# slasd5.f man page

slasd5.f —

## Synopsis

### Functions/Subroutines

subroutineslasd5(I, D, Z, DELTA, RHO, DSIGMA, WORK)SLASD5computes 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

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

slasd5(3) is an alias of slasd5.f(3).