SRC/sspgv.f(3)             Library Functions Manual             SRC/sspgv.f(3)

NAME
       SRC/sspgv.f

SYNOPSIS
   Functions/Subroutines
       subroutine sspgv (itype, jobz, uplo, n, ap, bp, w, z, ldz, work, info)
           SSPGV

Function/Subroutine Documentation
   subroutine sspgv (integer itype, character jobz, character uplo, integer n,
       real, dimension( * ) ap, real, dimension( * ) bp, real, dimension( * )
       w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work,
       integer info)
       SSPGV

       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
                               principal minor of order i of B is not positive.
                               The factorization of B could not be completed and
                               no eigenvalues or eigenvectors were computed.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 158 of file sspgv.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                  SRC/sspgv.f(3)