claev2 man page on Scientific

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```CLAEV2(1)	    LAPACK auxiliary routine (version 3.2)	     CLAEV2(1)

NAME
CLAEV2  -  computes the eigendecomposition of a 2-by-2 Hermitian matrix
[ A B ]	[ CONJG(B) C ]

SYNOPSIS
SUBROUTINE CLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

REAL		  CS1, RT1, RT2

COMPLEX	  A, B, C, SN1

PURPOSE
CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
[  A	       B  ]
[  CONJG(B)  C  ].  On return, RT1 is the eigenvalue of larger abso‐
lute  value,  RT2  is  the  eigenvalue  of  smaller absolute value, and
(CS1,SN1) is the unit right eigenvector for RT1, giving the  decomposi‐
tion
[  CS1	CONJG(SN1)  ] [	   A	 B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
[-SN1	 CS1	 ] [ CONJG(B) C ] [ SN1	    CS1	    ]	[  0  RT2 ].

ARGUMENTS
A      (input) COMPLEX
The (1,1) element of the 2-by-2 matrix.

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

C      (input) COMPLEX
The (2,2) element 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)	COMPLEX	 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  determi‐
nant  A*C-B*B; higher precision or correctly rounded or correctly trun‐
cated arithmetic would be needed	 to  compute  RT2  accurately  in  all
cases.
CS1  and	 SN1 are accurate to a few ulps barring over/underflow.	 Over‐
flow 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.

LAPACK auxiliary routine (versioNovember 2008			     CLAEV2(1)
```
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