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---
:name: dlaneg
:md5sum: c5a7742f33a7d96a4fed5f670646bf40
:category: :function
:type: integer
:arguments:
- n:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: input
:dims:
- n
- lld:
:type: doublereal
:intent: input
:dims:
- n-1
- sigma:
:type: doublereal
:intent: input
- pivmin:
:type: doublereal
:intent: input
- r:
:type: integer
:intent: input
:substitutions: {}
:fortran_help: " INTEGER FUNCTION DLANEG( N, D, LLD, SIGMA, PIVMIN, R )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLANEG computes the Sturm count, the number of negative pivots\n\
* encountered while factoring tridiagonal T - sigma I = L D L^T.\n\
* This implementation works directly on the factors without forming\n\
* the tridiagonal matrix T. The Sturm count is also the number of\n\
* eigenvalues of T less than sigma.\n\
*\n\
* This routine is called from DLARRB.\n\
*\n\
* The current routine does not use the PIVMIN parameter but rather\n\
* requires IEEE-754 propagation of Infinities and NaNs. This\n\
* routine also has no input range restrictions but does require\n\
* default exception handling such that x/0 produces Inf when x is\n\
* non-zero, and Inf/Inf produces NaN. For more information, see:\n\
*\n\
* Marques, Riedy, and Voemel, \"Benefits of IEEE-754 Features in\n\
* Modern Symmetric Tridiagonal Eigensolvers,\" SIAM Journal on\n\
* Scientific Computing, v28, n5, 2006. DOI 10.1137/050641624\n\
* (Tech report version in LAWN 172 with the same title.)\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix.\n\
*\n\
* D (input) DOUBLE PRECISION array, dimension (N)\n\
* The N diagonal elements of the diagonal matrix D.\n\
*\n\
* LLD (input) DOUBLE PRECISION array, dimension (N-1)\n\
* The (N-1) elements L(i)*L(i)*D(i).\n\
*\n\
* SIGMA (input) DOUBLE PRECISION\n\
* Shift amount in T - sigma I = L D L^T.\n\
*\n\
* PIVMIN (input) DOUBLE PRECISION\n\
* The minimum pivot in the Sturm sequence. May be used\n\
* when zero pivots are encountered on non-IEEE-754\n\
* architectures.\n\
*\n\
* R (input) INTEGER\n\
* The twist index for the twisted factorization that is used\n\
* for the negcount.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Osni Marques, LBNL/NERSC, USA\n\
* Christof Voemel, University of California, Berkeley, USA\n\
* Jason Riedy, University of California, Berkeley, USA\n\
*\n\
* =====================================================================\n\
*\n"
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