dlaev2(3)

NAME

DLAEV2 - compute the eigendecomposition of a 2-by-2 sym

metric 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 symmet

ric 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, giv

ing the decomposition

[ 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 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 ac

curately in all cases.

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

flow.

Overflow is possible only if RT1 is within a factor of 5

of overflow. Underflow is harmless if the input data is 0 or ex

ceeds

underflow_threshold / macheps.

LAPACK version 3.0 15 June 2000

DLAEV2(3)