mirror of https://github.com/opencv/opencv.git
Open Source Computer Vision Library
https://opencv.org/
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
422 lines
13 KiB
422 lines
13 KiB
/* slarrf.f -- translated by f2c (version 20061008). |
|
You must link the resulting object file with libf2c: |
|
on Microsoft Windows system, link with libf2c.lib; |
|
on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
|
or, if you install libf2c.a in a standard place, with -lf2c -lm |
|
-- in that order, at the end of the command line, as in |
|
cc *.o -lf2c -lm |
|
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
|
|
|
http://www.netlib.org/f2c/libf2c.zip |
|
*/ |
|
|
|
#include "clapack.h" |
|
|
|
|
|
/* Table of constant values */ |
|
|
|
static integer c__1 = 1; |
|
|
|
/* Subroutine */ int slarrf_(integer *n, real *d__, real *l, real *ld, |
|
integer *clstrt, integer *clend, real *w, real *wgap, real *werr, |
|
real *spdiam, real *clgapl, real *clgapr, real *pivmin, real *sigma, |
|
real *dplus, real *lplus, real *work, integer *info) |
|
{ |
|
/* System generated locals */ |
|
integer i__1; |
|
real r__1, r__2, r__3; |
|
|
|
/* Builtin functions */ |
|
double sqrt(doublereal); |
|
|
|
/* Local variables */ |
|
integer i__; |
|
real s, bestshift, smlgrowth, eps, tmp, max1, max2, rrr1, rrr2, znm2, |
|
growthbound, fail, fact, oldp; |
|
integer indx; |
|
real prod; |
|
integer ktry; |
|
real fail2, avgap, ldmax, rdmax; |
|
integer shift; |
|
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, |
|
integer *); |
|
logical dorrr1; |
|
real ldelta; |
|
extern doublereal slamch_(char *); |
|
logical nofail; |
|
real mingap, lsigma, rdelta; |
|
logical forcer; |
|
real rsigma, clwdth; |
|
extern logical sisnan_(real *); |
|
logical sawnan1, sawnan2, tryrrr1; |
|
|
|
|
|
/* -- LAPACK auxiliary routine (version 3.2) -- */ |
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
|
/* November 2006 */ |
|
/* * */ |
|
/* .. Scalar Arguments .. */ |
|
/* .. */ |
|
/* .. Array Arguments .. */ |
|
/* .. */ |
|
|
|
/* Purpose */ |
|
/* ======= */ |
|
|
|
/* Given the initial representation L D L^T and its cluster of close */ |
|
/* eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ... */ |
|
/* W( CLEND ), SLARRF finds a new relatively robust representation */ |
|
/* L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the */ |
|
/* eigenvalues of L(+) D(+) L(+)^T is relatively isolated. */ |
|
|
|
/* Arguments */ |
|
/* ========= */ |
|
|
|
/* N (input) INTEGER */ |
|
/* The order of the matrix (subblock, if the matrix splitted). */ |
|
|
|
/* D (input) REAL array, dimension (N) */ |
|
/* The N diagonal elements of the diagonal matrix D. */ |
|
|
|
/* L (input) REAL array, dimension (N-1) */ |
|
/* The (N-1) subdiagonal elements of the unit bidiagonal */ |
|
/* matrix L. */ |
|
|
|
/* LD (input) REAL array, dimension (N-1) */ |
|
/* The (N-1) elements L(i)*D(i). */ |
|
|
|
/* CLSTRT (input) INTEGER */ |
|
/* The index of the first eigenvalue in the cluster. */ |
|
|
|
/* CLEND (input) INTEGER */ |
|
/* The index of the last eigenvalue in the cluster. */ |
|
|
|
/* W (input) REAL array, dimension >= (CLEND-CLSTRT+1) */ |
|
/* The eigenvalue APPROXIMATIONS of L D L^T in ascending order. */ |
|
/* W( CLSTRT ) through W( CLEND ) form the cluster of relatively */ |
|
/* close eigenalues. */ |
|
|
|
/* WGAP (input/output) REAL array, dimension >= (CLEND-CLSTRT+1) */ |
|
/* The separation from the right neighbor eigenvalue in W. */ |
|
|
|
/* WERR (input) REAL array, dimension >= (CLEND-CLSTRT+1) */ |
|
/* WERR contain the semiwidth of the uncertainty */ |
|
/* interval of the corresponding eigenvalue APPROXIMATION in W */ |
|
|
|
/* SPDIAM (input) estimate of the spectral diameter obtained from the */ |
|
/* Gerschgorin intervals */ |
|
|
|
/* CLGAPL, CLGAPR (input) absolute gap on each end of the cluster. */ |
|
/* Set by the calling routine to protect against shifts too close */ |
|
/* to eigenvalues outside the cluster. */ |
|
|
|
/* PIVMIN (input) DOUBLE PRECISION */ |
|
/* The minimum pivot allowed in the Sturm sequence. */ |
|
|
|
/* SIGMA (output) REAL */ |
|
/* The shift used to form L(+) D(+) L(+)^T. */ |
|
|
|
/* DPLUS (output) REAL array, dimension (N) */ |
|
/* The N diagonal elements of the diagonal matrix D(+). */ |
|
|
|
/* LPLUS (output) REAL array, dimension (N-1) */ |
|
/* The first (N-1) elements of LPLUS contain the subdiagonal */ |
|
/* elements of the unit bidiagonal matrix L(+). */ |
|
|
|
/* WORK (workspace) REAL array, dimension (2*N) */ |
|
/* Workspace. */ |
|
|
|
/* 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 .. */ |
|
/* .. */ |
|
/* .. External Functions .. */ |
|
/* .. */ |
|
/* .. External Subroutines .. */ |
|
/* .. */ |
|
/* .. Intrinsic Functions .. */ |
|
/* .. */ |
|
/* .. Executable Statements .. */ |
|
|
|
/* Parameter adjustments */ |
|
--work; |
|
--lplus; |
|
--dplus; |
|
--werr; |
|
--wgap; |
|
--w; |
|
--ld; |
|
--l; |
|
--d__; |
|
|
|
/* Function Body */ |
|
*info = 0; |
|
fact = 2.f; |
|
eps = slamch_("Precision"); |
|
shift = 0; |
|
forcer = FALSE_; |
|
/* Note that we cannot guarantee that for any of the shifts tried, */ |
|
/* the factorization has a small or even moderate element growth. */ |
|
/* There could be Ritz values at both ends of the cluster and despite */ |
|
/* backing off, there are examples where all factorizations tried */ |
|
/* (in IEEE mode, allowing zero pivots & infinities) have INFINITE */ |
|
/* element growth. */ |
|
/* For this reason, we should use PIVMIN in this subroutine so that at */ |
|
/* least the L D L^T factorization exists. It can be checked afterwards */ |
|
/* whether the element growth caused bad residuals/orthogonality. */ |
|
/* Decide whether the code should accept the best among all */ |
|
/* representations despite large element growth or signal INFO=1 */ |
|
nofail = TRUE_; |
|
|
|
/* Compute the average gap length of the cluster */ |
|
clwdth = (r__1 = w[*clend] - w[*clstrt], dabs(r__1)) + werr[*clend] + |
|
werr[*clstrt]; |
|
avgap = clwdth / (real) (*clend - *clstrt); |
|
mingap = dmin(*clgapl,*clgapr); |
|
/* Initial values for shifts to both ends of cluster */ |
|
/* Computing MIN */ |
|
r__1 = w[*clstrt], r__2 = w[*clend]; |
|
lsigma = dmin(r__1,r__2) - werr[*clstrt]; |
|
/* Computing MAX */ |
|
r__1 = w[*clstrt], r__2 = w[*clend]; |
|
rsigma = dmax(r__1,r__2) + werr[*clend]; |
|
/* Use a small fudge to make sure that we really shift to the outside */ |
|
lsigma -= dabs(lsigma) * 2.f * eps; |
|
rsigma += dabs(rsigma) * 2.f * eps; |
|
/* Compute upper bounds for how much to back off the initial shifts */ |
|
ldmax = mingap * .25f + *pivmin * 2.f; |
|
rdmax = mingap * .25f + *pivmin * 2.f; |
|
/* Computing MAX */ |
|
r__1 = avgap, r__2 = wgap[*clstrt]; |
|
ldelta = dmax(r__1,r__2) / fact; |
|
/* Computing MAX */ |
|
r__1 = avgap, r__2 = wgap[*clend - 1]; |
|
rdelta = dmax(r__1,r__2) / fact; |
|
|
|
/* Initialize the record of the best representation found */ |
|
|
|
s = slamch_("S"); |
|
smlgrowth = 1.f / s; |
|
fail = (real) (*n - 1) * mingap / (*spdiam * eps); |
|
fail2 = (real) (*n - 1) * mingap / (*spdiam * sqrt(eps)); |
|
bestshift = lsigma; |
|
|
|
/* while (KTRY <= KTRYMAX) */ |
|
ktry = 0; |
|
growthbound = *spdiam * 8.f; |
|
L5: |
|
sawnan1 = FALSE_; |
|
sawnan2 = FALSE_; |
|
/* Ensure that we do not back off too much of the initial shifts */ |
|
ldelta = dmin(ldmax,ldelta); |
|
rdelta = dmin(rdmax,rdelta); |
|
/* Compute the element growth when shifting to both ends of the cluster */ |
|
/* accept the shift if there is no element growth at one of the two ends */ |
|
/* Left end */ |
|
s = -lsigma; |
|
dplus[1] = d__[1] + s; |
|
if (dabs(dplus[1]) < *pivmin) { |
|
dplus[1] = -(*pivmin); |
|
/* Need to set SAWNAN1 because refined RRR test should not be used */ |
|
/* in this case */ |
|
sawnan1 = TRUE_; |
|
} |
|
max1 = dabs(dplus[1]); |
|
i__1 = *n - 1; |
|
for (i__ = 1; i__ <= i__1; ++i__) { |
|
lplus[i__] = ld[i__] / dplus[i__]; |
|
s = s * lplus[i__] * l[i__] - lsigma; |
|
dplus[i__ + 1] = d__[i__ + 1] + s; |
|
if ((r__1 = dplus[i__ + 1], dabs(r__1)) < *pivmin) { |
|
dplus[i__ + 1] = -(*pivmin); |
|
/* Need to set SAWNAN1 because refined RRR test should not be used */ |
|
/* in this case */ |
|
sawnan1 = TRUE_; |
|
} |
|
/* Computing MAX */ |
|
r__2 = max1, r__3 = (r__1 = dplus[i__ + 1], dabs(r__1)); |
|
max1 = dmax(r__2,r__3); |
|
/* L6: */ |
|
} |
|
sawnan1 = sawnan1 || sisnan_(&max1); |
|
if (forcer || max1 <= growthbound && ! sawnan1) { |
|
*sigma = lsigma; |
|
shift = 1; |
|
goto L100; |
|
} |
|
/* Right end */ |
|
s = -rsigma; |
|
work[1] = d__[1] + s; |
|
if (dabs(work[1]) < *pivmin) { |
|
work[1] = -(*pivmin); |
|
/* Need to set SAWNAN2 because refined RRR test should not be used */ |
|
/* in this case */ |
|
sawnan2 = TRUE_; |
|
} |
|
max2 = dabs(work[1]); |
|
i__1 = *n - 1; |
|
for (i__ = 1; i__ <= i__1; ++i__) { |
|
work[*n + i__] = ld[i__] / work[i__]; |
|
s = s * work[*n + i__] * l[i__] - rsigma; |
|
work[i__ + 1] = d__[i__ + 1] + s; |
|
if ((r__1 = work[i__ + 1], dabs(r__1)) < *pivmin) { |
|
work[i__ + 1] = -(*pivmin); |
|
/* Need to set SAWNAN2 because refined RRR test should not be used */ |
|
/* in this case */ |
|
sawnan2 = TRUE_; |
|
} |
|
/* Computing MAX */ |
|
r__2 = max2, r__3 = (r__1 = work[i__ + 1], dabs(r__1)); |
|
max2 = dmax(r__2,r__3); |
|
/* L7: */ |
|
} |
|
sawnan2 = sawnan2 || sisnan_(&max2); |
|
if (forcer || max2 <= growthbound && ! sawnan2) { |
|
*sigma = rsigma; |
|
shift = 2; |
|
goto L100; |
|
} |
|
/* If we are at this point, both shifts led to too much element growth */ |
|
/* Record the better of the two shifts (provided it didn't lead to NaN) */ |
|
if (sawnan1 && sawnan2) { |
|
/* both MAX1 and MAX2 are NaN */ |
|
goto L50; |
|
} else { |
|
if (! sawnan1) { |
|
indx = 1; |
|
if (max1 <= smlgrowth) { |
|
smlgrowth = max1; |
|
bestshift = lsigma; |
|
} |
|
} |
|
if (! sawnan2) { |
|
if (sawnan1 || max2 <= max1) { |
|
indx = 2; |
|
} |
|
if (max2 <= smlgrowth) { |
|
smlgrowth = max2; |
|
bestshift = rsigma; |
|
} |
|
} |
|
} |
|
/* If we are here, both the left and the right shift led to */ |
|
/* element growth. If the element growth is moderate, then */ |
|
/* we may still accept the representation, if it passes a */ |
|
/* refined test for RRR. This test supposes that no NaN occurred. */ |
|
/* Moreover, we use the refined RRR test only for isolated clusters. */ |
|
if (clwdth < mingap / 128.f && dmin(max1,max2) < fail2 && ! sawnan1 && ! |
|
sawnan2) { |
|
dorrr1 = TRUE_; |
|
} else { |
|
dorrr1 = FALSE_; |
|
} |
|
tryrrr1 = TRUE_; |
|
if (tryrrr1 && dorrr1) { |
|
if (indx == 1) { |
|
tmp = (r__1 = dplus[*n], dabs(r__1)); |
|
znm2 = 1.f; |
|
prod = 1.f; |
|
oldp = 1.f; |
|
for (i__ = *n - 1; i__ >= 1; --i__) { |
|
if (prod <= eps) { |
|
prod = dplus[i__ + 1] * work[*n + i__ + 1] / (dplus[i__] * |
|
work[*n + i__]) * oldp; |
|
} else { |
|
prod *= (r__1 = work[*n + i__], dabs(r__1)); |
|
} |
|
oldp = prod; |
|
/* Computing 2nd power */ |
|
r__1 = prod; |
|
znm2 += r__1 * r__1; |
|
/* Computing MAX */ |
|
r__2 = tmp, r__3 = (r__1 = dplus[i__] * prod, dabs(r__1)); |
|
tmp = dmax(r__2,r__3); |
|
/* L15: */ |
|
} |
|
rrr1 = tmp / (*spdiam * sqrt(znm2)); |
|
if (rrr1 <= 8.f) { |
|
*sigma = lsigma; |
|
shift = 1; |
|
goto L100; |
|
} |
|
} else if (indx == 2) { |
|
tmp = (r__1 = work[*n], dabs(r__1)); |
|
znm2 = 1.f; |
|
prod = 1.f; |
|
oldp = 1.f; |
|
for (i__ = *n - 1; i__ >= 1; --i__) { |
|
if (prod <= eps) { |
|
prod = work[i__ + 1] * lplus[i__ + 1] / (work[i__] * |
|
lplus[i__]) * oldp; |
|
} else { |
|
prod *= (r__1 = lplus[i__], dabs(r__1)); |
|
} |
|
oldp = prod; |
|
/* Computing 2nd power */ |
|
r__1 = prod; |
|
znm2 += r__1 * r__1; |
|
/* Computing MAX */ |
|
r__2 = tmp, r__3 = (r__1 = work[i__] * prod, dabs(r__1)); |
|
tmp = dmax(r__2,r__3); |
|
/* L16: */ |
|
} |
|
rrr2 = tmp / (*spdiam * sqrt(znm2)); |
|
if (rrr2 <= 8.f) { |
|
*sigma = rsigma; |
|
shift = 2; |
|
goto L100; |
|
} |
|
} |
|
} |
|
L50: |
|
if (ktry < 1) { |
|
/* If we are here, both shifts failed also the RRR test. */ |
|
/* Back off to the outside */ |
|
/* Computing MAX */ |
|
r__1 = lsigma - ldelta, r__2 = lsigma - ldmax; |
|
lsigma = dmax(r__1,r__2); |
|
/* Computing MIN */ |
|
r__1 = rsigma + rdelta, r__2 = rsigma + rdmax; |
|
rsigma = dmin(r__1,r__2); |
|
ldelta *= 2.f; |
|
rdelta *= 2.f; |
|
++ktry; |
|
goto L5; |
|
} else { |
|
/* None of the representations investigated satisfied our */ |
|
/* criteria. Take the best one we found. */ |
|
if (smlgrowth < fail || nofail) { |
|
lsigma = bestshift; |
|
rsigma = bestshift; |
|
forcer = TRUE_; |
|
goto L5; |
|
} else { |
|
*info = 1; |
|
return 0; |
|
} |
|
} |
|
L100: |
|
if (shift == 1) { |
|
} else if (shift == 2) { |
|
/* store new L and D back into DPLUS, LPLUS */ |
|
scopy_(n, &work[1], &c__1, &dplus[1], &c__1); |
|
i__1 = *n - 1; |
|
scopy_(&i__1, &work[*n + 1], &c__1, &lplus[1], &c__1); |
|
} |
|
return 0; |
|
|
|
/* End of SLARRF */ |
|
|
|
} /* slarrf_ */
|
|
|