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ssbgvx.f(3)				      LAPACK				      ssbgvx.f(3)

NAME
       ssbgvx.f -

SYNOPSIS
   Functions/Subroutines
       subroutine ssbgvx (JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ, VL, VU, IL,
	   IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO)
	   SSBGST

Function/Subroutine Documentation
   subroutine ssbgvx (characterJOBZ, characterRANGE, characterUPLO, integerN, integerKA,
       integerKB, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldbb, * )BB,
       integerLDBB, 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)
       SSBGST

       Purpose:

	    SSBGVX computes selected eigenvalues, and optionally, eigenvectors
	    of a real generalized symmetric-definite banded eigenproblem, of
	    the form A*x=(lambda)*B*x.	Here A and B are assumed to be symmetric
	    and banded, and B is also positive definite.  Eigenvalues and
	    eigenvectors can be selected by specifying either all eigenvalues,
	    a range of values or a range of indices for the desired eigenvalues.

       Parameters:
	   JOBZ

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

	   RANGE

		     RANGE is CHARACTER*1
		     = '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

		     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.

	   KA

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

	   KB

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

	   AB

		     AB is REAL array, dimension (LDAB, N)
		     On entry, the upper or lower triangle of the symmetric band
		     matrix A, stored in the first ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
		     if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).

		     On exit, the contents of AB are destroyed.

	   LDAB

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

	   BB

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

		     On exit, the factor S from the split Cholesky factorization
		     B = S**T*S, as returned by SPBSTF.

	   LDBB

		     LDBB is INTEGER
		     The leading dimension of the array BB.  LDBB >= KB+1.

	   Q

		     Q is REAL array, dimension (LDQ, N)
		     If JOBZ = 'V', the n-by-n matrix used in the reduction of
		     A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x,
		     and consequently C to tridiagonal form.
		     If JOBZ = 'N', the array Q is not referenced.

	   LDQ

		     LDQ is INTEGER
		     The leading dimension of the array Q.  If JOBZ = 'N',
		     LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).

	   VL

		     VL is REAL

	   VU

		     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

		     IL is INTEGER

	   IU

		     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

		     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 A 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
		     2*SLAMCH('S').

	   M

		     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

		     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, with the i-th column of Z holding the
		     eigenvector associated with W(i).	The eigenvectors are
		     normalized so Z**T*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 (7N)

	   IWORK

		     IWORK is INTEGER array, dimension (5N)

	   IFAIL

		     IFAIL is INTEGER array, dimension (M)
		     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 eigenvalues that failed to converge.
		     If JOBZ = 'N', then IFAIL is not referenced.

	   INFO

		     INFO is INTEGER
		     = 0 : successful exit
		     < 0 : if INFO = -i, the i-th argument had an illegal value
		     <= N: if INFO = i, then i eigenvectors failed to converge.
			     Their indices are stored in IFAIL.
		     > N : SPBSTF returned an error code; i.e.,
			   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 2011

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

       Definition at line 284 of file ssbgvx.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

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