1SLAED4(1)                LAPACK routine (version 3.2)                SLAED4(1)
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NAME

6       SLAED4  - subroutine compute the I-th updated eigenvalue of a symmetric
7       rank-one modification to a diagonal matrix whose elements are given  in
8       the array d, and that   D(i) < D(j) for i < j  and that RHO > 0
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SYNOPSIS

11       SUBROUTINE SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )
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13           INTEGER        I, INFO, N
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15           REAL           DLAM, RHO
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17           REAL           D( * ), DELTA( * ), Z( * )
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PURPOSE

20       This  subroutine  computes  the  I-th updated eigenvalue of a symmetric
21       rank-one modification to a diagonal matrix whose elements are given  in
22       the  array  d,  and  that no loss in generality.  The rank-one modified
23       system is thus
24                  diag( D )  +  RHO *  Z * Z_transpose.
25       where we assume the Euclidean norm of Z is 1.
26       The method consists of approximating the rational functions in the sec‐
27       ular equation by simpler interpolating rational functions.
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ARGUMENTS

30       N      (input) INTEGER
31              The length of all arrays.
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33       I      (input) INTEGER
34              The index of the eigenvalue to be computed.  1 <= I <= N.
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36       D      (input) REAL array, dimension (N)
37              The original eigenvalues.  It is assumed that they are in order,
38              D(I) < D(J)  for I < J.
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40       Z      (input) REAL array, dimension (N)
41              The components of the updating vector.
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43       DELTA  (output) REAL array, dimension (N)
44              If N .GT. 2, DELTA contains (D(j) - lambda_I) in its  j-th  com‐
45              ponent.   If  N = 1, then DELTA(1) = 1. If N = 2, see SLAED5 for
46              detail. The vector DELTA contains the information  necessary  to
47              construct the eigenvectors by SLAED3 and SLAED9.
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49       RHO    (input) REAL
50              The scalar in the symmetric updating formula.
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52       DLAM   (output) REAL
53              The computed lambda_I, the I-th updated eigenvalue.
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55       INFO   (output) INTEGER
56              = 0:  successful exit
57              > 0:  if INFO = 1, the updating process failed.
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PARAMETERS

60       Logical  variable  ORGATI  (origin-at-i?)  is  used  for distinguishing
61       whether D(i) or D(i+1) is treated  as  the  origin.   ORGATI  =  .true.
62       origin  at  i  ORGATI = .false.   origin at i+1 Logical variable SWTCH3
63       (switch-for-3-poles?) is for noting if we are working with THREE poles!
64       MAXIT  is the maximum number of iterations allowed for each eigenvalue.
65       Further Details =============== Based on contributions by Ren-Cang  Li,
66       Computer Science Division, University of California at Berkeley, USA
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70 LAPACK routine (version 3.2)    November 2008                       SLAED4(1)