LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ dlaed5()

subroutine dlaed5 ( integer  I,
double precision, dimension( 2 )  D,
double precision, dimension( 2 )  Z,
double precision, dimension( 2 )  DELTA,
double precision  RHO,
double precision  DLAM 
)

DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation.

Download DLAED5 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 This subroutine computes the I-th eigenvalue of a symmetric rank-one
 modification of a 2-by-2 diagonal matrix

            diag( D )  +  RHO * Z * transpose(Z) .

 The diagonal elements in the array D are assumed to satisfy

            D(i) < D(j)  for  i < j .

 We also assume RHO > 0 and that the Euclidean norm of the vector
 Z is one.
Parameters
[in]I
          I is INTEGER
         The index of the eigenvalue to be computed.  I = 1 or I = 2.
[in]D
          D is DOUBLE PRECISION array, dimension (2)
         The original eigenvalues.  We assume D(1) < D(2).
[in]Z
          Z is DOUBLE PRECISION array, dimension (2)
         The components of the updating vector.
[out]DELTA
          DELTA is DOUBLE PRECISION array, dimension (2)
         The vector DELTA contains the information necessary
         to construct the eigenvectors.
[in]RHO
          RHO is DOUBLE PRECISION
         The scalar in the symmetric updating formula.
[out]DLAM
          DLAM is DOUBLE PRECISION
         The computed lambda_I, the I-th updated eigenvalue.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Definition at line 107 of file dlaed5.f.

108 *
109 * -- LAPACK computational routine --
110 * -- LAPACK is a software package provided by Univ. of Tennessee, --
111 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112 *
113 * .. Scalar Arguments ..
114  INTEGER I
115  DOUBLE PRECISION DLAM, RHO
116 * ..
117 * .. Array Arguments ..
118  DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 )
119 * ..
120 *
121 * =====================================================================
122 *
123 * .. Parameters ..
124  DOUBLE PRECISION ZERO, ONE, TWO, FOUR
125  parameter( zero = 0.0d0, one = 1.0d0, two = 2.0d0,
126  $ four = 4.0d0 )
127 * ..
128 * .. Local Scalars ..
129  DOUBLE PRECISION B, C, DEL, TAU, TEMP, W
130 * ..
131 * .. Intrinsic Functions ..
132  INTRINSIC abs, sqrt
133 * ..
134 * .. Executable Statements ..
135 *
136  del = d( 2 ) - d( 1 )
137  IF( i.EQ.1 ) THEN
138  w = one + two*rho*( z( 2 )*z( 2 )-z( 1 )*z( 1 ) ) / del
139  IF( w.GT.zero ) THEN
140  b = del + rho*( z( 1 )*z( 1 )+z( 2 )*z( 2 ) )
141  c = rho*z( 1 )*z( 1 )*del
142 *
143 * B > ZERO, always
144 *
145  tau = two*c / ( b+sqrt( abs( b*b-four*c ) ) )
146  dlam = d( 1 ) + tau
147  delta( 1 ) = -z( 1 ) / tau
148  delta( 2 ) = z( 2 ) / ( del-tau )
149  ELSE
150  b = -del + rho*( z( 1 )*z( 1 )+z( 2 )*z( 2 ) )
151  c = rho*z( 2 )*z( 2 )*del
152  IF( b.GT.zero ) THEN
153  tau = -two*c / ( b+sqrt( b*b+four*c ) )
154  ELSE
155  tau = ( b-sqrt( b*b+four*c ) ) / two
156  END IF
157  dlam = d( 2 ) + tau
158  delta( 1 ) = -z( 1 ) / ( del+tau )
159  delta( 2 ) = -z( 2 ) / tau
160  END IF
161  temp = sqrt( delta( 1 )*delta( 1 )+delta( 2 )*delta( 2 ) )
162  delta( 1 ) = delta( 1 ) / temp
163  delta( 2 ) = delta( 2 ) / temp
164  ELSE
165 *
166 * Now I=2
167 *
168  b = -del + rho*( z( 1 )*z( 1 )+z( 2 )*z( 2 ) )
169  c = rho*z( 2 )*z( 2 )*del
170  IF( b.GT.zero ) THEN
171  tau = ( b+sqrt( b*b+four*c ) ) / two
172  ELSE
173  tau = two*c / ( -b+sqrt( b*b+four*c ) )
174  END IF
175  dlam = d( 2 ) + tau
176  delta( 1 ) = -z( 1 ) / ( del+tau )
177  delta( 2 ) = -z( 2 ) / tau
178  temp = sqrt( delta( 1 )*delta( 1 )+delta( 2 )*delta( 2 ) )
179  delta( 1 ) = delta( 1 ) / temp
180  delta( 2 ) = delta( 2 ) / temp
181  END IF
182  RETURN
183 *
184 * End of DLAED5
185 *
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