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SLAEV2(3F)							    SLAEV2(3F)

NAME    [Toc]    [Back]

     SLAEV2 - compute the eigendecomposition of	a 2-by-2 symmetric matrix  [ A
     B ]  [ B C	]

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	SLAEV2(	A, B, C, RT1, RT2, CS1,	SN1 )

	 REAL		A, B, C, CS1, RT1, RT2,	SN1

PURPOSE    [Toc]    [Back]

     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    [Toc]    [Back]

     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 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






SLAEV2(3F)							    SLAEV2(3F)



	underflow_threshold / macheps.
SLAEV2(3F)							    SLAEV2(3F)

NAME    [Toc]    [Back]

     SLAEV2 - compute the eigendecomposition of	a 2-by-2 symmetric matrix  [ A
     B ]  [ B C	]

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	SLAEV2(	A, B, C, RT1, RT2, CS1,	SN1 )

	 REAL		A, B, C, CS1, RT1, RT2,	SN1

PURPOSE    [Toc]    [Back]

     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    [Toc]    [Back]

     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 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






SLAEV2(3F)							    SLAEV2(3F)



	underflow_threshold / macheps.


									PPPPaaaaggggeeee 2222
[ Back ]
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