---
name: "slaed1.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/slaed1.f"
---

# slaed1.f(3)

## NAME

SRC/slaed1.f

## SYNOPSIS

### Functions/Subroutines

subroutine **slaed1** (n, d, q, ldq, indxq, rho, cutpnt, work, iwork, info)\
 **SLAED1** used by SSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal.

## Function/Subroutine Documentation

### subroutine slaed1 (integer n, real, dimension( \* ) d, real, dimension( ldq, \* ) q, integer ldq, integer, dimension( \* ) indxq, real rho, integer cutpnt, real, dimension( \* ) work, integer, dimension( \* ) iwork, integer info)

**SLAED1** used by SSTEDC. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal.

**Purpose:**

```
!>
!> SLAED1 computes the updated eigensystem of a diagonal
!> matrix after modification by a rank-one symmetric matrix.  This
!> routine is used only for the eigenproblem which requires all
!> eigenvalues and eigenvectors of a tridiagonal matrix.  SLAED7 handles
!> the case in which eigenvalues only or eigenvalues and eigenvectors
!> of a full symmetric matrix (which was reduced to tridiagonal form)
!> are desired.
!>
!>   T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)
!>
!>    where Z = Q**T*u, u is a vector of length N with ones in the
!>    CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
!>
!>    The eigenvectors of the original matrix are stored in Q, and the
!>    eigenvalues are in D.  The algorithm consists of three stages:
!>
!>       The first stage consists of deflating the size of the problem
!>       when there are multiple eigenvalues or if there is a zero in
!>       the Z vector.  For each such occurrence the dimension of the
!>       secular equation problem is reduced by one.  This stage is
!>       performed by the routine SLAED2.
!>
!>       The second stage consists of calculating the updated
!>       eigenvalues. This is done by finding the roots of the secular
!>       equation via the routine SLAED4 (as called by SLAED3).
!>       This routine also calculates the eigenvectors of the current
!>       problem.
!>
!>       The final stage consists of computing the updated eigenvectors
!>       directly using the updated eigenvalues.  The eigenvectors for
!>       the current problem are multiplied with the eigenvectors from
!>       the overall problem.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>         The dimension of the symmetric tridiagonal matrix.  N >= 0.
!>
```

*D*

```
!>          D is REAL array, dimension (N)
!>         On entry, the eigenvalues of the rank-1-perturbed matrix.
!>         On exit, the eigenvalues of the repaired matrix.
!>
```

*Q*

```
!>          Q is REAL array, dimension (LDQ,N)
!>         On entry, the eigenvectors of the rank-1-perturbed matrix.
!>         On exit, the eigenvectors of the repaired tridiagonal matrix.
!>
```

*LDQ*

```
!>          LDQ is INTEGER
!>         The leading dimension of the array Q.  LDQ >= max(1,N).
!>
```

*INDXQ*

```
!>          INDXQ is INTEGER array, dimension (N)
!>         On entry, the permutation which separately sorts the two
!>         subproblems in D into ascending order.
!>         On exit, the permutation which will reintegrate the
!>         subproblems back into sorted order,
!>         i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
!>
```

*RHO*

```
!>          RHO is REAL
!>         The subdiagonal entry used to create the rank-1 modification.
!>
```

*CUTPNT*

```
!>          CUTPNT is INTEGER
!>         The location of the last eigenvalue in the leading sub-matrix.
!>         min(1,N) <= CUTPNT <= N/2.
!>
```

*WORK*

```
!>          WORK is REAL array, dimension (4*N + N**2)
!>
```

*IWORK*

```
!>          IWORK is INTEGER array, dimension (4*N)
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          > 0:  if INFO = 1, an eigenvalue did not converge
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Contributors:**

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA \
\
  Modified by Francoise Tisseur, University of Tennessee

Definition at line **161** of file **slaed1.f**.

## Author

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