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opencv/3rdparty/lapack/slarrj.c

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#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_ */
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