Visible to Intel only — GUID: GUID-4AAC4E4D-6A71-4CC7-94A7-E45B5796E3A6
Visible to Intel only — GUID: GUID-4AAC4E4D-6A71-4CC7-94A7-E45B5796E3A6
?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
call slasd5( i, d, z, delta, rho, dsigma, work )
call dlasd5( i, d, z, delta, rho, dsigma, work )
Include Files
- mkl.fi
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*ZT
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
-
INTEGER.The index of the eigenvalue to be computed. i = 1 or i = 2.
- d
-
REAL for slasd5
DOUBLE PRECISION for dlasd5
Array, dimension (2 ).
The original eigenvalues, 0 ≤ d(1) < d(2).
- z
-
REAL for slasd5
DOUBLE PRECISION for dlasd5
Array, dimension ( 2 ).
The components of the updating vector.
- rho
-
REAL for slasd5
DOUBLE PRECISION for dlasd5
The scalar in the symmetric updating formula.
- work
-
REAL for slasd5
DOUBLE PRECISION for dlasd5
Workspace array, dimension ( 2 ). Contains (d(j) + sigma_i) in its j-th component.
Output Parameters
- delta
-
REAL for slasd5
DOUBLE PRECISION for dlasd5
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
-
REAL for slasd5
DOUBLE PRECISION for dlasd5
The computed sigma_i, the i-th updated eigenvalue.