SRC/dlaev2.f(3)

NAME
SRC/dlaev2.f

SYNOPSIS

  Functions/Subroutines
subroutine dlaev2 (a, b, c, rt1, rt2, cs1, sn1)
DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Function/Subroutine Documentation

  subroutine dlaev2 (double precision a, double precision b, double precision c, double precision rt1, double precision rt2, double precision cs1, double precision sn1)

DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Purpose:

    !>
    !> DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
    !>    [  A   B  ]
    !>    [  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  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]
    !>    [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].
    !>

Parameters
    A

    !>          A is DOUBLE PRECISION
    !>          The (1,1) element of the 2-by-2 matrix.
    !>

    B

    !>          B is DOUBLE PRECISION
    !>          The (1,2) element and the conjugate of the (2,1) element of
    !>          the 2-by-2 matrix.
    !>

    C

    !>          C is DOUBLE PRECISION
    !>          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 DOUBLE PRECISION
    !>          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 119 of file dlaev2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.