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# NAME

PDLAED1 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix,

# SYNOPSIS

SUBROUTINE PDLAED1(
N, N1, D, ID, Q, IQ, JQ, DESCQ, RHO, WORK, IWORK, INFO )
INTEGER ID, INFO, IQ, JQ, N, N1 DOUBLE PRECISION RHO INTEGER DESCQ( * ), IWORK( * ) DOUBLE PRECISION D( * ), Q( * ), WORK( * )

# PURPOSE

PDLAED1 computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix, in parallel.

T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)

where Z = Q'u, u is a vector of length N with ones in the
N1 and N1 + 1 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 Z vector. For each such occurence the dimension of the
secular equation problem is reduced by one. This stage is
performed by the routine PDLAED2.

The second stage consists of calculating the updated
eigenvalues. This is done by finding the roots of the secular
equation via the routine SLAED4 (as called by PDLAED3).
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 eigenvectors for
the current problem are multiplied with the eigenvectors from
the overall problem.

# ARGUMENTS

N (global input) INTEGER
The order of the tridiagonal matrix T. N >= 0.
N1 (input) INTEGER
The location of the last eigenvalue in the leading sub-matrix. min(1,N) <= N1 <= N.
D (global input/output) DOUBLE PRECISION array, dimension (N)
On entry,the eigenvalues of the rank-1-perturbed matrix. On exit, the eigenvalues of the repaired matrix.
ID (global input) INTEGER
Q's global row/col index, which points to the beginning of the submatrix which is to be operated on.
Q (local output) DOUBLE PRECISION array,
global dimension (N, N), local dimension ( LLD_Q, LOCc(JQ+N-1)) Q contains the orthonormal eigenvectors of the symmetric tridiagonal matrix.
IQ (global input) INTEGER
Q's global row index, which points to the beginning of the submatrix which is to be operated on.
JQ (global input) INTEGER
Q's global column index, which points to the beginning of the submatrix which is to be operated on.
DESCQ (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix Z.
RHO (input) DOUBLE PRECISION
The subdiagonal entry used to create the rank-1 modification.
WORK (local workspace/output) DOUBLE PRECISION array,
dimension 6*N + 2*NP*NQ
IWORK (local workspace/output) INTEGER array,
dimension 7*N + 8*NPCOL + 2
INFO (global output) INTEGER
= 0: successful exit

< 0: If the i-th argument is an array and the j-entry had an illegal value, then INFO = -(i*100+j), if the i-th argument is a scalar and had an illegal value, then INFO = -i. > 0: The algorithm failed to compute the ith eigenvalue.
 13 August 2001 ScaLAPACK version 1.7

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