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/* sstebz.f -- translated by f2c (version 20061008).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "clapack.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static integer c_n1 = -1;
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static integer c__3 = 3;
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static integer c__2 = 2;
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static integer c__0 = 0;
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/* Subroutine */ int sstebz_(char *range, char *order, integer *n, real *vl,
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real *vu, integer *il, integer *iu, real *abstol, real *d__, real *e,
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integer *m, integer *nsplit, real *w, integer *iblock, integer *
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isplit, real *work, integer *iwork, integer *info)
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{
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/* System generated locals */
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integer i__1, i__2, i__3;
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real r__1, r__2, r__3, r__4, r__5;
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/* Builtin functions */
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double sqrt(doublereal), log(doublereal);
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/* Local variables */
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integer j, ib, jb, ie, je, nb;
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real gl;
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integer im, in;
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real gu;
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integer iw;
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real wl, wu;
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integer nwl;
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real ulp, wlu, wul;
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integer nwu;
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real tmp1, tmp2;
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integer iend, ioff, iout, itmp1, jdisc;
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extern logical lsame_(char *, char *);
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integer iinfo;
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real atoli;
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integer iwoff;
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real bnorm;
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integer itmax;
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real wkill, rtoli, tnorm;
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integer ibegin, irange, idiscl;
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extern doublereal slamch_(char *);
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real safemn;
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integer idumma[1];
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extern /* Subroutine */ int xerbla_(char *, integer *);
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *);
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integer idiscu;
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extern /* Subroutine */ int slaebz_(integer *, integer *, integer *,
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integer *, integer *, integer *, real *, real *, real *, real *,
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real *, real *, integer *, real *, real *, integer *, integer *,
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real *, integer *, integer *);
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integer iorder;
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logical ncnvrg;
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real pivmin;
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logical toofew;
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/* -- LAPACK routine (version 3.2) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* 8-18-00: Increase FUDGE factor for T3E (eca) */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* SSTEBZ computes the eigenvalues of a symmetric tridiagonal */
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/* matrix T. The user may ask for all eigenvalues, all eigenvalues */
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/* in the half-open interval (VL, VU], or the IL-th through IU-th */
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/* eigenvalues. */
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/* To avoid overflow, the matrix must be scaled so that its */
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/* largest element is no greater than overflow**(1/2) * */
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/* underflow**(1/4) in absolute value, and for greatest */
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/* accuracy, it should not be much smaller than that. */
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/* See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal */
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/* Matrix", Report CS41, Computer Science Dept., Stanford */
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/* University, July 21, 1966. */
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/* Arguments */
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/* ========= */
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/* RANGE (input) CHARACTER*1 */
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/* = 'A': ("All") all eigenvalues will be found. */
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/* = 'V': ("Value") all eigenvalues in the half-open interval */
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/* (VL, VU] will be found. */
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/* = 'I': ("Index") the IL-th through IU-th eigenvalues (of the */
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/* entire matrix) will be found. */
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/* ORDER (input) CHARACTER*1 */
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/* = 'B': ("By Block") the eigenvalues will be grouped by */
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/* split-off block (see IBLOCK, ISPLIT) and */
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/* ordered from smallest to largest within */
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/* the block. */
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/* = 'E': ("Entire matrix") */
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/* the eigenvalues for the entire matrix */
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/* will be ordered from smallest to */
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/* largest. */
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/* N (input) INTEGER */
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/* The order of the tridiagonal matrix T. N >= 0. */
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/* VL (input) REAL */
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/* VU (input) REAL */
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/* If RANGE='V', the lower and upper bounds of the interval to */
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/* be searched for eigenvalues. Eigenvalues less than or equal */
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/* to VL, or greater than VU, will not be returned. VL < VU. */
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/* Not referenced if RANGE = 'A' or 'I'. */
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/* IL (input) INTEGER */
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/* IU (input) INTEGER */
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/* If RANGE='I', the indices (in ascending order) of the */
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/* smallest and largest eigenvalues to be returned. */
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/* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. */
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/* Not referenced if RANGE = 'A' or 'V'. */
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/* ABSTOL (input) REAL */
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/* The absolute tolerance for the eigenvalues. An eigenvalue */
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/* (or cluster) is considered to be located if it has been */
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/* determined to lie in an interval whose width is ABSTOL or */
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/* less. If ABSTOL is less than or equal to zero, then ULP*|T| */
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/* will be used, where |T| means the 1-norm of T. */
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/* Eigenvalues will be computed most accurately when ABSTOL is */
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/* set to twice the underflow threshold 2*SLAMCH('S'), not zero. */
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/* D (input) REAL array, dimension (N) */
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/* The n diagonal elements of the tridiagonal matrix T. */
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/* E (input) REAL array, dimension (N-1) */
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/* The (n-1) off-diagonal elements of the tridiagonal matrix T. */
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/* M (output) INTEGER */
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/* The actual number of eigenvalues found. 0 <= M <= N. */
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/* (See also the description of INFO=2,3.) */
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/* NSPLIT (output) INTEGER */
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/* The number of diagonal blocks in the matrix T. */
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/* 1 <= NSPLIT <= N. */
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/* W (output) REAL array, dimension (N) */
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/* On exit, the first M elements of W will contain the */
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/* eigenvalues. (SSTEBZ may use the remaining N-M elements as */
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/* workspace.) */
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/* IBLOCK (output) INTEGER array, dimension (N) */
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/* At each row/column j where E(j) is zero or small, the */
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/* matrix T is considered to split into a block diagonal */
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/* matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which */
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/* block (from 1 to the number of blocks) the eigenvalue W(i) */
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/* belongs. (SSTEBZ may use the remaining N-M elements as */
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/* workspace.) */
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/* ISPLIT (output) INTEGER array, dimension (N) */
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/* The splitting points, at which T breaks up into submatrices. */
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/* The first submatrix consists of rows/columns 1 to ISPLIT(1), */
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/* the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), */
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/* etc., and the NSPLIT-th consists of rows/columns */
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/* ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. */
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/* (Only the first NSPLIT elements will actually be used, but */
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/* since the user cannot know a priori what value NSPLIT will */
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/* have, N words must be reserved for ISPLIT.) */
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/* WORK (workspace) REAL array, dimension (4*N) */
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/* IWORK (workspace) INTEGER array, dimension (3*N) */
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/* INFO (output) INTEGER */
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/* = 0: successful exit */
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/* < 0: if INFO = -i, the i-th argument had an illegal value */
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/* > 0: some or all of the eigenvalues failed to converge or */
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/* were not computed: */
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/* =1 or 3: Bisection failed to converge for some */
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/* eigenvalues; these eigenvalues are flagged by a */
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/* negative block number. The effect is that the */
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/* eigenvalues may not be as accurate as the */
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/* absolute and relative tolerances. This is */
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/* generally caused by unexpectedly inaccurate */
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/* arithmetic. */
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/* =2 or 3: RANGE='I' only: Not all of the eigenvalues */
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/* IL:IU were found. */
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/* Effect: M < IU+1-IL */
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/* Cause: non-monotonic arithmetic, causing the */
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/* Sturm sequence to be non-monotonic. */
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/* Cure: recalculate, using RANGE='A', and pick */
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/* out eigenvalues IL:IU. In some cases, */
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/* increasing the PARAMETER "FUDGE" may */
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/* make things work. */
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/* = 4: RANGE='I', and the Gershgorin interval */
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/* initially used was too small. No eigenvalues */
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/* were computed. */
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/* Probable cause: your machine has sloppy */
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/* floating-point arithmetic. */
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/* Cure: Increase the PARAMETER "FUDGE", */
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/* recompile, and try again. */
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/* Internal Parameters */
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/* =================== */
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/* RELFAC REAL, default = 2.0e0 */
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/* The relative tolerance. An interval (a,b] lies within */
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/* "relative tolerance" if b-a < RELFAC*ulp*max(|a|,|b|), */
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/* where "ulp" is the machine precision (distance from 1 to */
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/* the next larger floating point number.) */
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/* FUDGE REAL, default = 2 */
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/* A "fudge factor" to widen the Gershgorin intervals. Ideally, */
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/* a value of 1 should work, but on machines with sloppy */
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/* arithmetic, this needs to be larger. The default for */
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/* publicly released versions should be large enough to handle */
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/* the worst machine around. Note that this has no effect */
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/* on accuracy of the solution. */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. Local Arrays .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Parameter adjustments */
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--iwork;
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--work;
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--isplit;
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--iblock;
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--w;
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--e;
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--d__;
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/* Function Body */
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*info = 0;
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/* Decode RANGE */
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if (lsame_(range, "A")) {
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irange = 1;
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} else if (lsame_(range, "V")) {
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irange = 2;
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} else if (lsame_(range, "I")) {
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irange = 3;
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} else {
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irange = 0;
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}
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/* Decode ORDER */
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if (lsame_(order, "B")) {
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iorder = 2;
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} else if (lsame_(order, "E")) {
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iorder = 1;
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} else {
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iorder = 0;
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}
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/* Check for Errors */
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if (irange <= 0) {
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*info = -1;
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} else if (iorder <= 0) {
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*info = -2;
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} else if (*n < 0) {
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*info = -3;
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} else if (irange == 2) {
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if (*vl >= *vu) {
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*info = -5;
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}
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} else if (irange == 3 && (*il < 1 || *il > max(1,*n))) {
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*info = -6;
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} else if (irange == 3 && (*iu < min(*n,*il) || *iu > *n)) {
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*info = -7;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("SSTEBZ", &i__1);
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return 0;
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}
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/* Initialize error flags */
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*info = 0;
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ncnvrg = FALSE_;
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toofew = FALSE_;
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/* Quick return if possible */
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*m = 0;
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if (*n == 0) {
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return 0;
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}
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/* Simplifications: */
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if (irange == 3 && *il == 1 && *iu == *n) {
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irange = 1;
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}
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/* Get machine constants */
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/* NB is the minimum vector length for vector bisection, or 0 */
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/* if only scalar is to be done. */
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safemn = slamch_("S");
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ulp = slamch_("P");
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rtoli = ulp * 2.f;
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nb = ilaenv_(&c__1, "SSTEBZ", " ", n, &c_n1, &c_n1, &c_n1);
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if (nb <= 1) {
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nb = 0;
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}
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/* Special Case when N=1 */
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if (*n == 1) {
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*nsplit = 1;
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isplit[1] = 1;
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if (irange == 2 && (*vl >= d__[1] || *vu < d__[1])) {
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*m = 0;
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} else {
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w[1] = d__[1];
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iblock[1] = 1;
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*m = 1;
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}
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return 0;
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}
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/* Compute Splitting Points */
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*nsplit = 1;
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work[*n] = 0.f;
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pivmin = 1.f;
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/* DIR$ NOVECTOR */
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i__1 = *n;
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for (j = 2; j <= i__1; ++j) {
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|
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/* Computing 2nd power */
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r__1 = e[j - 1];
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tmp1 = r__1 * r__1;
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|
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/* Computing 2nd power */
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r__2 = ulp;
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|
|
if ((r__1 = d__[j] * d__[j - 1], dabs(r__1)) * (r__2 * r__2) + safemn
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> tmp1) {
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|
|
|
isplit[*nsplit] = j - 1;
|
|
|
|
++(*nsplit);
|
|
|
|
work[j - 1] = 0.f;
|
|
|
|
} else {
|
|
|
|
work[j - 1] = tmp1;
|
|
|
|
pivmin = dmax(pivmin,tmp1);
|
|
|
|
}
|
|
|
|
/* L10: */
|
|
|
|
}
|
|
|
|
isplit[*nsplit] = *n;
|
|
|
|
pivmin *= safemn;
|
|
|
|
|
|
|
|
/* Compute Interval and ATOLI */
|
|
|
|
|
|
|
|
if (irange == 3) {
|
|
|
|
|
|
|
|
/* RANGE='I': Compute the interval containing eigenvalues */
|
|
|
|
/* IL through IU. */
|
|
|
|
|
|
|
|
/* Compute Gershgorin interval for entire (split) matrix */
|
|
|
|
/* and use it as the initial interval */
|
|
|
|
|
|
|
|
gu = d__[1];
|
|
|
|
gl = d__[1];
|
|
|
|
tmp1 = 0.f;
|
|
|
|
|
|
|
|
i__1 = *n - 1;
|
|
|
|
for (j = 1; j <= i__1; ++j) {
|
|
|
|
tmp2 = sqrt(work[j]);
|
|
|
|
/* Computing MAX */
|
|
|
|
r__1 = gu, r__2 = d__[j] + tmp1 + tmp2;
|
|
|
|
gu = dmax(r__1,r__2);
|
|
|
|
/* Computing MIN */
|
|
|
|
r__1 = gl, r__2 = d__[j] - tmp1 - tmp2;
|
|
|
|
gl = dmin(r__1,r__2);
|
|
|
|
tmp1 = tmp2;
|
|
|
|
/* L20: */
|
|
|
|
}
|
|
|
|
|
|
|
|
/* Computing MAX */
|
|
|
|
r__1 = gu, r__2 = d__[*n] + tmp1;
|
|
|
|
gu = dmax(r__1,r__2);
|
|
|
|
/* Computing MIN */
|
|
|
|
r__1 = gl, r__2 = d__[*n] - tmp1;
|
|
|
|
gl = dmin(r__1,r__2);
|
|
|
|
/* Computing MAX */
|
|
|
|
r__1 = dabs(gl), r__2 = dabs(gu);
|
|
|
|
tnorm = dmax(r__1,r__2);
|
|
|
|
gl = gl - tnorm * 2.1f * ulp * *n - pivmin * 4.2000000000000002f;
|
|
|
|
gu = gu + tnorm * 2.1f * ulp * *n + pivmin * 2.1f;
|
|
|
|
|
|
|
|
/* Compute Iteration parameters */
|
|
|
|
|
|
|
|
itmax = (integer) ((log(tnorm + pivmin) - log(pivmin)) / log(2.f)) +
|
|
|
|
2;
|
|
|
|
if (*abstol <= 0.f) {
|
|
|
|
atoli = ulp * tnorm;
|
|
|
|
} else {
|
|
|
|
atoli = *abstol;
|
|
|
|
}
|
|
|
|
|
|
|
|
work[*n + 1] = gl;
|
|
|
|
work[*n + 2] = gl;
|
|
|
|
work[*n + 3] = gu;
|
|
|
|
work[*n + 4] = gu;
|
|
|
|
work[*n + 5] = gl;
|
|
|
|
work[*n + 6] = gu;
|
|
|
|
iwork[1] = -1;
|
|
|
|
iwork[2] = -1;
|
|
|
|
iwork[3] = *n + 1;
|
|
|
|
iwork[4] = *n + 1;
|
|
|
|
iwork[5] = *il - 1;
|
|
|
|
iwork[6] = *iu;
|
|
|
|
|
|
|
|
slaebz_(&c__3, &itmax, n, &c__2, &c__2, &nb, &atoli, &rtoli, &pivmin,
|
|
|
|
&d__[1], &e[1], &work[1], &iwork[5], &work[*n + 1], &work[*n
|
|
|
|
+ 5], &iout, &iwork[1], &w[1], &iblock[1], &iinfo);
|
|
|
|
|
|
|
|
if (iwork[6] == *iu) {
|
|
|
|
wl = work[*n + 1];
|
|
|
|
wlu = work[*n + 3];
|
|
|
|
nwl = iwork[1];
|
|
|
|
wu = work[*n + 4];
|
|
|
|
wul = work[*n + 2];
|
|
|
|
nwu = iwork[4];
|
|
|
|
} else {
|
|
|
|
wl = work[*n + 2];
|
|
|
|
wlu = work[*n + 4];
|
|
|
|
nwl = iwork[2];
|
|
|
|
wu = work[*n + 3];
|
|
|
|
wul = work[*n + 1];
|
|
|
|
nwu = iwork[3];
|
|
|
|
}
|
|
|
|
|
|
|
|
if (nwl < 0 || nwl >= *n || nwu < 1 || nwu > *n) {
|
|
|
|
*info = 4;
|
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
|
|
|
|
/* RANGE='A' or 'V' -- Set ATOLI */
|
|
|
|
|
|
|
|
/* Computing MAX */
|
|
|
|
r__3 = dabs(d__[1]) + dabs(e[1]), r__4 = (r__1 = d__[*n], dabs(r__1))
|
|
|
|
+ (r__2 = e[*n - 1], dabs(r__2));
|
|
|
|
tnorm = dmax(r__3,r__4);
|
|
|
|
|
|
|
|
i__1 = *n - 1;
|
|
|
|
for (j = 2; j <= i__1; ++j) {
|
|
|
|
/* Computing MAX */
|
|
|
|
r__4 = tnorm, r__5 = (r__1 = d__[j], dabs(r__1)) + (r__2 = e[j -
|
|
|
|
1], dabs(r__2)) + (r__3 = e[j], dabs(r__3));
|
|
|
|
tnorm = dmax(r__4,r__5);
|
|
|
|
/* L30: */
|
|
|
|
}
|
|
|
|
|
|
|
|
if (*abstol <= 0.f) {
|
|
|
|
atoli = ulp * tnorm;
|
|
|
|
} else {
|
|
|
|
atoli = *abstol;
|
|
|
|
}
|
|
|
|
|
|
|
|
if (irange == 2) {
|
|
|
|
wl = *vl;
|
|
|
|
wu = *vu;
|
|
|
|
} else {
|
|
|
|
wl = 0.f;
|
|
|
|
wu = 0.f;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
/* Find Eigenvalues -- Loop Over Blocks and recompute NWL and NWU. */
|
|
|
|
/* NWL accumulates the number of eigenvalues .le. WL, */
|
|
|
|
/* NWU accumulates the number of eigenvalues .le. WU */
|
|
|
|
|
|
|
|
*m = 0;
|
|
|
|
iend = 0;
|
|
|
|
*info = 0;
|
|
|
|
nwl = 0;
|
|
|
|
nwu = 0;
|
|
|
|
|
|
|
|
i__1 = *nsplit;
|
|
|
|
for (jb = 1; jb <= i__1; ++jb) {
|
|
|
|
ioff = iend;
|
|
|
|
ibegin = ioff + 1;
|
|
|
|
iend = isplit[jb];
|
|
|
|
in = iend - ioff;
|
|
|
|
|
|
|
|
if (in == 1) {
|
|
|
|
|
|
|
|
/* Special Case -- IN=1 */
|
|
|
|
|
|
|
|
if (irange == 1 || wl >= d__[ibegin] - pivmin) {
|
|
|
|
++nwl;
|
|
|
|
}
|
|
|
|
if (irange == 1 || wu >= d__[ibegin] - pivmin) {
|
|
|
|
++nwu;
|
|
|
|
}
|
|
|
|
if (irange == 1 || wl < d__[ibegin] - pivmin && wu >= d__[ibegin]
|
|
|
|
- pivmin) {
|
|
|
|
++(*m);
|
|
|
|
w[*m] = d__[ibegin];
|
|
|
|
iblock[*m] = jb;
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
|
|
|
|
/* General Case -- IN > 1 */
|
|
|
|
|
|
|
|
/* Compute Gershgorin Interval */
|
|
|
|
/* and use it as the initial interval */
|
|
|
|
|
|
|
|
gu = d__[ibegin];
|
|
|
|
gl = d__[ibegin];
|
|
|
|
tmp1 = 0.f;
|
|
|
|
|
|
|
|
i__2 = iend - 1;
|
|
|
|
for (j = ibegin; j <= i__2; ++j) {
|
|
|
|
tmp2 = (r__1 = e[j], dabs(r__1));
|
|
|
|
/* Computing MAX */
|
|
|
|
r__1 = gu, r__2 = d__[j] + tmp1 + tmp2;
|
|
|
|
gu = dmax(r__1,r__2);
|
|
|
|
/* Computing MIN */
|
|
|
|
r__1 = gl, r__2 = d__[j] - tmp1 - tmp2;
|
|
|
|
gl = dmin(r__1,r__2);
|
|
|
|
tmp1 = tmp2;
|
|
|
|
/* L40: */
|
|
|
|
}
|
|
|
|
|
|
|
|
/* Computing MAX */
|
|
|
|
r__1 = gu, r__2 = d__[iend] + tmp1;
|
|
|
|
gu = dmax(r__1,r__2);
|
|
|
|
/* Computing MIN */
|
|
|
|
r__1 = gl, r__2 = d__[iend] - tmp1;
|
|
|
|
gl = dmin(r__1,r__2);
|
|
|
|
/* Computing MAX */
|
|
|
|
r__1 = dabs(gl), r__2 = dabs(gu);
|
|
|
|
bnorm = dmax(r__1,r__2);
|
|
|
|
gl = gl - bnorm * 2.1f * ulp * in - pivmin * 2.1f;
|
|
|
|
gu = gu + bnorm * 2.1f * ulp * in + pivmin * 2.1f;
|
|
|
|
|
|
|
|
/* Compute ATOLI for the current submatrix */
|
|
|
|
|
|
|
|
if (*abstol <= 0.f) {
|
|
|
|
/* Computing MAX */
|
|
|
|
r__1 = dabs(gl), r__2 = dabs(gu);
|
|
|
|
atoli = ulp * dmax(r__1,r__2);
|
|
|
|
} else {
|
|
|
|
atoli = *abstol;
|
|
|
|
}
|
|
|
|
|
|
|
|
if (irange > 1) {
|
|
|
|
if (gu < wl) {
|
|
|
|
nwl += in;
|
|
|
|
nwu += in;
|
|
|
|
goto L70;
|
|
|
|
}
|
|
|
|
gl = dmax(gl,wl);
|
|
|
|
gu = dmin(gu,wu);
|
|
|
|
if (gl >= gu) {
|
|
|
|
goto L70;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
/* Set Up Initial Interval */
|
|
|
|
|
|
|
|
work[*n + 1] = gl;
|
|
|
|
work[*n + in + 1] = gu;
|
|
|
|
slaebz_(&c__1, &c__0, &in, &in, &c__1, &nb, &atoli, &rtoli, &
|
|
|
|
pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
|
|
|
|
work[*n + 1], &work[*n + (in << 1) + 1], &im, &iwork[1], &
|
|
|
|
w[*m + 1], &iblock[*m + 1], &iinfo);
|
|
|
|
|
|
|
|
nwl += iwork[1];
|
|
|
|
nwu += iwork[in + 1];
|
|
|
|
iwoff = *m - iwork[1];
|
|
|
|
|
|
|
|
/* Compute Eigenvalues */
|
|
|
|
|
|
|
|
itmax = (integer) ((log(gu - gl + pivmin) - log(pivmin)) / log(
|
|
|
|
2.f)) + 2;
|
|
|
|
slaebz_(&c__2, &itmax, &in, &in, &c__1, &nb, &atoli, &rtoli, &
|
|
|
|
pivmin, &d__[ibegin], &e[ibegin], &work[ibegin], idumma, &
|
|
|
|
work[*n + 1], &work[*n + (in << 1) + 1], &iout, &iwork[1],
|
|
|
|
&w[*m + 1], &iblock[*m + 1], &iinfo);
|
|
|
|
|
|
|
|
/* Copy Eigenvalues Into W and IBLOCK */
|
|
|
|
/* Use -JB for block number for unconverged eigenvalues. */
|
|
|
|
|
|
|
|
i__2 = iout;
|
|
|
|
for (j = 1; j <= i__2; ++j) {
|
|
|
|
tmp1 = (work[j + *n] + work[j + in + *n]) * .5f;
|
|
|
|
|
|
|
|
/* Flag non-convergence. */
|
|
|
|
|
|
|
|
if (j > iout - iinfo) {
|
|
|
|
ncnvrg = TRUE_;
|
|
|
|
ib = -jb;
|
|
|
|
} else {
|
|
|
|
ib = jb;
|
|
|
|
}
|
|
|
|
i__3 = iwork[j + in] + iwoff;
|
|
|
|
for (je = iwork[j] + 1 + iwoff; je <= i__3; ++je) {
|
|
|
|
w[je] = tmp1;
|
|
|
|
iblock[je] = ib;
|
|
|
|
/* L50: */
|
|
|
|
}
|
|
|
|
/* L60: */
|
|
|
|
}
|
|
|
|
|
|
|
|
*m += im;
|
|
|
|
}
|
|
|
|
L70:
|
|
|
|
;
|
|
|
|
}
|
|
|
|
|
|
|
|
/* If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU */
|
|
|
|
/* If NWL+1 < IL or NWU > IU, discard extra eigenvalues. */
|
|
|
|
|
|
|
|
if (irange == 3) {
|
|
|
|
im = 0;
|
|
|
|
idiscl = *il - 1 - nwl;
|
|
|
|
idiscu = nwu - *iu;
|
|
|
|
|
|
|
|
if (idiscl > 0 || idiscu > 0) {
|
|
|
|
i__1 = *m;
|
|
|
|
for (je = 1; je <= i__1; ++je) {
|
|
|
|
if (w[je] <= wlu && idiscl > 0) {
|
|
|
|
--idiscl;
|
|
|
|
} else if (w[je] >= wul && idiscu > 0) {
|
|
|
|
--idiscu;
|
|
|
|
} else {
|
|
|
|
++im;
|
|
|
|
w[im] = w[je];
|
|
|
|
iblock[im] = iblock[je];
|
|
|
|
}
|
|
|
|
/* L80: */
|
|
|
|
}
|
|
|
|
*m = im;
|
|
|
|
}
|
|
|
|
if (idiscl > 0 || idiscu > 0) {
|
|
|
|
|
|
|
|
/* Code to deal with effects of bad arithmetic: */
|
|
|
|
/* Some low eigenvalues to be discarded are not in (WL,WLU], */
|
|
|
|
/* or high eigenvalues to be discarded are not in (WUL,WU] */
|
|
|
|
/* so just kill off the smallest IDISCL/largest IDISCU */
|
|
|
|
/* eigenvalues, by simply finding the smallest/largest */
|
|
|
|
/* eigenvalue(s). */
|
|
|
|
|
|
|
|
/* (If N(w) is monotone non-decreasing, this should never */
|
|
|
|
/* happen.) */
|
|
|
|
|
|
|
|
if (idiscl > 0) {
|
|
|
|
wkill = wu;
|
|
|
|
i__1 = idiscl;
|
|
|
|
for (jdisc = 1; jdisc <= i__1; ++jdisc) {
|
|
|
|
iw = 0;
|
|
|
|
i__2 = *m;
|
|
|
|
for (je = 1; je <= i__2; ++je) {
|
|
|
|
if (iblock[je] != 0 && (w[je] < wkill || iw == 0)) {
|
|
|
|
iw = je;
|
|
|
|
wkill = w[je];
|
|
|
|
}
|
|
|
|
/* L90: */
|
|
|
|
}
|
|
|
|
iblock[iw] = 0;
|
|
|
|
/* L100: */
|
|
|
|
}
|
|
|
|
}
|
|
|
|
if (idiscu > 0) {
|
|
|
|
|
|
|
|
wkill = wl;
|
|
|
|
i__1 = idiscu;
|
|
|
|
for (jdisc = 1; jdisc <= i__1; ++jdisc) {
|
|
|
|
iw = 0;
|
|
|
|
i__2 = *m;
|
|
|
|
for (je = 1; je <= i__2; ++je) {
|
|
|
|
if (iblock[je] != 0 && (w[je] > wkill || iw == 0)) {
|
|
|
|
iw = je;
|
|
|
|
wkill = w[je];
|
|
|
|
}
|
|
|
|
/* L110: */
|
|
|
|
}
|
|
|
|
iblock[iw] = 0;
|
|
|
|
/* L120: */
|
|
|
|
}
|
|
|
|
}
|
|
|
|
im = 0;
|
|
|
|
i__1 = *m;
|
|
|
|
for (je = 1; je <= i__1; ++je) {
|
|
|
|
if (iblock[je] != 0) {
|
|
|
|
++im;
|
|
|
|
w[im] = w[je];
|
|
|
|
iblock[im] = iblock[je];
|
|
|
|
}
|
|
|
|
/* L130: */
|
|
|
|
}
|
|
|
|
*m = im;
|
|
|
|
}
|
|
|
|
if (idiscl < 0 || idiscu < 0) {
|
|
|
|
toofew = TRUE_;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
/* If ORDER='B', do nothing -- the eigenvalues are already sorted */
|
|
|
|
/* by block. */
|
|
|
|
/* If ORDER='E', sort the eigenvalues from smallest to largest */
|
|
|
|
|
|
|
|
if (iorder == 1 && *nsplit > 1) {
|
|
|
|
i__1 = *m - 1;
|
|
|
|
for (je = 1; je <= i__1; ++je) {
|
|
|
|
ie = 0;
|
|
|
|
tmp1 = w[je];
|
|
|
|
i__2 = *m;
|
|
|
|
for (j = je + 1; j <= i__2; ++j) {
|
|
|
|
if (w[j] < tmp1) {
|
|
|
|
ie = j;
|
|
|
|
tmp1 = w[j];
|
|
|
|
}
|
|
|
|
/* L140: */
|
|
|
|
}
|
|
|
|
|
|
|
|
if (ie != 0) {
|
|
|
|
itmp1 = iblock[ie];
|
|
|
|
w[ie] = w[je];
|
|
|
|
iblock[ie] = iblock[je];
|
|
|
|
w[je] = tmp1;
|
|
|
|
iblock[je] = itmp1;
|
|
|
|
}
|
|
|
|
/* L150: */
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
*info = 0;
|
|
|
|
if (ncnvrg) {
|
|
|
|
++(*info);
|
|
|
|
}
|
|
|
|
if (toofew) {
|
|
|
|
*info += 2;
|
|
|
|
}
|
|
|
|
return 0;
|
|
|
|
|
|
|
|
/* End of SSTEBZ */
|
|
|
|
|
|
|
|
} /* sstebz_ */
|