dlaed1 (l)  Linux Manuals
dlaed1: computes the updated eigensystem of a diagonal matrix after modification by a rankone symmetric matrix
NAME
DLAED1  computes the updated eigensystem of a diagonal matrix after modification by a rankone symmetric matrixSYNOPSIS
 SUBROUTINE DLAED1(
 N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO )
 INTEGER CUTPNT, INFO, LDQ, N
 DOUBLE PRECISION RHO
 INTEGER INDXQ( * ), IWORK( * )
 DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * )
PURPOSE
DLAED1 computes the updated eigensystem of a diagonal matrix after modification by a rankone symmetric matrix. This routine is used only for the eigenproblem which requires all eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles the case in which eigenvalues only or eigenvalues and eigenvectors of a full symmetric matrix (which was reduced to tridiagonal form) are desired.where Z
CUTPNT and CUTPNT
The eigenvectors of the original matrix are stored in Q, and the
eigenvalues are in D.
The first stage consists of deflating the size of the problem
when there are multiple eigenvalues or if there is a zero in
the Z vector.
secular equation problem is reduced by one.
performed by the routine DLAED2.
The second stage consists of calculating the updated
eigenvalues. This is done by finding the roots of the secular
equation via the routine DLAED4
This routine also calculates the eigenvectors of the current
problem.
The final stage consists of computing the updated eigenvectors
directly using the updated eigenvalues.
the current problem are multiplied with the eigenvectors from
the overall problem.
ARGUMENTS
 N (input) INTEGER
 The dimension of the symmetric tridiagonal matrix. N >= 0.
 D (input/output) DOUBLE PRECISION array, dimension (N)
 On entry, the eigenvalues of the rank1perturbed matrix. On exit, the eigenvalues of the repaired matrix.
 Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
 On entry, the eigenvectors of the rank1perturbed matrix. On exit, the eigenvectors of the repaired tridiagonal matrix.
 LDQ (input) INTEGER
 The leading dimension of the array Q. LDQ >= max(1,N).
 INDXQ (input/output) INTEGER array, dimension (N)
 On entry, the permutation which separately sorts the two subproblems in D into ascending order. On exit, the permutation which will reintegrate the subproblems back into sorted order, i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
 RHO (input) DOUBLE PRECISION
 The subdiagonal entry used to create the rank1 modification. CUTPNT (input) INTEGER The location of the last eigenvalue in the leading submatrix. min(1,N) <= CUTPNT <= N/2.
 WORK (workspace) DOUBLE PRECISION array, dimension (4*N + N**2)
 IWORK (workspace) INTEGER array, dimension (4*N)
 INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
> 0: if INFO = 1, an eigenvalue did not converge
FURTHER DETAILS
Based on contributions byJeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee.