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dlaed3 (3)
  • >> dlaed3 (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dlaed3 - find the roots of the secular equation, as  defined
         by the values in D, W, and RHO, between KSTART and KSTOP
    
    SYNOPSIS
         SUBROUTINE DLAED3( K, KSTART, KSTOP,  N,  D,  Q,  LDQ,  RHO,
                   CUTPNT,  DLAMDA, Q2, LDQ2, INDXC, CTOT, W, S, LDS,
                   INFO )
    
         INTEGER CUTPNT, INFO, K, KSTART, KSTOP, LDQ, LDQ2, LDS, N
    
         DOUBLE PRECISION RHO
    
         INTEGER CTOT( * ), INDXC( * )
    
         DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( LDQ2,
                   * ), S( LDS, * ), W( * )
    
    
    
         #include <sunperf.h>
    
         void dlaed3(int k, int kstart, int kstop, int n, double  *d,
                   double  *q, int ldq, double drho, int cutpnt, dou-
                   ble *dlamda, double *q2, int ldq2, int *indxc, int
                   *ctot, double *w, double *s, int lds, int *info) ;
    
    PURPOSE
         DLAED3 finds the roots of the secular equation,  as  defined
         by  the  values  in D, W, and RHO, between KSTART and KSTOP.
         It makes the appropriate calls to DLAED4  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) INTEGER
                   The number of terms in the rational function to be
                   solved by DLAED4.  K >= 0.
    
         KSTART    (input) INTEGER
                   KSTOP   (input) INTEGER  The  updated  eigenvalues
                   Lambda(I),   KSTART  <=  I  <=  KSTOP  are  to  be
                   computed.  1 <= KSTART <= KSTOP <= K.
    
         N         (input) INTEGER
                   The number of rows and columns in the Q matrix.  N
                   >= K (deflation may result in N>K).
    
         D         (output) DOUBLE PRECISION array, dimension (N)
                   D(I) contains the updated eigenvalues  for  KSTART
                   <= I <= KSTOP.
    
         Q         (output) DOUBLE PRECISION array, dimension (LDQ,N)
                   Initially  the  first  K  columns  are   used   as
                   workspace.   On output the columns KSTART to KSTOP
                   contain the updated eigenvectors.
    
         LDQ       (input) INTEGER
                   The leading dimension of  the  array  Q.   LDQ  >=
                   max(1,N).
    
         RHO       (input) DOUBLE PRECISION
                   The value of the parameter in the rank one  update
                   equation.  RHO >= 0 required.
    
         CUTPNT    (input) INTEGER
                   The location of the last eigenvalue in the leading
                   submatrix.  min(1,N) <= CUTPNT <= N.
    
         DLAMDA    (input/output) DOUBLE PRECISION  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) DOUBLE PRECISION array,  dimension  (LDQ2,
                   N)
                   The first K columns of  this  matrix  contain  the
                   non-deflated eigenvectors for the split problem.
    
         LDQ2      (input) INTEGER
                   The leading dimension of the array  Q2.   LDQ2  >=
                   max(1,N).
    
         INDXC     (input) 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
                   CUTPNT, the second contains non-zero elements only
                   below CUTPNT, and the third is dense.  The rows of
                   the  eigenvectors found by DLAED4 must be likewise
                   permuted  before  the  matrix  multiply  can  take
                   place.
    
         CTOT      (input) INTEGER array, dimension (4)
                   A count of the total number of the  various  types
                   of  columns  in  Q,  as  described  in INDXC.  The
                   fourth column type is any column  which  has  been
                   deflated.
    
         W         (input/output) DOUBLE PRECISION  array,  dimension
                   (K)
                   The first K elements of  this  array  contain  the
                   components of the deflation-adjusted updating vec-
                   tor. Destroyed on output.
    
         S         (workspace)  DOUBLE  PRECISION  array,   dimension
                   (LDS, K)
                   Will contain  the  eigenvectors  of  the  repaired
                   matrix  which will be multiplied by the previously
                   accumulated eigenvectors to update the system.
    
         LDS       (input) INTEGER
                   The leading dimension of S.  LDS >= max(1,K).
    
         INFO      (output) INTEGER
                   = 0:  successful exit.
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value.
                   > 0:  if INFO = 1, an eigenvalue did not converge
    
    
    
    


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