1SLASD8(1)           LAPACK auxiliary routine (version 3.1)           SLASD8(1)
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NAME

6       SLASD8 - the square roots of the roots of the secular equation,
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SYNOPSIS

9       SUBROUTINE SLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, DSIGMA,
10                          WORK, INFO )
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12           INTEGER        ICOMPQ, INFO, K, LDDIFR
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14           REAL           D( * ), DIFL( * ), DIFR( LDDIFR, * ), DSIGMA(  *  ),
15                          VF( * ), VL( * ), WORK( * ), Z( * )
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PURPOSE

18       SLASD8  finds the square roots of the roots of the secular equation, as
19       defined by the values in DSIGMA and Z. It makes the  appropriate  calls
20       to  SLASD4, and stores, for each  element in D, the distance to its two
21       nearest poles (elements in DSIGMA). It also updates the arrays  VF  and
22       VL,  the first and last components of all the right singular vectors of
23       the original bidiagonal matrix.
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25       SLASD8 is called from SLASD6.
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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:
32               = 0: Compute singular values only.
33               = 1: Compute singular vectors in factored form as well.
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35       K       (input) INTEGER
36               The  number  of  terms in the rational function to be solved by
37               SLASD4.  K >= 1.
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39       D       (output) REAL array, dimension ( K )
40               On output, D contains the updated singular values.
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42       Z       (input) REAL array, dimension ( K )
43               The first K elements of this array contain  the  components  of
44               the deflation-adjusted updating row vector.
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46       VF      (input/output) REAL array, dimension ( K )
47               On  entry,  VF contains  information passed through DBEDE8.  On
48               exit, VF contains the first K components of  the  first  compo‐
49               nents of all right singular vectors of the bidiagonal matrix.
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51       VL      (input/output) REAL array, dimension ( K )
52               On  entry,  VL contains  information passed through DBEDE8.  On
53               exit, VL contains the first K components of the last components
54               of all right singular vectors of the bidiagonal matrix.
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56       DIFL    (output) REAL array, dimension ( K )
57               On exit, DIFL(I) = D(I) - DSIGMA(I).
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59       DIFR    (output) REAL array,
60               dimension  (  LDDIFR,  2 ) if ICOMPQ = 1 and dimension ( K ) if
61               ICOMPQ = 0.  On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1)
62               is not defined and will not be referenced.
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64               If ICOMPQ = 1, DIFR(1:K,2) is an array containing the normaliz‐
65               ing factors for the right singular vector matrix.
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67       LDDIFR  (input) INTEGER
68               The leading dimension of DIFR, must be at least K.
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70       DSIGMA  (input) REAL array, dimension ( K )
71               The first K elements of this array contain the old roots of the
72               deflated  updating problem.  These are the poles of the secular
73               equation.
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75       WORK    (workspace) REAL array, dimension at least 3 * K
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77       INFO    (output) INTEGER
78               = 0:  successful exit.
79               < 0:  if INFO = -i, the i-th argument had an illegal value.
80               > 0:  if INFO = 1, an singular value did not converge
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FURTHER DETAILS

83       Based on contributions by
84          Ming Gu and Huan Ren, Computer Science Division, University of
85          California at Berkeley, USA
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90 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLASD8(1)