---
name: "dsteqr"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dsteqr/3lapack"
---

# dsteqr(3lapack)

computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method

## NAME

DSTEQR - computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method

## SYNOPSIS

- SUBROUTINE DSTEQR(

  COMPZ, N, D, E, Z, LDZ, WORK, INFO )

- CHARACTER

  COMPZ

- INTEGER

  INFO, LDZ, N

- DOUBLE

  PRECISION D( \* ), E( \* ), WORK( \* ), Z( LDZ, \* )

## PURPOSE

DSTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band symmetric matrix can also be found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to tridiagonal form.\

## ARGUMENTS

- COMPZ (input) CHARACTER\*1

  \= 'N':  Compute eigenvalues only.\
   \= 'V':  Compute eigenvalues and eigenvectors of the original symmetric matrix.  On entry, Z must contain the orthogonal matrix used to reduce the original matrix to tridiagonal form. = 'I':  Compute eigenvalues and eigenvectors of the tridiagonal matrix.  Z is initialized to the identity matrix.

- N (input) INTEGER

  The order of the matrix.  N \>= 0.

- D (input/output) DOUBLE PRECISION array, dimension (N)

  On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order.

- E (input/output) DOUBLE PRECISION array, dimension (N-1)

  On entry, the (n-1) subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed.

- Z (input/output) DOUBLE PRECISION array, dimension (LDZ, N)

  On entry, if  COMPZ = 'V', then Z contains the orthogonal matrix used in the reduction to tridiagonal form. On exit, if INFO = 0, then if  COMPZ = 'V', Z contains the orthonormal eigenvectors of the original symmetric matrix, and if COMPZ = 'I', Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If COMPZ = 'N', then Z is not referenced.

- LDZ (input) INTEGER

  The leading dimension of the array Z.  LDZ \>= 1, and if eigenvectors are desired, then  LDZ \>= max(1,N).

- WORK (workspace) DOUBLE PRECISION array, dimension (max(1,2\*N-2))

  If COMPZ = 'N', then WORK is not referenced.

- INFO (output) INTEGER

  \= 0:  successful exit\
   \< 0:  if INFO = -i, the i-th argument had an illegal value\
   \> 0:  the algorithm has failed to find all the eigenvalues in a total of 30\*N iterations; if INFO = i, then i elements of E have not converged to zero; on exit, D and E contain the elements of a symmetric tridiagonal matrix which is orthogonally similar to the original matrix.