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RedHat 9 (Linux i386) - man page for dsbevx (redhat section l)

DSBEVX(l)					)					DSBEVX(l)

NAME
       DSBEVX  -  compute  selected eigenvalues and, optionally, eigenvectors of a real symmetric
       band matrix A

SYNOPSIS
       SUBROUTINE DSBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL, VU, IL, IU, ABSTOL,  M,
			  W, Z, LDZ, WORK, IWORK, IFAIL, INFO )

	   CHARACTER	  JOBZ, RANGE, UPLO

	   INTEGER	  IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N

	   DOUBLE	  PRECISION ABSTOL, VL, VU

	   INTEGER	  IFAIL( * ), IWORK( * )

	   DOUBLE	  PRECISION AB( LDAB, * ), Q( LDQ, * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       DSBEVX  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.

ARGUMENTS
       JOBZ    (input) CHARACTER*1
	       = 'N':  Compute eigenvalues only;
	       = 'V':  Compute eigenvalues and eigenvectors.

       RANGE   (input) 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    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       KD      (input) INTEGER
	       The number of superdiagonals of the matrix A if UPLO = 'U', or the number of  sub-
	       diagonals if UPLO = 'L'.  KD >= 0.

       AB      (input/output) DOUBLE PRECISION 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 col-
	       umn  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    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KD + 1.

       Q       (output) DOUBLE PRECISION 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     (input) INTEGER
	       The leading dimension of the array Q.  If JOBZ = 'V', then LDQ >= max(1,N).

       VL      (input) DOUBLE PRECISION
	       VU      (input) DOUBLE PRECISION 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      (input) INTEGER
	       IU      (input) 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  (input) DOUBLE PRECISION
	       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*DLAMCH('S'), not zero.  If this routine returns with INFO>0,
	       indicating that	some  eigenvectors  did  not  converge,  try  setting  ABSTOL  to
	       2*DLAMCH('S').

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

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

       W       (output) DOUBLE PRECISION array, dimension (N)
	       The first M elements contain the selected eigenvalues in ascending order.

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

       WORK    (workspace) DOUBLE PRECISION array, dimension (7*N)

       IWORK   (workspace) INTEGER array, dimension (5*N)

       IFAIL   (output) 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    (output) 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.

LAPACK version 3.0			   15 June 2000 				DSBEVX(l)


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