# dsbev (l) - Linux Man Pages

## 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
= aqNaq: Compute eigenvalues only;
= aqVaq: Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1

= aqUaq: Upper triangle of A is stored;
= aqLaq: 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 = aqUaq, or the number of subdiagonals if UPLO = aqLaq. 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 = aqUaq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = aqLaq, 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 = aqUaq, the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = aqLaq, 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 = aqVaq, 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 = aqNaq, then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ = aqVaq, 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.