claesy man page on Scientific

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

NAME
CLAESY  -  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

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

COMPLEX	  A, B, C, CS1, EVSCAL, RT1, RT2, SN1

PURPOSE
CLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix
(  (	A, B );( B, C ) ) provided the norm of the matrix of eigenvec‐
tors 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 ]

ARGUMENTS
A       (input) COMPLEX
The ( 1, 1 ) element of input matrix.

B       (input) COMPLEX
The  ( 1, 2 ) element of input matrix.  The ( 2, 1 ) element is
also given by B, since the 2-by-2 matrix is symmetric.

C       (input) COMPLEX
The ( 2, 2 ) element of input matrix.

RT1     (output) COMPLEX
The eigenvalue of larger modulus.

RT2     (output) COMPLEX
The eigenvalue of smaller modulus.

EVSCAL  (output) COMPLEX
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 eigen‐
vectors before scaling was  larger  than	 the  threshold	 value
THRESH (set below).

CS1     (output) COMPLEX
SN1     (output) COMPLEX If EVSCAL .NE. 0,  ( CS1, SN1 ) is the
unit right eigenvector for RT1.

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