slaed7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used by sstedc, when the original matrix is dense
SUBROUTINE SLAED7(ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIV- COL, GIVNUM, WORK, IWORK, INFO) INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, QSIZ, TLVLS REAL RHO INTEGER GIVCOL(2,*), GIVPTR(*), INDXQ(*), IWORK(*), PERM(*), PRMPTR(*), QPTR(*) REAL D(*), GIVNUM(2,*), Q(LDQ,*), QSTORE(*), WORK(*) SUBROUTINE SLAED7_64(ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIV- COL, GIVNUM, WORK, IWORK, INFO) INTEGER*8 CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, QSIZ, TLVLS REAL RHO INTEGER*8 GIVCOL(2,*), GIVPTR(*), INDXQ(*), IWORK(*), PERM(*), PRMPTR(*), QPTR(*) REAL D(*), GIVNUM(2,*), Q(LDQ,*), QSTORE(*), WORK(*) F95 INTERFACE SUBROUTINE LAED7(ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIV- COL, GIVNUM, WORK, IWORK, INFO) REAL, DIMENSION(:,:) :: Q INTEGER :: ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, LDQ, CUTPNT, INFO INTEGER, DIMENSION(:) :: INDXQ, QPTR, PRMPTR, PERM, GIVPTR, IWORK REAL, DIMENSION(:) :: D, QSTORE, WORK REAL, DIMENSION(:,:) :: GIVNUM INTEGER, DIMENSION(:,:) :: GIVCOL REAL :: RHO SUBROUTINE LAED7_64(ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIV- COL, GIVNUM, WORK, IWORK, INFO) REAL, DIMENSION(:,:) :: Q INTEGER(8) :: ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, LDQ, CUTPNT, INFO INTEGER(8), DIMENSION(:) :: INDXQ, QPTR, PRMPTR, PERM, GIVPTR, IWORK REAL, DIMENSION(:) :: D, QSTORE, WORK REAL, DIMENSION(:,:) :: GIVNUM INTEGER(8), DIMENSION(:,:) :: GIVCOL REAL :: RHO C INTERFACE #include <sunperf.h> void slaed7 (int icompq, int n, int qsiz, int tlvls, int curlvl, int curpbm, float *d, float *q, int ldq, int *indxq, float rho, int cutpnt, float *qstore, int *qptr, int *prmptr, int *perm, int *givptr, int *givcol, float *givnum, int *info); void slaed7_64 (long icompq, long n, long qsiz, long tlvls, long curlvl, long curpbm, float *d, float *q, long ldq, long *indxq, float rho, long cutpnt, float *qstore, long *qptr, long *prmptr, long *perm, long *givptr, long *givcol, float *givnum, long *info);
Oracle Solaris Studio Performance Library slaed7(3P)
NAME
slaed7 - compute the updated eigensystem of a diagonal matrix after
modification by a rank-one symmetric matrix. Used by sstedc, when the
original matrix is dense
SYNOPSIS
SUBROUTINE SLAED7(ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ,
INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIV-
COL, GIVNUM, WORK, IWORK, INFO)
INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, QSIZ, TLVLS
REAL RHO
INTEGER GIVCOL(2,*), GIVPTR(*), INDXQ(*), IWORK(*), PERM(*), PRMPTR(*),
QPTR(*)
REAL D(*), GIVNUM(2,*), Q(LDQ,*), QSTORE(*), WORK(*)
SUBROUTINE SLAED7_64(ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ,
INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIV-
COL, GIVNUM, WORK, IWORK, INFO)
INTEGER*8 CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, QSIZ, TLVLS
REAL RHO
INTEGER*8 GIVCOL(2,*), GIVPTR(*), INDXQ(*), IWORK(*), PERM(*),
PRMPTR(*), QPTR(*)
REAL D(*), GIVNUM(2,*), Q(LDQ,*), QSTORE(*), WORK(*)
F95 INTERFACE
SUBROUTINE LAED7(ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ,
INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIV-
COL, GIVNUM, WORK, IWORK, INFO)
REAL, DIMENSION(:,:) :: Q
INTEGER :: ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, LDQ, CUTPNT, INFO
INTEGER, DIMENSION(:) :: INDXQ, QPTR, PRMPTR, PERM, GIVPTR, IWORK
REAL, DIMENSION(:) :: D, QSTORE, WORK
REAL, DIMENSION(:,:) :: GIVNUM
INTEGER, DIMENSION(:,:) :: GIVCOL
REAL :: RHO
SUBROUTINE LAED7_64(ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ,
INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIV-
COL, GIVNUM, WORK, IWORK, INFO)
REAL, DIMENSION(:,:) :: Q
INTEGER(8) :: ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, LDQ, CUTPNT, INFO
INTEGER(8), DIMENSION(:) :: INDXQ, QPTR, PRMPTR, PERM, GIVPTR, IWORK
REAL, DIMENSION(:) :: D, QSTORE, WORK
REAL, DIMENSION(:,:) :: GIVNUM
INTEGER(8), DIMENSION(:,:) :: GIVCOL
REAL :: RHO
C INTERFACE
#include <sunperf.h>
void slaed7 (int icompq, int n, int qsiz, int tlvls, int curlvl, int
curpbm, float *d, float *q, int ldq, int *indxq, float rho,
int cutpnt, float *qstore, int *qptr, int *prmptr, int *perm,
int *givptr, int *givcol, float *givnum, int *info);
void slaed7_64 (long icompq, long n, long qsiz, long tlvls, long
curlvl, long curpbm, float *d, float *q, long ldq, long
*indxq, float rho, long cutpnt, float *qstore, long *qptr,
long *prmptr, long *perm, long *givptr, long *givcol, float
*givnum, long *info);
PURPOSE
slaed7 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 symmetric matrix that has been reduced to tridiago-
nal form. SLAED1 handles the case in which all eigenvalues and eigen-
vectors of a symmetric tridiagonal matrix are desired.
T = Q(in) (D(in)+RHO*Z*Z**T) Q**T(in) = Q(out)*D(out)*Q**T(out)
where Z = Q**Tu, 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 SLAED8.
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 SLAED9). 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
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.
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.
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 REAL 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).
INDXQ (output)
INDXQ is INTEGER array, dimension (N)
The permutation which will reintegrate the subproblem just
solved back into sorted order, i.e., D(INDXQ(I = 1,N)) will
be in ascending order.
RHO (input)
RHO is REAL
The subdiagonal element used to create the rank-1 modifica-
tion.
CUTPNT (input)
CUTPNT is INTEGER
Contains the location of the last eigenvalue in the leading
sub-matrix. min(1,N) <= CUTPNT <= 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)
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.
WORK (output)
WORK is REAL array, dimension (3*N+2*QSIZ*N)
IWORK (output)
IWORK is INTEGER array, dimension (4*N)
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 slaed7(3P)