slaev2 (l) - Linux Man Pages

slaev2: computes the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]

NAME

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

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
    ]
    ]. 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     CS1 -SN1   RT1   ]

[-SN1  CS1     SN1  CS1       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.