slaed3.f(3)

NAME
slaed3.f -

SYNOPSIS

  Functions/Subroutines
subroutine slaed3 (K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W, S, INFO)
SLAED3 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal.

Function/Subroutine Documentation

  subroutine slaed3 (integerK, integerN, integerN1, real, dimension( * )D, real, dimension( ldq, * )Q, integerLDQ, realRHO, real, dimension( * )DLAMDA, real, dimension( * )Q2, integer, dimension( * )INDX, integer, dimension( * )CTOT, real, dimension( * )W, real, dimension( * )S, integerINFO)

SLAED3 used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal.

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.

Parameters:
    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.

    DLAMDA

              DLAMDA 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. 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

              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

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

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

Definition at line 185 of file slaed3.f.

Author

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