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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
|
| subroutine dlasd4 | ( | integer | N, |
| integer | I, | ||
| double precision, dimension( * ) | D, | ||
| double precision, dimension( * ) | Z, | ||
| double precision, dimension( * ) | DELTA, | ||
| double precision | RHO, | ||
| double precision | SIGMA, | ||
| double precision, dimension( * ) | WORK, | ||
| integer | INFO | ||
| ) |
DLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by dbdsdc.
Download DLASD4 + dependencies [TGZ] [ZIP] [TXT]
This subroutine computes the square root of the I-th updated
eigenvalue of a positive symmetric rank-one modification to
a positive diagonal matrix whose entries are given as the squares
of the corresponding entries in the array d, and that
0 <= 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 ) * 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 DOUBLE PRECISION array, dimension ( N )
The original eigenvalues. It is assumed that they are in
order, 0 <= D(I) < D(J) for I < J. |
| [in] | Z | Z is DOUBLE PRECISION array, dimension ( N )
The components of the updating vector. |
| [out] | DELTA | DELTA is DOUBLE PRECISION array, dimension ( N )
If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th
component. If N = 1, then DELTA(1) = 1. The vector DELTA
contains the information necessary to construct the
(singular) eigenvectors. |
| [in] | RHO | RHO is DOUBLE PRECISION
The scalar in the symmetric updating formula. |
| [out] | SIGMA | SIGMA is DOUBLE PRECISION
The computed sigma_I, the I-th updated eigenvalue. |
| [out] | WORK | WORK is DOUBLE PRECISION array, dimension ( N )
If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th
component. If N = 1, then WORK( 1 ) = 1. |
| [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.