165 const Real
zero(0), one(1), two(2), c1(0.1), c2(0.75), c3(0.25);
166 Real lamLower(0), lamUpper(0), lamNew(0), res(0), resLower(0), resUpper(0), s(0);
170 update_primal(*xnew_,x,lam);
171 res = residual(*xnew_);
176 std::ios_base::fmtflags streamFlags(stream.flags());
177 if (verbosity_ > 2) {
178 stream << std::scientific << std::setprecision(6);
180 stream <<
" Polyhedral Projection using the Dai-Fletcher Algorithm" << std::endl;
181 stream <<
" Bracketing Phase" << std::endl;
188 update_primal(*xnew_,x,lam);
189 res = residual(*xnew_);
190 if (verbosity_ > 2) {
192 stream << std::setw(6) << std::left <<
"iter";
193 stream << std::setw(15) << std::left <<
"lam";
194 stream << std::setw(15) << std::left <<
"res";
195 stream << std::setw(15) << std::left <<
"lower lam";
196 stream << std::setw(15) << std::left <<
"lower res";
199 stream << std::setw(6) << std::left << cnt;
200 stream << std::setw(15) << std::left << lam;
201 stream << std::setw(15) << std::left << res;
202 stream << std::setw(15) << std::left << lamLower;
203 stream << std::setw(15) << std::left << resLower;
206 while ( res <
zero && std::abs(res) > rtol && cnt < maxit_ ) {
207 s = std::max(resLower/res-one,c1);
212 update_primal(*xnew_,x,lam);
213 res = residual(*xnew_);
215 if (verbosity_ > 2) {
217 stream << std::setw(6) << std::left << cnt;
218 stream << std::setw(15) << std::left << lam;
219 stream << std::setw(15) << std::left << res;
220 stream << std::setw(15) << std::left << lamLower;
221 stream << std::setw(15) << std::left << resLower;
232 update_primal(*xnew_,x,lam);
233 res = residual(*xnew_);
234 if (verbosity_ > 2) {
236 stream << std::setw(6) << std::left <<
"iter";
237 stream << std::setw(15) << std::left <<
"lam";
238 stream << std::setw(15) << std::left <<
"res";
239 stream << std::setw(15) << std::left <<
"upper lam";
240 stream << std::setw(15) << std::left <<
"upper res";
243 stream << std::setw(6) << std::left << cnt;
244 stream << std::setw(15) << std::left << lam;
245 stream << std::setw(15) << std::left << res;
246 stream << std::setw(15) << std::left << lamUpper;
247 stream << std::setw(15) << std::left << resUpper;
250 while ( res >
zero && std::abs(res) > rtol && cnt < maxit_ ) {
251 s = std::max(resUpper/res-one,c1);
256 update_primal(*xnew_,x,lam);
257 res = residual(*xnew_);
259 if (verbosity_ > 2) {
261 stream << std::setw(6) << std::left << cnt;
262 stream << std::setw(15) << std::left << lam;
263 stream << std::setw(15) << std::left << res;
264 stream << std::setw(15) << std::left << lamUpper;
265 stream << std::setw(15) << std::left << resUpper;
272 if (verbosity_ > 2) {
273 stream <<
" Bracket: ";
274 stream << std::setw(15) << std::left << lamLower;
275 stream << std::setw(15) << std::left << lamUpper;
280 rtol = ctol_*std::max(one,std::min(std::abs(resLower),std::abs(resUpper)));
284 s = (resUpper - resLower) / resUpper;
285 lam = (resUpper * lamLower - resLower * lamUpper) / (resUpper - resLower);
286 dlam = lamUpper - lam;
287 update_primal(*xnew_,x,lam);
288 res = residual(*xnew_);
290 if (verbosity_ > 2) {
292 stream <<
" Secant Phase" << std::endl;
294 stream << std::setw(6) << std::left <<
"iter";
295 stream << std::setw(15) << std::left <<
"lam";
296 stream << std::setw(15) << std::left <<
"res";
297 stream << std::setw(15) << std::left <<
"stepsize";
298 stream << std::setw(15) << std::left <<
"rtol";
299 stream << std::setw(15) << std::left <<
"lbnd";
300 stream << std::setw(15) << std::left <<
"lres";
301 stream << std::setw(15) << std::left <<
"ubnd";
302 stream << std::setw(15) << std::left <<
"ures";
305 stream << std::setw(6) << std::left << cnt;
306 stream << std::setw(15) << std::left << lam;
307 stream << std::setw(15) << std::left << res;
308 stream << std::setw(15) << std::left << dlam;
309 stream << std::setw(15) << std::left << rtol;
310 stream << std::setw(15) << std::left << lamLower;
311 stream << std::setw(15) << std::left << resLower;
312 stream << std::setw(15) << std::left << lamUpper;
313 stream << std::setw(15) << std::left << resUpper;
316 for (cnt = 1; cnt < maxit_; cnt++) {
318 if ( std::abs(res) <= rtol ||
319 std::abs(lamUpper-lamLower) < ltol_*std::max(std::abs(lamUpper),std::abs(lamLower)) ) {
330 s = (resUpper - resLower) / resUpper;
331 lam = (lamLower * resUpper - lamUpper * resLower) / (resUpper - resLower);
332 dlam = lamUpper - lam;
338 if (resUpper <= (c1+one)*res) {
339 dlam = (lamUpper - lam) / c1;
340 lamNew = std::max(lam - dlam, c2*lamLower + c3*lam);
343 lamNew = std::max((lam * resUpper - lamUpper * res) / (resUpper - res),
344 c2*lamLower + c3*lam);
350 s = (lamUpper - lamLower) / (lamUpper - lam);
360 s = (resUpper - resLower) / resUpper;
361 lam = (lamLower * resUpper - lamUpper * resLower) / (resUpper - resLower);
362 dlam = lamUpper - lam;
368 if (resLower >= (c1+one)*res) {
369 dlam = (lam - lamLower) / c1;
370 lamNew = std::max(lam + dlam, c2*lamUpper + c3*lam);
373 lamNew = std::max((lamLower * res - lam * resLower) / (res - resLower),
374 c2*lamUpper + c3*lam);
375 dlam = lamNew - lamLower;
380 s = (lamUpper - lamLower) / (lamUpper - lam);
383 update_primal(*xnew_,x,lam);
384 res = residual(*xnew_);
386 if (verbosity_ > 2) {
388 stream << std::setw(6) << std::left << cnt;
389 stream << std::setw(15) << std::left << lam;
390 stream << std::setw(15) << std::left << res;
391 stream << std::setw(15) << std::left << dlam;
392 stream << std::setw(15) << std::left << rtol;
393 stream << std::setw(15) << std::left << lamLower;
394 stream << std::setw(15) << std::left << resLower;
395 stream << std::setw(15) << std::left << lamUpper;
396 stream << std::setw(15) << std::left << resUpper;
400 if (verbosity_ > 2) {
405 if (std::abs(res) > rtol ) {
407 stream <<
">>> ROL::PolyhedralProjection::project : Projection may be inaccurate! rnorm = ";
408 stream << std::abs(res) <<
" rtol = " << rtol << std::endl;
410 stream.flags(streamFlags);