1SLASD9(l)                              )                             SLASD9(l)
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NAME

6       SLASD9 - find the square roots of the roots of the secular equation,
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SYNOPSIS

9       SUBROUTINE SLASD9( ICOMPQ,  LDU,  K,  D, Z, VF, VL, DIFL, DIFR, DSIGMA,
10                          WORK, INFO )
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12           INTEGER        ICOMPQ, INFO, K, LDU
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14           REAL           D( * ), DIFL( * ), DIFR( LDU, * ), DSIGMA( * ),  VF(
15                          * ), VL( * ), WORK( * ), Z( * )
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PURPOSE

18       SLASD9  finds the square roots of the roots of the secular equation, as
19       defined by the values in DSIGMA and Z.  It makes the
20       appropriate calls to SLASD4, and stores, for each  element  in  D,  the
21       distance to its two nearest poles (elements in DSIGMA). It also updates
22       the arrays VF and VL, the first and last components of  all  the  right
23       singular vectors of the original bidiagonal matrix.
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25       SLASD9 is called from SLASD7.
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ARGUMENTS

29       ICOMPQ  (input) INTEGER
30               Specifies  whether  singular vectors are to be computed in fac‐
31               tored form in the calling routine:
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33               ICOMPQ = 0             Compute singular values only.
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35               ICOMPQ = 1             Compute singular vector matrices in fac‐
36               tored  form  also.  K       (input) INTEGER The number of terms
37               in the rational function to be solved by SLASD4.  K >= 1.
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39       D       (output) REAL array, dimension(K)
40               D(I) contains the updated singular values.
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42       DSIGMA  (input) REAL array, dimension(K)
43               The first K elements of this array contain the old roots of the
44               deflated  updating problem.  These are the poles of the secular
45               equation.
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47       Z       (input) REAL array, dimension (K)
48               The first K elements of this array contain  the  components  of
49               the deflation-adjusted updating row vector.
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51       VF      (input/output) REAL array, dimension(K)
52               On  entry,  VF contains  information passed through SBEDE8.f On
53               exit, VF contains the first K components of  the  first  compo‐
54               nents of all right singular vectors of the bidiagonal matrix.
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56       VL      (input/output) REAL array, dimension(K)
57               On  entry,  VL contains  information passed through SBEDE8.f On
58               exit, VL contains the first K components of the last components
59               of all right singular vectors of the bidiagonal matrix.
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61       DIFL    (output) REAL array, dimension (K).
62               On exit, DIFL(I) = D(I) - DSIGMA(I).
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64       DIFR    (output) REAL array,
65               dimension  (LDU,  2) if ICOMPQ =1 and dimension (K) if ICOMPQ =
66               0.  On exit, DIFR(I, 1) = D(I) - DSIGMA(I+1), DIFR(K, 1) is not
67               defined and will not be referenced.
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69               If  ICOMPQ = 1, DIFR(1:K, 2) is an array containing the normal‐
70               izing factors for the right singular vector matrix.
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72       WORK    (workspace) REAL array,
73               dimension at least (3 * K) Workspace.
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75       INFO    (output) INTEGER
76               = 0:  successful exit.
77               < 0:  if INFO = -i, the i-th argument had an illegal value.
78               > 0:  if INFO = 1, an singular value did not converge
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FURTHER DETAILS

81       Based on contributions by
82          Ming Gu and Huan Ren, Computer Science Division, University of
83          California at Berkeley, USA
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88LAPACK version 3.0               15 June 2000                        SLASD9(l)