---
name: "dlaed4.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/dlaed4.f"
---

# dlaed4.f(3)

## NAME

SRC/dlaed4.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dlaed4** (n, i, d, z, delta, rho, dlam, info)\
 **DLAED4** used by DSTEDC. Finds a single root of the secular equation.

## Function/Subroutine Documentation

### subroutine dlaed4 (integer n, integer i, double precision, dimension( \* ) d, double precision, dimension( \* ) z, double precision, dimension( \* ) delta, double precision rho, double precision dlam, integer info)

**DLAED4** used by DSTEDC. Finds a single root of the secular equation.

**Purpose:**

```
!>
!> This subroutine computes the I-th updated eigenvalue of a symmetric
!> rank-one modification to a diagonal matrix whose elements are
!> given in the array d, and that
!>
!>            D(i) < D(j)  for  i < j
!>
!> and that RHO > 0.  This is arranged by the calling routine, and is
!> no loss in generality.  The rank-one modified system is thus
!>
!>            diag( D )  +  RHO * Z * Z_transpose.
!>
!> where we assume the Euclidean norm of Z is 1.
!>
!> The method consists of approximating the rational functions in the
!> secular equation by simpler interpolating rational functions.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>         The length of all arrays.
!>
```

*I*

```
!>          I is INTEGER
!>         The index of the eigenvalue to be computed.  1 <= I <= N.
!>
```

*D*

```
!>          D is DOUBLE PRECISION array, dimension (N)
!>         The original eigenvalues.  It is assumed that they are in
!>         order, D(I) < D(J)  for I < J.
!>
```

*Z*

```
!>          Z is DOUBLE PRECISION array, dimension (N)
!>         The components of the updating vector.
!>
```

*DELTA*

```
!>          DELTA is DOUBLE PRECISION array, dimension (N)
!>         If N > 2, DELTA contains (D(j) - lambda_I) in its  j-th
!>         component.  If N = 1, then DELTA(1) = 1. If N = 2, see DLAED5
!>         for detail. The vector DELTA contains the information necessary
!>         to construct the eigenvectors by DLAED3 and DLAED9.
!>
```

*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.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>         = 0:  successful exit
!>         > 0:  if INFO = 1, the updating process failed.
!>
```

**Internal Parameters:**

```
!>  Logical variable ORGATI (origin-at-i?) is used for distinguishing
!>  whether D(i) or D(i+1) is treated as the origin.
!>
!>            ORGATI = .true.    origin at i
!>            ORGATI = .false.   origin at i+1
!>
!>   Logical variable SWTCH3 (switch-for-3-poles?) is for noting
!>   if we are working with THREE poles!
!>
!>   MAXIT is the maximum number of iterations allowed for each
!>   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 **144** of file **dlaed4.f**.

## Author

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