---
name: "dsteqr2"
section: "3"
platform: "linux"
package: "scalapack-doc"
version: "1.5-11"
release: "Debian 11 (Bullseye)"
platforms: ["linux"]
url: "https://new.carta.tech/dsteqr2"
---

# dsteqr2(3)

i a modified version of LAPACK routine DSTEQR

## NAME

DSTEQR2 - i a modified version of LAPACK routine DSTEQR

## SYNOPSIS

- SUBROUTINE DSTEQR2(

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

- CHARACTER

  COMPZ

- INTEGER

  INFO, LDZ, N, NR

- DOUBLE

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

## PURPOSE

DSTEQR2 is a modified version of LAPACK routine DSTEQR. DSTEQR2 computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. DSTEQR2 is modified from DSTEQR to allow each ScaLAPACK process running DSTEQR2 to perform updates on a distributed matrix Q. Proper usage of DSTEQR2 can be gleaned from examination of ScaLAPACK's PDSYEV.\

## ARGUMENTS

- COMPZ (input) CHARACTER\*1

  \= 'N':  Compute eigenvalues only.\
   \= 'I':  Compute eigenvalues and eigenvectors of the tridiagonal matrix.  Z must be initialized to the identity matrix by PDLASET or DLASET prior to entering this subroutine.

- 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 (local input/local output) DOUBLE PRECISION array, global

  dimension (N, N), local dimension (LDZ, NR). 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).

- NR (input) INTEGER

  NR = MAX(1, NUMROC( N, NB, MYPROW, 0, NPROCS ) ). If COMPZ = 'N', then NR is not referenced.

- 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.