redhat man page for zlaev2

ZLAEV2(l)								 )								 ZLAEV2(l)

NAME
       ZLAEV2 - compute the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]

SYNOPSIS
       SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

	   DOUBLE	  PRECISION CS1, RT1, RT2

	   COMPLEX*16	  A, B, C, SN1

PURPOSE
       ZLAEV2  computes  the  eigendecomposition  of  a 2-by-2 Hermitian matrix [ A B ] [ CONJG(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 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*16
	      The (1,1) element of the 2-by-2 matrix.

       B      (input) COMPLEX*16
	      The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix.

       C      (input) COMPLEX*16
	      The (2,2) element of the 2-by-2 matrix.

       RT1    (output) DOUBLE PRECISION
	      The eigenvalue of larger absolute value.

       RT2    (output) DOUBLE PRECISION
	      The eigenvalue of smaller absolute value.

       CS1    (output) DOUBLE PRECISION
	      SN1    (output) COMPLEX*16 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 							 ZLAEV2(l)