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ssbevx.f(3)				      LAPACK				      ssbevx.f(3)

       ssbevx.f -

       subroutine ssbevx (JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M,
	    SSBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors
	   for OTHER matrices

Function/Subroutine Documentation
   subroutine ssbevx (characterJOBZ, characterRANGE, characterUPLO, integerN, integerKD, real,
       dimension( ldab, * )AB, integerLDAB, real, dimension( ldq, * )Q, integerLDQ, realVL,
       realVU, integerIL, integerIU, realABSTOL, integerM, real, dimension( * )W, real,
       dimension( ldz, * )Z, integerLDZ, real, dimension( * )WORK, integer, dimension( * )IWORK,
       integer, dimension( * )IFAIL, integerINFO)
	SSBEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for
       OTHER matrices


	    SSBEVX computes selected eigenvalues and, optionally, eigenvectors
	    of a real symmetric band matrix A.	Eigenvalues and eigenvectors can
	    be selected by specifying either a range of values or a range of
	    indices for the desired eigenvalues.


		     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 is stored;
		     = 'L':  Lower triangle of A is stored.


		     N is INTEGER
		     The order of the matrix A.  N >= 0.


		     KD is INTEGER
		     The number of superdiagonals of the matrix A if UPLO = 'U',
		     or the number of subdiagonals if UPLO = 'L'.  KD >= 0.


		     AB is REAL array, dimension (LDAB, N)
		     On entry, the upper or lower triangle of the symmetric band
		     matrix A, stored in the first KD+1 rows of the array.  The
		     j-th column of A is stored in the j-th column of the array AB
		     as follows:
		     if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
		     if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

		     On exit, AB is overwritten by values generated during the
		     reduction to tridiagonal form.  If UPLO = 'U', the first
		     superdiagonal and the diagonal of the tridiagonal matrix T
		     are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
		     the diagonal and first subdiagonal of T are returned in the
		     first two rows of AB.


		     LDAB is INTEGER
		     The leading dimension of the array AB.  LDAB >= KD + 1.


		     Q is REAL array, dimension (LDQ, N)
		     If JOBZ = 'V', the N-by-N orthogonal matrix used in the
				    reduction to tridiagonal form.
		     If JOBZ = 'N', the array Q is not referenced.


		     LDQ is INTEGER
		     The leading dimension of the array Q.  If JOBZ = 'V', then
		     LDQ >= 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 AB to tridiagonal form.

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

		     See "Computing Small Singular Values of Bidiagonal Matrices
		     with Guaranteed High Relative Accuracy," by Demmel and
		     Kahan, LAPACK Working Note #3.


		     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)
		     The first M elements contain the selected eigenvalues in
		     ascending order.


		     Z is REAL array, dimension (LDZ, max(1,M))
		     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).
		     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.
		     If JOBZ = 'N', then Z is not referenced.
		     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 (7*N)


		     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:  if INFO = i, then i eigenvectors failed to converge.
			   Their indices are stored in array IFAIL.

	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

	   November 2011

       Definition at line 257 of file ssbevx.f.

       Generated automatically by Doxygen for LAPACK from the source code.

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