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DLAEV2(3F)							    DLAEV2(3F)

NAME    [Toc]    [Back]

     DLAEV2 - compute the eigendecomposition of	a 2-by-2 symmetric matrix  [ A
     B ]  [ B C	]

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DLAEV2(	A, B, C, RT1, RT2, CS1,	SN1 )

	 DOUBLE		PRECISION A, B,	C, CS1,	RT1, RT2, SN1

PURPOSE    [Toc]    [Back]

     DLAEV2 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    [Toc]    [Back]

     A	     (input) DOUBLE PRECISION
	     The (1,1) element of the 2-by-2 matrix.

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

     C	     (input) DOUBLE PRECISION
	     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) DOUBLE PRECISION 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.

     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



									Page 1






DLAEV2(3F)							    DLAEV2(3F)



	underflow_threshold / macheps.
DLAEV2(3F)							    DLAEV2(3F)

NAME    [Toc]    [Back]

     DLAEV2 - compute the eigendecomposition of	a 2-by-2 symmetric matrix  [ A
     B ]  [ B C	]

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DLAEV2(	A, B, C, RT1, RT2, CS1,	SN1 )

	 DOUBLE		PRECISION A, B,	C, CS1,	RT1, RT2, SN1

PURPOSE    [Toc]    [Back]

     DLAEV2 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    [Toc]    [Back]

     A	     (input) DOUBLE PRECISION
	     The (1,1) element of the 2-by-2 matrix.

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

     C	     (input) DOUBLE PRECISION
	     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) DOUBLE PRECISION 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.

     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



									Page 1






DLAEV2(3F)							    DLAEV2(3F)



	underflow_threshold / macheps.


									PPPPaaaaggggeeee 2222
[ Back ]
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