---
name: "dlaed2.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/dlaed2.f"
---

# dlaed2.f(3)

## NAME

SRC/dlaed2.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dlaed2** (k, n, n1, d, q, ldq, indxq, rho, z, dlambda, w, q2, indx, indxc, indxp, coltyp, info)\
 **DLAED2** used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

## Function/Subroutine Documentation

### subroutine dlaed2 (integer k, integer n, integer n1, double precision, dimension( \* ) d, double precision, dimension( ldq, \* ) q, integer ldq, integer, dimension( \* ) indxq, double precision rho, double precision, dimension( \* ) z, double precision, dimension( \* ) dlambda, double precision, dimension( \* ) w, double precision, dimension( \* ) q2, integer, dimension( \* ) indx, integer, dimension( \* ) indxc, integer, dimension( \* ) indxp, integer, dimension( \* ) coltyp, integer info)

**DLAED2** used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

**Purpose:**

```
!>
!> DLAED2 merges the two sets of eigenvalues together into a single
!> sorted set.  Then it tries to deflate the size of the problem.
!> There are two ways in which deflation can occur:  when two or more
!> eigenvalues are close together or if there is a tiny entry in the
!> Z vector.  For each such occurrence the order of the related secular
!> equation problem is reduced by one.
!>
```

**Parameters**

*K*

```
!>          K is INTEGER
!>         The number of non-deflated eigenvalues, and the order of the
!>         related secular equation. 0 <= K <=N.
!>
```

*N*

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

*N1*

```
!>          N1 is INTEGER
!>         The location of the last eigenvalue in the leading sub-matrix.
!>         min(1,N) <= N1 <= N/2.
!>
```

*D*

```
!>          D is DOUBLE PRECISION array, dimension (N)
!>         On entry, D contains the eigenvalues of the two submatrices to
!>         be combined.
!>         On exit, D contains the trailing (N-K) updated eigenvalues
!>         (those which were deflated) sorted into increasing order.
!>
```

*Q*

```
!>          Q is DOUBLE PRECISION array, dimension (LDQ, N)
!>         On entry, Q contains the eigenvectors of two submatrices in
!>         the two square blocks with corners at (1,1), (N1,N1)
!>         and (N1+1, N1+1), (N,N).
!>         On exit, Q contains the trailing (N-K) updated eigenvectors
!>         (those which were deflated) in its last N-K columns.
!>
```

*LDQ*

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

*INDXQ*

```
!>          INDXQ is INTEGER array, dimension (N)
!>         The permutation which separately sorts the two sub-problems
!>         in D into ascending order.  Note that elements in the second
!>         half of this permutation must first have N1 added to their
!>         values. Destroyed on exit.
!>
```

*RHO*

```
!>          RHO is DOUBLE PRECISION
!>         On entry, the off-diagonal element associated with the rank-1
!>         cut which originally split the two submatrices which are now
!>         being recombined.
!>         On exit, RHO has been modified to the value required by
!>         DLAED3.
!>
```

*Z*

```
!>          Z is DOUBLE PRECISION array, dimension (N)
!>         On entry, Z contains the updating vector (the last
!>         row of the first sub-eigenvector matrix and the first row of
!>         the second sub-eigenvector matrix).
!>         On exit, the contents of Z have been destroyed by the updating
!>         process.
!>
```

*DLAMBDA*

```
!>          DLAMBDA is DOUBLE PRECISION array, dimension (N)
!>         A copy of the first K eigenvalues which will be used by
!>         DLAED3 to form the secular equation.
!>
```

*W*

```
!>          W is DOUBLE PRECISION array, dimension (N)
!>         The first k values of the final deflation-altered z-vector
!>         which will be passed to DLAED3.
!>
```

*Q2*

```
!>          Q2 is DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2)
!>         A copy of the first K eigenvectors which will be used by
!>         DLAED3 in a matrix multiply (DGEMM) to solve for the new
!>         eigenvectors.
!>
```

*INDX*

```
!>          INDX is INTEGER array, dimension (N)
!>         The permutation used to sort the contents of DLAMBDA into
!>         ascending order.
!>
```

*INDXC*

```
!>          INDXC is INTEGER array, dimension (N)
!>         The permutation used to arrange the columns of the deflated
!>         Q matrix into three groups:  the first group contains non-zero
!>         elements only at and above N1, the second contains
!>         non-zero elements only below N1, and the third is dense.
!>
```

*INDXP*

```
!>          INDXP is INTEGER array, dimension (N)
!>         The permutation used to place deflated values of D at the end
!>         of the array.  INDXP(1:K) points to the nondeflated D-values
!>         and INDXP(K+1:N) points to the deflated eigenvalues.
!>
```

*COLTYP*

```
!>          COLTYP is INTEGER array, dimension (N)
!>         During execution, a label which will indicate which of the
!>         following types a column in the Q2 matrix is:
!>         1 : non-zero in the upper half only;
!>         2 : dense;
!>         3 : non-zero in the lower half only;
!>         4 : deflated.
!>         On exit, COLTYP(i) is the number of columns of type i,
!>         for i=1 to 4 only.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit.
!>          < 0:  if INFO = -i, the i-th argument had an illegal value.
!>
```

**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 **210** of file **dlaed2.f**.

## Author

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