LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dlaed9()

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.

Download DLAED9 + dependencies [TGZ] [ZIP] [TXT]

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
[in]K
!>          K is INTEGER
!>          The number of terms in the rational function to be solved by
!>          DLAED4.  K >= 0.
!>
[in]KSTART
!>          KSTART is INTEGER
!>
[in]KSTOP
!>          KSTOP is INTEGER
!>          The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP
!>          are to be computed.  1 <= KSTART <= KSTOP <= K.
!>
[in]N
!>          N is INTEGER
!>          The number of rows and columns in the Q matrix.
!>          N >= K (delation may result in N > K).
!>
[out]D
!>          D is DOUBLE PRECISION array, dimension (N)
!>          D(I) contains the updated eigenvalues
!>          for KSTART <= I <= KSTOP.
!>
[out]Q
!>          Q is DOUBLE PRECISION array, dimension (LDQ,N)
!>
[in]LDQ
!>          LDQ is INTEGER
!>          The leading dimension of the array Q.  LDQ >= max( 1, N ).
!>
[in]RHO
!>          RHO is DOUBLE PRECISION
!>          The value of the parameter in the rank one update equation.
!>          RHO >= 0 required.
!>
[in]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.
!>
[in]W
!>          W is DOUBLE PRECISION array, dimension (K)
!>          The first K elements of this array contain the components
!>          of the deflation-adjusted updating vector.
!>
[out]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.
!>
[in]LDS
!>          LDS is INTEGER
!>          The leading dimension of S.  LDS >= max( 1, K ).
!>
[out]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