?lasd5

Computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix.Used by ?bdsdc.

Syntax

void slasd5( lapack_int *i, float *d, float *z, float *delta, float *rho, float *dsigma, float *work );

void dlasd5( lapack_int *i, double *d, double *z, double *delta, double *rho, double *dsigma, double *work );

Include Files

mkl.h

Description

The routine computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix diag(d)*diag(d)+rho*Z*Z^T

The diagonal entries in the array d must satisfy 0 ≤ d(i) < d(j) for i<i, rho mustbe greater than 0, and that the Euclidean norm of the vector Z is equal to 1.

Input Parameters

i

The index of the eigenvalue to be computed. i = 1 or i = 2.

d

Array, dimension (2 ).

The original eigenvalues, 0 ≤ d(1) < d(2).

z

Array, dimension ( 2 ).

The components of the updating vector.

rho

The scalar in the symmetric updating formula.

work

Workspace array, dimension ( 2 ). Contains (d(j) + sigma_i) in its j-th component.

Output Parameters

delta

Array, dimension ( 2 ).

Contains (d(j) - sigma_i) in its j-th component. The vector delta contains the information necessary to construct the eigenvectors.

dsigma

The computed sigma_i, the i-th updated eigenvalue.