slaev2.f(3) LAPACK slaev2.f(3)
subroutine slaev2 (A, B, C, RT1, RT2, CS1, SN1)
SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian
subroutine slaev2 (realA, realB, realC, realRT1, realRT2, realCS1, realSN1)
SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
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 ].
A is REAL
The (1,1) element of the 2-by-2 matrix.
B is REAL
The (1,2) element and the conjugate of the (2,1) element of
the 2-by-2 matrix.
C is REAL
The (2,2) element of the 2-by-2 matrix.
RT1 is REAL
The eigenvalue of larger absolute value.
RT2 is REAL
The eigenvalue of smaller absolute value.
CS1 is REAL
SN1 is REAL
The vector (CS1, SN1) is a unit right eigenvector for RT1.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
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.
Definition at line 121 of file slaev2.f.
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Version 3.4.2 Tue Sep 25 2012 slaev2.f(3)