1SLAED9(1)                LAPACK routine (version 3.2)                SLAED9(1)
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NAME

6       SLAED9  -  finds  the  roots of the secular equation, as defined by the
7       values in D, Z, and RHO, between KSTART and KSTOP
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SYNOPSIS

10       SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA,  W,  S,
11                          LDS, INFO )
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13           INTEGER        INFO, K, KSTART, KSTOP, LDQ, LDS, N
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15           REAL           RHO
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17           REAL           D(  * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), W( *
18                          )
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PURPOSE

21       SLAED9 finds the roots of the secular equation, as defined by the  val‐
22       ues in D, Z, and RHO, between KSTART and KSTOP.  It makes the appropri‐
23       ate calls to SLAED4 and then stores the new matrix of eigenvectors  for
24       use in calculating the next level of Z vectors.
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ARGUMENTS

27       K       (input) INTEGER
28               The  number  of  terms in the rational function to be solved by
29               SLAED4.  K >= 0.
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31       KSTART  (input) INTEGER
32               KSTOP   (input)  INTEGER  The  updated  eigenvalues  Lambda(I),
33               KSTART  <= I <= KSTOP are to be computed.  1 <= KSTART <= KSTOP
34               <= K.
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36       N       (input) INTEGER
37               The number of rows and columns in the Q matrix.  N >= K  (dela‐
38               tion may result in N > K).
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40       D       (output) REAL array, dimension (N)
41               D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.
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43       Q       (workspace) REAL array, dimension (LDQ,N)
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45       LDQ     (input) INTEGER
46               The leading dimension of the array Q.  LDQ >= max( 1, N ).
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48       RHO     (input) REAL
49               The  value  of  the  parameter in the rank one update equation.
50               RHO >= 0 required.
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52       DLAMDA  (input) REAL array, dimension (K)
53               The first K elements of this array contain the old roots of the
54               deflated  updating problem.  These are the poles of the secular
55               equation.
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57       W       (input) REAL array, dimension (K)
58               The first K elements of this array contain  the  components  of
59               the deflation-adjusted updating vector.
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61       S       (output) REAL array, dimension (LDS, K)
62               Will contain the eigenvectors of the repaired matrix which will
63               be stored for subsequent Z vector calculation and multiplied by
64               the previously accumulated eigenvectors to update the system.
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66       LDS     (input) INTEGER
67               The leading dimension of S.  LDS >= max( 1, K ).
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69       INFO    (output) INTEGER
70               = 0:  successful exit.
71               < 0:  if INFO = -i, the i-th argument had an illegal value.
72               > 0:  if INFO = 1, an eigenvalue did not converge
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FURTHER DETAILS

75       Based on contributions by
76          Jeff Rutter, Computer Science Division, University of California
77          at Berkeley, USA
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81 LAPACK routine (version 3.2)    November 2008                       SLAED9(1)