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ZLAEV2(3F)							    ZLAEV2(3F)

NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

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

	 DOUBLE		PRECISION CS1, RT1, RT2

	 COMPLEX*16	A, B, C, SN1

PURPOSE    [Toc]    [Back]

     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 decomposition

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

ARGUMENTS    [Toc]    [Back]

     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 truncated
     arithmetic	would be needed	to compute RT2 accurately in all cases.

     CS1 and SN1 are accurate to a few ulps barring over/underflow.




									Page 1






ZLAEV2(3F)							    ZLAEV2(3F)



     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.
ZLAEV2(3F)							    ZLAEV2(3F)

NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

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

	 DOUBLE		PRECISION CS1, RT1, RT2

	 COMPLEX*16	A, B, C, SN1

PURPOSE    [Toc]    [Back]

     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 decomposition

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

ARGUMENTS    [Toc]    [Back]

     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 truncated
     arithmetic	would be needed	to compute RT2 accurately in all cases.

     CS1 and SN1 are accurate to a few ulps barring over/underflow.




									Page 1






ZLAEV2(3F)							    ZLAEV2(3F)



     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.


									PPPPaaaaggggeeee 2222
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