.TH "laneg" 3 "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,  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\&.
.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,  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

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