SRC/zlaev2.f(3)            Library Functions Manual            SRC/zlaev2.f(3)

NAME
       SRC/zlaev2.f

SYNOPSIS
   Functions/Subroutines
       subroutine zlaev2 (a, b, c, rt1, rt2, cs1, sn1)
           ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2
           symmetric/Hermitian matrix.

Function/Subroutine Documentation
   subroutine zlaev2 (complex*16 a, complex*16 b, complex*16 c, double
       precision rt1, double precision rt2, double precision cs1, complex*16
       sn1)
       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.

Author
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LAPACK                          Version 3.12.0                 SRC/zlaev2.f(3)