zlaev2.f - Man Page

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

          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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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 120 of file zlaev2.f.