dspgv(3)

NAME

DSPGV - compute all the eigenvalues and, optionally, the

eigenvectors of a real generalized symmetric-definite eigenprob

lem, 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 eigenprob

lem, 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 UP

LO = '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 sym

metric 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 ille

gal 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 version 3.0 15 June 2000

DSPGV(3)