laed9(3)

NAME
laed9 - laed9: D&C step: secular equation

SYNOPSIS

  Functions
subroutine dlaed9 (k, kstart, kstop, n, d, q, ldq, rho, dlambda, w, s, lds, info)
DLAED9 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.
subroutine slaed9 (k, kstart, kstop, n, d, q, ldq, rho, dlambda, w, s, lds, info)
SLAED9 used by SSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.

Detailed Description

Function Documentation

  subroutine dlaed9 (integer k, integer kstart, integer kstop, integer n, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, double precision rho, double precision, dimension( * ) dlambda, double precision, dimension( * ) w, double precision, dimension( lds, * ) s, integer lds, integer info)

DLAED9 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.

Purpose:

     DLAED9 finds the roots of the secular equation, as defined by the
     values in D, Z, and RHO, between KSTART and KSTOP.  It makes the
     appropriate calls to DLAED4 and then stores the new matrix of
     eigenvectors for use in calculating the next level of Z vectors.

Parameters
    K

              K is INTEGER
              The number of terms in the rational function to be solved by
              DLAED4.  K >= 0.

    KSTART

              KSTART is INTEGER

    KSTOP

              KSTOP is INTEGER
              The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP
              are to be computed.  1 <= KSTART <= KSTOP <= K.

    N

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

    D

              D is DOUBLE PRECISION array, dimension (N)
              D(I) contains the updated eigenvalues
              for KSTART <= I <= KSTOP.

    Q

              Q is DOUBLE PRECISION array, dimension (LDQ,N)

    LDQ

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

    RHO

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

    DLAMBDA

              DLAMBDA is DOUBLE PRECISION 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.

    W

              W is DOUBLE PRECISION array, dimension (K)
              The first K elements of this array contain the components
              of the deflation-adjusted updating vector.

    S

              S is DOUBLE PRECISION array, dimension (LDS, K)
              Will contain the eigenvectors of the repaired matrix which
              will be stored for subsequent Z vector calculation and
              multiplied by the previously accumulated eigenvectors
              to update the system.

    LDS

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

    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.

Contributors:
    Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 154 of file dlaed9.f.

  subroutine slaed9 (integer k, integer kstart, integer kstop, integer n, real, dimension( * ) d, real, dimension( ldq, * ) q, integer ldq, real rho, real, dimension( * ) dlambda, real, dimension( * ) w, real, dimension( lds, * ) s, integer lds, integer info)

SLAED9 used by SSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.

Purpose:

     SLAED9 finds the roots of the secular equation, as defined by the
     values in D, Z, and RHO, between KSTART and KSTOP.  It makes the
     appropriate calls to SLAED4 and then stores the new matrix of
     eigenvectors for use in calculating the next level of Z vectors.

Parameters
    K

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

    KSTART

              KSTART is INTEGER

    KSTOP

              KSTOP is INTEGER
              The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP
              are to be computed.  1 <= KSTART <= KSTOP <= K.

    N

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

    D

              D is REAL array, dimension (N)
              D(I) contains the updated eigenvalues
              for KSTART <= I <= KSTOP.

    Q

              Q is REAL array, dimension (LDQ,N)

    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.

    W

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

    S

              S is REAL array, dimension (LDS, K)
              Will contain the eigenvectors of the repaired matrix which
              will be stored for subsequent Z vector calculation and
              multiplied by the previously accumulated eigenvectors
              to update the system.

    LDS

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

    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.

Contributors:
    Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 154 of file slaed9.f.

Author

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