Visible to Intel only — GUID: GUID-08891D48-80E5-40C7-84FD-D538434481ED
Visible to Intel only — GUID: GUID-08891D48-80E5-40C7-84FD-D538434481ED
?laed4
Used by sstedc/dstedc. Finds a single root of the secular equation.
Syntax
call slaed4( n, i, d, z, delta, rho, dlam, info )
call dlaed4( n, i, d, z, delta, rho, dlam, info )
Include Files
- mkl.fi
Description
This routine computes the i-th updated eigenvalue of a symmetric rank-one 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. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus
diag(D) + rho*Z * transpose(Z).
where we assume the Euclidean norm of Z is 1.
The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.
Input Parameters
- n
-
INTEGER. The length of all arrays.
- i
-
INTEGER. The index of the eigenvalue to be computed; 1 ≤ i ≤ n.
- d, z
-
REAL for slaed4
DOUBLE PRECISION for dlaed4
Arrays, dimension (n) each. The array d contains the original eigenvalues. It is assumed that they are in order, d(i) < d(j) for i < j.
The array z contains the components of the updating vector Z.
- rho
-
REAL for slaed4
DOUBLE PRECISION for dlaed4
The scalar in the symmetric updating formula.
Output Parameters
- delta
-
REAL for slaed4
DOUBLE PRECISION for dlaed4
Array, dimension (n).
If n≠ 1, delta contains (d(j) - lambda_i) in its j-th component. If n = 1, then delta(1) = 1. The vector delta contains the information necessary to construct the eigenvectors.
- dlam
-
REAL for slaed4
DOUBLE PRECISION for dlaed4
The computed lambda_i, the i-th updated eigenvalue.
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = 1, the updating process failed.