SYNOPSIS
 SUBROUTINE SLAED8(
 ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO )
 INTEGER CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, QSIZ
 REAL RHO
 INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), INDXQ( * ), PERM( * )
 REAL D( * ), DLAMDA( * ), GIVNUM( 2, * ), Q( LDQ, * ), Q2( LDQ2, * ), W( * ), Z( * )
PURPOSE
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.ARGUMENTS
 ICOMPQ (input) 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.  K (output) INTEGER
 The number of nondeflated eigenvalues, and the order of the related secular equation.
 N (input) INTEGER
 The dimension of the symmetric tridiagonal matrix. N >= 0.
 QSIZ (input) INTEGER
 The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
 D (input/output) REAL array, dimension (N)
 On entry, the eigenvalues of the two submatrices to be combined. On exit, the trailing (NK) updated eigenvalues (those which were deflated) sorted into increasing order.
 Q (input/output) 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 (NK) updated eigenvectors (those which were deflated) in its last NK columns.
 LDQ (input) INTEGER
 The leading dimension of the array Q. LDQ >= max(1,N).
 INDXQ (input) INTEGER array, dimension (N)
 The permutation which separately sorts the two subproblems 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.
 RHO (input/output) REAL
 On entry, the offdiagonal element associated with the rank1 cut which originally split the two submatrices which are now being recombined. On exit, RHO has been modified to the value required by SLAED3. CUTPNT (input) INTEGER The location of the last eigenvalue in the leading submatrix. min(1,N) <= CUTPNT <= N.
 Z (input) REAL array, dimension (N)
 On entry, Z contains the updating vector (the last row of the first subeigenvector matrix and the first row of the second subeigenvector matrix). On exit, the contents of Z are destroyed by the updating process. DLAMDA (output) REAL array, dimension (N) A copy of the first K eigenvalues which will be used by SLAED3 to form the secular equation.
 Q2 (output) 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.
 LDQ2 (input) INTEGER
 The leading dimension of the array Q2. LDQ2 >= max(1,N).
 W (output) REAL array, dimension (N)
 The first k values of the final deflationaltered zvector and will be passed to SLAED3.
 PERM (output) INTEGER array, dimension (N)
 The permutations (from deflation and sorting) to be applied to each eigenblock. GIVPTR (output) INTEGER The number of Givens rotations which took place in this subproblem. GIVCOL (output) INTEGER array, dimension (2, N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation. GIVNUM (output) REAL array, dimension (2, N) Each number indicates the S value to be used in the corresponding Givens rotation.
 INDXP (workspace) 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 Dvalues
and INDXP(K+1:N) points to the deflated eigenvalues.  INDX (workspace) INTEGER array, dimension (N)
 The permutation used to sort the contents of D into ascending order.
 INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
FURTHER DETAILS
Based on contributions byJeff Rutter, Computer Science Division, University of California
at Berkeley, USA