slaed8 - edc, when the original matrix is dense
SUBROUTINE SLAED8(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 REAL RHO INTEGER GIVCOL(2,*), INDX(*), INDXP(*), INDXQ(*), PERM(*) REAL D(*), DLAMDA(*), GIVNUM(2,*), Q(LDQ,*), Q2(LDQ2,*), W(*), Z(*) SUBROUTINE SLAED8_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 REAL RHO INTEGER*8 GIVCOL(2,*), INDX(*), INDXP(*), INDXQ(*), PERM(*) REAL 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) REAL, DIMENSION(:,:) :: Q, Q2, GIVNUM INTEGER :: ICOMPQ, K, N, QSIZ, LDQ, CUTPNT, LDQ2, GIVPTR, INFO INTEGER, DIMENSION(:) :: INDXQ, PERM, INDXP, INDX REAL, DIMENSION(:) :: D, Z, DLAMDA, W INTEGER, DIMENSION(:,:) :: GIVCOL REAL :: 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) REAL, DIMENSION(:,:) :: Q, Q2, GIVNUM INTEGER(8) :: ICOMPQ, K, N, QSIZ, LDQ, CUTPNT, LDQ2, GIVPTR, INFO INTEGER(8), DIMENSION(:) :: INDXQ, PERM, INDXP, INDX REAL, DIMENSION(:) :: D, Z, DLAMDA, W INTEGER(8), DIMENSION(:,:) :: GIVCOL REAL :: RHO C INTERFACE #include <sunperf.h> void slaed8 (int icompq, int *k, int n, int qsiz, float *d, float *q, int ldq, int *indxq, float *rho, int cutpnt, float *z, float *dlamda, float *q2, int ldq2, float *w, int *perm, int *givptr, int *givcol, float *givnum, int *info); void slaed8_64 (long icompq, long *k, long n, long qsiz, float *d, float *q, long ldq, long *indxq, float *rho, long cutpnt, float *z, float *dlamda, float *q2, long ldq2, float *w, long *perm, long *givptr, long *givcol, float *givnum, long *info);
Oracle Solaris Studio Performance Library slaed8(3P)
NAME
slaed8 - merge eigenvalues and deflates secular equation. Used by sst-
edc, when the original matrix is dense
SYNOPSIS
SUBROUTINE SLAED8(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
REAL RHO
INTEGER GIVCOL(2,*), INDX(*), INDXP(*), INDXQ(*), PERM(*)
REAL D(*), DLAMDA(*), GIVNUM(2,*), Q(LDQ,*), Q2(LDQ2,*), W(*), Z(*)
SUBROUTINE SLAED8_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
REAL RHO
INTEGER*8 GIVCOL(2,*), INDX(*), INDXP(*), INDXQ(*), PERM(*)
REAL 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)
REAL, DIMENSION(:,:) :: Q, Q2, GIVNUM
INTEGER :: ICOMPQ, K, N, QSIZ, LDQ, CUTPNT, LDQ2, GIVPTR, INFO
INTEGER, DIMENSION(:) :: INDXQ, PERM, INDXP, INDX
REAL, DIMENSION(:) :: D, Z, DLAMDA, W
INTEGER, DIMENSION(:,:) :: GIVCOL
REAL :: 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)
REAL, DIMENSION(:,:) :: Q, Q2, GIVNUM
INTEGER(8) :: ICOMPQ, K, N, QSIZ, LDQ, CUTPNT, LDQ2, GIVPTR, INFO
INTEGER(8), DIMENSION(:) :: INDXQ, PERM, INDXP, INDX
REAL, DIMENSION(:) :: D, Z, DLAMDA, W
INTEGER(8), DIMENSION(:,:) :: GIVCOL
REAL :: RHO
C INTERFACE
#include <sunperf.h>
void slaed8 (int icompq, int *k, int n, int qsiz, float *d, float *q,
int ldq, int *indxq, float *rho, int cutpnt, float *z, float
*dlamda, float *q2, int ldq2, float *w, int *perm, int
*givptr, int *givcol, float *givnum, int *info);
void slaed8_64 (long icompq, long *k, long n, long qsiz, float *d,
float *q, long ldq, long *indxq, float *rho, long cutpnt,
float *z, float *dlamda, float *q2, long ldq2, float *w, long
*perm, long *givptr, long *givcol, float *givnum, long
*info);
PURPOSE
slaed8 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 REAL 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 REAL 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 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
SLAED3.
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 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 are destroyed by the updating
process.
DLAMDA (output)
DLAMDA is REAL array, dimension (N)
A copy of the first K eigenvalues which will be used by
SLAED3 to form the secular equation.
Q2 (output)
Q2 is REAL array, dimension (LDQ2,N)
If ICOMPQ = 0, Q2 is not referenced. Otherwise, a copy of the
first K eigenvectors which will be used by SLAED7 in a matrix
multiply (SGEMM) 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 REAL array, dimension (N)
The first k values of the final deflation-altered z-vector
and will be passed to SLAED3.
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 REAL 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 slaed8(3P)