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

# dsbev(3lapack)

computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

## NAME

DSBEV - computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

## SYNOPSIS

- SUBROUTINE DSBEV(

  JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, INFO )

- CHARACTER

  JOBZ, UPLO

- INTEGER

  INFO, KD, LDAB, LDZ, N

- DOUBLE

  PRECISION AB( LDAB, \* ), W( \* ), WORK( \* ), Z( LDZ, \* )

## PURPOSE

DSBEV computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A.

## ARGUMENTS

- JOBZ (input) CHARACTER\*1

  \= 'N':  Compute eigenvalues only;\
   \= 'V':  Compute eigenvalues and eigenvectors.

- UPLO (input) CHARACTER\*1

  \= 'U':  Upper triangle of A is stored;\
   \= 'L':  Lower triangle of A is stored.

- N (input) INTEGER

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

- KD (input) INTEGER

  The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'.  KD \>= 0.

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

  On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array.  The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)\<=i\<=j; if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j\<=i\<=min(n,j+kd). On exit, AB is overwritten by values generated during the reduction to tridiagonal form.  If UPLO = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of AB.

- LDAB (input) INTEGER

  The leading dimension of the array AB.  LDAB \>= KD + 1.

- W (output) DOUBLE PRECISION array, dimension (N)

  If INFO = 0, the eigenvalues in ascending order.

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

  If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = 'N', then Z is not referenced.

- LDZ (input) INTEGER

  The leading dimension of the array Z.  LDZ \>= 1, and if JOBZ = 'V', LDZ \>= max(1,N).

- WORK (workspace) DOUBLE PRECISION array, dimension (max(1,3\*N-2))

  - INFO (output) INTEGER

  \= 0:  successful exit\
   \< 0:  if INFO = -i, the i-th argument had an illegal value\
   \> 0:  if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.