LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dlaed3()

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.

Download DLAED3 + dependencies [TGZ] [ZIP] [TXT]

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
[in]K
!>          K is INTEGER
!>          The number of terms in the rational function to be solved by
!>          DLAED4.  K >= 0.
!>
[in]N
!>          N is INTEGER
!>          The number of rows and columns in the Q matrix.
!>          N >= K (deflation may result in N>K).
!>
[in]N1
!>          N1 is INTEGER
!>          The location of the last eigenvalue in the leading submatrix.
!>          min(1,N) <= N1 <= N/2.
!>
[out]D
!>          D is DOUBLE PRECISION array, dimension (N)
!>          D(I) contains the updated eigenvalues for
!>          1 <= I <= K.
!>
[out]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.
!>
[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]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.
!>
[in]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.
!>
[in]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.
!>
[in,out]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.
!>
[out]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.
!>
[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
Modified by Francoise Tisseur, University of Tennessee