.TH "laed8" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
laed8 \- laed8: D&C step: deflation
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclaed8\fP (k, n, qsiz, q, ldq, d, rho, cutpnt, z, dlambda, q2, ldq2, w, indxp, indx, indxq, perm, givptr, givcol, givnum, info)"
.br
.RI "\fBCLAED8\fP used by CSTEDC\&. Merges eigenvalues and deflates secular equation\&. Used when the original matrix is dense\&. "
.ti -1c
.RI "subroutine \fBdlaed8\fP (icompq, k, n, qsiz, d, q, ldq, indxq, rho, cutpnt, z, dlambda, q2, ldq2, w, perm, givptr, givcol, givnum, indxp, indx, info)"
.br
.RI "\fBDLAED8\fP used by DSTEDC\&. Merges eigenvalues and deflates secular equation\&. Used when the original matrix is dense\&. "
.ti -1c
.RI "subroutine \fBslaed8\fP (icompq, k, n, qsiz, d, q, ldq, indxq, rho, cutpnt, z, dlambda, q2, ldq2, w, perm, givptr, givcol, givnum, indxp, indx, info)"
.br
.RI "\fBSLAED8\fP used by SSTEDC\&. Merges eigenvalues and deflates secular equation\&. Used when the original matrix is dense\&. "
.ti -1c
.RI "subroutine \fBzlaed8\fP (k, n, qsiz, q, ldq, d, rho, cutpnt, z, dlambda, q2, ldq2, w, indxp, indx, indxq, perm, givptr, givcol, givnum, info)"
.br
.RI "\fBZLAED8\fP used by ZSTEDC\&. Merges eigenvalues and deflates secular equation\&. Used when the original matrix is dense\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine claed8 (integer k, integer n, integer qsiz, complex, dimension( ldq, * ) q, integer ldq, real, dimension( * ) d, real rho, integer cutpnt, real, dimension( * ) z, real, dimension( * ) dlambda, complex, dimension( ldq2, * ) q2, integer ldq2, real, dimension( * ) w, integer, dimension( * ) indxp, integer, dimension( * ) indx, integer, dimension( * ) indxq, integer, dimension( * ) perm, integer givptr, integer, dimension( 2, * ) givcol, real, dimension( 2, * ) givnum, integer info)"

.PP
\fBCLAED8\fP used by CSTEDC\&. Merges eigenvalues and deflates secular equation\&. Used when the original matrix is dense\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLAED8 merges the two sets of eigenvalues together into a single
 sorted set\&.  Then it tries to deflate the size of the problem\&.
 There are two ways in which deflation can occur:  when two or more
 eigenvalues are close together or if there is a tiny element in the
 Z vector\&.  For each such occurrence the order of the related secular
 equation problem is reduced by one\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIK\fP 
.PP
.nf
          K is INTEGER
         Contains the number of non-deflated eigenvalues\&.
         This is the order of the related secular equation\&.
.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 unitary matrix used to reduce
         the dense or band matrix to tridiagonal form\&.
         QSIZ >= N if ICOMPQ = 1\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is COMPLEX array, dimension (LDQ,N)
         On entry, Q contains the eigenvectors of the partially solved
         system which has been previously updated in matrix
         multiplies with other partially solved eigensystems\&.
         On exit, Q contains the trailing (N-K) updated eigenvectors
         (those which were deflated) in its last N-K columns\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
         The leading dimension of the array Q\&.  LDQ >= max( 1, N )\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
         On entry, D contains the eigenvalues of the two submatrices to
         be combined\&.  On exit, D contains the trailing (N-K) updated
         eigenvalues (those which were deflated) sorted into increasing
         order\&.
.fi
.PP
.br
\fIRHO\fP 
.PP
.nf
          RHO is REAL
         Contains the off diagonal element associated with the rank-1
         cut which originally split the two submatrices which are now
         being recombined\&. RHO is modified during the computation to
         the value required by SLAED3\&.
.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
\fIZ\fP 
.PP
.nf
          Z is REAL array, dimension (N)
         On input this vector contains the updating vector (the last
         row of the first sub-eigenvector matrix and the first row of
         the second sub-eigenvector matrix)\&.  The contents of Z are
         destroyed during the updating process\&.
.fi
.PP
.br
\fIDLAMBDA\fP 
.PP
.nf
          DLAMBDA is REAL array, dimension (N)
         Contains a copy of the first K eigenvalues which will be used
         by SLAED3 to form the secular equation\&.
.fi
.PP
.br
\fIQ2\fP 
.PP
.nf
          Q2 is COMPLEX array, dimension (LDQ2,N)
         If ICOMPQ = 0, Q2 is not referenced\&.  Otherwise,
         Contains a copy of the first K eigenvectors which will be used
         by SLAED7 in a matrix multiply (SGEMM) to update the new
         eigenvectors\&.
.fi
.PP
.br
\fILDQ2\fP 
.PP
.nf
          LDQ2 is INTEGER
         The leading dimension of the array Q2\&.  LDQ2 >= max( 1, N )\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is REAL array, dimension (N)
         This will hold the first k values of the final
         deflation-altered z-vector and will be passed to SLAED3\&.
.fi
.PP
.br
\fIINDXP\fP 
.PP
.nf
          INDXP is INTEGER array, dimension (N)
         This will contain the permutation used to place deflated
         values of D at the end of the array\&. On output INDXP(1:K)
         points to the nondeflated D-values and INDXP(K+1:N)
         points to the deflated eigenvalues\&.
.fi
.PP
.br
\fIINDX\fP 
.PP
.nf
          INDX is INTEGER array, dimension (N)
         This will contain the permutation used to sort the contents of
         D into ascending order\&.
.fi
.PP
.br
\fIINDXQ\fP 
.PP
.nf
          INDXQ is INTEGER array, dimension (N)
         This contains the permutation which separately sorts the two
         sub-problems in D into ascending order\&.  Note that elements in
         the second half of this permutation must first have CUTPNT
         added to their values in order to be accurate\&.
.fi
.PP
.br
\fIPERM\fP 
.PP
.nf
          PERM is INTEGER array, dimension (N)
         Contains the permutations (from deflation and sorting) to be
         applied to each eigenblock\&.
.fi
.PP
.br
\fIGIVPTR\fP 
.PP
.nf
          GIVPTR is INTEGER
         Contains the number of Givens rotations which took place in
         this subproblem\&.
.fi
.PP
.br
\fIGIVCOL\fP 
.PP
.nf
          GIVCOL is INTEGER array, dimension (2, 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)
         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\&.
.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

.SS "subroutine dlaed8 (integer icompq, integer k, integer n, integer qsiz, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) indxq, double precision rho, integer cutpnt, double precision, dimension( * ) z, double precision, dimension( * ) dlambda, double precision, dimension( ldq2, * ) q2, integer ldq2, double precision, dimension( * ) w, integer, dimension( * ) perm, integer givptr, integer, dimension( 2, * ) givcol, double precision, dimension( 2, * ) givnum, integer, dimension( * ) indxp, integer, dimension( * ) indx, integer info)"

.PP
\fBDLAED8\fP used by DSTEDC\&. Merges eigenvalues and deflates secular equation\&. Used when the original matrix is dense\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLAED8 merges the two sets of eigenvalues together into a single
 sorted set\&.  Then it tries to deflate the size of the problem\&.
 There are two ways in which deflation can occur:  when two or more
 eigenvalues are close together or if there is a tiny element in the
 Z vector\&.  For each such occurrence the order of the related secular
 equation problem is reduced by one\&.
.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
\fIK\fP 
.PP
.nf
          K is INTEGER
         The number of non-deflated eigenvalues, and the order of the
         related secular equation\&.
.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
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
         On entry, the eigenvalues of the two submatrices to be
         combined\&.  On exit, the trailing (N-K) updated eigenvalues
         (those which were deflated) sorted into increasing order\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is DOUBLE PRECISION array, dimension (LDQ,N)
         If ICOMPQ = 0, Q is not referenced\&.  Otherwise,
         on entry, Q contains the eigenvectors of the partially solved
         system which has been previously updated in matrix
         multiplies with other partially solved eigensystems\&.
         On exit, Q contains the trailing (N-K) updated eigenvectors
         (those which were deflated) in its last N-K columns\&.
.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 separately sorts the two sub-problems
         in D into ascending order\&.  Note that elements in the second
         half of this permutation must first have CUTPNT added to
         their values in order to be accurate\&.
.fi
.PP
.br
\fIRHO\fP 
.PP
.nf
          RHO is DOUBLE PRECISION
         On entry, the off-diagonal element associated with the rank-1
         cut which originally split the two submatrices which are now
         being recombined\&.
         On exit, RHO has been modified to the value required by
         DLAED3\&.
.fi
.PP
.br
\fICUTPNT\fP 
.PP
.nf
          CUTPNT is INTEGER
         The location of the last eigenvalue in the leading
         sub-matrix\&.  min(1,N) <= CUTPNT <= N\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is DOUBLE PRECISION array, dimension (N)
         On entry, Z contains the updating vector (the last row of
         the first sub-eigenvector matrix and the first row of the
         second sub-eigenvector matrix)\&.
         On exit, the contents of Z are destroyed by the updating
         process\&.
.fi
.PP
.br
\fIDLAMBDA\fP 
.PP
.nf
          DLAMBDA is DOUBLE PRECISION array, dimension (N)
         A copy of the first K eigenvalues which will be used by
         DLAED3 to form the secular equation\&.
.fi
.PP
.br
\fIQ2\fP 
.PP
.nf
          Q2 is DOUBLE PRECISION array, dimension (LDQ2,N)
         If ICOMPQ = 0, Q2 is not referenced\&.  Otherwise,
         a copy of the first K eigenvectors which will be used by
         DLAED7 in a matrix multiply (DGEMM) to update the new
         eigenvectors\&.
.fi
.PP
.br
\fILDQ2\fP 
.PP
.nf
          LDQ2 is INTEGER
         The leading dimension of the array Q2\&.  LDQ2 >= max(1,N)\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is DOUBLE PRECISION array, dimension (N)
         The first k values of the final deflation-altered z-vector and
         will be passed to DLAED3\&.
.fi
.PP
.br
\fIPERM\fP 
.PP
.nf
          PERM is INTEGER array, dimension (N)
         The permutations (from deflation and sorting) to be applied
         to each eigenblock\&.
.fi
.PP
.br
\fIGIVPTR\fP 
.PP
.nf
          GIVPTR is INTEGER
         The number of Givens rotations which took place in this
         subproblem\&.
.fi
.PP
.br
\fIGIVCOL\fP 
.PP
.nf
          GIVCOL is INTEGER array, dimension (2, 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 DOUBLE PRECISION array, dimension (2, N)
         Each number indicates the S value to be used in the
         corresponding Givens rotation\&.
.fi
.PP
.br
\fIINDXP\fP 
.PP
.nf
          INDXP is INTEGER array, dimension (N)
         The permutation used to place deflated values of D at the end
         of the array\&.  INDXP(1:K) points to the nondeflated D-values
         and INDXP(K+1:N) points to the deflated eigenvalues\&.
.fi
.PP
.br
\fIINDX\fP 
.PP
.nf
          INDX is INTEGER array, dimension (N)
         The permutation used to sort the contents of D into ascending
         order\&.
.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\&.
.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
\fBContributors:\fP
.RS 4
Jeff Rutter, Computer Science Division, University of California at Berkeley, USA 
.RE
.PP

.SS "subroutine slaed8 (integer icompq, integer k, integer n, integer qsiz, real, dimension( * ) d, real, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) indxq, real rho, integer cutpnt, real, dimension( * ) z, real, dimension( * ) dlambda, real, dimension( ldq2, * ) q2, integer ldq2, real, dimension( * ) w, integer, dimension( * ) perm, integer givptr, integer, dimension( 2, * ) givcol, real, dimension( 2, * ) givnum, integer, dimension( * ) indxp, integer, dimension( * ) indx, integer info)"

.PP
\fBSLAED8\fP used by SSTEDC\&. Merges eigenvalues and deflates secular equation\&. Used when the original matrix is dense\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLAED8 merges the two sets of eigenvalues together into a single
 sorted set\&.  Then it tries to deflate the size of the problem\&.
 There are two ways in which deflation can occur:  when two or more
 eigenvalues are close together or if there is a tiny element in the
 Z vector\&.  For each such occurrence the order of the related secular
 equation problem is reduced by one\&.
.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
\fIK\fP 
.PP
.nf
          K is INTEGER
         The number of non-deflated eigenvalues, and the order of the
         related secular equation\&.
.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
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
         On entry, the eigenvalues of the two submatrices to be
         combined\&.  On exit, the trailing (N-K) updated eigenvalues
         (those which were deflated) sorted into increasing order\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is REAL array, dimension (LDQ,N)
         If ICOMPQ = 0, Q is not referenced\&.  Otherwise,
         on entry, Q contains the eigenvectors of the partially solved
         system which has been previously updated in matrix
         multiplies with other partially solved eigensystems\&.
         On exit, Q contains the trailing (N-K) updated eigenvectors
         (those which were deflated) in its last N-K columns\&.
.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 separately sorts the two sub-problems
         in D into ascending order\&.  Note that elements in the second
         half of this permutation must first have CUTPNT added to
         their values in order to be accurate\&.
.fi
.PP
.br
\fIRHO\fP 
.PP
.nf
          RHO is REAL
         On entry, the off-diagonal element associated with the rank-1
         cut which originally split the two submatrices which are now
         being recombined\&.
         On exit, RHO has been modified to the value required by
         SLAED3\&.
.fi
.PP
.br
\fICUTPNT\fP 
.PP
.nf
          CUTPNT is INTEGER
         The location of the last eigenvalue in the leading
         sub-matrix\&.  min(1,N) <= CUTPNT <= N\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is REAL array, dimension (N)
         On entry, Z contains the updating vector (the last row of
         the first sub-eigenvector matrix and the first row of the
         second sub-eigenvector matrix)\&.
         On exit, the contents of Z are destroyed by the updating
         process\&.
.fi
.PP
.br
\fIDLAMBDA\fP 
.PP
.nf
          DLAMBDA is REAL array, dimension (N)
         A copy of the first K eigenvalues which will be used by
         SLAED3 to form the secular equation\&.
.fi
.PP
.br
\fIQ2\fP 
.PP
.nf
          Q2 is REAL array, dimension (LDQ2,N)
         If ICOMPQ = 0, Q2 is not referenced\&.  Otherwise,
         a copy of the first K eigenvectors which will be used by
         SLAED7 in a matrix multiply (SGEMM) to update the new
         eigenvectors\&.
.fi
.PP
.br
\fILDQ2\fP 
.PP
.nf
          LDQ2 is INTEGER
         The leading dimension of the array Q2\&.  LDQ2 >= max(1,N)\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is REAL array, dimension (N)
         The first k values of the final deflation-altered z-vector and
         will be passed to SLAED3\&.
.fi
.PP
.br
\fIPERM\fP 
.PP
.nf
          PERM is INTEGER array, dimension (N)
         The permutations (from deflation and sorting) to be applied
         to each eigenblock\&.
.fi
.PP
.br
\fIGIVPTR\fP 
.PP
.nf
          GIVPTR is INTEGER
         The number of Givens rotations which took place in this
         subproblem\&.
.fi
.PP
.br
\fIGIVCOL\fP 
.PP
.nf
          GIVCOL is INTEGER array, dimension (2, 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)
         Each number indicates the S value to be used in the
         corresponding Givens rotation\&.
.fi
.PP
.br
\fIINDXP\fP 
.PP
.nf
          INDXP is INTEGER array, dimension (N)
         The permutation used to place deflated values of D at the end
         of the array\&.  INDXP(1:K) points to the nondeflated D-values
         and INDXP(K+1:N) points to the deflated eigenvalues\&.
.fi
.PP
.br
\fIINDX\fP 
.PP
.nf
          INDX is INTEGER array, dimension (N)
         The permutation used to sort the contents of D into ascending
         order\&.
.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\&.
.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
\fBContributors:\fP
.RS 4
Jeff Rutter, Computer Science Division, University of California at Berkeley, USA 
.RE
.PP

.SS "subroutine zlaed8 (integer k, integer n, integer qsiz, complex*16, dimension( ldq, * ) q, integer ldq, double precision, dimension( * ) d, double precision rho, integer cutpnt, double precision, dimension( * ) z, double precision, dimension( * ) dlambda, complex*16, dimension( ldq2, * ) q2, integer ldq2, double precision, dimension( * ) w, integer, dimension( * ) indxp, integer, dimension( * ) indx, integer, dimension( * ) indxq, integer, dimension( * ) perm, integer givptr, integer, dimension( 2, * ) givcol, double precision, dimension( 2, * ) givnum, integer info)"

.PP
\fBZLAED8\fP used by ZSTEDC\&. Merges eigenvalues and deflates secular equation\&. Used when the original matrix is dense\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLAED8 merges the two sets of eigenvalues together into a single
 sorted set\&.  Then it tries to deflate the size of the problem\&.
 There are two ways in which deflation can occur:  when two or more
 eigenvalues are close together or if there is a tiny element in the
 Z vector\&.  For each such occurrence the order of the related secular
 equation problem is reduced by one\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIK\fP 
.PP
.nf
          K is INTEGER
         Contains the number of non-deflated eigenvalues\&.
         This is the order of the related secular equation\&.
.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 unitary matrix used to reduce
         the dense or band matrix to tridiagonal form\&.
         QSIZ >= N if ICOMPQ = 1\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is COMPLEX*16 array, dimension (LDQ,N)
         On entry, Q contains the eigenvectors of the partially solved
         system which has been previously updated in matrix
         multiplies with other partially solved eigensystems\&.
         On exit, Q contains the trailing (N-K) updated eigenvectors
         (those which were deflated) in its last N-K columns\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
         The leading dimension of the array Q\&.  LDQ >= max( 1, N )\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
         On entry, D contains the eigenvalues of the two submatrices to
         be combined\&.  On exit, D contains the trailing (N-K) updated
         eigenvalues (those which were deflated) sorted into increasing
         order\&.
.fi
.PP
.br
\fIRHO\fP 
.PP
.nf
          RHO is DOUBLE PRECISION
         Contains the off diagonal element associated with the rank-1
         cut which originally split the two submatrices which are now
         being recombined\&. RHO is modified during the computation to
         the value required by DLAED3\&.
.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
\fIZ\fP 
.PP
.nf
          Z is DOUBLE PRECISION array, dimension (N)
         On input this vector contains the updating vector (the last
         row of the first sub-eigenvector matrix and the first row of
         the second sub-eigenvector matrix)\&.  The contents of Z are
         destroyed during the updating process\&.
.fi
.PP
.br
\fIDLAMBDA\fP 
.PP
.nf
          DLAMBDA is DOUBLE PRECISION array, dimension (N)
         Contains a copy of the first K eigenvalues which will be used
         by DLAED3 to form the secular equation\&.
.fi
.PP
.br
\fIQ2\fP 
.PP
.nf
          Q2 is COMPLEX*16 array, dimension (LDQ2,N)
         If ICOMPQ = 0, Q2 is not referenced\&.  Otherwise,
         Contains a copy of the first K eigenvectors which will be used
         by DLAED7 in a matrix multiply (DGEMM) to update the new
         eigenvectors\&.
.fi
.PP
.br
\fILDQ2\fP 
.PP
.nf
          LDQ2 is INTEGER
         The leading dimension of the array Q2\&.  LDQ2 >= max( 1, N )\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is DOUBLE PRECISION array, dimension (N)
         This will hold the first k values of the final
         deflation-altered z-vector and will be passed to DLAED3\&.
.fi
.PP
.br
\fIINDXP\fP 
.PP
.nf
          INDXP is INTEGER array, dimension (N)
         This will contain the permutation used to place deflated
         values of D at the end of the array\&. On output INDXP(1:K)
         points to the nondeflated D-values and INDXP(K+1:N)
         points to the deflated eigenvalues\&.
.fi
.PP
.br
\fIINDX\fP 
.PP
.nf
          INDX is INTEGER array, dimension (N)
         This will contain the permutation used to sort the contents of
         D into ascending order\&.
.fi
.PP
.br
\fIINDXQ\fP 
.PP
.nf
          INDXQ is INTEGER array, dimension (N)
         This contains the permutation which separately sorts the two
         sub-problems in D into ascending order\&.  Note that elements in
         the second half of this permutation must first have CUTPNT
         added to their values in order to be accurate\&.
.fi
.PP
.br
\fIPERM\fP 
.PP
.nf
          PERM is INTEGER array, dimension (N)
         Contains the permutations (from deflation and sorting) to be
         applied to each eigenblock\&.
.fi
.PP
.br
\fIGIVPTR\fP 
.PP
.nf
          GIVPTR is INTEGER
         Contains the number of Givens rotations which took place in
         this subproblem\&.
.fi
.PP
.br
\fIGIVCOL\fP 
.PP
.nf
          GIVCOL is INTEGER array, dimension (2, 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 DOUBLE PRECISION array, dimension (2, 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\&.
.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

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.