# ssbgv.f man page

ssbgv.f

## Synopsis

### Functions/Subroutines

subroutine ssbgv (JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, INFO)
SSBGV

## Function/Subroutine Documentation

### subroutine ssbgv (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 INFO)

SSBGV

Purpose:

``` SSBGV 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.```
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(kb+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 that 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 >= N.```

WORK

`          WORK is REAL array, dimension (3*N)`

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.

Date:

December 2016

Definition at line 179 of file ssbgv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK