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claev2.f(3)				      LAPACK				      claev2.f(3)

NAME
       claev2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine claev2 (A, B, C, RT1, RT2, CS1, SN1)
	   CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian
	   matrix.

Function/Subroutine Documentation
   subroutine claev2 (complexA, complexB, complexC, realRT1, realRT2, realCS1, complexSN1)
       CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

       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 absolute value, RT2 is the
	    eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
	    eigenvector for RT1, giving the decomposition

	    [ CS1  CONJG(SN1) ] [    A	   B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
	    [-SN1     CS1     ] [ CONJG(B) C ] [ SN1	 CS1	 ]   [	0  RT2 ].

       Parameters:
	   A

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

	   B

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

	   C

		     C is COMPLEX
		    The (2,2) element of the 2-by-2 matrix.

	   RT1

		     RT1 is REAL
		    The eigenvalue of larger absolute value.

	   RT2

		     RT2 is REAL
		    The eigenvalue of smaller absolute value.

	   CS1

		     CS1 is REAL

	   SN1

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       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.

       Definition at line 122 of file claev2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      claev2.f(3)
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