dlae2 (l)  Linux Manuals
dlae2: computes the eigenvalues of a 2by2 symmetric matrix [ A B ] [ B C ]
Command to display dlae2
manual in Linux: $ man l dlae2
NAME
DLAE2  computes the eigenvalues of a 2by2 symmetric matrix [ A B ] [ B C ]
SYNOPSIS
 SUBROUTINE DLAE2(

A, B, C, RT1, RT2 )

DOUBLE
PRECISION A, B, C, RT1, RT2
PURPOSE
DLAE2 computes the eigenvalues of a 2by2 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.
ARGUMENTS
 A (input) DOUBLE PRECISION

The (1,1) element of the 2by2 matrix.
 B (input) DOUBLE PRECISION

The (1,2) and (2,1) elements of the 2by2 matrix.
 C (input) DOUBLE PRECISION

The (2,2) element of the 2by2 matrix.
 RT1 (output) DOUBLE PRECISION

The eigenvalue of larger absolute value.
 RT2 (output) DOUBLE PRECISION

The eigenvalue of smaller absolute value.
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*CB*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.
Pages related to dlae2
 dlae2 (3)
 dlaebz (l)  contains the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
 dlaed0 (l)  computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
 dlaed1 (l)  computes the updated eigensystem of a diagonal matrix after modification by a rankone symmetric matrix
 dlaed2 (l)  merges the two sets of eigenvalues together into a single sorted set
 dlaed3 (l)  finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
 dlaed4 (l)  subroutine compute the Ith updated eigenvalue of a symmetric rankone modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
 dlaed5 (l)  subroutine compute the Ith eigenvalue of a symmetric rankone modification of a 2by2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j
 dlaed6 (l)  computes the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho +  +  +  d(1)x d(2)x d(3)x It is assumed that if ORGATI = .true
 dlaed7 (l)  computes the updated eigensystem of a diagonal matrix after modification by a rankone symmetric matrix
 dlaed8 (l)  merges the two sets of eigenvalues together into a single sorted set