LAPACK  3.4.0
LAPACK: Linear Algebra PACKage
Functions/Subroutines
slaed8.f File Reference

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Functions/Subroutines

subroutine SLAED8 (ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO)
 SLAED8

Function/Subroutine Documentation

subroutine SLAED8 ( INTEGER  ICOMPQ,
INTEGER  K,
INTEGER  N,
INTEGER  QSIZ,
REAL, dimension( * )  D,
REAL, dimension( ldq, * )  Q,
INTEGER  LDQ,
INTEGER, dimension( * )  INDXQ,
REAL  RHO,
INTEGER  CUTPNT,
REAL, dimension( * )  Z,
REAL, dimension( * )  DLAMDA,
REAL, dimension( ldq2, * )  Q2,
INTEGER  LDQ2,
REAL, dimension( * )  W,
INTEGER, dimension( * )  PERM,
INTEGER  GIVPTR,
INTEGER, dimension( 2, * )  GIVCOL,
REAL, dimension( 2, * )  GIVNUM,
INTEGER, dimension( * )  INDXP,
INTEGER, dimension( * )  INDX,
INTEGER  INFO 
)

SLAED8

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Purpose: 

 SLAED8 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 element in the
 Z vector.  For each such occurrence the order of the related secular
 equation problem is reduced by one.
Parameters:
[in]ICOMPQ
          ICOMPQ is INTEGER
          = 0:  Compute eigenvalues only.
          = 1:  Compute eigenvectors of original dense symmetric matrix
                also.  On entry, Q contains the orthogonal matrix used
                to reduce the original matrix to tridiagonal form.
[out]K
          K is INTEGER
         The number of non-deflated eigenvalues, and the order of the
         related secular equation.
[in]N
          N is INTEGER
         The dimension of the symmetric tridiagonal matrix.  N >= 0.
[in]QSIZ
          QSIZ is INTEGER
         The dimension of the orthogonal matrix used to reduce
         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.
[in,out]D
          D is REAL array, dimension (N)
         On entry, the eigenvalues of the two submatrices to be
         combined.  On exit, the trailing (N-K) updated eigenvalues
         (those which were deflated) sorted into increasing order.
[in,out]Q
          Q is REAL array, dimension (LDQ,N)
         If ICOMPQ = 0, Q is not referenced.  Otherwise,
         on entry, Q contains the eigenvectors of the partially solved
         system which has been previously updated in matrix
         multiplies with other partially solved eigensystems.
         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]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 CUTPNT added to
         their values in order to be accurate.
[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]CUTPNT
          CUTPNT is INTEGER
         The location of the last eigenvalue in the leading
         sub-matrix.  min(1,N) <= CUTPNT <= N.
[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 are 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]Q2
          Q2 is REAL array, dimension (LDQ2,N)
         If ICOMPQ = 0, Q2 is not referenced.  Otherwise,
         a copy of the first K eigenvectors which will be used by
         SLAED7 in a matrix multiply (SGEMM) to update the new
         eigenvectors.
[in]LDQ2
          LDQ2 is INTEGER
         The leading dimension of the array Q2.  LDQ2 >= max(1,N).
[out]W
          W is REAL array, dimension (N)
         The first k values of the final deflation-altered z-vector and
         will be passed to SLAED3.
[out]PERM
          PERM is INTEGER array, dimension (N)
         The permutations (from deflation and sorting) to be applied
         to each eigenblock.
[out]GIVPTR
          GIVPTR is INTEGER
         The number of Givens rotations which took place in this
         subproblem.
[out]GIVCOL
          GIVCOL is INTEGER array, dimension (2, N)
         Each pair of numbers indicates a pair of columns to take place
         in a Givens rotation.
[out]GIVNUM
          GIVNUM is REAL array, dimension (2, N)
         Each number indicates the S value to be used in the
         corresponding Givens rotation.
[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]INDX
          INDX is INTEGER array, dimension (N)
         The permutation used to sort the contents of D into ascending
         order.
[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

Definition at line 242 of file slaed8.f.

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