sn1)"
.br
.RI "\fBSLAEV2\fP computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine slaev2 (real a, real b, real c, real rt1, real rt2, real cs1, real sn1)"

.PP
\fBSLAEV2\fP computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
!>    [  A   B  ]
!>    [  B   C  ]\&.
!> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
!> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
!> eigenvector for RT1, giving the decomposition
!>
!>    [ 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 REAL
!>          The (1,1) element of the 2-by-2 matrix\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is REAL
!>          The (1,2) element and the conjugate of the (2,1) element of
!>          the 2-by-2 matrix\&.
!> 
.fi
.PP
.br
\fIC\fP 
.PP
.nf
!>          C is REAL
!>          The (2,2) element of the 2-by-2 matrix\&.
!> 
.fi
.PP
.br
\fIRT1\fP 
.PP
.nf
!>          RT1 is REAL
!>          The eigenvalue of larger absolute value\&.
!> 
.fi
.PP
.br
\fIRT2\fP 
.PP
.nf
!>          RT2 is REAL
!>          The eigenvalue of smaller absolute value\&.
!> 
.fi
.PP
.br
\fICS1\fP 
.PP
.nf
!>          CS1 is REAL
!> 
.fi
.PP
.br
\fISN1\fP 
.PP
.nf
!>          SN1 is REAL
!>          The vector (CS1, SN1) is a 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
\fBFurther Details:\fP
.RS 4

.PP
.nf
!>
!>  RT1 is accurate to a few ulps barring over/underflow\&.
!>
!>  RT2 may be inaccurate if there is massive cancellation in the
!>  determinant A*C-B*B; higher precision or correctly rounded or
!>  correctly truncated arithmetic would be needed to compute RT2
!>  accurately in all cases\&.
!>
!>  CS1 and SN1 are accurate to a few ulps barring over/underflow\&.
!>
!>  Overflow is possible only if RT1 is within a factor of 5 of overflow\&.
!>  Underflow is harmless if the input data is 0 or exceeds
!>     underflow_threshold / macheps\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB119\fP of file \fBslaev2\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.