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template<typename T>
void lasd4(integer *n, integer *i, T *d, T *z, T *delta, T *rho, T *sigma, T *work, integer *info)# LASD4 computes the square root of the i-th updated eigenvalue
of a positive symmetric rank-one modification to a positive diagonal
matrix. Used by sbdsdc.Purpose:
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.
- Parameters:
N – [in]
N is INTEGER
The length of all arrays.
I – [in]
I is INTEGER
The index of the eigenvalue to be computed. 1 <= I <= N.
D – [in]
D is REAL array, dimension (N)
The original eigenvalues. It is assumed that they are in order, 0 <= D(I) < D(J) for I < J.
Z – [in]
Z is REAL array, dimension (N)
The components of the updating vector.
DELTA – [out]
DELTA is REAL 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.
RHO – [in]
RHO is REAL
The scalar in the symmetric updating formula.
SIGMA – [out]
SIGMA is REAL
The computed sigma_I, the I-th updated eigenvalue.
WORK – [out]
WORK is REAL 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.
INFO – [out]
INFO is INTEGER
= 0: successful exit
> 0: if INFO = 1, the updating process failed.