# ?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 )

## Description

This subroutine 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.

## Input Parameters

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.

## Output Parameters

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.

Parent topic: Auxiliary Routines