slaed2 - edc when the original matrix is tridiagonal
SUBROUTINE SLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO ) INTEGER INFO, K, LDQ, N, N1 REAL RHO INTEGER COLTYP(*), INDX(*), INDXC(*), INDXP(*), INDXQ(*) REAL D(*), DLAMDA(*), Q(LDQ,*), Q2(*), W(*), Z(*) SUBROUTINE SLAED2_64( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO ) INTEGER*8 INFO, K, LDQ, N, N1 REAL RHO INTEGER*8 COLTYP(*), INDX(*), INDXC(*), INDXP(*), INDXQ(*) REAL D(*), DLAMDA(*), Q(LDQ,*), Q2(*), W(*), Z(*) F95 INTERFACE SUBROUTINE LAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO ) REAL, DIMENSION(:,:) :: Q INTEGER :: K, N, N1, LDQ, INFO INTEGER, DIMENSION(:) :: INDXQ, INDX, INDXC, INDXP, COLTYP REAL, DIMENSION(:) :: D, Z, DLAMDA, W, Q2 REAL :: RHO SUBROUTINE LAED2_64( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO ) REAL, DIMENSION(:,:) :: Q INTEGER(8) :: K, N, N1, LDQ, INFO INTEGER(8), DIMENSION(:) :: INDXQ, INDX, INDXC, INDXP, COLTYP REAL, DIMENSION(:) :: D, Z, DLAMDA, W, Q2 REAL :: RHO C INTERFACE #include <sunperf.h> void slaed2 (int *k, int n, int n1, float *d, float *q, int ldq, int *indxq, float *rho, float *z, float *dlamda, float *w, float *q2, int *indxc, int *info); void slaed2_64 (long *k, long n, long n1, float *d, float *q, long ldq, long *indxq, float *rho, float *z, float *dlamda, float *w, float *q2, long *indxc, long *info);
Oracle Solaris Studio Performance Library slaed2(3P)
NAME
slaed2 - merge eigenvalues and deflates secular equation; used by sst-
edc when the original matrix is tridiagonal
SYNOPSIS
SUBROUTINE SLAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2,
INDX, INDXC, INDXP, COLTYP, INFO )
INTEGER INFO, K, LDQ, N, N1
REAL RHO
INTEGER COLTYP(*), INDX(*), INDXC(*), INDXP(*), INDXQ(*)
REAL D(*), DLAMDA(*), Q(LDQ,*), Q2(*), W(*), Z(*)
SUBROUTINE SLAED2_64( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W,
Q2, INDX, INDXC, INDXP, COLTYP, INFO )
INTEGER*8 INFO, K, LDQ, N, N1
REAL RHO
INTEGER*8 COLTYP(*), INDX(*), INDXC(*), INDXP(*), INDXQ(*)
REAL D(*), DLAMDA(*), Q(LDQ,*), Q2(*), W(*), Z(*)
F95 INTERFACE
SUBROUTINE LAED2( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2,
INDX, INDXC, INDXP, COLTYP, INFO )
REAL, DIMENSION(:,:) :: Q
INTEGER :: K, N, N1, LDQ, INFO
INTEGER, DIMENSION(:) :: INDXQ, INDX, INDXC, INDXP, COLTYP
REAL, DIMENSION(:) :: D, Z, DLAMDA, W, Q2
REAL :: RHO
SUBROUTINE LAED2_64( K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2,
INDX, INDXC, INDXP, COLTYP, INFO )
REAL, DIMENSION(:,:) :: Q
INTEGER(8) :: K, N, N1, LDQ, INFO
INTEGER(8), DIMENSION(:) :: INDXQ, INDX, INDXC, INDXP, COLTYP
REAL, DIMENSION(:) :: D, Z, DLAMDA, W, Q2
REAL :: RHO
C INTERFACE
#include <sunperf.h>
void slaed2 (int *k, int n, int n1, float *d, float *q, int ldq, int
*indxq, float *rho, float *z, float *dlamda, float *w, float
*q2, int *indxc, int *info);
void slaed2_64 (long *k, long n, long n1, float *d, float *q, long ldq,
long *indxq, float *rho, float *z, float *dlamda, float *w,
float *q2, long *indxc, long *info);
PURPOSE
slaed2 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 entry 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
The number of non-deflated eigenvalues, and the order of the
related secular equation. 0 <= K <=N.
N (input)
N is INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
N1 (input)
N1 is INTEGER
The location of the last eigenvalue in the leading sub-
matrix.
min(1,N) <= N1 <= N/2.
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.
Q (input/output)
Q is REAL array, dimension (LDQ, N)
On entry, Q contains the eigenvectors of two submatrices in
the two square blocks with corners at (1,1), (N1,N1) and
(N1+1, N1+1), (N,N).
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).
INDXQ (input/output)
INDXQ is INTEGER array, dimension (N)
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 N1 added to their
values. Destroyed on exit.
RHO (input/output)
RHO is REAL
On entry, the off-diagonal element associated with the rank-1
cut which originally split the two submatrices which are now
being recombined.
On exit, RHO has been modified to the value required by
SLAED3.
Z (input)
Z is REAL array, dimension (N)
On entry, Z contains the updating vector (the last row of the
first sub-eigenvector matrix and the first row of the second
sub-eigenvector matrix).
On exit, the contents of Z have been destroyed by the updat-
ing process.
DLAMDA (output)
DLAMDA is REAL array, dimension (N)
A copy of the first K eigenvalues which will be used by
SLAED3 to form the secular equation.
W (output)
W is REAL array, dimension (N)
The first k values of the final deflation-altered z-vector
which will be passed to SLAED3.
Q2 (output)
Q2 is REAL array, dimension (N1**2+(N-N1)**2)
A copy of the first K eigenvectors which will be used by
SLAED3 in a matrix multiply (SGEMM) to solve for the new
eigenvectors.
INDX (output)
INDX is INTEGER array, dimension (N)
The permutation used to sort the contents of DLAMDA into
ascending order.
INDXC (output)
INDXC is INTEGER array, dimension (N)
The permutation used to arrange the columns of the deflated Q
matrix into three groups: the first group contains non-zero
elements only at and above N1, the second contains non-zero
elements only below N1, and the third is dense.
INDXP (output)
INDXP is INTEGER array, dimension (N)
The permutation used to place deflated values of D at the end
of the array. INDXP(1:K) points to the nondeflated D-values
and INDXP(K+1:N) points to the deflated eigenvalues.
COLTYP (output)
COLTYP is INTEGER array, dimension (N)
During execution, a label which will indicate which of the
following types a column in the Q2 matrix is:
1 : non-zero in the upper half only;
2 : dense;
3 : non-zero in the lower half only;
4 : deflated.
On exit, COLTYP(i) is the number of columns of type i,
for i=1 to 4 only.
INFO (output)
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
7 Nov 2015 slaed2(3P)