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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine dlaed8 | ( | integer | ICOMPQ, |
| integer | K, | ||
| integer | N, | ||
| integer | QSIZ, | ||
| double precision, dimension( * ) | D, | ||
| double precision, dimension( ldq, * ) | Q, | ||
| integer | LDQ, | ||
| integer, dimension( * ) | INDXQ, | ||
| double precision | RHO, | ||
| integer | CUTPNT, | ||
| double precision, dimension( * ) | Z, | ||
| double precision, dimension( * ) | DLAMDA, | ||
| double precision, dimension( ldq2, * ) | Q2, | ||
| integer | LDQ2, | ||
| double precision, dimension( * ) | W, | ||
| integer, dimension( * ) | PERM, | ||
| integer | GIVPTR, | ||
| integer, dimension( 2, * ) | GIVCOL, | ||
| double precision, dimension( 2, * ) | GIVNUM, | ||
| integer, dimension( * ) | INDXP, | ||
| integer, dimension( * ) | INDX, | ||
| integer | INFO | ||
| ) |
DLAED8 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.
Download DLAED8 + dependencies [TGZ] [ZIP] [TXT]
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.
| [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 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. |
| [in,out] | Q | 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. |
| [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 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
DLAED3. |
| [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 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. |
| [out] | DLAMDA | DLAMDA is DOUBLE PRECISION array, dimension (N)
A copy of the first K eigenvalues which will be used by
DLAED3 to form the secular equation. |
| [out] | Q2 | 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
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)
The first k values of the final deflation-altered z-vector and
will be passed to DLAED3. |
| [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 DOUBLE PRECISION 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. |
1.9.4