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RedHat 9 (Linux i386) - man page for dlaev2 (redhat section l)

DLAEV2(l)					)					DLAEV2(l)

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

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

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

PURPOSE
       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 decomposi-
       tion

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

ARGUMENTS
       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	eigenvec-
	       tor 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  com-
       pute 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 harm-
       less if the input data is 0 or exceeds
	  underflow_threshold / macheps.

LAPACK version 3.0			   15 June 2000 				DLAEV2(l)


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