claed8 - edc, when the original matrix is dense
SUBROUTINE CLAED8(K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO) INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ REAL RHO INTEGER GIVCOL(2,*), INDX(*), INDXP(*), INDXQ(*), PERM(*) REAL D(*), DLAMDA(*), GIVNUM(2,*), W(*), Z(*) COMPLEX Q(LDQ,*), Q2(LDQ2,*) SUBROUTINE CLAED8_64(K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO) INTEGER*8 CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ REAL RHO INTEGER*8 GIVCOL(2,*), INDX(*), INDXP(*), INDXQ(*), PERM(*) REAL D(*), DLAMDA(*), GIVNUM(2,*), W(*), Z(*) COMPLEX Q(LDQ,*), Q2(LDQ2,*) F95 INTERFACE SUBROUTINE LAED8(K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO) REAL, DIMENSION(:,:) :: GIVNUM INTEGER :: K, N, QSIZ, LDQ, CUTPNT, LDQ2, GIVPTR, INFO INTEGER, DIMENSION(:) :: INDXP, INDX, INDXQ, PERM REAL, DIMENSION(:) :: D, Z, DLAMDA, W COMPLEX, DIMENSION(:,:) :: Q, Q2 INTEGER, DIMENSION(:,:) :: GIVCOL REAL :: RHO SUBROUTINE LAED8_64(K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM, INFO) REAL, DIMENSION(:,:) :: GIVNUM INTEGER(8) :: K, N, QSIZ, LDQ, CUTPNT, LDQ2, GIVPTR, INFO INTEGER(8), DIMENSION(:) :: INDXP, INDX, INDXQ, PERM REAL, DIMENSION(:) :: D, Z, DLAMDA, W COMPLEX, DIMENSION(:,:) :: Q, Q2 INTEGER(8), DIMENSION(:,:) :: GIVCOL REAL :: RHO C INTERFACE #include <sunperf.h> void claed8 (int *k, int n, int qsiz, floatcomplex *q, int ldq, float *d, float *rho, int cutpnt, float *z, float *dlamda, float- complex *q2, int ldq2, float *w, int *indxq, int *perm, int *givptr, int *givcol, float *givnum, int *info); void claed8_64 (long *k, long n, long qsiz, floatcomplex *q, long ldq, float *d, float *rho, long cutpnt, float *z, float *dlamda, floatcomplex *q2, long ldq2, float *w, long *indxq, long *perm, long *givptr, long *givcol, float *givnum, long *info);
Oracle Solaris Studio Performance Library claed8(3P)
NAME
claed8 - merge eigenvalues and deflates secular equation. Used by cst-
edc, when the original matrix is dense
SYNOPSIS
SUBROUTINE CLAED8(K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2,
LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM,
INFO)
INTEGER CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ
REAL RHO
INTEGER GIVCOL(2,*), INDX(*), INDXP(*), INDXQ(*), PERM(*)
REAL D(*), DLAMDA(*), GIVNUM(2,*), W(*), Z(*)
COMPLEX Q(LDQ,*), Q2(LDQ2,*)
SUBROUTINE CLAED8_64(K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2,
LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM,
INFO)
INTEGER*8 CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ
REAL RHO
INTEGER*8 GIVCOL(2,*), INDX(*), INDXP(*), INDXQ(*), PERM(*)
REAL D(*), DLAMDA(*), GIVNUM(2,*), W(*), Z(*)
COMPLEX Q(LDQ,*), Q2(LDQ2,*)
F95 INTERFACE
SUBROUTINE LAED8(K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2,
LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM,
INFO)
REAL, DIMENSION(:,:) :: GIVNUM
INTEGER :: K, N, QSIZ, LDQ, CUTPNT, LDQ2, GIVPTR, INFO
INTEGER, DIMENSION(:) :: INDXP, INDX, INDXQ, PERM
REAL, DIMENSION(:) :: D, Z, DLAMDA, W
COMPLEX, DIMENSION(:,:) :: Q, Q2
INTEGER, DIMENSION(:,:) :: GIVCOL
REAL :: RHO
SUBROUTINE LAED8_64(K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2,
LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL, GIVNUM,
INFO)
REAL, DIMENSION(:,:) :: GIVNUM
INTEGER(8) :: K, N, QSIZ, LDQ, CUTPNT, LDQ2, GIVPTR, INFO
INTEGER(8), DIMENSION(:) :: INDXP, INDX, INDXQ, PERM
REAL, DIMENSION(:) :: D, Z, DLAMDA, W
COMPLEX, DIMENSION(:,:) :: Q, Q2
INTEGER(8), DIMENSION(:,:) :: GIVCOL
REAL :: RHO
C INTERFACE
#include <sunperf.h>
void claed8 (int *k, int n, int qsiz, floatcomplex *q, int ldq, float
*d, float *rho, int cutpnt, float *z, float *dlamda, float-
complex *q2, int ldq2, float *w, int *indxq, int *perm, int
*givptr, int *givcol, float *givnum, int *info);
void claed8_64 (long *k, long n, long qsiz, floatcomplex *q, long ldq,
float *d, float *rho, long cutpnt, float *z, float *dlamda,
floatcomplex *q2, long ldq2, float *w, long *indxq, long
*perm, long *givptr, long *givcol, float *givnum, long
*info);
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.
ARGUMENTS
K (output)
K is INTEGER
Contains the number of non-deflated eigenvalues.
This is 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 unitary matrix used to reduce the dense
or band matrix to tridiagonal form.
QSIZ >= N if ICOMPQ = 1.
Q (input/output)
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 (input)
LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= max( 1, N ).
D (input/output)
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 (input/output)
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 (input)
CUTPNT is INTEGER
Contains 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 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 (output)
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 (output)
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 (input)
LDQ2 is INTEGER
The leading dimension of the array Q2.
LDQ2 >= max( 1, N ).
W (output)
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 (output)
INDXP is INTEGER array, dimension (N)
This will contain the permutation used to place deflated val-
ues 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 (output)
INDX is INTEGER array, dimension (N)
This will contain the permutation used to sort the contents
of D into ascending order.
INDXQ (input)
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 (output)
PERM is INTEGER array, dimension (N)
Contains the permutations (from deflation and sorting) to be
applied to each eigenblock.
GIVPTR (output)
GIVPTR is INTEGER
Contains the number of Givens rotations which took place in
this subproblem.
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.
INFO (output)
INFO is INTEGER
= 0: successful exit,
< 0: if INFO = -i, the i-th argument had an illegal value.
7 Nov 2015 claed8(3P)