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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 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 used by ZSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.
Download ZLAED8 + dependencies [TGZ] [ZIP] [TXT]
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.
| [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. |
1.9.4