?lasd5
?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 ≤
for d
(i) < d
(j)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.ori= 1.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 () in itsd(j) +sigma_ij-th component.
Output Parameters
- delta
- Array,dimension( 2 ).Contains () in itsd(j) -sigma_ij-th component. The vectordeltacontains the information necessary to construct the eigenvectors.
- dsigma
- The computedsigma_i, thei-th updated eigenvalue.