SRC/slaev2.f(3)

NAME
SRC/slaev2.f

SYNOPSIS

  Functions/Subroutines
subroutine slaev2 (a, b, c, rt1, rt2, cs1, sn1)
SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Function/Subroutine Documentation

  subroutine slaev2 (real a, real b, real c, real rt1, real rt2, real cs1, real sn1)

SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Purpose:

    !>
    !> SLAEV2 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 REAL
    !>          The (1,1) element of the 2-by-2 matrix.
    !>

    B

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

    C

    !>          C is REAL
    !>          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 REAL
    !>          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 slaev2.f.

Author

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