org.netlib.lapack
Class Sstebz
java.lang.Object
org.netlib.lapack.Sstebz
public class Sstebz
 extends java.lang.Object
Following is the description from the original
Fortran source. For each array argument, the Java
version will include an integer offset parameter, so
the arguments may not match the description exactly.
Contact seymour@cs.utk.edu with any questions.
* ..
*
* Purpose
* =======
*
* SSTEBZ computes the eigenvalues of a symmetric tridiagonal
* matrix T. The user may ask for all eigenvalues, all eigenvalues
* in the halfopen interval (VL, VU], or the ILth through IUth
* 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.
*
* Arguments
* =========
*
* RANGE (input) CHARACTER
* = 'A': ("All") all eigenvalues will be found.
* = 'V': ("Value") all eigenvalues in the halfopen interval
* (VL, VU] will be found.
* = 'I': ("Index") the ILth through IUth eigenvalues (of the
* entire matrix) will be found.
*
* ORDER (input) CHARACTER
* = 'B': ("By Block") the eigenvalues will be grouped by
* splitoff 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 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 1norm 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 (N1)
* The (n1) offdiagonal elements of the tridiagonal matrix T.
*
* M (output) INTEGER
* The actual number of eigenvalues found. 0 <= M <= N.
* (See also the description of INFO=2,3.)
*
* 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 NM 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 NM 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 NSPLITth consists of rows/columns
* ISPLIT(NSPLIT1)+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 ith 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+1IL
* Cause: nonmonotonic arithmetic, causing the
* Sturm sequence to be nonmonotonic.
* 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
* floatingpoint arithmetic.
* Cure: Increase the PARAMETER "FUDGE",
* recompile, and try again.
*
* Internal Parameters
* ===================
*
* RELFAC REAL, default = 2.0e0
* The relative tolerance. An interval (a,b] lies within
* "relative tolerance" if ba < 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.
*
* =====================================================================
*
* .. Parameters ..
Method Summary 
static void 
sstebz(java.lang.String range,
java.lang.String order,
int n,
float vl,
float vu,
int il,
int iu,
float abstol,
float[] d,
int _d_offset,
float[] e,
int _e_offset,
intW m,
intW nsplit,
float[] w,
int _w_offset,
int[] iblock,
int _iblock_offset,
int[] isplit,
int _isplit_offset,
float[] work,
int _work_offset,
int[] iwork,
int _iwork_offset,
intW info)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Sstebz
public Sstebz()
sstebz
public static void sstebz(java.lang.String range,
java.lang.String order,
int n,
float vl,
float vu,
int il,
int iu,
float abstol,
float[] d,
int _d_offset,
float[] e,
int _e_offset,
intW m,
intW nsplit,
float[] w,
int _w_offset,
int[] iblock,
int _iblock_offset,
int[] isplit,
int _isplit_offset,
float[] work,
int _work_offset,
int[] iwork,
int _iwork_offset,
intW info)