subroutine zlaev2 (A, B, C, RT1, RT2, CS1, SN1)
ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
Purpose:
ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
[ A B ]
[ CONJG(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 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ]
[-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ].
Parameters:
A is COMPLEX*16
The (1,1) element of the 2-by-2 matrix.
B
B is COMPLEX*16
The (1,2) element and the conjugate of the (2,1) element of
the 2-by-2 matrix.
C
C is COMPLEX*16
The (2,2) element of the 2-by-2 matrix.
RT1
RT1 is DOUBLE PRECISION
The eigenvalue of larger absolute value.
RT2
RT2 is DOUBLE PRECISION
The eigenvalue of smaller absolute value.
CS1
CS1 is DOUBLE PRECISION
SN1
SN1 is COMPLEX*16
The vector (CS1, SN1) is a unit right eigenvector for RT1.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
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.
Definition at line 123 of file zlaev2.f.
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