.TH "SRC/slasd4.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
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.SH NAME
SRC/slasd4.f
.SH SYNOPSIS
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.SS "Functions/Subroutines"

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.ti -1c
.RI "subroutine \fBslasd4\fP (n, i, d, z, delta, rho, sigma, work, info)"
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.RI "\fBSLASD4\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 sbdsdc\&. "
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.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine slasd4 (integer n, integer i, real, dimension( * ) d, real, dimension( * ) z, real, dimension( * ) delta, real rho, real sigma, real, dimension( * ) work, integer info)"

.PP
\fBSLASD4\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 sbdsdc\&.  
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\fBPurpose:\fP
.RS 4

.PP
.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\&.
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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 REAL array, dimension ( N )
         The original eigenvalues\&.  It is assumed that they are in
         order, 0 <= D(I) < D(J)  for I < J\&.
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\fIZ\fP 
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          Z is REAL array, dimension ( N )
         The components of the updating vector\&.
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\fIDELTA\fP 
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          DELTA is REAL 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\&.
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\fIRHO\fP 
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          RHO is REAL
         The scalar in the symmetric updating formula\&.
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\fISIGMA\fP 
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          SIGMA is REAL
         The computed sigma_I, the I-th updated eigenvalue\&.
.fi
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\fIWORK\fP 
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          WORK is REAL 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\&.
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\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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.nf
  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\&.
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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\&. 
.RE
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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 \fBslasd4\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.