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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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| subroutine slaed4 | ( | integer | N, |
| integer | I, | ||
| real, dimension( * ) | D, | ||
| real, dimension( * ) | Z, | ||
| real, dimension( * ) | DELTA, | ||
| real | RHO, | ||
| real | DLAM, | ||
| integer | INFO | ||
| ) |
SLAED4 used by sstedc. Finds a single root of the secular equation.
Download SLAED4 + dependencies [TGZ] [ZIP] [TXT]
This subroutine 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 * Z_transpose.
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. | [in] | N | N is INTEGER
The length of all arrays. |
| [in] | I | I is INTEGER
The index of the eigenvalue to be computed. 1 <= I <= N. |
| [in] | D | D is REAL array, dimension (N)
The original eigenvalues. It is assumed that they are in
order, D(I) < D(J) for I < J. |
| [in] | Z | Z is REAL array, dimension (N)
The components of the updating vector. |
| [out] | DELTA | DELTA is REAL array, dimension (N)
If N .GT. 2, DELTA contains (D(j) - lambda_I) in its j-th
component. If N = 1, then DELTA(1) = 1. If N = 2, see SLAED5
for detail. The vector DELTA contains the information necessary
to construct the eigenvectors by SLAED3 and SLAED9. |
| [in] | RHO | RHO is REAL
The scalar in the symmetric updating formula. |
| [out] | DLAM | DLAM is REAL
The computed lambda_I, the I-th updated eigenvalue. |
| [out] | INFO | INFO is INTEGER
= 0: successful exit
> 0: if INFO = 1, the updating process failed. |
Logical variable ORGATI (origin-at-i?) is used for distinguishing
whether D(i) or D(i+1) is treated as the origin.
ORGATI = .true. origin at i
ORGATI = .false. origin at i+1
Logical variable SWTCH3 (switch-for-3-poles?) is for noting
if we are working with THREE poles!
MAXIT is the maximum number of iterations allowed for each
eigenvalue.