163 const Real
zero(0), one(1), c1(0.1);
164 Real lamLower(0), lamUpper(0), res(0), resLower(0), resUpper(0), s(0);
168 update_primal(*xnew_,x,lam);
169 res = residual(*xnew_);
174 std::ios_base::fmtflags streamFlags(stream.flags());
175 if (verbosity_ > 2) {
176 stream << std::scientific << std::setprecision(6);
178 stream <<
" Polyhedral Projection using Ridders' Algorithm" << std::endl;
179 stream <<
" Bracketing Phase" << std::endl;
186 update_primal(*xnew_,x,lam);
187 res = residual(*xnew_);
188 if (verbosity_ > 2) {
190 stream << std::setw(6) << std::left <<
"iter";
191 stream << std::setw(15) << std::left <<
"lam";
192 stream << std::setw(15) << std::left <<
"res";
193 stream << std::setw(15) << std::left <<
"lower lam";
194 stream << std::setw(15) << std::left <<
"lower res";
197 stream << std::setw(6) << std::left << cnt;
198 stream << std::setw(15) << std::left << lam;
199 stream << std::setw(15) << std::left << res;
200 stream << std::setw(15) << std::left << lamLower;
201 stream << std::setw(15) << std::left << resLower;
204 while ( res <
zero && std::abs(res) > rtol && cnt < maxit_ ) {
205 s = std::max(resLower/res-one,c1);
210 update_primal(*xnew_,x,lam);
211 res = residual(*xnew_);
213 if (verbosity_ > 2) {
215 stream << std::setw(6) << std::left << cnt;
216 stream << std::setw(15) << std::left << lam;
217 stream << std::setw(15) << std::left << res;
218 stream << std::setw(15) << std::left << lamLower;
219 stream << std::setw(15) << std::left << resLower;
230 update_primal(*xnew_,x,lam);
231 res = residual(*xnew_);
232 if (verbosity_ > 2) {
234 stream << std::setw(6) << std::left <<
"iter";
235 stream << std::setw(15) << std::left <<
"lam";
236 stream << std::setw(15) << std::left <<
"res";
237 stream << std::setw(15) << std::left <<
"upper lam";
238 stream << std::setw(15) << std::left <<
"upper res";
241 stream << std::setw(6) << std::left << cnt;
242 stream << std::setw(15) << std::left << lam;
243 stream << std::setw(15) << std::left << res;
244 stream << std::setw(15) << std::left << lamUpper;
245 stream << std::setw(15) << std::left << resUpper;
248 while ( res >
zero && std::abs(res) > rtol && cnt < maxit_ ) {
249 s = std::max(resUpper/res-one,c1);
254 update_primal(*xnew_,x,lam);
255 res = residual(*xnew_);
257 if (verbosity_ > 2) {
259 stream << std::setw(6) << std::left << cnt;
260 stream << std::setw(15) << std::left << lam;
261 stream << std::setw(15) << std::left << res;
262 stream << std::setw(15) << std::left << lamUpper;
263 stream << std::setw(15) << std::left << resUpper;
270 if (verbosity_ > 2) {
271 stream <<
" Bracket: ";
272 stream << std::setw(15) << std::left << lamLower;
273 stream << std::setw(15) << std::left << lamUpper;
280 if (verbosity_ > 2) {
282 stream <<
" Ridders' Phase" << std::endl;
284 stream << std::setw(6) << std::left <<
"iter";
285 stream << std::setw(15) << std::left <<
"rtol";
286 stream << std::setw(15) << std::left <<
"lam";
287 stream << std::setw(15) << std::left <<
"res";
288 stream << std::setw(15) << std::left <<
"lam mid";
289 stream << std::setw(15) << std::left <<
"res mid";
290 stream << std::setw(15) << std::left <<
"lam low";
291 stream << std::setw(15) << std::left <<
"res low";
292 stream << std::setw(15) << std::left <<
"lam up";
293 stream << std::setw(15) << std::left <<
"res up";
296 const Real half(0.5);
297 Real lamMid(0), resMid(0);
298 for (cnt = 0; cnt < maxit_; cnt++) {
301 if (std::abs(lamUpper-lamLower) < ltol_)
break;
303 lamMid = half*(lamUpper+lamLower);
304 update_primal(*xnew_,x,lamMid);
305 resMid = residual(*xnew_);
306 if (std::abs(resMid) <= rtol) {
312 lam = lamMid-(lamMid-lamLower)*resMid/std::sqrt(resMid*resMid-resLower*resUpper);
313 update_primal(*xnew_,x,lam);
314 res = residual(*xnew_);
315 if (std::abs(res) <= rtol)
break;
318 if (resMid < -rtol) {
319 resLower = (lam < lamMid ? resMid : res);
320 lamLower = (lam < lamMid ? lamMid : lam);
330 if (resMid < -rtol) {
337 resUpper = (lam < lamMid ? res : resMid);
338 lamUpper = (lam < lamMid ? lam : lamMid);
343 if (verbosity_ > 2) {
345 stream << std::setw(6) << std::left << cnt;
346 stream << std::setw(15) << std::left << rtol;
347 stream << std::setw(15) << std::left << lam;
348 stream << std::setw(15) << std::left << res;
349 stream << std::setw(15) << std::left << lamMid;
350 stream << std::setw(15) << std::left << resMid;
351 stream << std::setw(15) << std::left << lamLower;
352 stream << std::setw(15) << std::left << resLower;
353 stream << std::setw(15) << std::left << lamUpper;
354 stream << std::setw(15) << std::left << resUpper;
358 if (verbosity_ > 2) {
361 stream << std::setw(6) << std::left << cnt;
362 stream << std::setw(15) << std::left << rtol;
363 stream << std::setw(15) << std::left << lam;
364 stream << std::setw(15) << std::left << res;
365 stream << std::setw(15) << std::left << lamMid;
366 stream << std::setw(15) << std::left << resMid;
367 stream << std::setw(15) << std::left << lamLower;
368 stream << std::setw(15) << std::left << resLower;
369 stream << std::setw(15) << std::left << lamUpper;
370 stream << std::setw(15) << std::left << resUpper;
377 if (std::abs(res) > rtol ) {
379 stream <<
">>> ROL::PolyhedralProjection::project : Projection may be inaccurate! rnorm = ";
380 stream << std::abs(res) <<
" rtol = " << rtol << std::endl;
382 stream.flags(streamFlags);