zlaed7 - nal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense
SUBROUTINE ZLAED7( 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 DOUBLE PRECISION RHO INTEGER GIVCOL(2,*), GIVPTR(*), INDXQ(*), IWORK(*), PERM(*), PRMPTR(*), QPTR(*) DOUBLE PRECISION D(*), GIVNUM(2,*), QSTORE(*), RWORK(*) DOUBLE COMPLEX Q(LDQ,*), WORK(*) SUBROUTINE ZLAED7_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 DOUBLE PRECISION RHO INTEGER*8 GIVCOL(2,*), GIVPTR(*), INDXQ(*), IWORK(*), PERM(*), PRMPTR(*), QPTR(*) DOUBLE PRECISION D(*), GIVNUM(2,*), QSTORE(*), RWORK(*) DOUBLE 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 ) INTEGER :: N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, LDQ, INFO INTEGER, DIMENSION(:) :: INDXQ, QPTR, PRMPTR, PERM, GIVPTR, IWORK REAL(8), DIMENSION(:,:) :: GIVNUM COMPLEX(8), DIMENSION(:,:) :: Q REAL(8), DIMENSION(:) :: D, QSTORE, RWORK INTEGER, DIMENSION(:,:) :: GIVCOL COMPLEX(8), DIMENSION(:) :: WORK REAL(8) :: 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 ) INTEGER(8) :: N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, LDQ, INFO INTEGER(8), DIMENSION(:) :: INDXQ, QPTR, PRMPTR, PERM, GIVPTR, IWORK REAL(8), DIMENSION(:,:) :: GIVNUM COMPLEX(8), DIMENSION(:,:) :: Q REAL(8), DIMENSION(:) :: D, QSTORE, RWORK INTEGER(8), DIMENSION(:,:) :: GIVCOL COMPLEX(8), DIMENSION(:) :: WORK REAL(8) :: RHO C INTERFACE #include <sunperf.h> void zlaed7 (int n, int cutpnt, int qsiz, int tlvls, int curlvl, int curpbm, double *d, doublecomplex *q, int ldq, double rho, int *indxq, double *qstore, int *qptr, int *prmptr, int *perm, int *givptr, int *givcol, double *givnum, int *info); void zlaed7_64 (long n, long cutpnt, long qsiz, long tlvls, long curlvl, long curpbm, double *d, doublecomplex *q, long ldq, double rho, long *indxq, double *qstore, long *qptr, long *prmptr, long *perm, long *givptr, long *givcol, double *givnum, long *info);
Oracle Solaris Studio Performance Library zlaed7(3P)
NAME
zlaed7 - is used by sstedc. Compute the updated eigensystem of a diago-
nal matrix after modification by a rank-one symmetric matrix. Used when
the original matrix is dense
SYNOPSIS
SUBROUTINE ZLAED7( 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
DOUBLE PRECISION RHO
INTEGER GIVCOL(2,*), GIVPTR(*), INDXQ(*), IWORK(*), PERM(*), PRMPTR(*),
QPTR(*)
DOUBLE PRECISION D(*), GIVNUM(2,*), QSTORE(*), RWORK(*)
DOUBLE COMPLEX Q(LDQ,*), WORK(*)
SUBROUTINE ZLAED7_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
DOUBLE PRECISION RHO
INTEGER*8 GIVCOL(2,*), GIVPTR(*), INDXQ(*), IWORK(*), PERM(*),
PRMPTR(*), QPTR(*)
DOUBLE PRECISION D(*), GIVNUM(2,*), QSTORE(*), RWORK(*)
DOUBLE 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 )
INTEGER :: N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, LDQ, INFO
INTEGER, DIMENSION(:) :: INDXQ, QPTR, PRMPTR, PERM, GIVPTR, IWORK
REAL(8), DIMENSION(:,:) :: GIVNUM
COMPLEX(8), DIMENSION(:,:) :: Q
REAL(8), DIMENSION(:) :: D, QSTORE, RWORK
INTEGER, DIMENSION(:,:) :: GIVCOL
COMPLEX(8), DIMENSION(:) :: WORK
REAL(8) :: 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 )
INTEGER(8) :: N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, LDQ, INFO
INTEGER(8), DIMENSION(:) :: INDXQ, QPTR, PRMPTR, PERM, GIVPTR, IWORK
REAL(8), DIMENSION(:,:) :: GIVNUM
COMPLEX(8), DIMENSION(:,:) :: Q
REAL(8), DIMENSION(:) :: D, QSTORE, RWORK
INTEGER(8), DIMENSION(:,:) :: GIVCOL
COMPLEX(8), DIMENSION(:) :: WORK
REAL(8) :: RHO
C INTERFACE
#include <sunperf.h>
void zlaed7 (int n, int cutpnt, int qsiz, int tlvls, int curlvl, int
curpbm, double *d, doublecomplex *q, int ldq, double rho, int
*indxq, double *qstore, int *qptr, int *prmptr, int *perm,
int *givptr, int *givcol, double *givnum, int *info);
void zlaed7_64 (long n, long cutpnt, long qsiz, long tlvls, long
curlvl, long curpbm, double *d, doublecomplex *q, long ldq,
double rho, long *indxq, double *qstore, long *qptr, long
*prmptr, long *perm, long *givptr, long *givcol, double
*givnum, long *info);
PURPOSE
zlaed7 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 DLAED2.
The second stage consists of calculating the updated eigenvalues. This
is done by finding the roots of the secular equation via the routine
DLAED4 (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 prob-
lem 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 DOUBLE PRECISION 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*16 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 DOUBLE PRECISION
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
subproblem 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 DOUBLE PRECISION array,
dimension (3*N+2*QSIZ*N)
WORK (output)
WORK is COMPLEX*16 array, dimension (QSIZ*N)
QSTORE (input/output)
QSTORE is DOUBLE PRECISION 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
bottom left of the divide and conquer tree, from left to
right and bottom to top.
PRMPTR (input)
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 rotations.
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 DOUBLE PRECISION array, dimension (2, N lg N)
Each number indicates the S value to be used in the
corresponding 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 zlaed7(3P)