.TH "slaneg.f" 3 "Tue Nov 14 2017" "Version 3.8.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
slaneg.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "integer function \fBslaneg\fP (\fBN\fP, D, LLD, SIGMA, PIVMIN, R)"
.br
.RI "\fBSLANEG\fP computes the Sturm count\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "integer function slaneg (integer N, real, dimension( * ) D, real, dimension( * ) LLD, real SIGMA, real PIVMIN, integer R)"

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

.PP
.nf
 SLANEG 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 SLARRB.

 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 REAL array, dimension (N)
          The N diagonal elements of the diagonal matrix D.
.fi
.PP
.br
\fILLD\fP 
.PP
.nf
          LLD is REAL array, dimension (N-1)
          The (N-1) elements L(i)*L(i)*D(i).
.fi
.PP
.br
\fISIGMA\fP 
.PP
.nf
          SIGMA is REAL
          Shift amount in T - sigma I = L D L^T.
.fi
.PP
.br
\fIPIVMIN\fP 
.PP
.nf
          PIVMIN is REAL
          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
\fBDate:\fP
.RS 4
December 2016 
.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 120 of file slaneg\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.
