PDLAED2(3) ScaLAPACK routine of NEC Numeric Library Collection PDLAED2(3)
NAME
PDLAED2 - sort the two sets of eigenvalues together into a single
sorted set
SYNOPSIS
SUBROUTINE PDLAED2( ICTXT, K, N, N1, NB, D, DROW, DCOL, Q, LDQ, RHO, Z,
W, DLAMDA, Q2, LDQ2, QBUF, CTOT, PSM, NPCOL, INDX,
INDXC, INDXP, INDCOL, COLTYP, NN, NN1, NN2, IB1,
IB2 )
INTEGER DCOL, DROW, IB1, IB2, ICTXT, K, LDQ, LDQ2, N, N1,
NB, NN, NN1, NN2, NPCOL
DOUBLE PRECISION RHO
INTEGER COLTYP( * ), CTOT( 0: NPCOL-1, 4 ), INDCOL( N ),
INDX( * ), INDXC( * ), INDXP( * ), PSM( 0: NPCOL-1,
4 )
DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2(
LDQ2, * ), QBUF( * ), W( * ), Z( * )
PURPOSE
PDLAED2 sorts 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 Z vector. For each
such occurrence the order of the related secular equation problem is
reduced by one.
ARGUMENTS
ICTXT (global input) INTEGER
The BLACS context handle, indicating the global context of the
operation on the matrix. The context itself is global.
K (output) INTEGER
The number of non-deflated eigenvalues, and the order of the
related secular equation. 0 <= K <=N.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
N1 (input) INTEGER
The location of the last eigenvalue in the leading sub-matrix.
min(1,N) < N1 < N.
NB (global input) INTEGER
The blocking factor used to distribute the columns of the
matrix. NB >= 1.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, D contains the eigenvalues of the two submatrices to
be combined. On exit, D contains the trailing (N-K) updated
eigenvalues (those which were deflated) sorted into increasing
order.
DROW (global input) INTEGER
The process row over which the first row of the matrix D is dis-
tributed. 0 <= DROW < NPROW.
DCOL (global input) INTEGER
The process column over which the first column of the matrix D
is distributed. 0 <= DCOL < NPCOL.
Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
On entry, Q contains the eigenvectors of two submatrices in the
two square blocks with corners at (1,1), (N1,N1) and (N1+1,
N1+1), (N,N). On exit, Q contains the trailing (N-K) updated
eigenvectors (those which were deflated) in its last N-K
columns.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,NQ).
RHO (global input/output) DOUBLE PRECISION
On entry, the off-diagonal element associated with the rank-1
cut which originally split the two submatrices which are now
being recombined. On exit, RHO has been modified to the value
required by PDLAED3.
Z (global input) DOUBLE PRECISION array, dimension (N)
On entry, Z contains the updating vector (the last row of the
first sub-eigenvector matrix and the first row of the second
sub-eigenvector matrix). On exit, the contents of Z have been
destroyed by the updating process.
DLAMDA (global output) DOUBLE PRECISION array, dimension (N) A
copy of the first K eigenvalues which will be used by SLAED3 to
form the secular equation.
W (global output) DOUBLE PRECISION array, dimension (N)
The first k values of the final deflation-altered z-vector which
will be passed to SLAED3.
Q2 (output) DOUBLE PRECISION array, dimension (LDQ2, NQ)
A copy of the first K eigenvectors which will be used by
LDQ2 (input) INTEGER
The leading dimension of the array Q2.
QBUF (workspace) DOUBLE PRECISION array, dimension 3*N
CTOT (workspace) INTEGER array, dimension( NPCOL, 4)
PSM (workspace) INTEGER array, dimension( NPCOL, 4)
NPCOL (global input) INTEGER
The total number of columns over which the distributed subma-
trix is distributed.
INDX (workspace) INTEGER array, dimension (N)
The permutation used to sort the contents of DLAMDA into ascend-
ing order.
INDXC (output) INTEGER array, dimension (N)
The permutation used to arrange the columns of the deflated Q
matrix into three groups: the first group contains non-zero
elements only at and above N1, the second contains non-zero ele-
ments only below N1, and the third is dense.
INDXP (workspace) INTEGER array, dimension (N)
The permutation used to place deflated values of D at the end of
the array. INDXP(1:K) points to the nondeflated D-values
and INDXP(K+1:N) points to the deflated eigenvalues.
INDCOL (workspace) INTEGER array, dimension (N)
COLTYP (workspace/output) INTEGER array, dimension (N) During
execution, a label which will indicate which of the following
types a column in the Q2 matrix is:
1 : non-zero in the upper half only;
2 : dense;
3 : non-zero in the lower half only;
4 : deflated.
NN (global output) INTEGER, the order of matrix U, (PDLAED1).
NN1 (global output) INTEGER, the order of matrix Q1,
(PDLAED1). NN2 (global output) INTEGER, the order of matrix
Q2, (PDLAED1). IB1 (global output) INTEGER, pointeur on Q1,
(PDLAED1). IB2 (global output) INTEGER, pointeur on Q2,
(PDLAED1).
ScaLAPACK routine 31 October 2017 PDLAED2(3)