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 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 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

   underflow_threshold / macheps.