redhat man page for slaev2

SLAEV2(l)								 )								 SLAEV2(l)

NAME
       SLAEV2 - compute the eigendecomposition of a 2-by-2 symmetric 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) element of the 2-by-2 matrix.

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

       C       (input) REAL
	       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) 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 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.

       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.

LAPACK version 3.0						   15 June 2000 							 SLAEV2(l)