.TH "SRC/dlarrf.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/dlarrf.f
.SH SYNOPSIS
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.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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.nf
!>          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
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\fIL\fP 
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.nf
!>          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 
.PP
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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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!>          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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.nf
!>          PIVMIN is DOUBLE PRECISION
!>          The minimum pivot allowed in the Sturm sequence\&.
!> 
.fi
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.br
\fISIGMA\fP 
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.nf
!>          SIGMA is DOUBLE PRECISION
!>          The shift used to form L(+) D(+) L(+)^T\&.
!> 
.fi
.PP
.br
\fIDPLUS\fP 
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.nf
!>          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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.nf
!>          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
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.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 
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Jim Demmel, University of California, Berkeley, USA 
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Inderjit Dhillon, University of Texas, Austin, USA 
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Osni Marques, LBNL/NERSC, USA 
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Christof Voemel, University of California, Berkeley, USA 
.RE
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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\&.