?laed5

Used by sstedc/dstedc. Solves the 2-by-2 secular equation.

Syntax

call slaed5( i, d, z, delta, rho, dlam )

call dlaed5( i, d, z, delta, rho, dlam )

The routine computes the i-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix

diag(D) + rho*Z * transpose(Z).

The diagonal elements in the array D are assumed to satisfy

D(i) < D(j) for i < j.

We also assume rho > 0 and that the Euclidean norm of the vector Z is one.

i

INTEGER. The index of the eigenvalue to be computed;

1 ≤ i ≤ 2.

d, z

REAL for slaed5

DOUBLE PRECISION for dlaed5

Arrays, dimension (2) each. The array d contains the original eigenvalues. It is assumed that d(1) < d(2).

The array z contains the components of the updating vector.

rho

REAL for slaed5

DOUBLE PRECISION for dlaed5

The scalar in the symmetric updating formula.

delta

REAL for slaed5

DOUBLE PRECISION for dlaed5

Array, dimension (2).

The vector delta contains the information necessary to construct the eigenvectors.

dlam

REAL for slaed5

DOUBLE PRECISION for dlaed5

The computed lambda_i, the i-th updated eigenvalue.