.TH "SRC/dlaed3.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
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.SH NAME
SRC/dlaed3.f
.SH SYNOPSIS
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.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdlaed3\fP (k, n, n1, d, q, ldq, rho, dlambda, q2, indx, ctot, w, s, info)"
.br
.RI "\fBDLAED3\fP used by DSTEDC\&. Finds the roots of the secular equation and updates the eigenvectors\&. Used when the original matrix is tridiagonal\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dlaed3 (integer k, integer n, integer n1, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, double precision rho, double precision, dimension( * ) dlambda, double precision, dimension( * ) q2, integer, dimension( * ) indx, integer, dimension( * ) ctot, double precision, dimension( * ) w, double precision, dimension( * ) s, integer info)"

.PP
\fBDLAED3\fP used by DSTEDC\&. Finds the roots of the secular equation and updates the eigenvectors\&. Used when the original matrix is tridiagonal\&.  
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\fBPurpose:\fP
.RS 4

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.nf
!>
!> DLAED3 finds the roots of the secular equation, as defined by the
!> values in D, W, and RHO, between 1 and K\&.  It makes the
!> appropriate calls to DLAED4 and then updates the eigenvectors by
!> multiplying the matrix of eigenvectors of the pair of eigensystems
!> being combined by the matrix of eigenvectors of the K-by-K system
!> which is solved here\&.
!>
!> 
.fi
.PP
 
.RE
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\fBParameters\fP
.RS 4
\fIK\fP 
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.nf
!>          K is INTEGER
!>          The number of terms in the rational function to be solved by
!>          DLAED4\&.  K >= 0\&.
!> 
.fi
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\fIN\fP 
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.nf
!>          N is INTEGER
!>          The number of rows and columns in the Q matrix\&.
!>          N >= K (deflation may result in N>K)\&.
!> 
.fi
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\fIN1\fP 
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!>          N1 is INTEGER
!>          The location of the last eigenvalue in the leading submatrix\&.
!>          min(1,N) <= N1 <= N/2\&.
!> 
.fi
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\fID\fP 
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!>          D is DOUBLE PRECISION array, dimension (N)
!>          D(I) contains the updated eigenvalues for
!>          1 <= I <= K\&.
!> 
.fi
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\fIQ\fP 
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!>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
!>          Initially the first K columns are used as workspace\&.
!>          On output the columns 1 to K contain
!>          the updated eigenvectors\&.
!> 
.fi
.PP
.br
\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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.br
\fIRHO\fP 
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.nf
!>          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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.nf
!>          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
.PP
.br
\fIQ2\fP 
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!>          Q2 is DOUBLE PRECISION array, dimension (LDQ2*N)
!>          The first K columns of this matrix contain the non-deflated
!>          eigenvectors for the split problem\&.
!> 
.fi
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.br
\fIINDX\fP 
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.nf
!>          INDX is INTEGER array, dimension (N)
!>          The permutation used to arrange the columns of the deflated
!>          Q matrix into three groups (see DLAED2)\&.
!>          The rows of the eigenvectors found by DLAED4 must be likewise
!>          permuted before the matrix multiply can take place\&.
!> 
.fi
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.br
\fICTOT\fP 
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!>          CTOT is INTEGER array, dimension (4)
!>          A count of the total number of the various types of columns
!>          in Q, as described in INDX\&.  The fourth column type is any
!>          column which has been deflated\&.
!> 
.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\&. Destroyed on
!>          output\&.
!> 
.fi
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.br
\fIS\fP 
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!>          S is DOUBLE PRECISION array, dimension (N1 + 1)*K
!>          Will contain the eigenvectors of the repaired matrix which
!>          will be multiplied by the previously accumulated eigenvectors
!>          to update the system\&.
!> 
.fi
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.br
\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 
.br
 Modified by Francoise Tisseur, University of Tennessee 
.RE
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Definition at line \fB175\fP of file \fBdlaed3\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.