.TH "SRC/slaed7.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/slaed7.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBslaed7\fP (icompq, n, qsiz, tlvls, curlvl, curpbm, d, q, ldq, indxq, rho, cutpnt, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, iwork, info)"
.br
.RI "\fBSLAED7\fP used by SSTEDC\&. 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 slaed7 (integer icompq, integer n, integer qsiz, integer tlvls, integer curlvl, integer curpbm, real, dimension( * ) d, real, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) indxq, real rho, integer cutpnt, real, dimension( * ) qstore, integer, dimension( * ) qptr, integer, dimension( * ) prmptr, integer, dimension( * ) perm, integer, dimension( * ) givptr, integer, dimension( 2, * ) givcol, real, dimension( 2, * ) givnum, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

.PP
\fBSLAED7\fP used by SSTEDC\&. 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
!>
!> SLAED7 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 symmetric matrix
!> that has been reduced to tridiagonal form\&.  SLAED1 handles
!> the case in which all eigenvalues and eigenvectors of a symmetric
!> tridiagonal matrix are desired\&.
!>
!>   T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)
!>
!>    where Z = Q**Tu, 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 SLAED8\&.
!>
!>       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 SLAED9)\&.
!>       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
\fIICOMPQ\fP 
.PP
.nf
!>          ICOMPQ is INTEGER
!>          = 0:  Compute eigenvalues only\&.
!>          = 1:  Compute eigenvectors of original dense symmetric matrix
!>                also\&.  On entry, Q contains the orthogonal matrix used
!>                to reduce the original matrix to tridiagonal form\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>         The dimension of the symmetric tridiagonal matrix\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIQSIZ\fP 
.PP
.nf
!>          QSIZ is INTEGER
!>         The dimension of the orthogonal matrix used to reduce
!>         the full matrix to tridiagonal form\&.  QSIZ >= N if ICOMPQ = 1\&.
!> 
.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 REAL 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
\fIINDXQ\fP 
.PP
.nf
!>          INDXQ is INTEGER array, dimension (N)
!>         The permutation which will reintegrate the subproblem just
!>         solved back into sorted order, i\&.e\&., D( INDXQ( I = 1, N ) )
!>         will be in ascending order\&.
!> 
.fi
.PP
.br
\fIRHO\fP 
.PP
.nf
!>          RHO is REAL
!>         The subdiagonal element used to create the rank-1
!>         modification\&.
!> 
.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
\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
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.br
\fIGIVPTR\fP 
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.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
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.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
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (3*N+2*QSIZ*N)
!> 
.fi
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.br
\fIIWORK\fP 
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.nf
!>          IWORK is INTEGER array, dimension (4*N)
!> 
.fi
.PP
.br
\fIINFO\fP 
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.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
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
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 \fB256\fP of file \fBslaed7\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.