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# Manual Reference Pages  -  PSLAED2 (l)

### NAME

PSLAED2 - sort the two sets of eigenvalues together into a single sorted set

Synopsis
Purpose
Arguments

### SYNOPSIS

 SUBROUTINE PSLAED2( 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 REAL RHO INTEGER COLTYP( * ), CTOT( 0: NPCOL-1, 4 ), INDCOL( N ), INDX( * ), INDXC( * ), INDXP( * ), PSM( 0: NPCOL-1, 4 ) REAL D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( LDQ2, * ), QBUF( * ), W( * ), Z( * )

### PURPOSE

PSLAED2 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) REAL 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 distributed. 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) REAL 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) REAL 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 PSLAED3. Z (global input) REAL 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) REAL array, dimension (N) A copy of the first K eigenvalues which will be used by SLAED3 to form the secular equation. W (global output) REAL array, dimension (N) The first k values of the final deflation-altered z-vector which will be passed to SLAED3. Q2 (output) REAL 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) REAL 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 submatrix is distributed. INDX (workspace) INTEGER array, dimension (N) The permutation used to sort the contents of DLAMDA into ascending 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 elements 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, (PSLAED1). NN1 (global output) INTEGER, the order of matrix Q1, (PSLAED1). NN2 (global output) INTEGER, the order of matrix Q2, (PSLAED1). IB1 (global output) INTEGER, pointeur on Q1, (PSLAED1). IB2 (global output) INTEGER, pointeur on Q2, (PSLAED1).
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 ScaLAPACK version 1.7 PSLAED2 (l) 13 August 2001

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