---
name: "slasd5.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/slasd5.f"
---

# slasd5.f(3)

## NAME

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

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**

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

Definition at line **115** of file **slasd5.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.