.TH "laneg" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
laneg \- laneg: Sturm count
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "integer function \fBdlaneg\fP (n, d, lld, sigma, pivmin, r)"
.br
.RI "\fBDLANEG\fP computes the Sturm count\&. "
.ti -1c
.RI "integer function \fBslaneg\fP (n, d, lld, sigma, pivmin, r)"
.br
.RI "\fBSLANEG\fP computes the Sturm count\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function 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

.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
\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

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.