.TH "SRC/claed7.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/claed7.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBclaed7\fP (n, cutpnt, qsiz, tlvls, curlvl, curpbm, d, q, ldq, rho, indxq, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, rwork, iwork, info)"
.br
.RI "\fBCLAED7\fP used by CSTEDC\&. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix\&. Used when the original matrix is dense\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine claed7 (integer n, integer cutpnt, integer qsiz, integer tlvls, integer curlvl, integer curpbm, real, dimension( * ) d, complex, dimension( ldq, * ) q, integer ldq, real rho, integer, dimension( * ) indxq, real, dimension( * ) qstore, integer, dimension( * ) qptr, integer, dimension( * ) prmptr, integer, dimension( * ) perm, integer, dimension( * ) givptr, integer, dimension( 2, * ) givcol, real, dimension( 2, * ) givnum, complex, dimension( * ) work, real, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)"

.PP
\fBCLAED7\fP used by CSTEDC\&. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix\&. Used when the original matrix is dense\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLAED7 computes the updated eigensystem of a diagonal
 matrix after modification by a rank-one symmetric matrix\&. This
 routine is used only for the eigenproblem which requires all
 eigenvalues and optionally eigenvectors of a dense or banded
 Hermitian matrix that has been reduced to tridiagonal form\&.

   T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out)

   where Z = Q**Hu, u is a vector of length N with ones in the
   CUTPNT and CUTPNT + 1 th elements and zeros elsewhere\&.

    The eigenvectors of the original matrix are stored in Q, and the
    eigenvalues are in D\&.  The algorithm consists of three stages:

       The first stage consists of deflating the size of the problem
       when there are multiple eigenvalues or if there is a zero in
       the Z vector\&.  For each such occurrence the dimension of the
       secular equation problem is reduced by one\&.  This stage is
       performed by the routine SLAED2\&.

       The second stage consists of calculating the updated
       eigenvalues\&. This is done by finding the roots of the secular
       equation via the routine SLAED4 (as called by SLAED3)\&.
       This routine also calculates the eigenvectors of the current
       problem\&.

       The final stage consists of computing the updated eigenvectors
       directly using the updated eigenvalues\&.  The eigenvectors for
       the current problem are multiplied with the eigenvectors from
       the overall problem\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
         The dimension of the symmetric tridiagonal matrix\&.  N >= 0\&.
.fi
.PP
.br
\fICUTPNT\fP 
.PP
.nf
          CUTPNT is INTEGER
         Contains the location of the last eigenvalue in the leading
         sub-matrix\&.  min(1,N) <= CUTPNT <= N\&.
.fi
.PP
.br
\fIQSIZ\fP 
.PP
.nf
          QSIZ is INTEGER
         The dimension of the unitary matrix used to reduce
         the full matrix to tridiagonal form\&.  QSIZ >= N\&.
.fi
.PP
.br
\fITLVLS\fP 
.PP
.nf
          TLVLS is INTEGER
         The total number of merging levels in the overall divide and
         conquer tree\&.
.fi
.PP
.br
\fICURLVL\fP 
.PP
.nf
          CURLVL is INTEGER
         The current level in the overall merge routine,
         0 <= curlvl <= tlvls\&.
.fi
.PP
.br
\fICURPBM\fP 
.PP
.nf
          CURPBM is INTEGER
         The current problem in the current level in the overall
         merge routine (counting from upper left to lower right)\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
         On entry, the eigenvalues of the rank-1-perturbed matrix\&.
         On exit, the eigenvalues of the repaired matrix\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is COMPLEX array, dimension (LDQ,N)
         On entry, the eigenvectors of the rank-1-perturbed matrix\&.
         On exit, the eigenvectors of the repaired tridiagonal matrix\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
         The leading dimension of the array Q\&.  LDQ >= max(1,N)\&.
.fi
.PP
.br
\fIRHO\fP 
.PP
.nf
          RHO is REAL
         Contains the subdiagonal element used to create the rank-1
         modification\&.
.fi
.PP
.br
\fIINDXQ\fP 
.PP
.nf
          INDXQ is INTEGER array, dimension (N)
         This contains the permutation which will reintegrate the
         subproblem just solved back into sorted order,
         ie\&. D( INDXQ( I = 1, N ) ) will be in ascending order\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (4*N)
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is REAL array,
                                 dimension (3*N+2*QSIZ*N)
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (QSIZ*N)
.fi
.PP
.br
\fIQSTORE\fP 
.PP
.nf
          QSTORE is REAL array, dimension (N**2+1)
         Stores eigenvectors of submatrices encountered during
         divide and conquer, packed together\&. QPTR points to
         beginning of the submatrices\&.
.fi
.PP
.br
\fIQPTR\fP 
.PP
.nf
          QPTR is INTEGER array, dimension (N+2)
         List of indices pointing to beginning of submatrices stored
         in QSTORE\&. The submatrices are numbered starting at the
         bottom left of the divide and conquer tree, from left to
         right and bottom to top\&.
.fi
.PP
.br
\fIPRMPTR\fP 
.PP
.nf
          PRMPTR is INTEGER array, dimension (N lg N)
         Contains a list of pointers which indicate where in PERM a
         level's permutation is stored\&.  PRMPTR(i+1) - PRMPTR(i)
         indicates the size of the permutation and also the size of
         the full, non-deflated problem\&.
.fi
.PP
.br
\fIPERM\fP 
.PP
.nf
          PERM is INTEGER array, dimension (N lg N)
         Contains the permutations (from deflation and sorting) to be
         applied to each eigenblock\&.
.fi
.PP
.br
\fIGIVPTR\fP 
.PP
.nf
          GIVPTR is INTEGER array, dimension (N lg N)
         Contains a list of pointers which indicate where in GIVCOL a
         level's Givens rotations are stored\&.  GIVPTR(i+1) - GIVPTR(i)
         indicates the number of Givens rotations\&.
.fi
.PP
.br
\fIGIVCOL\fP 
.PP
.nf
          GIVCOL is INTEGER array, dimension (2, N lg N)
         Each pair of numbers indicates a pair of columns to take place
         in a Givens rotation\&.
.fi
.PP
.br
\fIGIVNUM\fP 
.PP
.nf
          GIVNUM is REAL array, dimension (2, N lg N)
         Each number indicates the S value to be used in the
         corresponding Givens rotation\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB245\fP of file \fBclaed7\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.