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dlaed2-f(3)

dlaed2.f –

Synopsis

Functions/Subroutines

subroutine dlaed2 (K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO)
DLAED2 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

Function/Subroutine Documentation

subroutine dlaed2 (integerK, integerN, integerN1, double precision, dimension( * )D, double precision, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )INDXQ, double precisionRHO, double precision, dimension( * )Z, double precision, dimension( * )DLAMDA, double precision, dimension( * )W, double precision, dimension( * )Q2, integer, dimension( * )INDX, integer, dimension( * )INDXC, integer, dimension( * )INDXP, integer, dimension( * )COLTYP, integerINFO)

DLAED2 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

Purpose:

 DLAED2 merges 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.

 

Parameters:

K

 K is INTEGER
 The number of non-deflated eigenvalues, and the order of the
 related secular equation. 0 <= K <=N.

N

 N is INTEGER
 The dimension of the symmetric tridiagonal matrix. N >= 0.

N1

 N1 is INTEGER
 The location of the last eigenvalue in the leading sub-matrix.
 min(1,N) <= N1 <= N/2.

D

 D is 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.

Q

 Q is 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

 LDQ is INTEGER
 The leading dimension of the array Q. LDQ >= max(1,N).

INDXQ

 INDXQ is INTEGER array, dimension (N)
 The permutation which separately sorts the two sub-problems
 in D into ascending order. Note that elements in the second
 half of this permutation must first have N1 added to their
 values. Destroyed on exit.

RHO

 RHO is 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
 DLAED3.

Z

 Z is 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

 DLAMDA is DOUBLE PRECISION array, dimension (N)
 A copy of the first K eigenvalues which will be used by
 DLAED3 to form the secular equation.

W

 W is DOUBLE PRECISION array, dimension (N)
 The first k values of the final deflation-altered z-vector
 which will be passed to DLAED3.

Q2

 Q2 is DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2)
 A copy of the first K eigenvectors which will be used by
 DLAED3 in a matrix multiply (DGEMM) to solve for the new
 eigenvectors.

INDX

 INDX is INTEGER array, dimension (N)
 The permutation used to sort the contents of DLAMDA into
 ascending order.

INDXC

 INDXC is 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

 INDXP is 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.

COLTYP

 COLTYP is 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.
 On exit, COLTYP(i) is the number of columns of type i,
 for i=1 to 4 only.

INFO

 INFO is INTEGER
 = 0: successful exit.
 < 0: if INFO = -i, the i-th argument had an illegal value.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

 Modified by Francoise Tisseur, University of Tennessee 

Definition at line 212 of file dlaed2.f.

Author

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