dlaed1 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used by dstedc, when the original matrix is tridiagonal
SUBROUTINE DLAED1(N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO) INTEGER CUTPNT, INFO, LDQ, N DOUBLE PRECISION RHO INTEGER INDXQ(*), IWORK(*) DOUBLE PRECISION D(*), Q(LDQ,*), WORK(*) SUBROUTINE DLAED1_64(N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO) INTEGER*8 CUTPNT, INFO, LDQ, N DOUBLE PRECISION RHO INTEGER*8 INDXQ(*), IWORK(*) DOUBLE PRECISION D(*), Q(LDQ,*), WORK(*) F95 INTERFACE SUBROUTINE LAED1(N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO) INTEGER :: N, LDQ, CUTPNT, INFO INTEGER, DIMENSION(:) :: INDXQ, IWORK REAL(8), DIMENSION(:,:) :: Q REAL(8), DIMENSION(:) :: D, WORK REAL(8) :: RHO SUBROUTINE LAED1_64(N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO) INTEGER(8) :: N, LDQ, CUTPNT, INFO INTEGER(8), DIMENSION(:) :: INDXQ, IWORK REAL(8), DIMENSION(:,:) :: Q REAL(8), DIMENSION(:) :: D, WORK REAL(8) :: RHO C INTERFACE #include <sunperf.h> void dlaed1 (int n, double *d, double *q, int ldq, int *indxq, double rho, int cutpnt, int *info); void dlaed1_64 (long n, double *d, double *q, long ldq, long *indxq, double rho, long cutpnt, long *info);
Oracle Solaris Studio Performance Library dlaed1(3P)
NAME
dlaed1 - compute the updated eigensystem of a diagonal matrix after
modification by a rank-one symmetric matrix. Used by dstedc, when the
original matrix is tridiagonal
SYNOPSIS
SUBROUTINE DLAED1(N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO)
INTEGER CUTPNT, INFO, LDQ, N
DOUBLE PRECISION RHO
INTEGER INDXQ(*), IWORK(*)
DOUBLE PRECISION D(*), Q(LDQ,*), WORK(*)
SUBROUTINE DLAED1_64(N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
INFO)
INTEGER*8 CUTPNT, INFO, LDQ, N
DOUBLE PRECISION RHO
INTEGER*8 INDXQ(*), IWORK(*)
DOUBLE PRECISION D(*), Q(LDQ,*), WORK(*)
F95 INTERFACE
SUBROUTINE LAED1(N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO)
INTEGER :: N, LDQ, CUTPNT, INFO
INTEGER, DIMENSION(:) :: INDXQ, IWORK
REAL(8), DIMENSION(:,:) :: Q
REAL(8), DIMENSION(:) :: D, WORK
REAL(8) :: RHO
SUBROUTINE LAED1_64(N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
INFO)
INTEGER(8) :: N, LDQ, CUTPNT, INFO
INTEGER(8), DIMENSION(:) :: INDXQ, IWORK
REAL(8), DIMENSION(:,:) :: Q
REAL(8), DIMENSION(:) :: D, WORK
REAL(8) :: RHO
C INTERFACE
#include <sunperf.h>
void dlaed1 (int n, double *d, double *q, int ldq, int *indxq, double
rho, int cutpnt, int *info);
void dlaed1_64 (long n, double *d, double *q, long ldq, long *indxq,
double rho, long cutpnt, long *info);
PURPOSE
dlaed1 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 eigenvectors of a
tridiagonal matrix. DLAED7 handles the case in which eigenvalues only
or eigenvalues and eigenvectors of a full symmetric matrix (which was
reduced to tridiagonal form) are desired.
T = Q(in) (D(in)+RHO* Z*Z**T) Q**T(in) = Q(out)*D(out)* Q**T(out)
where Z = Q**T*u, 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 DLAED3). 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.
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 DOUBLE PRECISION 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 (input/output)
INDXQ is INTEGER array, dimension (N)
On entry, the permutation which separately sorts the two sub-
problems in D into ascending order.
On exit, the permutation which will reintegrate the subprob-
lems back into sorted order, i.e., D(INDXQ(I=1,N)) will be in
ascending order.
RHO (input)
RHO is DOUBLE PRECISION
The subdiagonal entry used to create the rank-1 modification.
CUTPNT (input)
CUTPNT is INTEGER
The location of the last eigenvalue in the leading sub-
matrix. min(1,N) <= CUTPNT <= N/2.
WORK (output)
WORK is DOUBLE PRECISION array, dimension (4*N+N**2)
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 dlaed1(3P)