---
name: "slaed0.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/slaed0.f"
---

# slaed0.f(3)

## NAME

SRC/slaed0.f

## SYNOPSIS

### Functions/Subroutines

subroutine **slaed0** (icompq, qsiz, n, d, e, q, ldq, qstore, ldqs, work, iwork, info)\
 **SLAED0** used by SSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.

## Function/Subroutine Documentation

### subroutine slaed0 (integer icompq, integer qsiz, integer n, real, dimension( \* ) d, real, dimension( \* ) e, real, dimension( ldq, \* ) q, integer ldq, real, dimension( ldqs, \* ) qstore, integer ldqs, real, dimension( \* ) work, integer, dimension( \* ) iwork, integer info)

**SLAED0** used by SSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.

**Purpose:**

```
!>
!> SLAED0 computes all eigenvalues and corresponding eigenvectors of a
!> symmetric tridiagonal matrix using the divide and conquer method.
!>
```

**Parameters**

*ICOMPQ*

```
!>          ICOMPQ is INTEGER
!>          = 0:  Compute eigenvalues only.
!>          = 1:  Compute eigenvectors of original dense symmetric matrix
!>                also.  On entry, Q contains the orthogonal matrix used
!>                to reduce the original matrix to tridiagonal form.
!>          = 2:  Compute eigenvalues and eigenvectors of tridiagonal
!>                matrix.
!>
```

*QSIZ*

```
!>          QSIZ is INTEGER
!>         The dimension of the orthogonal matrix used to reduce
!>         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.
!>
```

*N*

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

*D*

```
!>          D is REAL array, dimension (N)
!>         On entry, the main diagonal of the tridiagonal matrix.
!>         On exit, its eigenvalues.
!>
```

*E*

```
!>          E is REAL array, dimension (N-1)
!>         The off-diagonal elements of the tridiagonal matrix.
!>         On exit, E has been destroyed.
!>
```

*Q*

```
!>          Q is REAL array, dimension (LDQ, N)
!>         On entry, Q must contain an N-by-N orthogonal matrix.
!>         If ICOMPQ = 0    Q is not referenced.
!>         If ICOMPQ = 1    On entry, Q is a subset of the columns of the
!>                          orthogonal matrix used to reduce the full
!>                          matrix to tridiagonal form corresponding to
!>                          the subset of the full matrix which is being
!>                          decomposed at this time.
!>         If ICOMPQ = 2    On entry, Q will be the identity matrix.
!>                          On exit, Q contains the eigenvectors of the
!>                          tridiagonal matrix.
!>
```

*LDQ*

```
!>          LDQ is INTEGER
!>         The leading dimension of the array Q.  If eigenvectors are
!>         desired, then  LDQ >= max(1,N).  In any case,  LDQ >= 1.
!>
```

*QSTORE*

```
!>          QSTORE is REAL array, dimension (LDQS, N)
!>         Referenced only when ICOMPQ = 1.  Used to store parts of
!>         the eigenvector matrix when the updating matrix multiplies
!>         take place.
!>
```

*LDQS*

```
!>          LDQS is INTEGER
!>         The leading dimension of the array QSTORE.  If ICOMPQ = 1,
!>         then  LDQS >= max(1,N).  In any case,  LDQS >= 1.
!>
```

*WORK*

```
!>          WORK is REAL array,
!>         If ICOMPQ = 0 or 1, the dimension of WORK must be at least
!>                     1 + 3*N + 2*N*lg N + 3*N**2
!>                     ( lg( N ) = smallest integer k
!>                                 such that 2^k >= N )
!>         If ICOMPQ = 2, the dimension of WORK must be at least
!>                     4*N + N**2.
!>
```

*IWORK*

```
!>          IWORK is INTEGER array,
!>         If ICOMPQ = 0 or 1, the dimension of IWORK must be at least
!>                        6 + 6*N + 5*N*lg N.
!>                        ( lg( N ) = smallest integer k
!>                                    such that 2^k >= N )
!>         If ICOMPQ = 2, the dimension of IWORK must be at least
!>                        3 + 5*N.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>          > 0:  The algorithm failed to compute an eigenvalue while
!>                working on the submatrix lying in rows and columns
!>                INFO/(N+1) through mod(INFO,N+1).
!>
```

**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

Definition at line **170** of file **slaed0.f**.

## Author

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