PLASMA 2.8.0 PLASMA - Parallel Linear Algebra for Scalable Multi-core Architectures

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void CORE_slaed2_computeK | ( | int * | Kptr,
|  | int | n,
|  | int | n1,
|  | float * | betaptr,
|  | float * | D,
|  | float * | Q,
|  | int | LDQ,
|  | float * | Z,
|  | float * | DLAMBDA,
|  | float * | W,
|  | int * | INDX,
|  | int * | INDXC,
|  | int * | INDXP,
|  | int * | INDXQ,
|  | int * | COLTYP
| ) |  |

CORE_slaed2_computeK - Computes the number of deflated eigenvalues of a symmetric tridiagonal matrix. A eigenvalue is deflated if it's close enough to another eigenvalue or if the vector Z contains a tiny entry. This operation is useful when two subproblems, which were previously solved, are merge into a larger problem.

Parameters

  [out] | Kptr | On exit, Kptr stores the number of non-deflated eigenvalues
  [in] | n | n specifies the dimension of the symmetric tridiagonal matrix
  [in] | n1 | n1 specifies the location of the last eigenvalue of the first subproblem min(1, n) <= n1 <= n/2
  [in,out] | betaptr | betaptr[0] specifies the rank-1 approximation that was used for splitting the problem into two subproblems. On exit, it contains the updated beta for LAED3.
  [in,out] | D | On entry, D contains the eigenvalues of the two submatrices to be merged. On exit, D contains the updated eigenvalues sorted into increasing order.
  [in,out] | Q | On entry, Q contains the eigenvectors of each subproblem. On exit, Q contains the updated eigenvectors, which can be modified through givens rotation (with close eigenvalues).
  [in] | LDQ | LDQ specifies the leading direction of Q
  [out] | Z | Z will contain the updating vectors, composed of the last row of the first subproblem and the first row of the second subproblem.
  [out] | DLAMBDA | DLAMBDA will contain a copy of the first K eigenvalues and then an update of those eigenvalues for usage in LAED3. In LAPACK, the call of slamc3 is done at the beginning of LAED3.
  [out] | W | W will contain the fisrt K values of the final Z vector, for future use in LAED3.
  [out] | INDX | The permutation used to sort the contents of DLAMBDA into ascending order
  [out] | INDXC | The permutation used to arrange the columns of the deflated Q matrix 1- non-zero elements only at and above n1 2- non-zero elements only below n1 3- dense
  [out] | INDXP | INDXP is the permutation used to place deflated eigenvalues at the end of the array INDXP(0:K-1) points to the non-deflated D values INDXP(K-1:N-1) points to the deflated D values
  [in,out] | INDXQ | The permutation which separetely sorts each subprobem in D into ascending order. In the second half of the permutation, elements will have n1 added to their value.
  [out] | COLTYP | COLTYP indicate the type of the Q matrix columns during the process. 1- non-zero in the upper half only 2- dense 3- non-zero in the lower half only 4- deflated