claev2.f File Reference

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Functions/Subroutines
subroutine	CLAEV2 (A, B, C, RT1, RT2, CS1, SN1)
	CLAEV2

---

Function/Subroutine Documentation

subroutine CLAEV2	(	COMPLEX	A,
		COMPLEX	B,
		COMPLEX	C,
		REAL	RT1,
		REAL	RT2,
		REAL	CS1,
		COMPLEX	SN1
	)

CLAEV2

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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:

[in]	A	A is COMPLEX The (1,1) element of the 2-by-2 matrix.
[in]	B	B is COMPLEX The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix.
[in]	C	C is COMPLEX The (2,2) element of the 2-by-2 matrix.
[out]	RT1	RT1 is REAL The eigenvalue of larger absolute value.
[out]	RT2	RT2 is REAL The eigenvalue of smaller absolute value.
[out]	CS1	CS1 is REAL
[out]	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:

November 2011

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.

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