dlaed7 (l)  Linux Man Pages
dlaed7: computes the updated eigensystem of a diagonal matrix after modification by a rankone symmetric matrix
NAME
DLAED7  computes the updated eigensystem of a diagonal matrix after modification by a rankone symmetric matrixSYNOPSIS
 SUBROUTINE DLAED7(
 ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, INFO )
 INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, QSIZ, TLVLS
 DOUBLE PRECISION RHO
 INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * )
 DOUBLE PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ), QSTORE( * ), WORK( * )
PURPOSE
DLAED7 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 optionally eigenvectors of a dense symmetric matrix that has been reduced to tridiagonal form. DLAED1 handles the case in which all eigenvalues and eigenvectors of a symmetric tridiagonal matrix 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 DLAED8.
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
 ICOMPQ (input) INTEGER

= 0: Compute eigenvalues only.
= 1: Compute eigenvectors of original dense symmetric matrix also. On entry, Q contains the orthogonal matrix used to reduce the original matrix to tridiagonal form.  N (input) INTEGER
 The dimension of the symmetric tridiagonal matrix. N >= 0.
 QSIZ (input) INTEGER
 The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
 TLVLS (input) INTEGER
 The total number of merging levels in the overall divide and conquer tree. CURLVL (input) INTEGER The current level in the overall merge routine, 0 <= CURLVL <= TLVLS. CURPBM (input) INTEGER The current problem in the current level in the overall merge routine (counting from upper left to lower right).
 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 (output) INTEGER array, dimension (N)
 The permutation which will reintegrate the subproblem just solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) will be in ascending order.
 RHO (input) DOUBLE PRECISION
 The subdiagonal element used to create the rank1 modification. CUTPNT (input) INTEGER Contains the location of the last eigenvalue in the leading submatrix. min(1,N) <= CUTPNT <= N. QSTORE (input/output) DOUBLE PRECISION array, dimension (N**2+1) Stores eigenvectors of submatrices encountered during divide and conquer, packed together. QPTR points to beginning of the submatrices.
 QPTR (input/output) INTEGER array, dimension (N+2)
 List of indices pointing to beginning of submatrices stored in QSTORE. The submatrices are numbered starting at the bottom left of the divide and conquer tree, from left to right and bottom to top. PRMPTR (input) INTEGER array, dimension (N lg N) Contains a list of pointers which indicate where in PERM a levelaqs permutation is stored. PRMPTR(i+1)  PRMPTR(i) indicates the size of the permutation and also the size of the full, nondeflated problem.
 PERM (input) INTEGER array, dimension (N lg N)
 Contains the permutations (from deflation and sorting) to be applied to each eigenblock. GIVPTR (input) INTEGER array, dimension (N lg N) Contains a list of pointers which indicate where in GIVCOL a levelaqs Givens rotations are stored. GIVPTR(i+1)  GIVPTR(i) indicates the number of Givens rotations. GIVCOL (input) INTEGER array, dimension (2, N lg N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation. GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N) Each number indicates the S value to be used in the corresponding Givens rotation.
 WORK (workspace) DOUBLE PRECISION array, dimension (3*N+QSIZ*N)
 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