SYNOPSIS

SUBROUTINE SLAEV2(

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

    

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

PURPOSE

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

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

   underflow_threshold / macheps.