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DLAED4(l)) DLAED4(l)DLAED4 - 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 > 0NAMESUBROUTINE DLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO ) INTEGER I, INFO, N DOUBLE PRECISION DLAM, RHO DOUBLE PRECISION D( * ), DELTA( * ), Z( * )SYNOPSISThis 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.PURPOSEN (input) INTEGER The length of all arrays. I (input) INTEGER The index of the eigenvalue to be computed. 1 <= I <= N. D (input) DOUBLE PRECISION array, dimension (N) The original eigenvalues. It is assumed that they are in order, D(I) < D(J) for I < J. Z (input) DOUBLE PRECISION array, dimension (N) The components of the updating vector. DELTA (output) DOUBLE PRECISION 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) DOUBLE PRECISION The scalar in the symmetric updating formula. DLAM (output) DOUBLE PRECISION The computed lambda_I, the I-th updated eigenvalue. INFO (output) INTEGER = 0: successful exit > 0: if INFO = 1, the updating process failed.ARGUMENTSLogical 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. Further Details =============== Based on contributions by Ren-Cang Li, Computer Science Division, University of California at Berkeley, USAPARAMETERSLAPACK version 3.015 June 2000 DLAED4(l)

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