ssygvd.f(3)

NAME
ssygvd.f

SYNOPSIS

  Functions/Subroutines
subroutine ssygvd (ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, IWORK, LIWORK, INFO)
SSYGVD

Function/Subroutine Documentation

  subroutine ssygvd (integer ITYPE, character JOBZ, character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( ldb, * ) B, integer LDB, real, dimension( * ) W, real, dimension( * ) WORK, integer LWORK, integer, dimension( * ) IWORK, integer LIWORK, integer INFO)

Purpose:

     SSYGVD 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 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.

    A

              A is REAL array, dimension (LDA, N)
              On entry, the symmetric matrix A.  If UPLO = 'U', the
              leading N-by-N upper triangular part of A contains the
              upper triangular part of the matrix A.  If UPLO = 'L',
              the leading N-by-N lower triangular part of A contains
              the lower triangular part of the matrix A.
              On exit, if JOBZ = 'V', then if INFO = 0, A 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 on exit the upper triangle (if UPLO='U')
              or the lower triangle (if UPLO='L') of A, including the
              diagonal, is destroyed.

    LDA

              LDA is INTEGER
              The leading dimension of the array A.  LDA >= max(1,N).

    B

              B is REAL array, dimension (LDB, N)
              On entry, the symmetric matrix B.  If UPLO = 'U', the
              leading N-by-N upper triangular part of B contains the
              upper triangular part of the matrix B.  If UPLO = 'L',
              the leading N-by-N lower triangular part of B contains
              the lower triangular part of the matrix B.
              On exit, if INFO <= N, the part of B containing the matrix is
              overwritten by the triangular factor U or L from the Cholesky
              factorization B = U**T*U or B = L*L**T.

    LDB

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).

    W

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

    WORK

              WORK is REAL array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal 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+1.
              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 optimal 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 optimal LIWORK.

    LIWORK

              LIWORK is INTEGER
              The dimension of the array IWORK.
              If N <= 1,                LIWORK >= 1.
              If JOBZ  = 'N' and 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 optimal 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:  SPOTRF or SSYEVD returned an error code:
                 <= N:  if INFO = i and JOBZ = 'N', then the algorithm
                        failed to converge; i off-diagonal elements of an
                        intermediate tridiagonal form did not converge to
                        zero;
                        if INFO = i and JOBZ = 'V', then the algorithm
                        failed to compute an eigenvalue while working on
                        the submatrix lying in rows and columns INFO/(N+1)
                        through mod(INFO,N+1);
                 > 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.

Further Details:

      Modified so that no backsubstitution is performed if SSYEVD fails to
      converge (NEIG in old code could be greater than N causing out of
      bounds reference to A - reported by Ralf Meyer).  Also corrected the
      description of INFO and the test on ITYPE. Sven, 16 Feb 05.

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

Definition at line 225 of file ssygvd.f.

Author

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