--- /dev/null
+#include "clapack.h"
+
+/* Subroutine */ int slarrj_(integer *n, real *d__, real *e2, integer *ifirst,
+ integer *ilast, real *rtol, integer *offset, real *w, real *werr,
+ real *work, integer *iwork, real *pivmin, real *spdiam, integer *info)
+{
+ /* System generated locals */
+ integer i__1, i__2;
+ real r__1, r__2;
+
+ /* Builtin functions */
+ double log(doublereal);
+
+ /* Local variables */
+ integer i__, j, k, p;
+ real s;
+ integer i1, i2, ii;
+ real fac, mid;
+ integer cnt;
+ real tmp, left;
+ integer iter, nint, prev, next, savi1;
+ real right, width, dplus;
+ integer olnint, maxitr;
+
+
+/* -- LAPACK auxiliary routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+/* .. Array Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* Given the initial eigenvalue approximations of T, SLARRJ */
+/* does bisection to refine the eigenvalues of T, */
+/* W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial */
+/* guesses for these eigenvalues are input in W, the corresponding estimate */
+/* of the error in these guesses in WERR. During bisection, intervals */
+/* [left, right] are maintained by storing their mid-points and */
+/* semi-widths in the arrays W and WERR respectively. */
+
+/* Arguments */
+/* ========= */
+
+/* N (input) INTEGER */
+/* The order of the matrix. */
+
+/* D (input) REAL array, dimension (N) */
+/* The N diagonal elements of T. */
+
+/* E2 (input) REAL array, dimension (N-1) */
+/* The Squares of the (N-1) subdiagonal elements of T. */
+
+/* IFIRST (input) INTEGER */
+/* The index of the first eigenvalue to be computed. */
+
+/* ILAST (input) INTEGER */
+/* The index of the last eigenvalue to be computed. */
+
+/* RTOL (input) REAL */
+/* Tolerance for the convergence of the bisection intervals. */
+/* An interval [LEFT,RIGHT] has converged if */
+/* RIGHT-LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|). */
+
+/* OFFSET (input) INTEGER */
+/* Offset for the arrays W and WERR, i.e., the IFIRST-OFFSET */
+/* through ILAST-OFFSET elements of these arrays are to be used. */
+
+/* W (input/output) REAL array, dimension (N) */
+/* On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are */
+/* estimates of the eigenvalues of L D L^T indexed IFIRST through */
+/* ILAST. */
+/* On output, these estimates are refined. */
+
+/* WERR (input/output) REAL array, dimension (N) */
+/* On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are */
+/* the errors in the estimates of the corresponding elements in W. */
+/* On output, these errors are refined. */
+
+/* WORK (workspace) REAL array, dimension (2*N) */
+/* Workspace. */
+
+/* IWORK (workspace) INTEGER array, dimension (2*N) */
+/* Workspace. */
+
+/* PIVMIN (input) DOUBLE PRECISION */
+/* The minimum pivot in the Sturm sequence for T. */
+
+/* SPDIAM (input) DOUBLE PRECISION */
+/* The spectral diameter of T. */
+
+/* INFO (output) INTEGER */
+/* Error flag. */
+
+/* Further Details */
+/* =============== */
+
+/* Based on contributions by */
+/* Beresford Parlett, University of California, Berkeley, USA */
+/* Jim Demmel, University of California, Berkeley, USA */
+/* Inderjit Dhillon, University of Texas, Austin, USA */
+/* Osni Marques, LBNL/NERSC, USA */
+/* Christof Voemel, University of California, Berkeley, USA */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+ /* Parameter adjustments */
+ --iwork;
+ --work;
+ --werr;
+ --w;
+ --e2;
+ --d__;
+
+ /* Function Body */
+ *info = 0;
+
+ maxitr = (integer) ((log(*spdiam + *pivmin) - log(*pivmin)) / log(2.f)) +
+ 2;
+
+/* Initialize unconverged intervals in [ WORK(2*I-1), WORK(2*I) ]. */
+/* The Sturm Count, Count( WORK(2*I-1) ) is arranged to be I-1, while */
+/* Count( WORK(2*I) ) is stored in IWORK( 2*I ). The integer IWORK( 2*I-1 ) */
+/* for an unconverged interval is set to the index of the next unconverged */
+/* interval, and is -1 or 0 for a converged interval. Thus a linked */
+/* list of unconverged intervals is set up. */
+
+ i1 = *ifirst;
+ i2 = *ilast;
+/* The number of unconverged intervals */
+ nint = 0;
+/* The last unconverged interval found */
+ prev = 0;
+ i__1 = i2;
+ for (i__ = i1; i__ <= i__1; ++i__) {
+ k = i__ << 1;
+ ii = i__ - *offset;
+ left = w[ii] - werr[ii];
+ mid = w[ii];
+ right = w[ii] + werr[ii];
+ width = right - mid;
+/* Computing MAX */
+ r__1 = dabs(left), r__2 = dabs(right);
+ tmp = dmax(r__1,r__2);
+/* The following test prevents the test of converged intervals */
+ if (width < *rtol * tmp) {
+/* This interval has already converged and does not need refinement. */
+/* (Note that the gaps might change through refining the */
+/* eigenvalues, however, they can only get bigger.) */
+/* Remove it from the list. */
+ iwork[k - 1] = -1;
+/* Make sure that I1 always points to the first unconverged interval */
+ if (i__ == i1 && i__ < i2) {
+ i1 = i__ + 1;
+ }
+ if (prev >= i1 && i__ <= i2) {
+ iwork[(prev << 1) - 1] = i__ + 1;
+ }
+ } else {
+/* unconverged interval found */
+ prev = i__;
+/* Make sure that [LEFT,RIGHT] contains the desired eigenvalue */
+
+/* Do while( CNT(LEFT).GT.I-1 ) */
+
+ fac = 1.f;
+L20:
+ cnt = 0;
+ s = left;
+ dplus = d__[1] - s;
+ if (dplus < 0.f) {
+ ++cnt;
+ }
+ i__2 = *n;
+ for (j = 2; j <= i__2; ++j) {
+ dplus = d__[j] - s - e2[j - 1] / dplus;
+ if (dplus < 0.f) {
+ ++cnt;
+ }
+/* L30: */
+ }
+ if (cnt > i__ - 1) {
+ left -= werr[ii] * fac;
+ fac *= 2.f;
+ goto L20;
+ }
+
+/* Do while( CNT(RIGHT).LT.I ) */
+
+ fac = 1.f;
+L50:
+ cnt = 0;
+ s = right;
+ dplus = d__[1] - s;
+ if (dplus < 0.f) {
+ ++cnt;
+ }
+ i__2 = *n;
+ for (j = 2; j <= i__2; ++j) {
+ dplus = d__[j] - s - e2[j - 1] / dplus;
+ if (dplus < 0.f) {
+ ++cnt;
+ }
+/* L60: */
+ }
+ if (cnt < i__) {
+ right += werr[ii] * fac;
+ fac *= 2.f;
+ goto L50;
+ }
+ ++nint;
+ iwork[k - 1] = i__ + 1;
+ iwork[k] = cnt;
+ }
+ work[k - 1] = left;
+ work[k] = right;
+/* L75: */
+ }
+ savi1 = i1;
+
+/* Do while( NINT.GT.0 ), i.e. there are still unconverged intervals */
+/* and while (ITER.LT.MAXITR) */
+
+ iter = 0;
+L80:
+ prev = i1 - 1;
+ i__ = i1;
+ olnint = nint;
+ i__1 = olnint;
+ for (p = 1; p <= i__1; ++p) {
+ k = i__ << 1;
+ ii = i__ - *offset;
+ next = iwork[k - 1];
+ left = work[k - 1];
+ right = work[k];
+ mid = (left + right) * .5f;
+/* semiwidth of interval */
+ width = right - mid;
+/* Computing MAX */
+ r__1 = dabs(left), r__2 = dabs(right);
+ tmp = dmax(r__1,r__2);
+ if (width < *rtol * tmp || iter == maxitr) {
+/* reduce number of unconverged intervals */
+ --nint;
+/* Mark interval as converged. */
+ iwork[k - 1] = 0;
+ if (i1 == i__) {
+ i1 = next;
+ } else {
+/* Prev holds the last unconverged interval previously examined */
+ if (prev >= i1) {
+ iwork[(prev << 1) - 1] = next;
+ }
+ }
+ i__ = next;
+ goto L100;
+ }
+ prev = i__;
+
+/* Perform one bisection step */
+
+ cnt = 0;
+ s = mid;
+ dplus = d__[1] - s;
+ if (dplus < 0.f) {
+ ++cnt;
+ }
+ i__2 = *n;
+ for (j = 2; j <= i__2; ++j) {
+ dplus = d__[j] - s - e2[j - 1] / dplus;
+ if (dplus < 0.f) {
+ ++cnt;
+ }
+/* L90: */
+ }
+ if (cnt <= i__ - 1) {
+ work[k - 1] = mid;
+ } else {
+ work[k] = mid;
+ }
+ i__ = next;
+L100:
+ ;
+ }
+ ++iter;
+/* do another loop if there are still unconverged intervals */
+/* However, in the last iteration, all intervals are accepted */
+/* since this is the best we can do. */
+ if (nint > 0 && iter <= maxitr) {
+ goto L80;
+ }
+
+
+/* At this point, all the intervals have converged */
+ i__1 = *ilast;
+ for (i__ = savi1; i__ <= i__1; ++i__) {
+ k = i__ << 1;
+ ii = i__ - *offset;
+/* All intervals marked by '0' have been refined. */
+ if (iwork[k - 1] == 0) {
+ w[ii] = (work[k - 1] + work[k]) * .5f;
+ werr[ii] = work[k] - w[ii];
+ }
+/* L110: */
+ }
+
+ return 0;
+
+/* End of SLARRJ */
+
+} /* slarrj_ */
projects / opencv / blobdiff