NAME

       sspgvd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sspgvd (ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
           INFO)
           SSPGVD

Function/Subroutine Documentation

   subroutine sspgvd (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 LWORK, integer, dimension( * ) IWORK,
       integer LIWORK, integer INFO)
       SSPGVD

       Purpose:

            SSPGVD 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.
            If eigenvectors are desired, it uses a divide and conquer algorithm.

            The divide and conquer algorithm makes very mild assumptions about
            floating point arithmetic. It will work on machines with a guard
            digit in add/subtract, or on those binary machines without guard
            digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
            Cray-2. It could conceivably fail on hexadecimal or decimal machines
            without guard digits, but we know of none.

       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 (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the required LWORK.

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     If N <= 1,               LWORK >= 1.
                     If JOBZ = 'N' and N > 1, LWORK >= 2*N.
                     If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the required sizes of the WORK and IWORK
                     arrays, returns these values as the first entries of the WORK
                     and IWORK arrays, and no error message related to LWORK or
                     LIWORK is issued by XERBLA.

           IWORK

                     IWORK is INTEGER array, dimension (MAX(1,LIWORK))
                     On exit, if INFO = 0, IWORK(1) returns the required LIWORK.

           LIWORK

                     LIWORK is INTEGER
                     The dimension of the array IWORK.
                     If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
                     If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.

                     If LIWORK = -1, then a workspace query is assumed; the
                     routine only calculates the required sizes of the WORK and
                     IWORK arrays, returns these values as the first entries of
                     the WORK and IWORK arrays, and no error message related to
                     LWORK or LIWORK is issued by XERBLA.

           INFO

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

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2015

       Contributors:
           Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Author

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