claed7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used by cstedc, when the original matrix is dense
SUBROUTINE CLAED7(N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, INFO) INTEGER CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, TLVLS REAL RHO INTEGER GIVCOL(2,*), GIVPTR(*), INDXQ(*), IWORK(*), PERM(*), PRMPTR(*), QPTR(*) REAL D(*), GIVNUM(2,*), QSTORE(*), RWORK(*) COMPLEX Q(LDQ,*), WORK(*) SUBROUTINE CLAED7_64(N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, INFO) INTEGER*8 CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, TLVLS REAL RHO INTEGER*8 GIVCOL(2,*), GIVPTR(*), INDXQ(*), IWORK(*), PERM(*), PRMPTR(*), QPTR(*) REAL D(*), GIVNUM(2,*), QSTORE(*), RWORK(*) COMPLEX Q(LDQ,*), WORK(*) F95 INTERFACE SUBROUTINE LAED7(N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, INFO) REAL, DIMENSION(:,:) :: GIVNUM INTEGER :: N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, LDQ, INFO INTEGER, DIMENSION(:) :: INDXQ, QPTR, PRMPTR, PERM, GIVPTR, IWORK REAL, DIMENSION(:) :: D, QSTORE, RWORK COMPLEX, DIMENSION(:,:) :: Q INTEGER, DIMENSION(:,:) :: GIVCOL COMPLEX, DIMENSION(:) :: WORK REAL :: RHO SUBROUTINE LAED7_64(N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, INFO) REAL, DIMENSION(:,:) :: GIVNUM INTEGER(8) :: N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, LDQ, INFO INTEGER(8), DIMENSION(:) :: INDXQ, QPTR, PRMPTR, PERM, GIVPTR, IWORK REAL, DIMENSION(:) :: D, QSTORE, RWORK COMPLEX, DIMENSION(:,:) :: Q INTEGER(8), DIMENSION(:,:) :: GIVCOL COMPLEX, DIMENSION(:) :: WORK REAL :: RHO C INTERFACE #include <sunperf.h> void claed7 (int n, int cutpnt, int qsiz, int tlvls, int curlvl, int curpbm, float *d, floatcomplex *q, int ldq, float rho, int *indxq, float *qstore, int *qptr, int *prmptr, int *perm, int *givptr, int *givcol, float *givnum, int *info); void claed7_64 (long n, long cutpnt, long qsiz, long tlvls, long curlvl, long curpbm, float *d, floatcomplex *q, long ldq, float rho, long *indxq, float *qstore, long *qptr, long *prmptr, long *perm, long *givptr, long *givcol, float *givnum, long *info);
Oracle Solaris Studio Performance Library claed7(3P)
NAME
claed7 - compute the updated eigensystem of a diagonal matrix after
modification by a rank-one symmetric matrix. Used by cstedc, when the
original matrix is dense
SYNOPSIS
SUBROUTINE CLAED7(N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ,
RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL,
GIVNUM, WORK, RWORK, IWORK, INFO)
INTEGER CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, TLVLS
REAL RHO
INTEGER GIVCOL(2,*), GIVPTR(*), INDXQ(*), IWORK(*), PERM(*), PRMPTR(*),
QPTR(*)
REAL D(*), GIVNUM(2,*), QSTORE(*), RWORK(*)
COMPLEX Q(LDQ,*), WORK(*)
SUBROUTINE CLAED7_64(N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ,
RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL,
GIVNUM, WORK, RWORK, IWORK, INFO)
INTEGER*8 CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, TLVLS
REAL RHO
INTEGER*8 GIVCOL(2,*), GIVPTR(*), INDXQ(*), IWORK(*), PERM(*),
PRMPTR(*), QPTR(*)
REAL D(*), GIVNUM(2,*), QSTORE(*), RWORK(*)
COMPLEX Q(LDQ,*), WORK(*)
F95 INTERFACE
SUBROUTINE LAED7(N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ,
RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL,
GIVNUM, WORK, RWORK, IWORK, INFO)
REAL, DIMENSION(:,:) :: GIVNUM
INTEGER :: N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, LDQ, INFO
INTEGER, DIMENSION(:) :: INDXQ, QPTR, PRMPTR, PERM, GIVPTR, IWORK
REAL, DIMENSION(:) :: D, QSTORE, RWORK
COMPLEX, DIMENSION(:,:) :: Q
INTEGER, DIMENSION(:,:) :: GIVCOL
COMPLEX, DIMENSION(:) :: WORK
REAL :: RHO
SUBROUTINE LAED7_64(N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ,
RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL,
GIVNUM, WORK, RWORK, IWORK, INFO)
REAL, DIMENSION(:,:) :: GIVNUM
INTEGER(8) :: N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, LDQ, INFO
INTEGER(8), DIMENSION(:) :: INDXQ, QPTR, PRMPTR, PERM, GIVPTR, IWORK
REAL, DIMENSION(:) :: D, QSTORE, RWORK
COMPLEX, DIMENSION(:,:) :: Q
INTEGER(8), DIMENSION(:,:) :: GIVCOL
COMPLEX, DIMENSION(:) :: WORK
REAL :: RHO
C INTERFACE
#include <sunperf.h>
void claed7 (int n, int cutpnt, int qsiz, int tlvls, int curlvl, int
curpbm, float *d, floatcomplex *q, int ldq, float rho, int
*indxq, float *qstore, int *qptr, int *prmptr, int *perm, int
*givptr, int *givcol, float *givnum, int *info);
void claed7_64 (long n, long cutpnt, long qsiz, long tlvls, long
curlvl, long curpbm, float *d, floatcomplex *q, long ldq,
float rho, long *indxq, float *qstore, long *qptr, long
*prmptr, long *perm, long *givptr, long *givcol, float
*givnum, long *info);
PURPOSE
claed7 computes the updated eigensystem of a diagonal matrix after mod-
ification by a rank-one symmetric matrix. This routine is used only for
the eigenproblem which requires all eigenvalues and optionally eigen-
vectors of a dense or banded Hermitian matrix that has been reduced to
tridiagonal form.
T=Q(in)(D(in)+RHO*Z*Z**H ) Q**H(in) = Q(out)*D(out)*Q**H(out)
where Z = Q**Hu, u is a vector of length N with ones in the CUTPNT and
CUTPNT + 1 th elements and zeros elsewhere.
The eigenvectors of the original matrix are stored in Q, and the eigen-
values are in D. The algorithm consists of three stages:
The first stage consists of deflating the size of the problem when
there are multiple eigenvalues or if there is a zero in the Z vector.
For each such occurence the dimension of the secular equation problem
is reduced by one. This stage is performed by the routine SLAED2.
The second stage consists of calculating the updated eigenvalues. This
is done by finding the roots of the secular equation via the routine
SLAED4 (as called by SLAED3). This routine also calculates the eigen-
vectors of the current problem.
The final stage consists of computing the updated eigenvectors directly
using the updated eigenvalues. The eigenvectors for the current problem
are multiplied with the eigenvectors from the overall problem.
ARGUMENTS
N (input)
N is INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
CUTPNT (input)
CUTPNT is INTEGER
Contains the location of the last eigenvalue in the leading
sub-matrix. min(1,N) <= CUTPNT <= N.
QSIZ (input)
QSIZ is INTEGER
The dimension of the unitary matrix used to reduce the full
matrix to tridiagonal form. QSIZ >= N.
TLVLS (input)
TLVLS is INTEGER
The total number of merging levels in the overall divide and
conquer tree.
CURLVL (input)
CURLVL is INTEGER
The current level in the overall merge routine,
0 <= curlvl <= tlvls.
CURPBM (input)
CURPBM is INTEGER
The current problem in the current level in the overall merge
routine (counting from upper left to lower right).
D (input/output)
D is REAL array, dimension (N)
On entry, the eigenvalues of the rank-1-perturbed matrix.
On exit, the eigenvalues of the repaired matrix.
Q (input/output)
Q is COMPLEX array, dimension (LDQ,N)
On entry, the eigenvectors of the rank-1-perturbed matrix.
On exit, the eigenvectors of the repaired tridiagonal matrix.
LDQ (input)
LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= max(1,N).
RHO (input)
RHO is REAL
Contains the subdiagonal element used to create the rank-1
modification.
INDXQ (output)
INDXQ is INTEGER array, dimension (N)
This contains the permutation which will reintegrate the sub-
problem just solved back into sorted order, ie. D(INDXQ(I =
1, N)) will be in ascending order.
IWORK (output)
IWORK is INTEGER array, dimension (4*N)
RWORK (output)
RWORK is REAL array, dimension (3*N+2*QSIZ*N)
WORK (output)
WORK is COMPLEX array, dimension (QSIZ*N)
QSTORE (input/output)
QSTORE is REAL array, dimension (N**2+1)
Stores eigenvectors of submatrices encountered during divide
and conquer, packed together. QPTR points to beginning of the
submatrices.
QPTR (input/output)
QPTR is INTEGER array, dimension (N+2)
List of indices pointing to beginning of submatrices stored
in QSTORE. The submatrices are numbered starting at the bot-
tom left of the divide and conquer tree, from left to right
and bottom to top.
PRMPTR (input/output)
PRMPTR is INTEGER array, dimension (N lg N)
Contains a list of pointers which indicate where in PERM a
level's permutation is stored.
PRMPTR(i+1) - PRMPTR(i) indicates the size of the permutation
and also the size of the full, non-deflated problem.
PERM (input)
PERM is INTEGER array, dimension (N lg N)
Contains the permutations (from deflation and sorting) to be
applied to each eigenblock.
GIVPTR (input/output)
GIVPTR is INTEGER array, dimension (N lg N)
Contains a list of pointers which indicate where in GIVCOL a
level's Givens rotations are stored.
GIVPTR(i+1) - GIVPTR(i) indicates the number of Givens rota-
tions.
GIVCOL (input)
GIVCOL is INTEGER array, dimension (2, N lg N)
Each pair of numbers indicates a pair of columns to take
place in a Givens rotation.
GIVNUM (input)
GIVNUM is REAL array, dimension (2, N lg 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,
> 0: if INFO = 1, an eigenvalue did not converge.
7 Nov 2015 claed7(3P)