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SUBROUTINE <a name="SLAED9.1"></a><a href="slaed9.f.html#SLAED9.1">SLAED9</a>( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W,
$ S, LDS, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK 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 INFO, K, KSTART, KSTOP, LDQ, LDS, N
REAL RHO
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ),
$ W( * )
<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="SLAED9.20"></a><a href="slaed9.f.html#SLAED9.1">SLAED9</a> finds the roots of the secular equation, as defined by the
</span><span class="comment">*</span><span class="comment"> values in D, Z, and RHO, between KSTART and KSTOP. It makes the
</span><span class="comment">*</span><span class="comment"> appropriate calls to <a name="SLAED4.22"></a><a href="slaed4.f.html#SLAED4.1">SLAED4</a> and then stores the new matrix of
</span><span class="comment">*</span><span class="comment"> eigenvectors for use in calculating the next level of Z vectors.
</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"> K (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of terms in the rational function to be solved by
</span><span class="comment">*</span><span class="comment"> <a name="SLAED4.30"></a><a href="slaed4.f.html#SLAED4.1">SLAED4</a>. K >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KSTART (input) INTEGER
</span><span class="comment">*</span><span class="comment"> KSTOP (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP
</span><span class="comment">*</span><span class="comment"> are to be computed. 1 <= KSTART <= KSTOP <= K.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of rows and columns in the Q matrix.
</span><span class="comment">*</span><span class="comment"> N >= K (delation may result in N > K).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> D (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> D(I) contains the updated eigenvalues
</span><span class="comment">*</span><span class="comment"> for KSTART <= I <= KSTOP.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q (workspace) REAL array, dimension (LDQ,N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDQ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Q. LDQ >= max( 1, N ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RHO (input) REAL
</span><span class="comment">*</span><span class="comment"> The value of the parameter in the rank one update equation.
</span><span class="comment">*</span><span class="comment"> RHO >= 0 required.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DLAMDA (input) REAL 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"> W (input) REAL 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 vector.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> S (output) REAL array, dimension (LDS, K)
</span><span class="comment">*</span><span class="comment"> Will contain the eigenvectors of the repaired matrix which
</span><span class="comment">*</span><span class="comment"> will be stored for subsequent Z vector calculation and
</span><span class="comment">*</span><span class="comment"> multiplied by the previously accumulated eigenvectors
</span><span class="comment">*</span><span class="comment"> to update the system.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDS (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of S. LDS >= max( 1, 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 eigenvalue 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"> Jeff Rutter, Computer Science Division, University of California
</span><span class="comment">*</span><span class="comment"> 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"> .. Local Scalars ..
</span> INTEGER I, J
REAL TEMP
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> REAL <a name="SLAMC3.91"></a><a href="slamch.f.html#SLAMC3.574">SLAMC3</a>, SNRM2
EXTERNAL <a name="SLAMC3.92"></a><a href="slamch.f.html#SLAMC3.574">SLAMC3</a>, SNRM2
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL SCOPY, <a name="SLAED4.95"></a><a href="slaed4.f.html#SLAED4.1">SLAED4</a>, <a name="XERBLA.95"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
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