dsbev.f -

## SYNOPSIS

### Functions/Subroutines

subroutine dsbev (JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, INFO)
DSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

## Function/Subroutine Documentation

### subroutine dsbev (characterJOBZ, characterUPLO, integerN, integerKD, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )W, double precision, dimension( ldz, * )Z, integerLDZ, double precision, dimension( * )WORK, integerINFO)

DSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

``` DSBEV computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A.
```

Parameters:

JOBZ

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

UPLO

```          UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.
```

N

```          N is INTEGER
The order of the matrix A.  N >= 0.
```

KD

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

AB

```          AB is 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 = '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

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

W

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

Z

```          Z is DOUBLE PRECISION array, dimension (LDZ, N)
If JOBZ = 'V', 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 = '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 DOUBLE PRECISION array, dimension (max(1,3*N-2))
```

INFO

```          INFO is 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.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley