.TH "SRC/zlar1v.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
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.SH NAME
SRC/zlar1v.f
.SH SYNOPSIS
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.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzlar1v\fP (n, b1, bn, lambda, d, l, ld, lld, pivmin, gaptol, z, wantnc, negcnt, ztz, mingma, r, isuppz, nrminv, resid, rqcorr, work)"
.br
.RI "\fBZLAR1V\fP computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zlar1v (integer n, integer b1, integer bn, double precision lambda, double precision, dimension( * ) d, double precision, dimension( * ) l, double precision, dimension( * ) ld, double precision, dimension( * ) lld, double precision pivmin, double precision gaptol, complex*16, dimension( * ) z, logical wantnc, integer negcnt, double precision ztz, double precision mingma, integer r, integer, dimension( * ) isuppz, double precision nrminv, double precision resid, double precision rqcorr, double precision, dimension( * ) work)"

.PP
\fBZLAR1V\fP computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI\&.  
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\fBPurpose:\fP
.RS 4

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.nf
!>
!> ZLAR1V computes the (scaled) r-th column of the inverse of
!> the sumbmatrix in rows B1 through BN of the tridiagonal matrix
!> L D L**T - sigma I\&. When sigma is close to an eigenvalue, the
!> computed vector is an accurate eigenvector\&. Usually, r corresponds
!> to the index where the eigenvector is largest in magnitude\&.
!> The following steps accomplish this computation :
!> (a) Stationary qd transform,  L D L**T - sigma I = L(+) D(+) L(+)**T,
!> (b) Progressive qd transform, L D L**T - sigma I = U(-) D(-) U(-)**T,
!> (c) Computation of the diagonal elements of the inverse of
!>     L D L**T - sigma I by combining the above transforms, and choosing
!>     r as the index where the diagonal of the inverse is (one of the)
!>     largest in magnitude\&.
!> (d) Computation of the (scaled) r-th column of the inverse using the
!>     twisted factorization obtained by combining the top part of the
!>     the stationary and the bottom part of the progressive transform\&.
!> 
.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 L D L**T\&.
!> 
.fi
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.br
\fIB1\fP 
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!>          B1 is INTEGER
!>           First index of the submatrix of L D L**T\&.
!> 
.fi
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.br
\fIBN\fP 
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!>          BN is INTEGER
!>           Last index of the submatrix of L D L**T\&.
!> 
.fi
.PP
.br
\fILAMBDA\fP 
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!>          LAMBDA is DOUBLE PRECISION
!>           The shift\&. In order to compute an accurate eigenvector,
!>           LAMBDA should be a good approximation to an eigenvalue
!>           of L D L**T\&.
!> 
.fi
.PP
.br
\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, in elements 1 to N-1\&.
!> 
.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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\fILD\fP 
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!>          LD is DOUBLE PRECISION array, dimension (N-1)
!>           The n-1 elements L(i)*D(i)\&.
!> 
.fi
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.br
\fILLD\fP 
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!>          LLD is DOUBLE PRECISION array, dimension (N-1)
!>           The n-1 elements L(i)*L(i)*D(i)\&.
!> 
.fi
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.br
\fIPIVMIN\fP 
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!>          PIVMIN is DOUBLE PRECISION
!>           The minimum pivot in the Sturm sequence\&.
!> 
.fi
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.br
\fIGAPTOL\fP 
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!>          GAPTOL is DOUBLE PRECISION
!>           Tolerance that indicates when eigenvector entries are negligible
!>           w\&.r\&.t\&. their contribution to the residual\&.
!> 
.fi
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.br
\fIZ\fP 
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!>          Z is COMPLEX*16 array, dimension (N)
!>           On input, all entries of Z must be set to 0\&.
!>           On output, Z contains the (scaled) r-th column of the
!>           inverse\&. The scaling is such that Z(R) equals 1\&.
!> 
.fi
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.br
\fIWANTNC\fP 
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!>          WANTNC is LOGICAL
!>           Specifies whether NEGCNT has to be computed\&.
!> 
.fi
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.br
\fINEGCNT\fP 
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!>          NEGCNT is INTEGER
!>           If WANTNC is \&.TRUE\&. then NEGCNT = the number of pivots < pivmin
!>           in the  matrix factorization L D L**T, and NEGCNT = -1 otherwise\&.
!> 
.fi
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.br
\fIZTZ\fP 
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!>          ZTZ is DOUBLE PRECISION
!>           The square of the 2-norm of Z\&.
!> 
.fi
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.br
\fIMINGMA\fP 
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!>          MINGMA is DOUBLE PRECISION
!>           The reciprocal of the largest (in magnitude) diagonal
!>           element of the inverse of L D L**T - sigma I\&.
!> 
.fi
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.br
\fIR\fP 
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!>          R is INTEGER
!>           The twist index for the twisted factorization used to
!>           compute Z\&.
!>           On input, 0 <= R <= N\&. If R is input as 0, R is set to
!>           the index where (L D L**T - sigma I)^{-1} is largest
!>           in magnitude\&. If 1 <= R <= N, R is unchanged\&.
!>           On output, R contains the twist index used to compute Z\&.
!>           Ideally, R designates the position of the maximum entry in the
!>           eigenvector\&.
!> 
.fi
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.br
\fIISUPPZ\fP 
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!>          ISUPPZ is INTEGER array, dimension (2)
!>           The support of the vector in Z, i\&.e\&., the vector Z is
!>           nonzero only in elements ISUPPZ(1) through ISUPPZ( 2 )\&.
!> 
.fi
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.br
\fINRMINV\fP 
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!>          NRMINV is DOUBLE PRECISION
!>           NRMINV = 1/SQRT( ZTZ )
!> 
.fi
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\fIRESID\fP 
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!>          RESID is DOUBLE PRECISION
!>           The residual of the FP vector\&.
!>           RESID = ABS( MINGMA )/SQRT( ZTZ )
!> 
.fi
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.br
\fIRQCORR\fP 
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.nf
!>          RQCORR is DOUBLE PRECISION
!>           The Rayleigh Quotient correction to LAMBDA\&.
!>           RQCORR = MINGMA*TMP
!> 
.fi
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.br
\fIWORK\fP 
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!>          WORK is DOUBLE PRECISION array, dimension (4*N)
!> 
.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\&. 
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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 \fB227\fP of file \fBzlar1v\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.