slaed3 - vectors; used by sstedc when the original matrix is tridiagonal
SUBROUTINE SLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W, S, INFO ) INTEGER INFO, K, LDQ, N, N1 REAL RHO INTEGER CTOT(*),INDX(*) REAL D(*),DLAMDA(*), Q(LDQ,*), Q2(*), S(*), W(*) SUBROUTINE SLAED3_64( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W, S, INFO ) INTEGER*8 INFO, K, LDQ, N, N1 REAL RHO INTEGER*8 CTOT(*),INDX(*) REAL D(*),DLAMDA(*), Q(LDQ,*), Q2(*), S(*), W(*) F95 INTERFACE SUBROUTINE LAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W, S, INFO ) REAL, DIMENSION(:,:) :: Q INTEGER :: K, N, N1, LDQ, INFO INTEGER, DIMENSION(:) :: INDX, CTOT REAL, DIMENSION(:) :: D, DLAMDA, Q2, W, S REAL :: RHO SUBROUTINE LAED3_64( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W, S, INFO ) REAL, DIMENSION(:,:) :: Q INTEGER(8) :: K, N, N1, LDQ, INFO INTEGER(8), DIMENSION(:) :: INDX, CTOT REAL, DIMENSION(:) :: D, DLAMDA, Q2, W, S REAL :: RHO C INTERFACE #include <sunperf.h> void slaed3 (int k, int n, int n1, float *d, float *q, int ldq, float rho, float *dlamda, float *q2, int *indx, int *ctot, float *w, int *info); void slaed3_64 (long k, long n, long n1, float *d, float *q, long ldq, float rho, float *dlamda, float *q2, long *indx, long *ctot, float *w, long *info);
Oracle Solaris Studio Performance Library slaed3(3P)
NAME
slaed3 - find the roots of the secular equation and updates the eigen-
vectors; used by sstedc when the original matrix is tridiagonal
SYNOPSIS
SUBROUTINE SLAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W,
S, INFO )
INTEGER INFO, K, LDQ, N, N1
REAL RHO
INTEGER CTOT(*),INDX(*)
REAL D(*),DLAMDA(*), Q(LDQ,*), Q2(*), S(*), W(*)
SUBROUTINE SLAED3_64( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT,
W, S, INFO )
INTEGER*8 INFO, K, LDQ, N, N1
REAL RHO
INTEGER*8 CTOT(*),INDX(*)
REAL D(*),DLAMDA(*), Q(LDQ,*), Q2(*), S(*), W(*)
F95 INTERFACE
SUBROUTINE LAED3( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT, W,
S, INFO )
REAL, DIMENSION(:,:) :: Q
INTEGER :: K, N, N1, LDQ, INFO
INTEGER, DIMENSION(:) :: INDX, CTOT
REAL, DIMENSION(:) :: D, DLAMDA, Q2, W, S
REAL :: RHO
SUBROUTINE LAED3_64( K, N, N1, D, Q, LDQ, RHO, DLAMDA, Q2, INDX, CTOT,
W, S, INFO )
REAL, DIMENSION(:,:) :: Q
INTEGER(8) :: K, N, N1, LDQ, INFO
INTEGER(8), DIMENSION(:) :: INDX, CTOT
REAL, DIMENSION(:) :: D, DLAMDA, Q2, W, S
REAL :: RHO
C INTERFACE
#include <sunperf.h>
void slaed3 (int k, int n, int n1, float *d, float *q, int ldq, float
rho, float *dlamda, float *q2, int *indx, int *ctot, float
*w, int *info);
void slaed3_64 (long k, long n, long n1, float *d, float *q, long ldq,
float rho, float *dlamda, float *q2, long *indx, long *ctot,
float *w, long *info);
PURPOSE
slaed3 finds the roots of the secular equation, as defined by the val-
ues in D, W, and RHO, between 1 and K. It makes the appropriate calls
to SLAED4 and then updates the eigenvectors by multiplying the matrix
of eigenvectors of the pair of eigensystems being combined by the
matrix of eigenvectors of the K-by-K system which is solved here.
This code makes very mild assumptions about floating point arithmetic.
It will work on machines with a guard digit in add/subtract, or on
those binary machines without guard digits which subtract like the Cray
X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on
hexadecimal or decimal machines without guard digits, but we know of
none.
ARGUMENTS
K (input)
K is INTEGER
The number of terms in the rational function to be solved by
SLAED4. K >= 0.
N (input)
N is INTEGER
The number of rows and columns in the Q matrix.
N >= K (deflation may result in N>K).
N1 (input)
N1 is INTEGER
The location of the last eigenvalue in the leading submatrix.
min(1,N) <= N1 <= N/2.
D (output)
D is REAL array, dimension (N)
D(I) contains the updated eigenvalues for
1 <= I <= K.
Q (output)
Q is REAL array, dimension (LDQ,N)
Initially the first K columns are used as workspace.
On output the columns 1 to K contain the updated eigenvec-
tors.
LDQ (input)
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
RHO (input)
RHO is REAL
The value of the parameter in the rank one update equation.
RHO >= 0 required.
DLAMDA (input/output)
DLAMDA is REAL array, dimension (K)
The first K elements of this array contain the old roots of
the deflated updating problem. These are the poles of the
secular equation. May be changed on output by having lowest
order bit set to zero on Cray X-MP, Cray Y-MP, Cray-2, or
Cray C-90, as described above.
Q2 (input)
Q2 is REAL array, dimension (LDQ2, N)
The first K columns of this matrix contain the non-deflated
eigenvectors for the split problem.
INDX (input)
INDX is INTEGER array, dimension (N)
The permutation is used to arrange the columns of the
deflated Q matrix into three groups (see SLAED2).
The rows of the eigenvectors found by SLAED4 must be likewise
permuted before the matrix multiply can take place.
CTOT (input)
CTOT is INTEGER array, dimension (4)
A count of the total number of the various types of columns
in Q, as described in INDX. The fourth column type is any
column which has been deflated.
W (input/output)
W is REAL array, dimension (K)
The first K elements of this array contain the components of
the deflation-adjusted updating vector. Destroyed on output.
S (output)
S is REAL array, dimension (N1 + 1)*K
Will contain the eigenvectors of the repaired matrix which
will be multiplied by the previously accumulated eigenvectors
to update the system.
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 slaed3(3P)