claev2.f (3) Linux Manual Page
claev2.f –
Synopsis
Functions/Subroutines
subroutine claev2 (A, B, C, RT1, RT2, CS1, SN1)CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
Function/Subroutine Documentation
subroutine claev2 (complexA, complexB, complexC, realRT1, realRT2, realCS1, complexSN1)
CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose:
CLAEV2 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
A is COMPLEX
B
The (1,1) element of the 2-by-2 matrix.B is COMPLEX
C
The (1,2) element and the conjugate of the (2,1) element of
the 2-by-2 matrix.C is COMPLEX
RT1
The (2,2) element of the 2-by-2 matrix.RT1 is REAL
RT2
The eigenvalue of larger absolute value.RT2 is REAL
CS1
The eigenvalue of smaller absolute value.CS1 is REAL
SN1SN1 is COMPLEX
The vector (CS1, SN1) is a unit right eigenvector for RT1.
Author:
- Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
- September 2012
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 122 of file claev2.f.