# dlaneg(3) [centos man page]

dlaneg.f(3) LAPACK dlaneg.f(3)NAME

dlaneg.f-SYNOPSIS

Functions/Subroutines INTEGER function dlaneg (N, D, LLD, SIGMA, PIVMIN, R) DLANEG computes the Sturm count.Function/Subroutine Documentation INTEGER function dlaneg (integerN, double precision, dimension( * )D, double precision, dimension( * )LLD, double precisionSIGMA, double precisionPIVMIN, integerR) DLANEG computes the Sturm count. Purpose: DLANEG computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T - sigma I = L D L^T. This implementation works directly on the factors without forming the tridiagonal matrix T. The Sturm count is also the number of eigenvalues of T less than sigma. This routine is called from DLARRB. The current routine does not use the PIVMIN parameter but rather requires IEEE-754 propagation of Infinities and NaNs. This routine also has no input range restrictions but does require default exception handling such that x/0 produces Inf when x is non-zero, and Inf/Inf produces NaN. For more information, see: Marques, Riedy, and Voemel, "Benefits of IEEE-754 Features in Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on Scientific Computing, v28, n5, 2006. DOI 10.1137/050641624 (Tech report version in LAWN 172 with the same title.) Parameters: N N is INTEGER The order of the matrix. D D is DOUBLE PRECISION array, dimension (N) The N diagonal elements of the diagonal matrix D. LLD LLD is DOUBLE PRECISION array, dimension (N-1) The (N-1) elements L(i)*L(i)*D(i). SIGMA SIGMA is DOUBLE PRECISION Shift amount in T - sigma I = L D L^T. PIVMIN PIVMIN is DOUBLE PRECISION The minimum pivot in the Sturm sequence. May be used when zero pivots are encountered on non-IEEE-754 architectures. R R is INTEGER The twist index for the twisted factorization that is used for the negcount. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Contributors: Osni Marques, LBNL/NERSC, USA Christof Voemel, University of California, Berkeley, USA Jason Riedy, University of California, Berkeley, USA Definition at line 119 of file dlaneg.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 dlaneg.f(3)

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dlarrc.f(3) LAPACK dlarrc.f(3)NAME

dlarrc.f-SYNOPSIS

Functions/Subroutines subroutine dlarrc (JOBT, N, VL, VU, D, E, PIVMIN, EIGCNT, LCNT, RCNT, INFO) DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.Function/Subroutine Documentation subroutine dlarrc (characterJOBT, integerN, double precisionVL, double precisionVU, double precision, dimension( * )D, double precision, dimension( * )E, double precisionPIVMIN, integerEIGCNT, integerLCNT, integerRCNT, integerINFO) DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix. Purpose: Find the number of eigenvalues of the symmetric tridiagonal matrix T that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T if JOBT = 'L'. Parameters: JOBT JOBT is CHARACTER*1 = 'T': Compute Sturm count for matrix T. = 'L': Compute Sturm count for matrix L D L^T. N N is INTEGER The order of the matrix. N > 0. VL VL is DOUBLE PRECISION VU VU is DOUBLE PRECISION The lower and upper bounds for the eigenvalues. D D is DOUBLE PRECISION array, dimension (N) JOBT = 'T': The N diagonal elements of the tridiagonal matrix T. JOBT = 'L': The N diagonal elements of the diagonal matrix D. E E is DOUBLE PRECISION array, dimension (N) JOBT = 'T': The N-1 offdiagonal elements of the matrix T. JOBT = 'L': The N-1 offdiagonal elements of the matrix L. PIVMIN PIVMIN is DOUBLE PRECISION The minimum pivot in the Sturm sequence for T. EIGCNT EIGCNT is INTEGER The number of eigenvalues of the symmetric tridiagonal matrix T that are in the interval (VL,VU] LCNT LCNT is INTEGER RCNT RCNT is INTEGER The left and right negcounts of the interval. INFO INFO is INTEGER Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Contributors: 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 Definition at line 136 of file dlarrc.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 dlarrc.f(3)