.TH "slarrf.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
slarrf.f \- 
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBslarrf\fP (N, D, L, LD, CLSTRT, CLEND, W, WGAP, WERR, SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA, DPLUS, LPLUS, WORK, INFO)"
.br
.RI "\fI\fBSLARRF\fP finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated\&. \fP"
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine slarrf (integerN, real, dimension( * )D, real, dimension( * )L, real, dimension( * )LD, integerCLSTRT, integerCLEND, real, dimension( * )W, real, dimension( * )WGAP, real, dimension( * )WERR, realSPDIAM, realCLGAPL, realCLGAPR, realPIVMIN, realSIGMA, real, dimension( * )DPLUS, real, dimension( * )LPLUS, real, dimension( * )WORK, integerINFO)"

.PP
\fBSLARRF\fP finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated\&.  
.PP
\fBPurpose: \fP
.RS 4

.PP
.nf
 Given the initial representation L D L^T and its cluster of close
 eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ...
 W( CLEND ), SLARRF finds a new relatively robust representation
 L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the
 eigenvalues of L(+) D(+) L(+)^T is relatively isolated.
.fi
.PP
 
.RE
.PP
\fBParameters:\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix (subblock, if the matrix splitted).
.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
\fIL\fP 
.PP
.nf
          L is REAL array, dimension (N-1)
          The (N-1) subdiagonal elements of the unit bidiagonal
          matrix L.
.fi
.PP
.br
\fILD\fP 
.PP
.nf
          LD is REAL array, dimension (N-1)
          The (N-1) elements L(i)*D(i).
.fi
.PP
.br
\fICLSTRT\fP 
.PP
.nf
          CLSTRT is INTEGER
          The index of the first eigenvalue in the cluster.
.fi
.PP
.br
\fICLEND\fP 
.PP
.nf
          CLEND is INTEGER
          The index of the last eigenvalue in the cluster.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is REAL array, dimension
          dimension is >=  (CLEND-CLSTRT+1)
          The eigenvalue APPROXIMATIONS of L D L^T in ascending order.
          W( CLSTRT ) through W( CLEND ) form the cluster of relatively
          close eigenalues.
.fi
.PP
.br
\fIWGAP\fP 
.PP
.nf
          WGAP is REAL array, dimension
          dimension is >=  (CLEND-CLSTRT+1)
          The separation from the right neighbor eigenvalue in W.
.fi
.PP
.br
\fIWERR\fP 
.PP
.nf
          WERR is REAL array, dimension
          dimension is >=  (CLEND-CLSTRT+1)
          WERR contain the semiwidth of the uncertainty
          interval of the corresponding eigenvalue APPROXIMATION in W
.fi
.PP
.br
\fISPDIAM\fP 
.PP
.nf
          SPDIAM is REAL
          estimate of the spectral diameter obtained from the
          Gerschgorin intervals
.fi
.PP
.br
\fICLGAPL\fP 
.PP
.nf
          CLGAPL is REAL
.fi
.PP
.br
\fICLGAPR\fP 
.PP
.nf
          CLGAPR is REAL
          absolute gap on each end of the cluster.
          Set by the calling routine to protect against shifts too close
          to eigenvalues outside the cluster.
.fi
.PP
.br
\fIPIVMIN\fP 
.PP
.nf
          PIVMIN is REAL
          The minimum pivot allowed in the Sturm sequence.
.fi
.PP
.br
\fISIGMA\fP 
.PP
.nf
          SIGMA is REAL
          The shift used to form L(+) D(+) L(+)^T.
.fi
.PP
.br
\fIDPLUS\fP 
.PP
.nf
          DPLUS is REAL array, dimension (N)
          The N diagonal elements of the diagonal matrix D(+).
.fi
.PP
.br
\fILPLUS\fP 
.PP
.nf
          LPLUS is REAL array, dimension (N-1)
          The first (N-1) elements of LPLUS contain the subdiagonal
          elements of the unit bidiagonal matrix L(+).
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (2*N)
          Workspace.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          Signals processing OK (=0) or failure (=1)
.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
September 2012 
.RE
.PP
\fBContributors: \fP
.RS 4
Beresford Parlett, University of California, Berkeley, USA 
.br
 Jim Demmel, University of California, Berkeley, USA 
.br
 Inderjit Dhillon, University of Texas, Austin, USA 
.br
 Osni Marques, LBNL/NERSC, USA 
.br
 Christof Voemel, University of California, Berkeley, USA 
.RE
.PP

.PP
Definition at line 191 of file slarrf\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.