lae2(3)

NAME
lae2 - lae2: 2x2 eig, step in steqr, stemr

SYNOPSIS

  Functions

subroutine dlae2 (a, b, c, rt1, rt2)
DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
subroutine slae2 (a, b, c, rt1, rt2)
SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Detailed Description

Function Documentation

  subroutine dlae2 (double precision a, double precision b, double precision c, double precision rt1, double precision rt2)

DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Purpose:

    !>
    !> DLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
    !>    [  A   B  ]
    !>    [  B   C  ].
    !> On return, RT1 is the eigenvalue of larger absolute value, and RT2
    !> is the eigenvalue of smaller absolute value.
    !>

Parameters
    A

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

    B

    !>          B is DOUBLE PRECISION
    !>          The (1,2) and (2,1) elements 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.
    !>

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.
    !>
    !>  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.
    !>

  subroutine slae2 (real a, real b, real c, real rt1, real rt2)

SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Purpose:

    !>
    !> SLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
    !>    [  A   B  ]
    !>    [  B   C  ].
    !> On return, RT1 is the eigenvalue of larger absolute value, and RT2
    !> is the eigenvalue of smaller absolute value.
    !>

Parameters
    A

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

    B

    !>          B is REAL
    !>          The (1,2) and (2,1) elements 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.
    !>

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.
    !>
    !>  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.
    !>

Author

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