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slasd5.f(3) LAPACK slasd5.f(3)

NAME

slasd5.f -

SYNOPSIS

Functions/Subroutines


subroutine slasd5 (I, D, Z, DELTA, RHO, DSIGMA, WORK)
 
SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.

Function/Subroutine Documentation

subroutine slasd5 (integerI, real, dimension( 2 )D, real, dimension( 2 )Z, real, dimension( 2 )DELTA, realRHO, realDSIGMA, real, dimension( 2 )WORK)

SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.
Purpose: 
 This subroutine computes the square root of the I-th eigenvalue
 of a positive symmetric rank-one modification of a 2-by-2 diagonal
 matrix


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


 The diagonal entries in the array D are assumed to satisfy


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


 We also assume RHO > 0 and that the Euclidean norm of the vector
 Z is one.
Parameters:
I 
          I is INTEGER
         The index of the eigenvalue to be computed.  I = 1 or I = 2.
D 
          D is REAL array, dimension (2)
         The original eigenvalues.  We assume 0 <= D(1) < D(2).
Z 
          Z is REAL array, dimension (2)
         The components of the updating vector.
DELTA 
          DELTA is REAL array, dimension (2)
         Contains (D(j) - sigma_I) in its  j-th component.
         The vector DELTA contains the information necessary
         to construct the eigenvectors.
RHO 
          RHO is REAL
         The scalar in the symmetric updating formula.
DSIGMA 
          DSIGMA is REAL
         The computed sigma_I, the I-th updated eigenvalue.
WORK 
          WORK is REAL array, dimension (2)
         WORK contains (D(j) + sigma_I) in its  j-th component.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Contributors:
Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA
Definition at line 117 of file slasd5.f.

Author

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