laed9 - Man Page

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.

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.

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.