# ssbgvd.f - Man Page

SRC/ssbgvd.f

## Synopsis

### Functions/Subroutines

subroutine ssbgvd (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, lwork, iwork, liwork, info)
SSBGVD

## Function/Subroutine Documentation

### subroutine ssbgvd (character jobz, character uplo, integer n, integer ka, integer kb, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldbb, * ) bb, integer ldbb, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

SSBGVD

Purpose:

SSBGVD computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of the
form A*x=(lambda)*B*x.  Here A and B are assumed to be symmetric and
banded, and B is also positive definite.  If eigenvectors are
desired, it uses a divide and conquer algorithm.
Parameters

JOBZ

JOBZ is CHARACTER*1
= 'N':  Compute eigenvalues only;
= 'V':  Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangles of A and B are stored;
= 'L':  Lower triangles of A and B are stored.

N

N is INTEGER
The order of the matrices A and B.  N >= 0.

KA

KA is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'.  KA >= 0.

KB

KB is INTEGER
The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'.  KB >= 0.

AB

AB is REAL array, dimension (LDAB, N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).

On exit, the contents of AB are destroyed.

LDAB

LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= KA+1.

BB

BB is REAL array, dimension (LDBB, N)
On entry, the upper or lower triangle of the symmetric band
matrix B, stored in the first kb+1 rows of the array.  The
j-th column of B is stored in the j-th column of the array BB
as follows:
if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).

On exit, the factor S from the split Cholesky factorization
B = S**T*S, as returned by SPBSTF.

LDBB

LDBB is INTEGER
The leading dimension of the array BB.  LDBB >= KB+1.

W

W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is REAL array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
eigenvectors, with the i-th column of Z holding the
eigenvector associated with W(i).  The eigenvectors are
normalized so Z**T*B*Z = I.
If JOBZ = 'N', then Z is not referenced.

LDZ

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

WORK

WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If N <= 1,               LWORK >= 1.
If JOBZ = 'N' and N > 1, LWORK >= 3*N.
If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK and IWORK
arrays, returns these values as the first entries of the WORK
and IWORK arrays, and no error message related to LWORK or
LIWORK is issued by XERBLA.

IWORK

IWORK is INTEGER array, dimension (MAX(1,LIWORK))
On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.

LIWORK

LIWORK is INTEGER
The dimension of the array IWORK.
If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK and
IWORK arrays, returns these values as the first entries of
the WORK and IWORK arrays, and no error message related to
LWORK or LIWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, and i is:
<= N:  the algorithm failed to converge:
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> N:   if INFO = N + i, for 1 <= i <= N, then SPBSTF
returned INFO = i: B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Contributors:

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 219 of file ssbgvd.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page ssbgvd(3) is an alias of ssbgvd.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK