1DLASD5(1)           LAPACK auxiliary routine (version 3.1)           DLASD5(1)
2
3
4

NAME

6       DLASD5  -  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
10

SYNOPSIS

12       SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )
13
14           INTEGER        I
15
16           DOUBLE         PRECISION DSIGMA, RHO
17
18           DOUBLE         PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )
19

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
23
24       We  also  assume RHO > 0 and that the Euclidean norm of the vector Z is
25       one.
26
27

ARGUMENTS

29       I      (input) INTEGER
30              The index of the eigenvalue to be computed.  I = 1 or I = 2.
31
32       D      (input) DOUBLE PRECISION array, dimension ( 2 )
33              The original eigenvalues.  We assume 0 <= D(1) < D(2).
34
35       Z      (input) DOUBLE PRECISION array, dimension ( 2 )
36              The components of the updating vector.
37
38       DELTA  (output) DOUBLE PRECISION 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.
42
43       RHO    (input) DOUBLE PRECISION
44              The scalar in the symmetric updating formula.
45
46              DSIGMA (output) DOUBLE PRECISION The computed sigma_I, the  I-th
47              updated eigenvalue.
48
49       WORK   (workspace) DOUBLE PRECISION array, dimension ( 2 )
50              WORK contains (D(j) + sigma_I) in its  j-th component.
51

FURTHER DETAILS

53       Based on contributions by
54          Ren-Cang Li, Computer Science Division, University of California
55          at Berkeley, USA
56
57
58
59
60 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       DLASD5(1)
Impressum