LAPACK  3.4.0
LAPACK: Linear Algebra PACKage
Functions/Subroutines
slaed2.f File Reference

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Functions/Subroutines

subroutine SLAED2 (K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO)
 SLAED2

Function/Subroutine Documentation

subroutine SLAED2 ( INTEGER  K,
INTEGER  N,
INTEGER  N1,
REAL, dimension( * )  D,
REAL, dimension( ldq, * )  Q,
INTEGER  LDQ,
INTEGER, dimension( * )  INDXQ,
REAL  RHO,
REAL, dimension( * )  Z,
REAL, dimension( * )  DLAMDA,
REAL, dimension( * )  W,
REAL, dimension( * )  Q2,
INTEGER, dimension( * )  INDX,
INTEGER, dimension( * )  INDXC,
INTEGER, dimension( * )  INDXP,
INTEGER, dimension( * )  COLTYP,
INTEGER  INFO 
)

SLAED2

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Purpose: 

 SLAED2 merges the two sets of eigenvalues together into a single
 sorted set.  Then it tries to deflate the size of the problem.
 There are two ways in which deflation can occur:  when two or more
 eigenvalues are close together or if there is a tiny entry in the
 Z vector.  For each such occurrence the order of the related secular
 equation problem is reduced by one.
Parameters:
[out]K
          K is INTEGER
         The number of non-deflated eigenvalues, and the order of the
         related secular equation. 0 <= K <=N.
[in]N
          N is INTEGER
         The dimension of the symmetric tridiagonal matrix.  N >= 0.
[in]N1
          N1 is INTEGER
         The location of the last eigenvalue in the leading sub-matrix.
         min(1,N) <= N1 <= N/2.
[in,out]D
          D is REAL array, dimension (N)
         On entry, D contains the eigenvalues of the two submatrices to
         be combined.
         On exit, D contains the trailing (N-K) updated eigenvalues
         (those which were deflated) sorted into increasing order.
[in,out]Q
          Q is REAL array, dimension (LDQ, N)
         On entry, Q contains the eigenvectors of two submatrices in
         the two square blocks with corners at (1,1), (N1,N1)
         and (N1+1, N1+1), (N,N).
         On exit, Q contains the trailing (N-K) updated eigenvectors
         (those which were deflated) in its last N-K columns.
[in]LDQ
          LDQ is INTEGER
         The leading dimension of the array Q.  LDQ >= max(1,N).
[in,out]INDXQ
          INDXQ is INTEGER array, dimension (N)
         The permutation which separately sorts the two sub-problems
         in D into ascending order.  Note that elements in the second
         half of this permutation must first have N1 added to their
         values. Destroyed on exit.
[in,out]RHO
          RHO is REAL
         On entry, the off-diagonal element associated with the rank-1
         cut which originally split the two submatrices which are now
         being recombined.
         On exit, RHO has been modified to the value required by
         SLAED3.
[in]Z
          Z is REAL array, dimension (N)
         On entry, Z contains the updating vector (the last
         row of the first sub-eigenvector matrix and the first row of
         the second sub-eigenvector matrix).
         On exit, the contents of Z have been destroyed by the updating
         process.
[out]DLAMDA
          DLAMDA is REAL array, dimension (N)
         A copy of the first K eigenvalues which will be used by
         SLAED3 to form the secular equation.
[out]W
          W is REAL array, dimension (N)
         The first k values of the final deflation-altered z-vector
         which will be passed to SLAED3.
[out]Q2
          Q2 is REAL array, dimension (N1**2+(N-N1)**2)
         A copy of the first K eigenvectors which will be used by
         SLAED3 in a matrix multiply (SGEMM) to solve for the new
         eigenvectors.
[out]INDX
          INDX is INTEGER array, dimension (N)
         The permutation used to sort the contents of DLAMDA into
         ascending order.
[out]INDXC
          INDXC is INTEGER array, dimension (N)
         The permutation used to arrange the columns of the deflated
         Q matrix into three groups:  the first group contains non-zero
         elements only at and above N1, the second contains
         non-zero elements only below N1, and the third is dense.
[out]INDXP
          INDXP is INTEGER array, dimension (N)
         The permutation used to place deflated values of D at the end
         of the array.  INDXP(1:K) points to the nondeflated D-values
         and INDXP(K+1:N) points to the deflated eigenvalues.
[out]COLTYP
          COLTYP is INTEGER array, dimension (N)
         During execution, a label which will indicate which of the
         following types a column in the Q2 matrix is:
         1 : non-zero in the upper half only;
         2 : dense;
         3 : non-zero in the lower half only;
         4 : deflated.
         On exit, COLTYP(i) is the number of columns of type i,
         for i=1 to 4 only.
[out]INFO
          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Contributors:
Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee

Definition at line 212 of file slaed2.f.

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