dlarra (l) - Linux Manuals

dlarra: the splitting points with threshold SPLTOL

NAME

DLARRA - the splitting points with threshold SPLTOL

SYNOPSIS

SUBROUTINE DLARRA(
N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO )

    
IMPLICIT NONE

    
INTEGER INFO, N, NSPLIT

    
DOUBLE PRECISION SPLTOL, TNRM

    
INTEGER ISPLIT( * )

    
DOUBLE PRECISION D( * ), E( * ), E2( * )

PURPOSE

Compute the splitting points with threshold SPLTOL. DLARRA sets any "small" off-diagonal elements to zero.

ARGUMENTS

N (input) INTEGER
The order of the matrix. N > 0.
D (input) DOUBLE PRECISION array, dimension (N)
On entry, the N diagonal elements of the tridiagonal matrix T.
E (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the first (N-1) entries contain the subdiagonal elements of the tridiagonal matrix T; E(N) need not be set. On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT, are set to zero, the other entries of E are untouched.
E2 (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the first (N-1) entries contain the SQUARES of the subdiagonal elements of the tridiagonal matrix T; E2(N) need not be set. On exit, the entries E2( ISPLIT( I ) ), 1 <= I <= NSPLIT, have been set to zero SPLTOL (input) DOUBLE PRECISION The threshold for splitting. Two criteria can be used:
SPLTOL<0 : criterion based on absolute off-diagonal value
SPLTOL>0 : criterion that preserves relative accuracy TNRM (input) DOUBLE PRECISION The norm of the matrix.
NSPLIT (output) INTEGER
The number of blocks T splits into. 1 <= NSPLIT <= N.
ISPLIT (output) INTEGER array, dimension (N)
The splitting points, at which T breaks up into blocks. The first block consists of rows/columns 1 to ISPLIT(1), the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), etc., and the NSPLIT-th consists of rows/columns ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
INFO (output) INTEGER
= 0: successful exit

FURTHER DETAILS

Based on contributions by

Beresford Parlett, University of California, Berkeley, USA
Jim Demmel, University of California, Berkeley, USA

Inderjit Dhillon, University of Texas, Austin, USA

Osni Marques, LBNL/NERSC, USA

Christof Voemel, University of California, Berkeley, USA

Pages related to dlarra

  • dlarra (3)
  • dlarrb (l) - the relatively robust representation(RRR) L D L^T, DLARRB does &quot;limited&quot; bisection to refine the eigenvalues of L D L^T,
  • dlarrc (l) - the number of eigenvalues of the symmetric tridiagonal matrix T that are in the interval (VL,VU] if JOBT = aqTaq, and of L D L^T if JOBT = aqLaq
  • dlarrd (l) - computes the eigenvalues of a symmetric tridiagonal matrix T to suitable accuracy
  • dlarre (l) - find the desired eigenvalues of a given real symmetric tridiagonal matrix T, DLARRE sets any &quot;small&quot; off-diagonal elements to zero, and for each unreduced block T_i, it finds (a) a suitable shift at one end of the blockaqs spectrum,
  • dlarrf (l) - the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ..
  • dlarrj (l) - the initial eigenvalue approximations of T, DLARRJ does bisection to refine the eigenvalues of T,
  • dlarrk (l) - computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy
  • dlarrr (l) - tests to decide whether the symmetric tridiagonal matrix T warrants expensive computations which guarantee high relative accuracy in the eigenvalues
  • dlarrv (l) - computes the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and APPROXIMATIONS to the eigenvalues of L D L^T
  • dlar1v (l) - computes the (scaled) r-th column of the inverse of the sumbmatrix in rows B1 through BN of the tridiagonal matrix L D L^T - sigma I