.TH "lar1v" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lar1v \- lar1v: step in larrv, hence stemr & stegr
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclar1v\fP (n, b1, bn, lambda, d, l, ld, lld, pivmin, gaptol, z, wantnc, negcnt, ztz, mingma, r, isuppz, nrminv, resid, rqcorr, work)"
.br
.RI "\fBCLAR1V\fP computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI\&. "
.ti -1c
.RI "subroutine \fBdlar1v\fP (n, b1, bn, lambda, d, l, ld, lld, pivmin, gaptol, z, wantnc, negcnt, ztz, mingma, r, isuppz, nrminv, resid, rqcorr, work)"
.br
.RI "\fBDLAR1V\fP computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI\&. "
.ti -1c
.RI "subroutine \fBslar1v\fP (n, b1, bn, lambda, d, l, ld, lld, pivmin, gaptol, z, wantnc, negcnt, ztz, mingma, r, isuppz, nrminv, resid, rqcorr, work)"
.br
.RI "\fBSLAR1V\fP computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI\&. "
.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 "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine clar1v (integer n, integer b1, integer bn, real lambda, real, dimension( * ) d, real, dimension( * ) l, real, dimension( * ) ld, real, dimension( * ) lld, real pivmin, real gaptol, complex, dimension( * ) z, logical wantnc, integer negcnt, real ztz, real mingma, integer r, integer, dimension( * ) isuppz, real nrminv, real resid, real rqcorr, real, dimension( * ) work)"

.PP
\fBCLAR1V\fP computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLAR1V 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
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
           The order of the matrix L D L**T\&.
.fi
.PP
.br
\fIB1\fP 
.PP
.nf
          B1 is INTEGER
           First index of the submatrix of L D L**T\&.
.fi
.PP
.br
\fIBN\fP 
.PP
.nf
          BN is INTEGER
           Last index of the submatrix of L D L**T\&.
.fi
.PP
.br
\fILAMBDA\fP 
.PP
.nf
          LAMBDA is REAL
           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 
.PP
.nf
          L is REAL array, dimension (N-1)
           The (n-1) subdiagonal elements of the unit bidiagonal matrix
           L, in elements 1 to N-1\&.
.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
\fILD\fP 
.PP
.nf
          LD is REAL array, dimension (N-1)
           The n-1 elements L(i)*D(i)\&.
.fi
.PP
.br
\fILLD\fP 
.PP
.nf
          LLD is REAL array, dimension (N-1)
           The n-1 elements L(i)*L(i)*D(i)\&.
.fi
.PP
.br
\fIPIVMIN\fP 
.PP
.nf
          PIVMIN is REAL
           The minimum pivot in the Sturm sequence\&.
.fi
.PP
.br
\fIGAPTOL\fP 
.PP
.nf
          GAPTOL is REAL
           Tolerance that indicates when eigenvector entries are negligible
           w\&.r\&.t\&. their contribution to the residual\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is COMPLEX 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
.PP
.br
\fIWANTNC\fP 
.PP
.nf
          WANTNC is LOGICAL
           Specifies whether NEGCNT has to be computed\&.
.fi
.PP
.br
\fINEGCNT\fP 
.PP
.nf
          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
.PP
.br
\fIZTZ\fP 
.PP
.nf
          ZTZ is REAL
           The square of the 2-norm of Z\&.
.fi
.PP
.br
\fIMINGMA\fP 
.PP
.nf
          MINGMA is REAL
           The reciprocal of the largest (in magnitude) diagonal
           element of the inverse of L D L**T - sigma I\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          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
.PP
.br
\fIISUPPZ\fP 
.PP
.nf
          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
.PP
.br
\fINRMINV\fP 
.PP
.nf
          NRMINV is REAL
           NRMINV = 1/SQRT( ZTZ )
.fi
.PP
.br
\fIRESID\fP 
.PP
.nf
          RESID is REAL
           The residual of the FP vector\&.
           RESID = ABS( MINGMA )/SQRT( ZTZ )
.fi
.PP
.br
\fIRQCORR\fP 
.PP
.nf
          RQCORR is REAL
           The Rayleigh Quotient correction to LAMBDA\&.
           RQCORR = MINGMA*TMP
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (4*N)
.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 dlar1v (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, double precision, 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
\fBDLAR1V\fP computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLAR1V 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
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
           The order of the matrix L D L**T\&.
.fi
.PP
.br
\fIB1\fP 
.PP
.nf
          B1 is INTEGER
           First index of the submatrix of L D L**T\&.
.fi
.PP
.br
\fIBN\fP 
.PP
.nf
          BN is INTEGER
           Last index of the submatrix of L D L**T\&.
.fi
.PP
.br
\fILAMBDA\fP 
.PP
.nf
          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 
.PP
.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
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
           The n diagonal elements of the diagonal matrix D\&.
.fi
.PP
.br
\fILD\fP 
.PP
.nf
          LD is DOUBLE PRECISION array, dimension (N-1)
           The n-1 elements L(i)*D(i)\&.
.fi
.PP
.br
\fILLD\fP 
.PP
.nf
          LLD is DOUBLE PRECISION array, dimension (N-1)
           The n-1 elements L(i)*L(i)*D(i)\&.
.fi
.PP
.br
\fIPIVMIN\fP 
.PP
.nf
          PIVMIN is DOUBLE PRECISION
           The minimum pivot in the Sturm sequence\&.
.fi
.PP
.br
\fIGAPTOL\fP 
.PP
.nf
          GAPTOL is DOUBLE PRECISION
           Tolerance that indicates when eigenvector entries are negligible
           w\&.r\&.t\&. their contribution to the residual\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is DOUBLE PRECISION 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
.PP
.br
\fIWANTNC\fP 
.PP
.nf
          WANTNC is LOGICAL
           Specifies whether NEGCNT has to be computed\&.
.fi
.PP
.br
\fINEGCNT\fP 
.PP
.nf
          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
.PP
.br
\fIZTZ\fP 
.PP
.nf
          ZTZ is DOUBLE PRECISION
           The square of the 2-norm of Z\&.
.fi
.PP
.br
\fIMINGMA\fP 
.PP
.nf
          MINGMA is DOUBLE PRECISION
           The reciprocal of the largest (in magnitude) diagonal
           element of the inverse of L D L**T - sigma I\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          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
.PP
.br
\fIISUPPZ\fP 
.PP
.nf
          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
.PP
.br
\fINRMINV\fP 
.PP
.nf
          NRMINV is DOUBLE PRECISION
           NRMINV = 1/SQRT( ZTZ )
.fi
.PP
.br
\fIRESID\fP 
.PP
.nf
          RESID is DOUBLE PRECISION
           The residual of the FP vector\&.
           RESID = ABS( MINGMA )/SQRT( ZTZ )
.fi
.PP
.br
\fIRQCORR\fP 
.PP
.nf
          RQCORR is DOUBLE PRECISION
           The Rayleigh Quotient correction to LAMBDA\&.
           RQCORR = MINGMA*TMP
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (4*N)
.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 slar1v (integer n, integer b1, integer bn, real lambda, real, dimension( * ) d, real, dimension( * ) l, real, dimension( * ) ld, real, dimension( * ) lld, real pivmin, real gaptol, real, dimension( * ) z, logical wantnc, integer negcnt, real ztz, real mingma, integer r, integer, dimension( * ) isuppz, real nrminv, real resid, real rqcorr, real, dimension( * ) work)"

.PP
\fBSLAR1V\fP computes the (scaled) r-th column of the inverse of the submatrix in rows b1 through bn of the tridiagonal matrix LDLT - λI\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLAR1V 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
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
           The order of the matrix L D L**T\&.
.fi
.PP
.br
\fIB1\fP 
.PP
.nf
          B1 is INTEGER
           First index of the submatrix of L D L**T\&.
.fi
.PP
.br
\fIBN\fP 
.PP
.nf
          BN is INTEGER
           Last index of the submatrix of L D L**T\&.
.fi
.PP
.br
\fILAMBDA\fP 
.PP
.nf
          LAMBDA is REAL
           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 
.PP
.nf
          L is REAL array, dimension (N-1)
           The (n-1) subdiagonal elements of the unit bidiagonal matrix
           L, in elements 1 to N-1\&.
.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
\fILD\fP 
.PP
.nf
          LD is REAL array, dimension (N-1)
           The n-1 elements L(i)*D(i)\&.
.fi
.PP
.br
\fILLD\fP 
.PP
.nf
          LLD is REAL array, dimension (N-1)
           The n-1 elements L(i)*L(i)*D(i)\&.
.fi
.PP
.br
\fIPIVMIN\fP 
.PP
.nf
          PIVMIN is REAL
           The minimum pivot in the Sturm sequence\&.
.fi
.PP
.br
\fIGAPTOL\fP 
.PP
.nf
          GAPTOL is REAL
           Tolerance that indicates when eigenvector entries are negligible
           w\&.r\&.t\&. their contribution to the residual\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          Z is REAL 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
.PP
.br
\fIWANTNC\fP 
.PP
.nf
          WANTNC is LOGICAL
           Specifies whether NEGCNT has to be computed\&.
.fi
.PP
.br
\fINEGCNT\fP 
.PP
.nf
          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
.PP
.br
\fIZTZ\fP 
.PP
.nf
          ZTZ is REAL
           The square of the 2-norm of Z\&.
.fi
.PP
.br
\fIMINGMA\fP 
.PP
.nf
          MINGMA is REAL
           The reciprocal of the largest (in magnitude) diagonal
           element of the inverse of L D L**T - sigma I\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          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
.PP
.br
\fIISUPPZ\fP 
.PP
.nf
          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
.PP
.br
\fINRMINV\fP 
.PP
.nf
          NRMINV is REAL
           NRMINV = 1/SQRT( ZTZ )
.fi
.PP
.br
\fIRESID\fP 
.PP
.nf
          RESID is REAL
           The residual of the FP vector\&.
           RESID = ABS( MINGMA )/SQRT( ZTZ )
.fi
.PP
.br
\fIRQCORR\fP 
.PP
.nf
          RQCORR is REAL
           The Rayleigh Quotient correction to LAMBDA\&.
           RQCORR = MINGMA*TMP
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (4*N)
.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 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\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.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
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
           The order of the matrix L D L**T\&.
.fi
.PP
.br
\fIB1\fP 
.PP
.nf
          B1 is INTEGER
           First index of the submatrix of L D L**T\&.
.fi
.PP
.br
\fIBN\fP 
.PP
.nf
          BN is INTEGER
           Last index of the submatrix of L D L**T\&.
.fi
.PP
.br
\fILAMBDA\fP 
.PP
.nf
          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 
.PP
.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
.PP
.br
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
           The n diagonal elements of the diagonal matrix D\&.
.fi
.PP
.br
\fILD\fP 
.PP
.nf
          LD is DOUBLE PRECISION array, dimension (N-1)
           The n-1 elements L(i)*D(i)\&.
.fi
.PP
.br
\fILLD\fP 
.PP
.nf
          LLD is DOUBLE PRECISION array, dimension (N-1)
           The n-1 elements L(i)*L(i)*D(i)\&.
.fi
.PP
.br
\fIPIVMIN\fP 
.PP
.nf
          PIVMIN is DOUBLE PRECISION
           The minimum pivot in the Sturm sequence\&.
.fi
.PP
.br
\fIGAPTOL\fP 
.PP
.nf
          GAPTOL is DOUBLE PRECISION
           Tolerance that indicates when eigenvector entries are negligible
           w\&.r\&.t\&. their contribution to the residual\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          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
.PP
.br
\fIWANTNC\fP 
.PP
.nf
          WANTNC is LOGICAL
           Specifies whether NEGCNT has to be computed\&.
.fi
.PP
.br
\fINEGCNT\fP 
.PP
.nf
          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
.PP
.br
\fIZTZ\fP 
.PP
.nf
          ZTZ is DOUBLE PRECISION
           The square of the 2-norm of Z\&.
.fi
.PP
.br
\fIMINGMA\fP 
.PP
.nf
          MINGMA is DOUBLE PRECISION
           The reciprocal of the largest (in magnitude) diagonal
           element of the inverse of L D L**T - sigma I\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          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
.PP
.br
\fIISUPPZ\fP 
.PP
.nf
          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
.PP
.br
\fINRMINV\fP 
.PP
.nf
          NRMINV is DOUBLE PRECISION
           NRMINV = 1/SQRT( ZTZ )
.fi
.PP
.br
\fIRESID\fP 
.PP
.nf
          RESID is DOUBLE PRECISION
           The residual of the FP vector\&.
           RESID = ABS( MINGMA )/SQRT( ZTZ )
.fi
.PP
.br
\fIRQCORR\fP 
.PP
.nf
          RQCORR is DOUBLE PRECISION
           The Rayleigh Quotient correction to LAMBDA\&.
           RQCORR = MINGMA*TMP
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (4*N)
.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\&.