dlaed8 - edc, when the original matrix is dense
SUBROUTINE DLAED8(ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO) INTEGER CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, QSIZ DOUBLE PRECISION RHO INTEGER GIVCOL(2,*), INDX(*), INDXP(*), INDXQ(*), PERM(*) DOUBLE PRECISION D(*), DLAMDA(*), GIVNUM(2,*), Q(LDQ,*), Q2(LDQ2,*), W(*), Z(*) SUBROUTINE DLAED8_64(ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO) INTEGER*8 CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, QSIZ DOUBLE PRECISION RHO INTEGER*8 GIVCOL(2,*), INDX(*), INDXP(*), INDXQ(*), PERM(*) DOUBLE PRECISION D(*), DLAMDA(*), GIVNUM(2,*), Q(LDQ,*), Q2(LDQ2,*), W(*), Z(*) F95 INTERFACE SUBROUTINE LAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO ) INTEGER :: ICOMPQ, K, N, QSIZ, LDQ, CUTPNT, LDQ2, GIVPTR, INFO INTEGER, DIMENSION(:) :: INDXQ, PERM, INDXP, INDX REAL(8), DIMENSION(:,:) :: Q, Q2, GIVNUM REAL(8), DIMENSION(:) :: D, Z, DLAMDA, W INTEGER, DIMENSION(:,:) :: GIVCOL REAL(8) :: RHO SUBROUTINE LAED8_64(ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO) INTEGER(8) :: ICOMPQ, K, N, QSIZ, LDQ, CUTPNT, LDQ2, GIVPTR, INFO INTEGER(8), DIMENSION(:) :: INDXQ, PERM, INDXP, INDX REAL(8), DIMENSION(:,:) :: Q, Q2, GIVNUM REAL(8), DIMENSION(:) :: D, Z, DLAMDA, W INTEGER(8), DIMENSION(:,:) :: GIVCOL REAL(8) :: RHO C INTERFACE #include <sunperf.h> void dlaed8 (int icompq, int *k, int n, int qsiz, double *d, double *q, int ldq, int *indxq, double *rho, int cutpnt, double *z, dou- ble *dlamda, double *q2, int ldq2, double *w, int *perm, int *givptr, int *givcol, double *givnum, int *info); void dlaed8_64 (long icompq, long *k, long n, long qsiz, double *d, double *q, long ldq, long *indxq, double *rho, long cutpnt, double *z, double *dlamda, double *q2, long ldq2, double *w, long *perm, long *givptr, long *givcol, double *givnum, long *info);
Oracle Solaris Studio Performance Library dlaed8(3P)
NAME
dlaed8 - merge eigenvalues and deflates secular equation. Used by dst-
edc, when the original matrix is dense
SYNOPSIS
SUBROUTINE DLAED8(ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z,
DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP,
INDX, INFO)
INTEGER CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, QSIZ
DOUBLE PRECISION RHO
INTEGER GIVCOL(2,*), INDX(*), INDXP(*), INDXQ(*), PERM(*)
DOUBLE PRECISION D(*), DLAMDA(*), GIVNUM(2,*), Q(LDQ,*), Q2(LDQ2,*),
W(*), Z(*)
SUBROUTINE DLAED8_64(ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT,
Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP,
INDX, INFO)
INTEGER*8 CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, QSIZ
DOUBLE PRECISION RHO
INTEGER*8 GIVCOL(2,*), INDX(*), INDXP(*), INDXQ(*), PERM(*)
DOUBLE PRECISION D(*), DLAMDA(*), GIVNUM(2,*), Q(LDQ,*), Q2(LDQ2,*),
W(*), Z(*)
F95 INTERFACE
SUBROUTINE LAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z,
DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP,
INDX, INFO )
INTEGER :: ICOMPQ, K, N, QSIZ, LDQ, CUTPNT, LDQ2, GIVPTR, INFO
INTEGER, DIMENSION(:) :: INDXQ, PERM, INDXP, INDX
REAL(8), DIMENSION(:,:) :: Q, Q2, GIVNUM
REAL(8), DIMENSION(:) :: D, Z, DLAMDA, W
INTEGER, DIMENSION(:,:) :: GIVCOL
REAL(8) :: RHO
SUBROUTINE LAED8_64(ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT,
Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP,
INDX, INFO)
INTEGER(8) :: ICOMPQ, K, N, QSIZ, LDQ, CUTPNT, LDQ2, GIVPTR, INFO
INTEGER(8), DIMENSION(:) :: INDXQ, PERM, INDXP, INDX
REAL(8), DIMENSION(:,:) :: Q, Q2, GIVNUM
REAL(8), DIMENSION(:) :: D, Z, DLAMDA, W
INTEGER(8), DIMENSION(:,:) :: GIVCOL
REAL(8) :: RHO
C INTERFACE
#include <sunperf.h>
void dlaed8 (int icompq, int *k, int n, int qsiz, double *d, double *q,
int ldq, int *indxq, double *rho, int cutpnt, double *z, dou-
ble *dlamda, double *q2, int ldq2, double *w, int *perm, int
*givptr, int *givcol, double *givnum, int *info);
void dlaed8_64 (long icompq, long *k, long n, long qsiz, double *d,
double *q, long ldq, long *indxq, double *rho, long cutpnt,
double *z, double *dlamda, double *q2, long ldq2, double *w,
long *perm, long *givptr, long *givcol, double *givnum, long
*info);
PURPOSE
dlaed8 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.
ARGUMENTS
ICOMPQ (input)
ICOMPQ is INTEGER
= 0: Compute eigenvalues only.
= 1: Compute eigenvectors of original dense symmetric matrix
also. On entry, Q contains the orthogonal matrix used to
reduce the original matrix to tridiagonal form.
K (output)
K is INTEGER
The number of non-deflated eigenvalues, and the order of the
related secular equation.
N (input)
N is INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
QSIZ (input)
QSIZ is INTEGER
The dimension of the orthogonal matrix used to reduce the
full matrix to tridiagonal form.
QSIZ >= N if ICOMPQ = 1.
D (input/output)
D is DOUBLE PRECISION array, dimension (N)
On entry, the eigenvalues of the two submatrices to be com-
bined.
On exit, the trailing (N-K) updated eigenvalues (those which
were deflated) sorted into increasing order.
Q (input/output)
Q is DOUBLE PRECISION array, dimension (LDQ,N)
If ICOMPQ = 0, Q is not referenced. Otherwise, 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 (input)
LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= max(1,N).
INDXQ (input)
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 CUTPNT added to
their values in order to be accurate.
RHO (input/output)
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.
CUTPNT (input)
CUTPNT is INTEGER
The location of the last eigenvalue in the leading sub-
matrix. min(1,N) <= CUTPNT <= N.
Z (input)
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 are destroyed by the updating
process.
DLAMDA (output)
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.
Q2 (output)
Q2 is DOUBLE PRECISION array, dimension (LDQ2,N)
If ICOMPQ = 0, Q2 is not referenced. Otherwise, a copy of
the first K eigenvectors which will be used by DLAED7 in a
matrix multiply (DGEMM) to update the new eigenvectors.
LDQ2 (input)
LDQ2 is INTEGER
The leading dimension of the array Q2.
LDQ2 >= max(1,N).
W (output)
W is DOUBLE PRECISION array, dimension (N)
The first k values of the final deflation-altered z-vector
and will be passed to DLAED3.
PERM (output)
PERM is INTEGER array, dimension (N)
The permutations (from deflation and sorting) to be applied
to each eigenblock.
GIVPTR (output)
GIVPTR is INTEGER
The number of Givens rotations which took place in this sub-
problem.
GIVCOL (output)
GIVCOL is INTEGER array, dimension (2, N)
Each pair of numbers indicates a pair of columns to take
place in a Givens rotation.
GIVNUM (output)
GIVNUM is DOUBLE PRECISION array, dimension (2, N)
Each number indicates the S value to be used in the corre-
sponding Givens rotation.
INDXP (output)
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.
INDX (output)
INDX is INTEGER array, dimension (N)
The permutation used to sort the contents of D into ascending
order.
INFO (output)
INFO is INTEGER
= 0: successful exit,
< 0: if INFO = -i, the i-th argument had an illegal value.
7 Nov 2015 dlaed8(3P)