lasd5(3) LAPACK lasd5(3)

lasd5 - lasd5: D&C step: secular equation, 2x2


subroutine dlasd5 (i, d, z, delta, rho, dsigma, work)
DLASD5 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. 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.

DLASD5 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 DOUBLE PRECISION array, dimension ( 2 )
         The original eigenvalues.  We assume 0 <= D(1) < D(2).

Z

          Z is DOUBLE PRECISION array, dimension ( 2 )
         The components of the updating vector.

DELTA

          DELTA is DOUBLE PRECISION 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 DOUBLE PRECISION
         The scalar in the symmetric updating formula.

DSIGMA

          DSIGMA is DOUBLE PRECISION
         The computed sigma_I, the I-th updated eigenvalue.

WORK

          WORK is DOUBLE PRECISION 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.

Contributors:

Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

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.

Contributors:

Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

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