laed3(3)

NAME
laed3 - laed3: D&C step: secular equation

SYNOPSIS

  Functions
subroutine dlaed3 (k, n, n1, d, q, ldq, rho, dlambda, q2, indx, ctot, w, s, info)
DLAED3 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal.
subroutine slaed3 (k, n, n1, d, q, ldq, rho, dlambda, 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.

Detailed Description

Function Documentation

  subroutine dlaed3 (integer k, integer n, integer n1, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, double precision rho, double precision, dimension( * ) dlambda, double precision, dimension( * ) q2, integer, dimension( * ) indx, integer, dimension( * ) ctot, double precision, dimension( * ) w, double precision, dimension( * ) s, integer info)

DLAED3 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is tridiagonal.

Purpose:

     DLAED3 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 DLAED4 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.

Parameters
    K

              K is INTEGER
              The number of terms in the rational function to be solved by
              DLAED4.  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 DOUBLE PRECISION array, dimension (N)
              D(I) contains the updated eigenvalues for
              1 <= I <= K.

    Q

              Q is DOUBLE PRECISION 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 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.

    Q2

              Q2 is DOUBLE PRECISION 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 DLAED2).
              The rows of the eigenvectors found by DLAED4 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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.

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

Definition at line 175 of file dlaed3.f.

  subroutine slaed3 (integer k, integer n, integer n1, real, dimension( * ) d, real, dimension( ldq, * ) q, integer ldq, real rho, real, dimension( * ) dlambda, real, dimension( * ) q2, integer, dimension( * ) indx, integer, dimension( * ) ctot, real, dimension( * ) w, real, dimension( * ) s, integer info)

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.

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.

    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

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
     Modified by Francoise Tisseur, University of Tennessee

Definition at line 175 of file slaed3.f.

Author

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