dstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal.
?laed1computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. This routine is used only for the eigenproblem which requires all eigenvalues and eigenvectors of a tridiagonal matrix.
?laed7handles the case in which eigenvalues only or eigenvalues and eigenvectors of a full symmetric matrix (which was reduced to tridiagonal form) are desired.
is a vector of length
nwith ones in the
) -th elements and zeros elsewhere. The eigenvectors of the original matrix are stored in
Q, and the eigenvalues are in
D. The algorithm consists of three stages:
The first stage consists of deflating the size of the problem when there are multiple eigenvalues or if there is a zero in the
zvector. For each such occurrence the dimension of the secular equation problem is reduced by one. This stage is performed by the routine
The final stage consists of computing the updated eigenvectors directly using the updated eigenvalues. The eigenvectors for the current problem are multiplied with the eigenvectors from the overall problem.
- INTEGER. The dimension of the symmetric tridiagonal matrix ().n≥0
- REALforslaed1DOUBLE PRECISIONfordlaed1.Arrays:contains the eigenvalues of the rank-1-perturbed matrix. The dimension ofd(*)dmust be at leastmax(1,.n)contains the eigenvectors of the rank-1-perturbed matrix. The second dimension ofq(ldq, *)qmust be at leastmax(1,.n)is a workspace array, dimension at least (work(*)4).n+n2
- 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.
- REALforslaed1DOUBLE PRECISIONfordlaed1.The subdiagonal entry used to create the rank-1 modification. This parameter can be modified by?laed2, where it is input/output.
- INTEGER.The location of the last eigenvalue in the leading sub-matrix.min(1,.n) ≤cutpnt≤n/2
- INTEGER.Workspace array, dimension (4n).
- On exit, contains the eigenvalues of the repaired matrix.
- On exit,qcontains the eigenvectors of the repaired tridiagonal matrix.
- On exit