ssbgv (3) - Linux Man Pages

ssbgv.f -

SYNOPSIS

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine ssbgv (characterJOBZ, characterUPLO, integerN, integerKA, integerKB, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldbb, * )BB, integerLDBB, real, dimension( * )W, real, dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integerINFO)

SSBGST

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