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ssygvx.f(3)				      LAPACK				      ssygvx.f(3)

       ssygvx.f -

       subroutine ssygvx (ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL, VU, IL, IU, ABSTOL, M,

Function/Subroutine Documentation
   subroutine ssygvx (integerITYPE, characterJOBZ, characterRANGE, characterUPLO, integerN, real,
       dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, realVL, realVU,
       integerIL, integerIU, realABSTOL, integerM, real, dimension( * )W, real, dimension( ldz, *
       )Z, integerLDZ, real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK,
       integer, dimension( * )IFAIL, integerINFO)


	    SSYGVX computes selected eigenvalues, and optionally, 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.
	    Eigenvalues and eigenvectors can be selected by specifying either a
	    range of values or a range of indices for the desired eigenvalues.


		     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 is CHARACTER*1
		     = 'N':  Compute eigenvalues only;
		     = 'V':  Compute eigenvalues and eigenvectors.


		     = 'A': all eigenvalues will be found.
		     = 'V': all eigenvalues in the half-open interval (VL,VU]
			    will be found.
		     = 'I': the IL-th through IU-th eigenvalues will be found.


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


		     N is INTEGER
		     The order of the matrix pencil (A,B).  N >= 0.


		     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, the lower triangle (if UPLO='L') or the upper
		     triangle (if UPLO='U') of A, including the diagonal, is


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


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


		     VL is REAL


		     VU is REAL
		     If RANGE='V', the lower and upper bounds of the interval to
		     be searched for eigenvalues. VL < VU.
		     Not referenced if RANGE = 'A' or 'I'.


		     IL is INTEGER


		     IU is INTEGER
		     If RANGE='I', the indices (in ascending order) of the
		     smallest and largest eigenvalues to be returned.
		     1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
		     Not referenced if RANGE = 'A' or 'V'.


		     ABSTOL is REAL
		     The absolute error tolerance for the eigenvalues.
		     An approximate eigenvalue is accepted as converged
		     when it is determined to lie in an interval [a,b]
		     of width less than or equal to

			     ABSTOL + EPS *   max( |a|,|b| ) ,

		     where EPS is the machine precision.  If ABSTOL is less than
		     or equal to zero, then  EPS*|T|  will be used in its place,
		     where |T| is the 1-norm of the tridiagonal matrix obtained
		     by reducing C to tridiagonal form, where C is the symmetric
		     matrix of the standard symmetric problem to which the
		     generalized problem is transformed.

		     Eigenvalues will be computed most accurately when ABSTOL is
		     set to twice the underflow threshold 2*DLAMCH('S'), not zero.
		     If this routine returns with INFO>0, indicating that some
		     eigenvectors did not converge, try setting ABSTOL to


		     M is INTEGER
		     The total number of eigenvalues found.  0 <= M <= N.
		     If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.


		     W is REAL array, dimension (N)
		     On normal exit, the first M elements contain the selected
		     eigenvalues in ascending order.


		     Z is REAL array, dimension (LDZ, max(1,M))
		     If JOBZ = 'N', then Z is not referenced.
		     If JOBZ = 'V', then if INFO = 0, the first M columns of Z
		     contain the orthonormal eigenvectors of the matrix A
		     corresponding to the selected eigenvalues, with the i-th
		     column of Z holding the eigenvector associated with W(i).
		     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 an eigenvector fails to converge, then that column of Z
		     contains the latest approximation to the eigenvector, and the
		     index of the eigenvector is returned in IFAIL.
		     Note: the user must ensure that at least max(1,M) columns are
		     supplied in the array Z; if RANGE = 'V', the exact value of M
		     is not known in advance and an upper bound must be used.


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


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


		     The length of the array WORK.  LWORK >= max(1,8*N).
		     For optimal efficiency, LWORK >= (NB+3)*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.


		     IWORK is INTEGER array, dimension (5*N)


		     IFAIL is INTEGER array, dimension (N)
		     If JOBZ = 'V', then if INFO = 0, the first M elements of
		     IFAIL are zero.  If INFO > 0, then IFAIL contains the
		     indices of the eigenvectors that failed to converge.
		     If JOBZ = 'N', then IFAIL is not referenced.


		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value
		     > 0:  SPOTRF or SSYEVX returned an error code:
			<= N:  if INFO = i, SSYEVX failed to converge;
			       i eigenvectors failed to converge.  Their indices
			       are stored in array IFAIL.
			> 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.

	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

	   November 2011

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

       Definition at line 289 of file ssygvx.f.

       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      ssygvx.f(3)
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