LAPACK
3.6.1
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 sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.
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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. |
Definition at line 230 of file zlaed8.f.