claed8-f(3)

claed8.f –

Synopsis

Functions/Subroutines

subroutine claed8 (K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO)
CLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

Function/Subroutine Documentation

subroutine claed8 (integerK, integerN, integerQSIZ, complex, dimension( ldq, * )Q, integerLDQ, real, dimension( * )D, realRHO, integerCUTPNT, real, dimension( * )Z, real, dimension( * )DLAMDA, complex, dimension( ldq2, * )Q2, integerLDQ2, real, dimension( * )W, integer, dimension( * )INDXP, integer, dimension( * )INDX, integer, dimension( * )INDXQ, integer, dimension( * )PERM, integerGIVPTR, integer, dimension( 2, * )GIVCOL, real, dimension( 2, * )GIVNUM, integerINFO)

CLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

Purpose:

 CLAED8 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 element in the
 Z vector. For each such occurrence the order of the related secular
 equation problem is reduced by one.

Parameters:

 K is INTEGER
 Contains the number of non-deflated eigenvalues.
 This is the order of the related secular equation.

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

QSIZ

 QSIZ is INTEGER
 The dimension of the unitary matrix used to reduce
 the dense or band matrix to tridiagonal form.
 QSIZ >= N if ICOMPQ = 1.

 Q is COMPLEX array, dimension (LDQ,N)
 On entry, Q contains the eigenvectors of the partially solved
 system which has been previously updated in matrix
 multiplies with other partially solved eigensystems.
 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 ).

 D is 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.

RHO

 RHO is REAL
 Contains the off diagonal element associated with the rank-1
 cut which originally split the two submatrices which are now
 being recombined. RHO is modified during the computation to
 the value required by SLAED3.

CUTPNT

 CUTPNT is INTEGER
 Contains the location of the last eigenvalue in the leading
 sub-matrix. MIN(1,N) <= CUTPNT <= N.

 Z is REAL array, dimension (N)
 On input this vector contains the updating vector (the last
 row of the first sub-eigenvector matrix and the first row of
 the second sub-eigenvector matrix). The contents of Z are
 destroyed during the updating process.

DLAMDA

 DLAMDA is REAL array, dimension (N)
 Contains a copy of the first K eigenvalues which will be used
 by SLAED3 to form the secular equation.

 Q2 is COMPLEX array, dimension (LDQ2,N)
 If ICOMPQ = 0, Q2 is not referenced. Otherwise,
 Contains a copy of the first K eigenvectors which will be used
 by SLAED7 in a matrix multiply (SGEMM) to update the new
 eigenvectors.

LDQ2

 LDQ2 is INTEGER
 The leading dimension of the array Q2. LDQ2 >= max( 1, N ).

 W is REAL array, dimension (N)
 This will hold the first k values of the final
 deflation-altered z-vector and will be passed to SLAED3.

INDXP

 INDXP is INTEGER array, dimension (N)
 This will contain the permutation used to place deflated
 values of D at the end of the array. On output INDXP(1:K)
 points to the nondeflated D-values and INDXP(K+1:N)
 points to the deflated eigenvalues.

INDX

 INDX is INTEGER array, dimension (N)
 This will contain the permutation used to sort the contents of
 D into ascending order.

INDXQ

 INDXQ is INTEGER array, dimension (N)
 This contains 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 CUTPNT
 added to their values in order to be accurate.

PERM

 PERM is INTEGER array, dimension (N)
 Contains the permutations (from deflation and sorting) to be
 applied to each eigenblock.

GIVPTR

 GIVPTR is INTEGER
 Contains the number of Givens rotations which took place in
 this subproblem.

GIVCOL

 GIVCOL is INTEGER array, dimension (2, N)
 Each pair of numbers indicates a pair of columns to take place
 in a Givens rotation.

GIVNUM

 GIVNUM is REAL array, dimension (2, N)
 Each number indicates the S value to be used in the
 corresponding Givens rotation.

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

Definition at line 227 of file claed8.f.

Author

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