claev2-f(3)

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 is COMPLEX
 The (1,1) element of the 2-by-2 matrix.

 B is COMPLEX
 The (1,2) element and the conjugate of the (2,1) element of
 the 2-by-2 matrix.

 C is COMPLEX
 The (2,2) element of the 2-by-2 matrix.

RT1

 RT1 is REAL
 The eigenvalue of larger absolute value.

RT2

 RT2 is REAL
 The eigenvalue of smaller absolute value.

CS1

 CS1 is REAL

SN1

 SN1 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.

Author

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