!>
!> SLAED3 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 SLAED4 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.
!>
!> 

K

!>          K is INTEGER
!>          The number of terms in the rational function to be solved by
!>          SLAED4.  K >= 0.
!> 

N

!>          N is INTEGER
!>          The number of rows and columns in the Q matrix.
!>          N >= K (deflation may result in N>K).
!> 

N1

!>          N1 is INTEGER
!>          The location of the last eigenvalue in the leading submatrix.
!>          min(1,N) <= N1 <= N/2.
!> 

D

!>          D is REAL array, dimension (N)
!>          D(I) contains the updated eigenvalues for
!>          1 <= I <= K.
!> 

Q

!>          Q is REAL array, dimension (LDQ,N)
!>          Initially the first K columns are used as workspace.
!>          On output the columns 1 to K contain
!>          the updated eigenvectors.
!> 

LDQ

!>          LDQ is INTEGER
!>          The leading dimension of the array Q.  LDQ >= max(1,N).
!> 

RHO

!>          RHO is REAL
!>          The value of the parameter in the rank one update equation.
!>          RHO >= 0 required.
!> 

DLAMBDA

!>          DLAMBDA is REAL 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.
!> 

Q2

!>          Q2 is REAL array, dimension (LDQ2*N)
!>          The first K columns of this matrix contain the non-deflated
!>          eigenvectors for the split problem.
!> 

INDX

!>          INDX is INTEGER array, dimension (N)
!>          The permutation used to arrange the columns of the deflated
!>          Q matrix into three groups (see SLAED2).
!>          The rows of the eigenvectors found by SLAED4 must be likewise
!>          permuted before the matrix multiply can take place.
!> 

CTOT

!>          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.
!> 

W

!>          W is REAL array, dimension (K)
!>          The first K elements of this array contain the components
!>          of the deflation-adjusted updating vector. Destroyed on
!>          output.
!> 

S

!>          S is REAL 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.
!> 

INFO

!>          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
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee