dlarrc (l) - Linux Manuals

dlarrc: 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

NAME

DLARRC - 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

SYNOPSIS

SUBROUTINE DLARRC(
JOBT, N, VL, VU, D, E, PIVMIN, EIGCNT, LCNT, RCNT, INFO )

    
CHARACTER JOBT

    
INTEGER EIGCNT, INFO, LCNT, N, RCNT

    
DOUBLE PRECISION PIVMIN, VL, VU

    
DOUBLE PRECISION D( * ), E( * )

PURPOSE

Find 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.

ARGUMENTS

JOBT (input) CHARACTER*1
= aqTaq: Compute Sturm count for matrix T.
= aqLaq: Compute Sturm count for matrix L D L^T.
N (input) INTEGER
The order of the matrix. N > 0.
VL (input) DOUBLE PRECISION
VU (input) DOUBLE PRECISION The lower and upper bounds for the eigenvalues.
D (input) DOUBLE PRECISION array, dimension (N)
JOBT = aqTaq: The N diagonal elements of the tridiagonal matrix T.
JOBT = aqLaq: The N diagonal elements of the diagonal matrix D.
E (input) DOUBLE PRECISION array, dimension (N)

JOBT = aqTaq: The N-1 offdiagonal elements of the matrix T.
JOBT = aqLaq: The N-1 offdiagonal elements of the matrix L.
PIVMIN (input) DOUBLE PRECISION
The minimum pivot in the Sturm sequence for T.
EIGCNT (output) INTEGER
The number of eigenvalues of the symmetric tridiagonal matrix T that are in the interval (VL,VU]
LCNT (output) INTEGER
RCNT (output) INTEGER The left and right negcounts of the interval.
INFO (output) INTEGER

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 dlarrc

  • dlarrc (3)
  • dlarra (l) - the splitting points with threshold SPLTOL
  • dlarrb (l) - the relatively robust representation(RRR) L D L^T, DLARRB does "limited" bisection to refine the eigenvalues of L D L^T,
  • 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 "small" 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