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

# ssbevx(3lapack)

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

## NAME

SSBEVX - computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A

## SYNOPSIS

- SUBROUTINE SSBEVX(

  JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO )

- CHARACTER

  JOBZ, RANGE, UPLO

- INTEGER

  IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N

- REAL

  ABSTOL, VL, VU

- INTEGER

  IFAIL( \* ), IWORK( \* )

- REAL

  AB( LDAB, \* ), Q( LDQ, \* ), W( \* ), WORK( \* ), Z( LDZ, \* )

## PURPOSE

SSBEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A.  Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.\

## ARGUMENTS

- JOBZ (input) CHARACTER\*1

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

- RANGE (input) CHARACTER\*1

  \= 'A': all eigenvalues will be found;\
   \= 'V': all eigenvalues in the half-open interval (VL,VU\] will be found; = 'I': the IL-th through IU-th eigenvalues will be found.

- 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) REAL 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.

- Q (output) REAL array, dimension (LDQ, N)

  If JOBZ = 'V', the N-by-N orthogonal matrix used in the reduction to tridiagonal form. If JOBZ = 'N', the array Q is not referenced.

- LDQ (input) INTEGER

  The leading dimension of the array Q.  If JOBZ = 'V', then LDQ \>= max(1,N).

- VL (input) REAL

  VU      (input) REAL If RANGE='V', the lower and upper bounds of the interval to be searched for eigenvalues. VL \< VU. Not referenced if RANGE = 'A' or 'I'.

- IL (input) INTEGER

  IU      (input) INTEGER If RANGE='I', the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 \<= IL \<= IU \<= N, if N \> 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'.

- ABSTOL (input) REAL

  The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval \[a,b\] of width less than or equal to ABSTOL + EPS \*   max( \|a\|,\|b\| ) , where EPS is the machine precision.  If ABSTOL is less than or equal to zero, then  EPS\*\|T\|  will be used in its place, where \|T\| is the 1-norm of the tridiagonal matrix obtained by reducing AB to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2\*SLAMCH('S'), not zero. If this routine returns with INFO\>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2\*SLAMCH('S'). See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3.

- M (output) INTEGER

  The total number of eigenvalues found.  0 \<= M \<= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

- W (output) REAL array, dimension (N)

  The first M elements contain the selected eigenvalues in ascending order.

- Z (output) REAL array, dimension (LDZ, max(1,M))

  If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. If JOBZ = 'N', then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used.

- LDZ (input) INTEGER

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

- WORK (workspace) REAL array, dimension (7\*N)

  - IWORK (workspace) INTEGER array, dimension (5\*N)

  - IFAIL (output) INTEGER array, dimension (N)

  If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero.  If INFO \> 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = 'N', then IFAIL is not referenced.

- INFO (output) INTEGER

  \= 0:  successful exit.\
   \< 0:  if INFO = -i, the i-th argument had an illegal value.\
   \> 0:  if INFO = i, then i eigenvectors failed to converge. Their indices are stored in array IFAIL.