Man page - lasd5(3)

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lasd5

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine dlasd5 (integer i, double precision, dimension( 2 ) d, doubleprecision, dimension( 2 ) z, double precision, dimension( 2 ) delta,double precision rho, double precision dsigma, double precision,dimension( 2 ) work)
subroutine slasd5 (integer i, real, dimension( 2 ) d, real, dimension( 2 )z, real, dimension( 2 ) delta, real rho, real dsigma, real, dimension(2 ) work)
Author

NAME

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

SYNOPSIS

Functions

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.

Detailed Description

Function Documentation

subroutine dlasd5 (integer i, double precision, dimension( 2 ) d, doubleprecision, dimension( 2 ) z, double precision, dimension( 2 ) delta,double precision rho, double precision dsigma, double precision,dimension( 2 ) 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.

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

subroutine slasd5 (integer i, real, dimension( 2 ) d, real, dimension( 2 )z, real, dimension( 2 ) delta, real rho, real dsigma, 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.

Contributors:

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

Author

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