SLAED4(3F) SLAED4(3F)
SLAED4 - 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
SUBROUTINE SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )
INTEGER I, INFO, N
REAL DLAM, RHO
REAL D( * ), DELTA( * ), Z( * )
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 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.
N (input) INTEGER
The length of all arrays.
I (input) INTEGER
The index of the eigenvalue to be computed. 1 <= I <= N.
D (input) REAL array, dimension (N)
The original eigenvalues. It is assumed that they are in order,
D(I) < D(J) for I < J.
Z (input) REAL array, dimension (N)
The components of the updating vector.
DELTA (output) REAL array, dimension (N)
If N .ne. 1, DELTA contains (D(j) - lambda_I) in its j-th
component. If N = 1, then DELTA(1) = 1. The vector DELTA
contains the information necessary to construct the eigenvectors.
RHO (input) REAL
The scalar in the symmetric updating formula.
Page 1
SLAED4(3F) SLAED4(3F)
DLAM (output) REAL
The computed lambda_I, the I-th updated eigenvalue.
INFO (output) 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.
SLAED4(3F) SLAED4(3F)
SLAED4 - 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
SUBROUTINE SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )
INTEGER I, INFO, N
REAL DLAM, RHO
REAL D( * ), DELTA( * ), Z( * )
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 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.
N (input) INTEGER
The length of all arrays.
I (input) INTEGER
The index of the eigenvalue to be computed. 1 <= I <= N.
D (input) REAL array, dimension (N)
The original eigenvalues. It is assumed that they are in order,
D(I) < D(J) for I < J.
Z (input) REAL array, dimension (N)
The components of the updating vector.
DELTA (output) REAL array, dimension (N)
If N .ne. 1, DELTA contains (D(j) - lambda_I) in its j-th
component. If N = 1, then DELTA(1) = 1. The vector DELTA
contains the information necessary to construct the eigenvectors.
RHO (input) REAL
The scalar in the symmetric updating formula.
Page 1
SLAED4(3F) SLAED4(3F)
DLAM (output) REAL
The computed lambda_I, the I-th updated eigenvalue.
INFO (output) 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.
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