Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  - finds the roots of the secular equation, as defined by the values in D, W, and
       RHO, between 1 and K

SYNOPSIS

       SUBROUTINE SLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W, S, INFO )

           INTEGER        INFO, K, LDQ, N, N1

           REAL           RHO

           INTEGER        CTOT( * ), INDX( * )

           REAL           D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( * ), S( * ), W( * )

PURPOSE

       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.
        This code makes very mild assumptions about floating point
        arithmetic. It will work on machines with a guard digit in
        add/subtract, or on those binary machines without guard digits
        which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
        It could conceivably fail on hexadecimal or decimal machines
        without guard digits, but we know of none.

ARGUMENTS

        K       (input) INTEGER
                The number of terms in the rational function to be solved by
                SLAED4.  K >= 0.

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

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

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

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

        RHO     (input) REAL
                The value of the parameter in the rank one update equation.
                RHO >= 0 required.

        DLAMDA  (input/output) 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. May be changed on output by
                having lowest order bit set to zero on Cray X-MP, Cray Y-MP,
                Cray-2, or Cray C-90, as described above.

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

        INDX    (input) 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    (input) 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       (input/output) REAL array, dimension (K)
                The first K elements of this array contain the components
                of the deflation-adjusted updating vector. Destroyed on
                output.

        S       (workspace) 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.

        LDS     (input) INTEGER
                The leading dimension of S.  LDS >= max(1,K).

        INFO    (output) 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

FURTHER DETAILS

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

 LAPACK routine (version 3.2)               April 2011                            SLAED3(3lapack)