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SSTEBZ(l)					)					SSTEBZ(l)

       SSTEBZ - compute the eigenvalues of a symmetric tridiagonal matrix T





	   INTEGER	  IBLOCK( * ), ISPLIT( * ), IWORK( * )

	   REAL 	  D( * ), E( * ), W( * ), WORK( * )

       SSTEBZ computes the eigenvalues of a symmetric tridiagonal matrix T. The user may ask  for
       all  eigenvalues, all eigenvalues in the half-open interval (VL, VU], or the IL-th through
       IU-th eigenvalues.

       To avoid overflow, the matrix must be scaled so that its
       largest element is no greater than overflow**(1/2) *
       underflow**(1/4) in absolute value, and for greatest
       accuracy, it should not be much smaller than that.

       See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal Matrix", Report  CS41,  Com-
       puter Science Dept., Stanford
       University, July 21, 1966.

       RANGE   (input) CHARACTER
	       = 'A': ("All")	all eigenvalues will be found.
	       = 'V': ("Value") all eigenvalues in the half-open interval (VL, VU] will be found.
	       = 'I': ("Index") the IL-th through IU-th eigenvalues (of the entire  matrix)  will
	       be found.

       ORDER   (input) CHARACTER
	       =  'B':	("By  Block")  the  eigenvalues  will  be grouped by split-off block (see
	       IBLOCK, ISPLIT) and ordered from smallest to largest within  the  block.   =  'E':
	       ("Entire  matrix")  the	eigenvalues  for  the  entire matrix will be ordered from
	       smallest to largest.

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

       VL      (input) REAL
	       VU      (input) REAL If RANGE='V', the lower and upper bounds of the  interval  to
	       be  searched  for  eigenvalues.	 Eigenvalues less than or equal to VL, or greater
	       than VU, will not be returned.  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) REAL
	       The absolute tolerance for the eigenvalues.  An eigenvalue (or cluster) is consid-
	       ered  to be located if it has been determined to lie in an interval whose width is
	       ABSTOL or less.	If ABSTOL is less than or equal to zero,  then	ULP*|T|  will  be
	       used, where |T| means the 1-norm of T.

	       Eigenvalues  will  be  computed	most  accurately  when ABSTOL is set to twice the
	       underflow threshold 2*SLAMCH('S'), not zero.

       D       (input) REAL array, dimension (N)
	       The n diagonal elements of the tridiagonal matrix T.

       E       (input) REAL array, dimension (N-1)
	       The (n-1) off-diagonal elements of the tridiagonal matrix T.

       M       (output) INTEGER
	       The actual number of eigenvalues found. 0 <= M <= N.  (See also the description of

       NSPLIT  (output) INTEGER
	       The number of diagonal blocks in the matrix T.  1 <= NSPLIT <= N.

       W       (output) REAL array, dimension (N)
	       On  exit, the first M elements of W will contain the eigenvalues.  (SSTEBZ may use
	       the remaining N-M elements as workspace.)

       IBLOCK  (output) INTEGER array, dimension (N)
	       At each row/column j where E(j) is zero or small, the matrix T  is  considered  to
	       split  into a block diagonal matrix.  On exit, if INFO = 0, IBLOCK(i) specifies to
	       which block (from 1 to the number of blocks) the eigenvalue W(i) belongs.  (SSTEBZ
	       may use the remaining N-M elements as workspace.)

       ISPLIT  (output) INTEGER array, dimension (N)
	       The  splitting points, at which T breaks up into submatrices.  The first submatrix
	       consists of rows/columns 1 to ISPLIT(1), the second  of	rows/columns  ISPLIT(1)+1
	       through	 ISPLIT(2),   etc.,   and   the   NSPLIT-th   consists	 of  rows/columns
	       ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.  (Only the first NSPLIT elements will
	       actually  be  used, but since the user cannot know a priori what value NSPLIT will
	       have, N words must be reserved for ISPLIT.)

       WORK    (workspace) REAL array, dimension (4*N)

       IWORK   (workspace) INTEGER array, dimension (3*N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       > 0:  some or all of the eigenvalues failed to converge or
	       were not computed:
	       =1 or 3: Bisection failed to converge for some eigenvalues; these eigenvalues  are
	       flagged by a negative block number.  The effect is that the eigenvalues may not be
	       as accurate as the absolute and relative tolerances.  This is generally caused  by
	       unexpectedly  inaccurate  arithmetic.  =2 or 3: RANGE='I' only: Not all of the ei-
	       IL:IU were found.
	       Effect: M < IU+1-IL
	       Cause:  non-monotonic arithmetic, causing the Sturm sequence to be  non-monotonic.
	       Cure:   recalculate, using RANGE='A', and pick
	       out  eigenvalues  IL:IU.  In some cases, increasing the PARAMETER "FUDGE" may make
	       things work.  = 4:    RANGE='I', and the Gershgorin interval  initially	used  was
	       too small.  No eigenvalues were computed.  Probable cause: your machine has sloppy
	       floating-point arithmetic.  Cure: Increase the PARAMETER "FUDGE",  recompile,  and
	       try again.

       RELFAC  REAL, default = 2.0e0
	       The relative tolerance.	An interval (a,b] lies within "relative tolerance" if  b-
	       a < RELFAC*ulp*max(|a|,|b|), where "ulp" is the machine precision (distance from 1
	       to the next larger floating point number.)

       FUDGE   REAL, default = 2
	       A  "fudge factor" to widen the Gershgorin intervals.  Ideally, a value of 1 should
	       work, but on machines with sloppy  arithmetic,  this  needs  to	be  larger.   The
	       default	for publicly released versions should be large enough to handle the worst
	       machine around.	Note that this has no effect on accuracy of the solution.

LAPACK version 3.0			   15 June 2000 				SSTEBZ(l)
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