LAPACK  3.4.0
LAPACK: Linear Algebra PACKage
Functions/Subroutines
zlaed8.f File Reference

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Functions/Subroutines

subroutine ZLAED8 (K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO)
 ZLAED8

Function/Subroutine Documentation

subroutine ZLAED8 ( INTEGER  K,
INTEGER  N,
INTEGER  QSIZ,
COMPLEX*16, dimension( ldq, * )  Q,
INTEGER  LDQ,
DOUBLE PRECISION, dimension( * )  D,
DOUBLE PRECISION  RHO,
INTEGER  CUTPNT,
DOUBLE PRECISION, dimension( * )  Z,
DOUBLE PRECISION, dimension( * )  DLAMDA,
COMPLEX*16, dimension( ldq2, * )  Q2,
INTEGER  LDQ2,
DOUBLE PRECISION, dimension( * )  W,
INTEGER, dimension( * )  INDXP,
INTEGER, dimension( * )  INDX,
INTEGER, dimension( * )  INDXQ,
INTEGER, dimension( * )  PERM,
INTEGER  GIVPTR,
INTEGER, dimension( 2, * )  GIVCOL,
DOUBLE PRECISION, dimension( 2, * )  GIVNUM,
INTEGER  INFO 
)

ZLAED8

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Purpose: 

 ZLAED8 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:
[out]K
          K is INTEGER
         Contains the number of non-deflated eigenvalues.
         This is 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 unitary matrix used to reduce
         the dense or band matrix to tridiagonal form.
         QSIZ >= N if ICOMPQ = 1.
[in,out]Q
          Q is COMPLEX*16 array, dimension (LDQ,N)
         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,out]D
          D is DOUBLE PRECISION 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]RHO
          RHO is DOUBLE PRECISION
         Contains the off diagonal element associated with the rank-1
         cut which originally split the two submatrices which are now
         being recombined. RHO is modified during the computation to
         the value required by DLAED3.
[in]CUTPNT
          CUTPNT is INTEGER
         Contains the location of the last eigenvalue in the leading
         sub-matrix.  MIN(1,N) <= CUTPNT <= N.
[in]Z
          Z is DOUBLE PRECISION array, dimension (N)
         On input this vector contains the updating vector (the last
         row of the first sub-eigenvector matrix and the first row of
         the second sub-eigenvector matrix).  The contents of Z are
         destroyed during the updating process.
[out]DLAMDA
          DLAMDA is DOUBLE PRECISION array, dimension (N)
         Contains a copy of the first K eigenvalues which will be used
         by DLAED3 to form the secular equation.
[out]Q2
          Q2 is COMPLEX*16 array, dimension (LDQ2,N)
         If ICOMPQ = 0, Q2 is not referenced.  Otherwise,
         Contains a copy of the first K eigenvectors which will be used
         by DLAED7 in a matrix multiply (DGEMM) 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 DOUBLE PRECISION array, dimension (N)
         This will hold the first k values of the final
         deflation-altered z-vector and will be passed to DLAED3.
[out]INDXP
          INDXP is INTEGER array, dimension (N)
         This will contain the permutation used to place deflated
         values of D at the end of the array. On output 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)
         This will contain the permutation used to sort the contents of
         D into ascending order.
[in]INDXQ
          INDXQ is INTEGER array, dimension (N)
         This contains 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.
[out]PERM
          PERM is INTEGER array, dimension (N)
         Contains the permutations (from deflation and sorting) to be
         applied to each eigenblock.
[out]GIVPTR
          GIVPTR is INTEGER
         Contains 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 DOUBLE PRECISION array, dimension (2, N)
         Each number indicates the S value to be used in the
         corresponding Givens rotation.
[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

Definition at line 227 of file zlaed8.f.

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