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lae2(3) Library Functions Manual 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.
!>

Definition at line 101 of file dlae2.f.

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.
!>

Definition at line 101 of file slae2.f.

Author

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