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

.in +1c
.ti -1c
.RI "subroutine \fBdlarrf\fP (n, d, l, ld, clstrt, clend, w, wgap, werr, spdiam, clgapl, clgapr, pivmin, sigma, dplus, lplus, work, info)"
.br
.RI "\fBDLARRF\fP finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dlarrf (integer n, double precision, dimension( * ) d, double precision, dimension( * ) l, double precision, dimension( * ) ld, integer clstrt, integer clend, double precision, dimension( * ) w, double precision, dimension( * ) wgap, double precision, dimension( * ) werr, double precision spdiam, double precision clgapl, double precision clgapr, double precision pivmin, double precision sigma, double precision, dimension( * ) dplus, double precision, dimension( * ) lplus, double precision, dimension( * ) work, integer info)"

.PP
\fBDLARRF\fP finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated\&.  
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\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 ), DLARRF 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
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\fBParameters\fP
.RS 4
\fIN\fP 
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          N is INTEGER
          The order of the matrix (subblock, if the matrix split)\&.
.fi
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.br
\fID\fP 
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          D is DOUBLE PRECISION array, dimension (N)
          The N diagonal elements of the diagonal matrix D\&.
.fi
.PP
.br
\fIL\fP 
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          L is DOUBLE PRECISION array, dimension (N-1)
          The (N-1) subdiagonal elements of the unit bidiagonal
          matrix L\&.
.fi
.PP
.br
\fILD\fP 
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          LD is DOUBLE PRECISION array, dimension (N-1)
          The (N-1) elements L(i)*D(i)\&.
.fi
.PP
.br
\fICLSTRT\fP 
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          CLSTRT is INTEGER
          The index of the first eigenvalue in the cluster\&.
.fi
.PP
.br
\fICLEND\fP 
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          CLEND is INTEGER
          The index of the last eigenvalue in the cluster\&.
.fi
.PP
.br
\fIW\fP 
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          W is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 
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.nf
          SPDIAM is DOUBLE PRECISION
          estimate of the spectral diameter obtained from the
          Gerschgorin intervals
.fi
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.br
\fICLGAPL\fP 
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.nf
          CLGAPL is DOUBLE PRECISION
.fi
.PP
.br
\fICLGAPR\fP 
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.nf
          CLGAPR is DOUBLE PRECISION
          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 
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          PIVMIN is DOUBLE PRECISION
          The minimum pivot allowed in the Sturm sequence\&.
.fi
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\fISIGMA\fP 
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          SIGMA is DOUBLE PRECISION
          The shift used to form L(+) D(+) L(+)^T\&.
.fi
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\fIDPLUS\fP 
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          DPLUS is DOUBLE PRECISION array, dimension (N)
          The N diagonal elements of the diagonal matrix D(+)\&.
.fi
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.br
\fILPLUS\fP 
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          LPLUS is DOUBLE PRECISION 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 
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.nf
          WORK is DOUBLE PRECISION array, dimension (2*N)
          Workspace\&.
.fi
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.br
\fIINFO\fP 
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.nf
          INFO is INTEGER
          Signals processing OK (=0) or failure (=1)
.fi
.PP
 
.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
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Univ\&. of California Berkeley 
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Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.RE
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\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 
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 Osni Marques, LBNL/NERSC, USA 
.br
 Christof Voemel, University of California, Berkeley, USA 
.RE
.PP

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Definition at line \fB189\fP of file \fBdlarrf\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.