.TH "SRC/dlaed9.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
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.SH NAME
SRC/dlaed9.f
.SH SYNOPSIS
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.SS "Functions/Subroutines"

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.ti -1c
.RI "subroutine \fBdlaed9\fP (k, kstart, kstop, n, d, q, ldq, rho, dlambda, w, s, lds, info)"
.br
.RI "\fBDLAED9\fP used by DSTEDC\&. Finds the roots of the secular equation and updates the eigenvectors\&. Used when the original matrix is dense\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dlaed9 (integer k, integer kstart, integer kstop, integer n, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, double precision rho, double precision, dimension( * ) dlambda, double precision, dimension( * ) w, double precision, dimension( lds, * ) s, integer lds, integer info)"

.PP
\fBDLAED9\fP used by DSTEDC\&. Finds the roots of the secular equation and updates the eigenvectors\&. Used when the original matrix is dense\&.  
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\fBPurpose:\fP
.RS 4

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.nf
!>
!> DLAED9 finds the roots of the secular equation, as defined by the
!> values in D, Z, and RHO, between KSTART and KSTOP\&.  It makes the
!> appropriate calls to DLAED4 and then stores the new matrix of
!> eigenvectors for use in calculating the next level of Z vectors\&.
!> 
.fi
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.RE
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\fBParameters\fP
.RS 4
\fIK\fP 
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!>          K is INTEGER
!>          The number of terms in the rational function to be solved by
!>          DLAED4\&.  K >= 0\&.
!> 
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\fIKSTART\fP 
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!>          KSTART is INTEGER
!> 
.fi
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\fIKSTOP\fP 
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!>          KSTOP is INTEGER
!>          The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP
!>          are to be computed\&.  1 <= KSTART <= KSTOP <= K\&.
!> 
.fi
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\fIN\fP 
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!>          N is INTEGER
!>          The number of rows and columns in the Q matrix\&.
!>          N >= K (delation may result in N > K)\&.
!> 
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\fID\fP 
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!>          D is DOUBLE PRECISION array, dimension (N)
!>          D(I) contains the updated eigenvalues
!>          for KSTART <= I <= KSTOP\&.
!> 
.fi
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\fIQ\fP 
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!>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
!> 
.fi
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\fILDQ\fP 
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!>          LDQ is INTEGER
!>          The leading dimension of the array Q\&.  LDQ >= max( 1, N )\&.
!> 
.fi
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\fIRHO\fP 
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!>          RHO is DOUBLE PRECISION
!>          The value of the parameter in the rank one update equation\&.
!>          RHO >= 0 required\&.
!> 
.fi
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\fIDLAMBDA\fP 
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!>          DLAMBDA is DOUBLE PRECISION array, dimension (K)
!>          The first K elements of this array contain the old roots
!>          of the deflated updating problem\&.  These are the poles
!>          of the secular equation\&.
!> 
.fi
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.br
\fIW\fP 
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!>          W is DOUBLE PRECISION array, dimension (K)
!>          The first K elements of this array contain the components
!>          of the deflation-adjusted updating vector\&.
!> 
.fi
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\fIS\fP 
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!>          S is DOUBLE PRECISION array, dimension (LDS, K)
!>          Will contain the eigenvectors of the repaired matrix which
!>          will be stored for subsequent Z vector calculation and
!>          multiplied by the previously accumulated eigenvectors
!>          to update the system\&.
!> 
.fi
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\fILDS\fP 
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!>          LDS is INTEGER
!>          The leading dimension of S\&.  LDS >= max( 1, K )\&.
!> 
.fi
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\fIINFO\fP 
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!>          INFO is INTEGER
!>          = 0:  successful exit\&.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value\&.
!>          > 0:  if INFO = 1, an eigenvalue did not converge
!> 
.fi
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.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

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Univ\&. of California Berkeley 

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Univ\&. of Colorado Denver 

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NAG Ltd\&. 
.RE
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\fBContributors:\fP
.RS 4
Jeff Rutter, Computer Science Division, University of California at Berkeley, USA 
.RE
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Definition at line \fB154\fP of file \fBdlaed9\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.