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SUBROUTINE <a name="DLASD8.1"></a><a href="dlasd8.f.html#DLASD8.1">DLASD8</a>( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR,
$ DSIGMA, WORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> INTEGER ICOMPQ, INFO, K, LDDIFR
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> DOUBLE PRECISION D( * ), DIFL( * ), DIFR( LDDIFR, * ),
$ DSIGMA( * ), VF( * ), VL( * ), WORK( * ),
$ Z( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DLASD8.20"></a><a href="dlasd8.f.html#DLASD8.1">DLASD8</a> finds the square roots of the roots of the secular equation,
</span><span class="comment">*</span><span class="comment"> as defined by the values in DSIGMA and Z. It makes the appropriate
</span><span class="comment">*</span><span class="comment"> calls to <a name="DLASD4.22"></a><a href="dlasd4.f.html#DLASD4.1">DLASD4</a>, and stores, for each element in D, the distance
</span><span class="comment">*</span><span class="comment"> to its two nearest poles (elements in DSIGMA). It also updates
</span><span class="comment">*</span><span class="comment"> the arrays VF and VL, the first and last components of all the
</span><span class="comment">*</span><span class="comment"> right singular vectors of the original bidiagonal matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DLASD8.27"></a><a href="dlasd8.f.html#DLASD8.1">DLASD8</a> is called from <a name="DLASD6.27"></a><a href="dlasd6.f.html#DLASD6.1">DLASD6</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ICOMPQ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> Specifies whether singular vectors are to be computed in
</span><span class="comment">*</span><span class="comment"> factored form in the calling routine:
</span><span class="comment">*</span><span class="comment"> = 0: Compute singular values only.
</span><span class="comment">*</span><span class="comment"> = 1: Compute singular vectors in factored form as well.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> K (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of terms in the rational function to be solved
</span><span class="comment">*</span><span class="comment"> by <a name="DLASD4.40"></a><a href="dlasd4.f.html#DLASD4.1">DLASD4</a>. K >= 1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> D (output) DOUBLE PRECISION array, dimension ( K )
</span><span class="comment">*</span><span class="comment"> On output, D contains the updated singular values.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Z (input) DOUBLE PRECISION array, dimension ( K )
</span><span class="comment">*</span><span class="comment"> The first K elements of this array contain the components
</span><span class="comment">*</span><span class="comment"> of the deflation-adjusted updating row vector.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> VF (input/output) DOUBLE PRECISION array, dimension ( K )
</span><span class="comment">*</span><span class="comment"> On entry, VF contains information passed through DBEDE8.
</span><span class="comment">*</span><span class="comment"> On exit, VF contains the first K components of the first
</span><span class="comment">*</span><span class="comment"> components of all right singular vectors of the bidiagonal
</span><span class="comment">*</span><span class="comment"> matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> VL (input/output) DOUBLE PRECISION array, dimension ( K )
</span><span class="comment">*</span><span class="comment"> On entry, VL contains information passed through DBEDE8.
</span><span class="comment">*</span><span class="comment"> On exit, VL contains the first K components of the last
</span><span class="comment">*</span><span class="comment"> components of all right singular vectors of the bidiagonal
</span><span class="comment">*</span><span class="comment"> matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DIFL (output) DOUBLE PRECISION array, dimension ( K )
</span><span class="comment">*</span><span class="comment"> On exit, DIFL(I) = D(I) - DSIGMA(I).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DIFR (output) DOUBLE PRECISION array,
</span><span class="comment">*</span><span class="comment"> dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and
</span><span class="comment">*</span><span class="comment"> dimension ( K ) if ICOMPQ = 0.
</span><span class="comment">*</span><span class="comment"> On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not
</span><span class="comment">*</span><span class="comment"> defined and will not be referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If ICOMPQ = 1, DIFR(1:K,2) is an array containing the
</span><span class="comment">*</span><span class="comment"> normalizing factors for the right singular vector matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDDIFR (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of DIFR, must be at least K.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DSIGMA (input) DOUBLE PRECISION array, dimension ( K )
</span><span class="comment">*</span><span class="comment"> The first K elements of this array contain the old roots
</span><span class="comment">*</span><span class="comment"> of the deflated updating problem. These are the poles
</span><span class="comment">*</span><span class="comment"> of the secular equation.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) DOUBLE PRECISION array, dimension at least 3 * K
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit.
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment"> > 0: if INFO = 1, an singular value did not converge
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Based on contributions by
</span><span class="comment">*</span><span class="comment"> Ming Gu and Huan Ren, Computer Science Division, University of
</span><span class="comment">*</span><span class="comment"> California at Berkeley, USA
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> INTEGER I, IWK1, IWK2, IWK2I, IWK3, IWK3I, J
DOUBLE PRECISION DIFLJ, DIFRJ, DJ, DSIGJ, DSIGJP, RHO, TEMP
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL DCOPY, <a name="DLASCL.106"></a><a href="dlascl.f.html#DLASCL.1">DLASCL</a>, <a name="DLASD4.106"></a><a href="dlasd4.f.html#DLASD4.1">DLASD4</a>, <a name="DLASET.106"></a><a href="dlaset.f.html#DLASET.1">DLASET</a>, <a name="XERBLA.106"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> DOUBLE PRECISION DDOT, <a name="DLAMC3.109"></a><a href="dlamch.f.html#DLAMC3.574">DLAMC3</a>, DNRM2
EXTERNAL DDOT, <a name="DLAMC3.110"></a><a href="dlamch.f.html#DLAMC3.574">DLAMC3</a>, DNRM2
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS, SIGN, SQRT
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
<span class="comment">*</span><span class="comment">
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