Provided by: liblapack-doc_3.3.1-1_all bug

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)