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dlaed2 (3)
  • >> dlaed2 (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         dlaed2 - merge the two sets of eigenvalues together  into  a
         single sorted set
    
    SYNOPSIS
         SUBROUTINE DLAED2( K, N, D, Q, LDQ, INDXQ, RHO,  CUTPNT,  Z,
                   DLAMDA,  Q2,  LDQ2, INDXC, W, INDXP, INDX, COLTYP,
                   INFO )
    
         INTEGER CUTPNT, INFO, K, LDQ, LDQ2, N
    
         DOUBLE PRECISION RHO
    
         INTEGER COLTYP( * ), INDX( * ), INDXC(  *  ),  INDXP(  *  ),
                   INDXQ( * )
    
         DOUBLE PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), Q2( LDQ2,
                   * ), W( * ), Z( * )
    
    
    
         #include <sunperf.h>
    
         void dlaed2(int *k, int n, double *d, double  *q,  int  ldq,
                   int  *indxq, double *drho, int cutpnt, double *dz,
                   double *dlamda, double *q2, int ldq2, int  *indxc,
                   double *w, int *indxp, int *indx, int *coltyp, int
                   *info) ;
    
    PURPOSE
         DLAED2 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) INTEGER
                   The number of non-deflated  eigenvalues,  and  the
                   order of the related secular equation. 0 <= K <=N.
    
         N         (input) INTEGER
                   The dimension of the symmetric tridiagonal matrix.
                   N >= 0.
    
         D         (input/output) DOUBLE PRECISION  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) DOUBLE PRECISION  array,  dimension
                   (LDQ, N)
                   On entry, Q contains the eigenvectors of two  sub-
                   matrices  in the two square blocks with corners at
                   (1,1), (CUTPNT,CUTPNT) and  (CUTPNT+1,  CUTPNT+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) INTEGER
                   The leading dimension of  the  array  Q.   LDQ  >=
                   max(1,N).
    
         INDXQ     (input/output) 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 CUTPNT added to their values. Des-
                   troyed on exit.
    
         RHO       (input/output) DOUBLE PRECISION
                   On entry, the off-diagonal element associated with
                   the rank-1 cut which originally split the two sub-
                   matrices which are now being recombined.  On exit,
                   RHO  has  been  modified  to the value required by
                   DLAED3.
    
                   CUTPNT (input) INTEGER The location  of  the  last
                   eigenvalue in the leading sub-matrix.  min(1,N) <=
                   CUTPNT <= N.
    
         Z         (input) DOUBLE PRECISION 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 updating process.
    
                   DLAMDA (output) DOUBLE PRECISION array,  dimension
                   (N)  A  copy of the first K eigenvalues which will
                   be used by DLAED3 to form the secular equation.
    
         Q2        (output) DOUBLE PRECISION array, dimension  (LDQ2,
                   N)
                   A copy of the first K eigenvectors which  will  be
                   used  by  DLAED3  in  a matrix multiply (DGEMM) to
                   solve for the new eigenvectors.   Q2  is  arranged
                   into  three blocks.  The first block contains non-
                   zero elements only at and above CUTPNT, the second
                   contains  non-zero elements only below CUTPNT, and
                   the third is dense.
    
         LDQ2      (input) INTEGER
                   The leading dimension of the array  Q2.   LDQ2  >=
                   max(1,N).
    
         INDXC     (output) 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.
    
         W         (output) DOUBLE PRECISION array, dimension (N)
                   The first k values of the final  deflation-altered
                   z-vector which will be passed to DLAED3.
    
         INDXP     (workspace) 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  eigen-
                   values.
    
         INDX      (workspace) INTEGER array, dimension (N)
                   The permutation used to sort  the  contents  of  D
                   into ascending order.
    
                   COLTYP (workspace/output) 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 : non-zero in the lower half only;
                   3 : dense;
                   4 : deflated.  On exit, COLTYP(i) is the number of
                   columns of type i, for i=1 to 4 only.
    
         INFO      (output) INTEGER
                   = 0:  successful exit.
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value.
    
    
    
    


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