slasd5.f - Man Page

SRC/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 (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

NAG Ltd.

Contributors:

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

Definition at line 115 of file slasd5.f.

Author

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Referenced By

The man page slasd5(3) is an alias of slasd5.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK