slaed9 (3p)

Name

slaed9 - is used by sstedc. Find the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense

Synopsis

SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA,  W,  S,
LDS, INFO )


INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N

REAL RHO

REAL D(*),DLAMDA(*), Q(LDQ,*), S(LDS,*), W(*)


SUBROUTINE  SLAED9_64(  K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W,
S, LDS, INFO )


INTEGER*8 INFO, K, KSTART, KSTOP, LDQ, LDS, N

REAL RHO

REAL D(*),DLAMDA(*), Q(LDQ,*), S(LDS,*), W(*)


F95 INTERFACE
SUBROUTINE LAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO,  DLAMDA,  W,  S,
LDS, INFO )


REAL, DIMENSION(:,:) :: Q, S

INTEGER :: K, KSTART, KSTOP, N, LDQ, LDS, INFO

REAL, DIMENSION(:) :: D, DLAMDA, W

REAL :: RHO


SUBROUTINE LAED9_64( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S,
LDS, INFO )


REAL, DIMENSION(:,:) :: Q, S

INTEGER(8) :: K, KSTART, KSTOP, N, LDQ, LDS, INFO

REAL, DIMENSION(:) :: D, DLAMDA, W

REAL :: RHO


C INTERFACE
#include <sunperf.h>

void slaed9 (int k, int kstart, int kstop, int n, float *d,  float  *q,
int  ldq,  float  rho, float *dlamda, float *w, float *s, int
lds, int *info);


void slaed9_64 (long k, long kstart, long  kstop,  long  n,  float  *d,
float *q, long ldq, float rho, float *dlamda, float *w, float
*s, long lds, long *info);

Description

Oracle Solaris Studio Performance Library                           slaed9(3P)



NAME
       slaed9  - is used by sstedc. Find the roots of the secular equation and
       updates the eigenvectors. Used when the original matrix is dense


SYNOPSIS
       SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA,  W,  S,
                 LDS, INFO )


       INTEGER INFO, K, KSTART, KSTOP, LDQ, LDS, N

       REAL RHO

       REAL D(*),DLAMDA(*), Q(LDQ,*), S(LDS,*), W(*)


       SUBROUTINE  SLAED9_64(  K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W,
                 S, LDS, INFO )


       INTEGER*8 INFO, K, KSTART, KSTOP, LDQ, LDS, N

       REAL RHO

       REAL D(*),DLAMDA(*), Q(LDQ,*), S(LDS,*), W(*)


   F95 INTERFACE
       SUBROUTINE LAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO,  DLAMDA,  W,  S,
                 LDS, INFO )


       REAL, DIMENSION(:,:) :: Q, S

       INTEGER :: K, KSTART, KSTOP, N, LDQ, LDS, INFO

       REAL, DIMENSION(:) :: D, DLAMDA, W

       REAL :: RHO


       SUBROUTINE LAED9_64( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S,
                 LDS, INFO )


       REAL, DIMENSION(:,:) :: Q, S

       INTEGER(8) :: K, KSTART, KSTOP, N, LDQ, LDS, INFO

       REAL, DIMENSION(:) :: D, DLAMDA, W

       REAL :: RHO


   C INTERFACE
       #include <sunperf.h>

       void slaed9 (int k, int kstart, int kstop, int n, float *d,  float  *q,
                 int  ldq,  float  rho, float *dlamda, float *w, float *s, int
                 lds, int *info);


       void slaed9_64 (long k, long kstart, long  kstop,  long  n,  float  *d,
                 float *q, long ldq, float rho, float *dlamda, float *w, float
                 *s, long lds, long *info);


PURPOSE
       slaed9 finds the roots of the secular equation, as defined by the  val-
       ues in D, Z, and RHO, between KSTART and KSTOP.  It makes the appropri-
       ate calls to SLAED4 and then stores the new matrix of eigenvectors  for
       use in calculating the next level of Z vectors.


ARGUMENTS
       K (input)
                 K is INTEGER
                 The number of terms in the rational function to be solved by
                 SLAED4.  K >= 0.


       KSTART (input)
                 KSTART is INTEGER


       KSTOP (input)
                 KSTOP is INTEGER
                 The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP
                 are to be computed.  1 <= KSTART <= KSTOP <= K.


       N (input)
                 N is INTEGER
                 The number of rows and columns in the Q matrix.
                 N >= K (delation may result in N > K).


       D (output)
                 D is REAL array, dimension (N)
                 D(I) contains the updated eigenvalues
                 for KSTART <= I <= KSTOP.


       Q (output)
                 Q is REAL array, dimension (LDQ,N)


       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)
                 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.


       W (input)
                 W is REAL array, dimension (K)
                 The first K elements of this array contain the components
                 of the deflation-adjusted updating vector.


       S (output)
                 S is REAL array, dimension (LDS, K)
                 Will contain the eigenvectors of the repaired matrix which
                 will be stored for subsequent Z vector calculation and
                 multiplied by the previously accumulated eigenvectors
                 to update the system.


       LDS (input)
                 LDS is INTEGER
                 The leading dimension of S.  LDS >= max( 1, K ).


       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                        slaed9(3P)