dstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.
?laed2merges 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 entry in the
zvector. For each such occurrence the order of the related secular equation problem is reduced by one.
- INTEGER. The number of non-deflated eigenvalues, and the order of the related secular equation (0 ≤.k≤n)
- INTEGER. The dimension of the symmetric tridiagonal matrix ().n≥0
- INTEGER. The location of the last eigenvalue in the leading sub-matrix;min(1,.n) ≤n1≤n/2
- REALforslaed2DOUBLE PRECISIONfordlaed2.Arrays:contains the eigenvalues of the two submatrices to be combined. The dimension ofd(*)dmust be at leastmax(1,.n)contains the eigenvectors of the two submatrices in the two square blocks with corners at (1,1), (q(ldq, *)n1,n1) and (n1+1,n1+1), (n,n). The second dimension ofqmust be at leastmax(1,.n)contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix).z(*)
- INTEGER. The leading dimension of the arrayq;.ldq≥max(1,n)
- INTEGER. Array, dimension (n).On entry, the permutation which separately sorts the two subproblems indinto ascending order. Note that elements in the second half of this permutation must first haven1added to their values.
- REALforslaed2DOUBLE PRECISIONfordlaed2.On entry, the off-diagonal element associated with the rank-1 cut which originally split the two submatrices which are now being recombined.
- INTEGER.Workspace arrays, dimension (n) each. Arrayindxcontains the permutation used to sort the contents ofdlamdainto ascending order.Arrayindxpcontains the permutation used to place deflated values ofdat the end of the array.indxp(1:k) points to the nondeflatedd-values andindxp(k+1:n) points to the deflated eigenvalues.
- INTEGER.Workspace array, dimension (n).During execution, a label which will indicate which of the following types a column in theq2matrix is:1 : non-zero in the upper half only;2 : dense;3 : non-zero in the lower half only;4 : deflated.
- On exit,dcontains the trailing (n-k) updated eigenvalues (those which were deflated) sorted into increasing order.
- On exit,qcontains the trailing (n-k) updated eigenvectors (those which were deflated) in its lastn-kcolumns.
- On exit,zcontent is destroyed by the updating process.