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# slaev2

```
NAME
SLAEV2 - compute the eigendecomposition of a 2-by-2 sym-
metric matrix  [ A B ]  [ B C ]

SYNOPSIS
SUBROUTINE SLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

REAL           A, B, C, CS1, RT1, RT2, SN1

PURPOSE
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 ].

ARGUMENTS
A       (input) REAL
The (1,1) entry of the 2-by-2 matrix.

B       (input) REAL
The (1,2) entry and the conjugate of the (2,1) entry
of the 2-by-2 matrix.

C       (input) REAL
The (2,2) entry of the 2-by-2 matrix.

RT1     (output) REAL
The eigenvalue of larger absolute value.

RT2     (output) REAL
The eigenvalue of smaller absolute value.

CS1     (output) REAL
SN1     (output) REAL The vector (CS1, SN1) is a
unit right eigenvector for RT1.

FURTHER DETAILS
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.
```