SSPGV(3)       LAPACK routine of NEC Numeric Library Collection       SSPGV(3)



NAME
       SSPGV

SYNOPSIS
       SUBROUTINE SSPGV (ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO)



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.




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

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

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

           AP        (input/output)
                     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        (input/output)
                     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         (output)
                     W is REAL array, dimension (N)
                     If INFO = 0, the eigenvalues in ascending order.

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

           WORK      (output)
                     WORK is REAL array, dimension (3*N)

           INFO      (output)
                     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.



LAPACK routine                  31 October 2017                       SSPGV(3)