# SSPGV (3) - Linux Manuals

sspgv.f -

## SYNOPSIS

### Functions/Subroutines

subroutine sspgv (ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO)
SSPGST

## Function/Subroutine Documentation

### subroutine sspgv (integerITYPE, characterJOBZ, characterUPLO, integerN, real, dimension( * )AP, real, dimension( * )BP, real, dimension( * )W, real, dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integerINFO)

SSPGST

Purpose:

``` SSPGV 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.
```

Parameters:

ITYPE

```          ITYPE is 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

```          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.
```

AP

```          AP is REAL 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

```          BP is REAL 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

```          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.  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

```          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 (3*N)
```

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  SPPTRF or SSPEV returned an error code:
<= N:  if INFO = i, SSPEV 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.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley