claev2.f (3)  Linux Manuals
NAME
claev2.f 
SYNOPSIS
Functions/Subroutines
subroutine claev2 (A, B, C, RT1, RT2, CS1, SN1)
CLAEV2 computes the eigenvalues and eigenvectors of a 2by2 symmetric/Hermitian matrix.
Function/Subroutine Documentation
subroutine claev2 (complexA, complexB, complexC, realRT1, realRT2, realCS1, complexSN1)
CLAEV2 computes the eigenvalues and eigenvectors of a 2by2 symmetric/Hermitian matrix.
Purpose:

CLAEV2 computes the eigendecomposition of a 2by2 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 The (1,1) element of the 2by2 matrix.
BB is COMPLEX The (1,2) element and the conjugate of the (2,1) element of the 2by2 matrix.
CC is COMPLEX The (2,2) element of the 2by2 matrix.
RT1RT1 is REAL The eigenvalue of larger absolute value.
RT2RT2 is REAL The eigenvalue of smaller absolute value.
CS1CS1 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*CB*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.
Author
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