lasd5

slasd5

Functions

void slasd5(
    const INT           i,
    const f32* restrict D,
    const f32* restrict Z,
          f32* restrict delta,
    const f32           rho,
          f32*          dsigma,
          f32* restrict work
);

void slasd5(const INT i, const f32 *restrict D, const f32 *restrict Z, f32 *restrict delta, const f32 rho, f32 *dsigma, f32 *restrict work)

SLASD5 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 D are assumed to satisfy 0 <= D[0] < D[1]. We also assume RHO > 0 and that the Euclidean norm of Z is one.

Parameters

in

i

The index of the eigenvalue to be computed. i = 0 or i = 1.

in

D

Array of dimension 2. The original eigenvalues. 0 <= D[0] < D[1].

in

Z

Array of dimension 2. The components of the updating vector.

out

delta

Array of dimension 2. Contains (D[j] - sigma_i) in its j-th component.

in

rho

The scalar in the symmetric updating formula.

out

dsigma

The computed sigma_i, the i-th updated eigenvalue.

out

work

Array of dimension 2. Contains (D[j] + sigma_i) in its j-th component.

dlasd5

Functions

void dlasd5(
    const INT           i,
    const f64* restrict D,
    const f64* restrict Z,
          f64* restrict delta,
    const f64           rho,
          f64*          dsigma,
          f64* restrict work
);

void dlasd5(const INT i, const f64 *restrict D, const f64 *restrict Z, f64 *restrict delta, const f64 rho, f64 *dsigma, f64 *restrict work)

DLASD5 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 D are assumed to satisfy 0 <= D[0] < D[1]. We also assume RHO > 0 and that the Euclidean norm of Z is one.

Parameters

in

i

The index of the eigenvalue to be computed. i = 0 or i = 1.

in

D

Array of dimension 2. The original eigenvalues. 0 <= D[0] < D[1].

in

Z

Array of dimension 2. The components of the updating vector.

out

delta

Array of dimension 2. Contains (D[j] - sigma_i) in its j-th component.

in

rho

The scalar in the symmetric updating formula.

out

dsigma

The computed sigma_i, the i-th updated eigenvalue.

out

work

Array of dimension 2. Contains (D[j] + sigma_i) in its j-th component.