1SLASD5(1)           LAPACK auxiliary routine (version 3.1)           SLASD5(1)
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NAME

6       SLASD5  -  compute the square root of the I-th eigenvalue of a positive
7       symmetric rank-one modification of a 2-by-2 diagonal matrix   diag( D )
8       *  diag(  D ) + RHO  The diagonal entries in the array D are assumed to
9       satisfy   0 <= D(i) < D(j) for i < j
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SYNOPSIS

12       SUBROUTINE SLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )
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14           INTEGER        I
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16           REAL           DSIGMA, RHO
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18           REAL           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
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24       We  also  assume RHO > 0 and that the Euclidean norm of the vector Z is
25       one.
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ARGUMENTS

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

53       Based on contributions by
54          Ren-Cang Li, Computer Science Division, University of California
55          at Berkeley, USA
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60 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLASD5(1)
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