man dlaev2 (Fonctions bibliothèques) - compute the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]
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 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.