1DLASD5(1)           LAPACK auxiliary routine (version 3.2)           DLASD5(1)
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NAME

6       DLASD5 - subroutine compute the square root of the I-th eigenvalue of a
7       positive symmetric rank-one modification of a  2-by-2  diagonal  matrix
8       diag(  D  )  * diag( D ) + RHO  The diagonal entries in the array D are
9       assumed to satisfy   0 <= D(i) < D(j) for i < j
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SYNOPSIS

12       SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )
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14           INTEGER        I
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16           DOUBLE         PRECISION DSIGMA, RHO
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18           DOUBLE         PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )
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PURPOSE

21       This subroutine computes the square root of the I-th  eigenvalue  of  a
22       positive symmetric rank-one modification of a 2-by-2 diagonal matrix We
23       also assume RHO > 0 and that the Euclidean norm of the vector Z is one.
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ARGUMENTS

26       I      (input) INTEGER
27              The index of the eigenvalue to be computed.  I = 1 or I = 2.
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29       D      (input) DOUBLE PRECISION array, dimension ( 2 )
30              The original eigenvalues.  We assume 0 <= D(1) < D(2).
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32       Z      (input) DOUBLE PRECISION array, dimension ( 2 )
33              The components of the updating vector.
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35       DELTA  (output) DOUBLE PRECISION array, dimension ( 2 )
36              Contains (D(j) - sigma_I) in its  j-th  component.   The  vector
37              DELTA contains the information necessary to construct the eigen‐
38              vectors.
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40       RHO    (input) DOUBLE PRECISION
41              The scalar in the symmetric updating formula.   DSIGMA  (output)
42              DOUBLE  PRECISION  The computed sigma_I, the I-th updated eigen‐
43              value.
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45       WORK   (workspace) DOUBLE PRECISION array, dimension ( 2 )
46              WORK contains (D(j) + sigma_I) in its  j-th component.
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FURTHER DETAILS

49       Based on contributions by
50          Ren-Cang Li, Computer Science Division, University of California
51          at Berkeley, USA
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55 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       DLASD5(1)
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