SRC/ssygv.f(3)

NAME
SRC/ssygv.f

SYNOPSIS

  Functions/Subroutines
subroutine ssygv (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, info)
SSYGV

Function/Subroutine Documentation

  subroutine ssygv (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 info)

SSYGV

Purpose:

     SSYGV 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.

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 positive definite 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 length of the array WORK.  LWORK >= max(1,3*N-1).
              For optimal efficiency, LWORK >= (NB+2)*N,
              where NB is the blocksize for SSYTRD returned by ILAENV.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK 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 SSYEV returned an error code:
                 <= N:  if INFO = i, SSYEV 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 173 of file ssygv.f.

Author

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