.TH "SRC/dlaneg.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/dlaneg.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "integer function \fBdlaneg\fP (n, d, lld, sigma, pivmin, r)"
.br
.RI "\fBDLANEG\fP computes the Sturm count\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "integer function dlaneg (integer n, double precision, dimension( * ) d, double precision, dimension( * ) lld, double precision sigma, double precision pivmin, integer r)"

.PP
\fBDLANEG\fP computes the Sturm count\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.)
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The N diagonal elements of the diagonal matrix D\&.
.fi
.PP
.br
\fILLD\fP 
.PP
.nf
          LLD is DOUBLE PRECISION array, dimension (N-1)
          The (N-1) elements L(i)*L(i)*D(i)\&.
.fi
.PP
.br
\fISIGMA\fP 
.PP
.nf
          SIGMA is DOUBLE PRECISION
          Shift amount in T - sigma I = L D L^T\&.
.fi
.PP
.br
\fIPIVMIN\fP 
.PP
.nf
          PIVMIN is DOUBLE PRECISION
          The minimum pivot in the Sturm sequence\&.  May be used
          when zero pivots are encountered on non-IEEE-754
          architectures\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          R is INTEGER
          The twist index for the twisted factorization that is used
          for the negcount\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Osni Marques, LBNL/NERSC, USA 
.br
 Christof Voemel, University of California, Berkeley, USA 
.br
 Jason Riedy, University of California, Berkeley, USA 
.br
.RE
.PP

.PP
Definition at line \fB117\fP of file \fBdlaneg\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.