.TH "larrj" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
larrj \- larrj: step in stemr, refine eigval estimates
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBdlarrj\fP (n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info)"
.br
.RI "\fBDLARRJ\fP performs refinement of the initial estimates of the eigenvalues of the matrix T\&. "
.ti -1c
.RI "subroutine \fBslarrj\fP (n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info)"
.br
.RI "\fBSLARRJ\fP performs refinement of the initial estimates of the eigenvalues of the matrix T\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine dlarrj (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e2, integer ifirst, integer ilast, double precision rtol, integer offset, double precision, dimension( * ) w, double precision, dimension( * ) werr, double precision, dimension( * ) work, integer, dimension( * ) iwork, double precision pivmin, double precision spdiam, integer info)"

.PP
\fBDLARRJ\fP performs refinement of the initial estimates of the eigenvalues of the matrix T\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 Given the initial eigenvalue approximations of T, DLARRJ
 does  bisection to refine the eigenvalues of T,
 W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy\&. Initial
 guesses for these eigenvalues are input in W, the corresponding estimate
 of the error in these guesses in WERR\&. During bisection, intervals
 [left, right] are maintained by storing their mid-points and
 semi-widths in the arrays W and WERR respectively\&.
.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 T\&.
.fi
.PP
.br
\fIE2\fP 
.PP
.nf
          E2 is DOUBLE PRECISION array, dimension (N-1)
          The Squares of the (N-1) subdiagonal elements of T\&.
.fi
.PP
.br
\fIIFIRST\fP 
.PP
.nf
          IFIRST is INTEGER
          The index of the first eigenvalue to be computed\&.
.fi
.PP
.br
\fIILAST\fP 
.PP
.nf
          ILAST is INTEGER
          The index of the last eigenvalue to be computed\&.
.fi
.PP
.br
\fIRTOL\fP 
.PP
.nf
          RTOL is DOUBLE PRECISION
          Tolerance for the convergence of the bisection intervals\&.
          An interval [LEFT,RIGHT] has converged if
          RIGHT-LEFT < RTOL*MAX(|LEFT|,|RIGHT|)\&.
.fi
.PP
.br
\fIOFFSET\fP 
.PP
.nf
          OFFSET is INTEGER
          Offset for the arrays W and WERR, i\&.e\&., the IFIRST-OFFSET
          through ILAST-OFFSET elements of these arrays are to be used\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is DOUBLE PRECISION array, dimension (N)
          On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are
          estimates of the eigenvalues of L D L^T indexed IFIRST through
          ILAST\&.
          On output, these estimates are refined\&.
.fi
.PP
.br
\fIWERR\fP 
.PP
.nf
          WERR is DOUBLE PRECISION array, dimension (N)
          On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are
          the errors in the estimates of the corresponding elements in W\&.
          On output, these errors are refined\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (2*N)
          Workspace\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (2*N)
          Workspace\&.
.fi
.PP
.br
\fIPIVMIN\fP 
.PP
.nf
          PIVMIN is DOUBLE PRECISION
          The minimum pivot in the Sturm sequence for T\&.
.fi
.PP
.br
\fISPDIAM\fP 
.PP
.nf
          SPDIAM is DOUBLE PRECISION
          The spectral diameter of T\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          Error flag\&.
.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
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

.SS "subroutine slarrj (integer n, real, dimension( * ) d, real, dimension( * ) e2, integer ifirst, integer ilast, real rtol, integer offset, real, dimension( * ) w, real, dimension( * ) werr, real, dimension( * ) work, integer, dimension( * ) iwork, real pivmin, real spdiam, integer info)"

.PP
\fBSLARRJ\fP performs refinement of the initial estimates of the eigenvalues of the matrix T\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 Given the initial eigenvalue approximations of T, SLARRJ
 does  bisection to refine the eigenvalues of T,
 W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy\&. Initial
 guesses for these eigenvalues are input in W, the corresponding estimate
 of the error in these guesses in WERR\&. During bisection, intervals
 [left, right] are maintained by storing their mid-points and
 semi-widths in the arrays W and WERR respectively\&.
.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 T\&.
.fi
.PP
.br
\fIE2\fP 
.PP
.nf
          E2 is REAL array, dimension (N-1)
          The Squares of the (N-1) subdiagonal elements of T\&.
.fi
.PP
.br
\fIIFIRST\fP 
.PP
.nf
          IFIRST is INTEGER
          The index of the first eigenvalue to be computed\&.
.fi
.PP
.br
\fIILAST\fP 
.PP
.nf
          ILAST is INTEGER
          The index of the last eigenvalue to be computed\&.
.fi
.PP
.br
\fIRTOL\fP 
.PP
.nf
          RTOL is REAL
          Tolerance for the convergence of the bisection intervals\&.
          An interval [LEFT,RIGHT] has converged if
          RIGHT-LEFT < RTOL*MAX(|LEFT|,|RIGHT|)\&.
.fi
.PP
.br
\fIOFFSET\fP 
.PP
.nf
          OFFSET is INTEGER
          Offset for the arrays W and WERR, i\&.e\&., the IFIRST-OFFSET
          through ILAST-OFFSET elements of these arrays are to be used\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is REAL array, dimension (N)
          On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are
          estimates of the eigenvalues of L D L^T indexed IFIRST through
          ILAST\&.
          On output, these estimates are refined\&.
.fi
.PP
.br
\fIWERR\fP 
.PP
.nf
          WERR is REAL array, dimension (N)
          On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are
          the errors in the estimates of the corresponding elements in W\&.
          On output, these errors are refined\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (2*N)
          Workspace\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (2*N)
          Workspace\&.
.fi
.PP
.br
\fIPIVMIN\fP 
.PP
.nf
          PIVMIN is REAL
          The minimum pivot in the Sturm sequence for T\&.
.fi
.PP
.br
\fISPDIAM\fP 
.PP
.nf
          SPDIAM is REAL
          The spectral diameter of T\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          Error flag\&.
.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
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

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