Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  -  computes  all  the  eigenvalues  and,  optionally, the eigenvectors of a real
generalized   symmetric-definite   eigenproblem,    of    the    form    A*x=(lambda)*B*x,
A*Bx=(lambda)*x, or B*A*x=(lambda)*x

```

#### SYNOPSIS

```       SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO )

CHARACTER     JOBZ, UPLO

INTEGER       INFO, ITYPE, LDZ, N

DOUBLE        PRECISION AP( * ), BP( * ), W( * ), WORK( * ), Z( LDZ, * )

```

#### PURPOSE

```       DSPGV computes all the eigenvalues and, optionally, the eigenvectors of a real generalized
symmetric-definite eigenproblem,  of  the  form  A*x=(lambda)*B*x,   A*Bx=(lambda)*x,   or
B*A*x=(lambda)*x.
Here A and B are assumed to be symmetric, stored in packed format,
and B is also positive definite.

```

#### ARGUMENTS

```        ITYPE   (input) INTEGER
Specifies the problem type to be solved:
= 1:  A*x = (lambda)*B*x
= 2:  A*B*x = (lambda)*x
= 3:  B*A*x = (lambda)*x

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

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

N       (input) INTEGER
The order of the matrices A and B.  N >= 0.

AP      (input/output) DOUBLE PRECISION array, dimension
(N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array.  The j-th column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
On exit, the contents of AP are destroyed.

BP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
B, packed columnwise in a linear array.  The j-th column of B
is stored in the array BP as follows:
if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
On exit, the triangular factor U or L from the Cholesky
factorization B = U**T*U or B = L*L**T, in the same storage
format as B.

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

Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
eigenvectors.  The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.
If JOBZ = 'N', then Z is not referenced.

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

WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  DPPTRF or DSPEV returned an error code:
<= N:  if INFO = i, DSPEV 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 the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

LAPACK driver routine (version 3.3.1)      April 2011                             DSPGV(3lapack)
```