.TH "SRC/dlasd4.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
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.SH NAME
SRC/dlasd4.f
.SH SYNOPSIS
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.SS "Functions/Subroutines"

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.RI "subroutine \fBdlasd4\fP (n, i, d, z, delta, rho, sigma, work, info)"
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.RI "\fBDLASD4\fP computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix\&. Used by dbdsdc\&. "
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.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dlasd4 (integer n, integer i, double precision, dimension( * ) d, double precision, dimension( * ) z, double precision, dimension( * ) delta, double precision rho, double precision sigma, double precision, dimension( * ) work, integer info)"

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\fBDLASD4\fP computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix\&. Used by dbdsdc\&.  
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\fBPurpose:\fP
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.nf
!>
!> This subroutine computes the square root of the I-th updated
!> eigenvalue of a positive symmetric rank-one modification to
!> a positive diagonal matrix whose entries are given as the squares
!> of the corresponding entries in the array d, and that
!>
!>        0 <= D(i) < D(j)  for  i < j
!>
!> and that RHO > 0\&. This is arranged by the calling routine, and is
!> no loss in generality\&.  The rank-one modified system is thus
!>
!>        diag( D ) * diag( D ) +  RHO * Z * Z_transpose\&.
!>
!> where we assume the Euclidean norm of Z is 1\&.
!>
!> The method consists of approximating the rational functions in the
!> secular equation by simpler interpolating rational functions\&.
!> 
.fi
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.RE
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\fBParameters\fP
.RS 4
\fIN\fP 
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!>          N is INTEGER
!>         The length of all arrays\&.
!> 
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\fII\fP 
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!>          I is INTEGER
!>         The index of the eigenvalue to be computed\&.  1 <= I <= N\&.
!> 
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\fID\fP 
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!>          D is DOUBLE PRECISION array, dimension ( N )
!>         The original eigenvalues\&.  It is assumed that they are in
!>         order, 0 <= D(I) < D(J)  for I < J\&.
!> 
.fi
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\fIZ\fP 
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!>          Z is DOUBLE PRECISION array, dimension ( N )
!>         The components of the updating vector\&.
!> 
.fi
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\fIDELTA\fP 
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!>          DELTA is DOUBLE PRECISION array, dimension ( N )
!>         If N \&.ne\&. 1, DELTA contains (D(j) - sigma_I) in its  j-th
!>         component\&.  If N = 1, then DELTA(1) = 1\&.  The vector DELTA
!>         contains the information necessary to construct the
!>         (singular) eigenvectors\&.
!> 
.fi
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\fIRHO\fP 
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!>          RHO is DOUBLE PRECISION
!>         The scalar in the symmetric updating formula\&.
!> 
.fi
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\fISIGMA\fP 
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!>          SIGMA is DOUBLE PRECISION
!>         The computed sigma_I, the I-th updated eigenvalue\&.
!> 
.fi
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\fIWORK\fP 
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!>          WORK is DOUBLE PRECISION array, dimension ( N )
!>         If N \&.ne\&. 1, WORK contains (D(j) + sigma_I) in its  j-th
!>         component\&.  If N = 1, then WORK( 1 ) = 1\&.
!> 
.fi
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.br
\fIINFO\fP 
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!>          INFO is INTEGER
!>         = 0:  successful exit
!>         > 0:  if INFO = 1, the updating process failed\&.
!> 
.fi
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.RE
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\fBInternal Parameters:\fP
.RS 4

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!>  Logical variable ORGATI (origin-at-i?) is used for distinguishing
!>  whether D(i) or D(i+1) is treated as the origin\&.
!>
!>            ORGATI = \&.true\&.    origin at i
!>            ORGATI = \&.false\&.   origin at i+1
!>
!>  Logical variable SWTCH3 (switch-for-3-poles?) is for noting
!>  if we are working with THREE poles!
!>
!>  MAXIT is the maximum number of iterations allowed for each
!>  eigenvalue\&.
!> 
.fi
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.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
Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA 
.RE
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Definition at line \fB152\fP of file \fBdlasd4\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.