\brief \b ESMF_DLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense. \htmlonly Download ESMF_DLAED8 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:
\verbatim
ESMF_DLAED8 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. \endverbatim \param[in] ICOMPQ \verbatim 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. \endverbatim
\param[out] K \verbatim K is INTEGER The number of non-deflated eigenvalues, and the order of the related secular equation. \endverbatim
\param[in] N \verbatim N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0. \endverbatim
\param[in] QSIZ \verbatim QSIZ is INTEGER The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. \endverbatim
\param[in,out] D \verbatim D is DOUBLE PRECISION 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. \endverbatim
\param[in,out] Q \verbatim Q is DOUBLE PRECISION 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. \endverbatim
\param[in] LDQ \verbatim LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N). \endverbatim
\param[in] INDXQ \verbatim 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. \endverbatim
\param[in,out] RHO \verbatim RHO is DOUBLE PRECISION 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 ESMF_DLAED3. \endverbatim
\param[in] CUTPNT \verbatim CUTPNT is INTEGER The location of the last eigenvalue in the leading sub-matrix. min(1,N) <= CUTPNT <= N. \endverbatim
\param[in] Z \verbatim Z is DOUBLE PRECISION 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. \endverbatim
\param[out] DLAMDA \verbatim DLAMDA is DOUBLE PRECISION array, dimension (N) A copy of the first K eigenvalues which will be used by ESMF_DLAED3 to form the secular equation. \endverbatim
\param[out] Q2 \verbatim Q2 is DOUBLE PRECISION array, dimension (LDQ2,N) If ICOMPQ = 0, Q2 is not referenced. Otherwise, a copy of the first K eigenvectors which will be used by ESMF_DLAED7 in a matrix multiply (ESMF_DGEMM) to update the new eigenvectors. \endverbatim
\param[in] LDQ2 \verbatim LDQ2 is INTEGER The leading dimension of the array Q2. LDQ2 >= max(1,N). \endverbatim
\param[out] W \verbatim W is DOUBLE PRECISION array, dimension (N) The first k values of the final deflation-altered z-vector and will be passed to ESMF_DLAED3. \endverbatim
\param[out] PERM \verbatim PERM is INTEGER array, dimension (N) The permutations (from deflation and sorting) to be applied to each eigenblock. \endverbatim
\param[out] GIVPTR \verbatim GIVPTR is INTEGER The number of Givens rotations which took place in this subproblem. \endverbatim
\param[out] GIVCOL \verbatim GIVCOL is INTEGER array, dimension (2, N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation. \endverbatim
\param[out] GIVNUM \verbatim GIVNUM is DOUBLE PRECISION array, dimension (2, N) Each number indicates the S value to be used in the corresponding Givens rotation. \endverbatim
\param[out] INDXP \verbatim 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. \endverbatim
\param[out] INDX \verbatim INDX is INTEGER array, dimension (N) The permutation used to sort the contents of D into ascending order. \endverbatim
\param[out] INFO \verbatim INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date December 2016 \ingroup auxOTHERcomputational \par Contributors:
Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer | :: | ICOMPQ | ||||
| integer | :: | K | ||||
| integer | :: | N | ||||
| integer | :: | QSIZ | ||||
| double precision | :: | D(*) | ||||
| double precision | :: | Q(LDQ,*) | ||||
| integer | :: | LDQ | ||||
| integer | :: | INDXQ(*) | ||||
| double precision | :: | RHO | ||||
| integer | :: | CUTPNT | ||||
| double precision | :: | Z(*) | ||||
| double precision | :: | DLAMDA(*) | ||||
| double precision | :: | Q2(LDQ2,*) | ||||
| integer | :: | LDQ2 | ||||
| double precision | :: | W(*) | ||||
| integer | :: | PERM(*) | ||||
| integer | :: | GIVPTR | ||||
| integer | :: | GIVCOL(2,*) | ||||
| double precision | :: | GIVNUM(2,*) | ||||
| integer | :: | INDXP(*) | ||||
| integer | :: | INDX(*) | ||||
| integer | :: | INFO |