---
name: "dlaed5"
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/dlaed5.f"
---

# dlaed5(3)

Part of [dlaed5.f(3)](/dlaed5.f/3.md).

## NAME

SRC/dlaed5.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dlaed5** (i, d, z, delta, rho, dlam)\
 **DLAED5** used by DSTEDC. Solves the 2-by-2 secular equation.

## Function/Subroutine Documentation

### subroutine dlaed5 (integer i, double precision, dimension( 2 ) d, double precision, dimension( 2 ) z, double precision, dimension( 2 ) delta, double precision rho, double precision dlam)

**DLAED5** used by DSTEDC. Solves the 2-by-2 secular equation.

**Purpose:**

```
!>
!> This subroutine computes the I-th eigenvalue of a symmetric rank-one
!> modification of a 2-by-2 diagonal matrix
!>
!>            diag( D )  +  RHO * Z * transpose(Z) .
!>
!> The diagonal elements in the array D are assumed to satisfy
!>
!>            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 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)
!>         The vector DELTA contains the information necessary
!>         to construct the eigenvectors.
!>
```

*RHO*

```
!>          RHO is DOUBLE PRECISION
!>         The scalar in the symmetric updating formula.
!>
```

*DLAM*

```
!>          DLAM is DOUBLE PRECISION
!>         The computed lambda_I, the I-th updated eigenvalue.
!>
```

**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 **107** of file **dlaed5.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.