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CentOS 7.0 - man page for dstebz.f (centos section 3)

dstebz.f(3)				      LAPACK				      dstebz.f(3)

NAME
       dstebz.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dstebz (RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK,
	   ISPLIT, WORK, IWORK, INFO)
	   DSTEBZ

Function/Subroutine Documentation
   subroutine dstebz (characterRANGE, characterORDER, integerN, double precisionVL, double
       precisionVU, integerIL, integerIU, double precisionABSTOL, double precision, dimension( *
       )D, double precision, dimension( * )E, integerM, integerNSPLIT, double precision,
       dimension( * )W, integer, dimension( * )IBLOCK, integer, dimension( * )ISPLIT, double
       precision, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)
       DSTEBZ

       Purpose:

	    DSTEBZ 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, Computer Science Dept., Stanford
	    University, July 21, 1966.

       Parameters:
	   RANGE

		     RANGE is CHARACTER*1
		     = '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

		     ORDER is CHARACTER*1
		     = '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

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

	   VL

		     VL is DOUBLE PRECISION

	   VU

		     VU is DOUBLE PRECISION

		     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

		     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 DOUBLE PRECISION
		     The absolute tolerance for the eigenvalues.  An eigenvalue
		     (or cluster) is considered 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*DLAMCH('S'), not zero.

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		     The n diagonal elements of the tridiagonal matrix T.

	   E

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

	   M

		     M is INTEGER
		     The actual number of eigenvalues found. 0 <= M <= N.
		     (See also the description of INFO=2,3.)

	   NSPLIT

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

	   W

		     W is DOUBLE PRECISION array, dimension (N)
		     On exit, the first M elements of W will contain the
		     eigenvalues.  (DSTEBZ may use the remaining N-M elements as
		     workspace.)

	   IBLOCK

		     IBLOCK is 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.  (DSTEBZ may use the remaining N-M elements as
		     workspace.)

	   ISPLIT

		     ISPLIT is 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

		     WORK is DOUBLE PRECISION array, dimension (4*N)

	   IWORK

		     IWORK is INTEGER array, dimension (3*N)

	   INFO

		     INFO is 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 eigenvalues
				   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.

       Internal Parameters:

	     RELFAC  DOUBLE PRECISION, 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   DOUBLE PRECISION, 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 262 of file dstebz.f.

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

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


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