1SLASD8(1)           LAPACK auxiliary routine (version 3.2)           SLASD8(1)
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NAME

6       SLASD8 - finds 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.  SLASD8 is called from SLASD6.
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ARGUMENTS

26       ICOMPQ  (input) INTEGER
27               Specifies whether singular vectors are to be computed  in  fac‐
28               tored form in the calling routine:
29               = 0: Compute singular values only.
30               = 1: Compute singular vectors in factored form as well.
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32       K       (input) INTEGER
33               The  number  of  terms in the rational function to be solved by
34               SLASD4.  K >= 1.
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36       D       (output) REAL array, dimension ( K )
37               On output, D contains the updated singular values.
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39       Z       (input/output) REAL array, dimension ( K )
40               On entry, the first K elements of this array contain the compo‐
41               nents  of the deflation-adjusted updating row vector.  On exit,
42               Z is updated.
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44       VF      (input/output) REAL array, dimension ( K )
45               On entry, VF contains  information passed through  DBEDE8.   On
46               exit,  VF  contains  the first K components of the first compo‐
47               nents of all right singular vectors of the bidiagonal matrix.
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49       VL      (input/output) REAL array, dimension ( K )
50               On entry, VL contains  information passed through  DBEDE8.   On
51               exit, VL contains the first K components of the last components
52               of all right singular vectors of the bidiagonal matrix.
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54       DIFL    (output) REAL array, dimension ( K )
55               On exit, DIFL(I) = D(I) - DSIGMA(I).
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57       DIFR    (output) REAL array,
58               dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and dimension (  K  )  if
59               ICOMPQ = 0.  On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1)
60               is not defined and will not be  referenced.   If  ICOMPQ  =  1,
61               DIFR(1:K,2)  is an array containing the normalizing factors for
62               the right singular vector matrix.
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64       LDDIFR  (input) INTEGER
65               The leading dimension of DIFR, must be at least K.
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67       DSIGMA  (input/output) REAL array, dimension ( K )
68               On entry, the first K elements of this array  contain  the  old
69               roots of the deflated updating problem.  These are the poles of
70               the secular equation.  On exit, the elements of DSIGMA  may  be
71               very slightly altered in value.
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73       WORK    (workspace) REAL array, dimension at least 3 * K
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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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87 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLASD8(1)