ROL
ROL_BrentsProjection_Def.hpp
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43 
44 
45 #ifndef ROL_BRENTSPROJECTION_DEF_H
46 #define ROL_BRENTSPROJECTION_DEF_H
47 
48 namespace ROL {
49 
50 template<typename Real>
51 BrentsProjection<Real>::BrentsProjection(const Vector<Real> &xprim,
52  const Vector<Real> &xdual,
53  const Ptr<BoundConstraint<Real>> &bnd,
54  const Ptr<Constraint<Real>> &con,
55  const Vector<Real> &mul,
56  const Vector<Real> &res)
57  : PolyhedralProjection<Real>(xprim,xdual,bnd,con,mul,res),
58  DEFAULT_atol_ (std::sqrt(ROL_EPSILON<Real>()*std::sqrt(ROL_EPSILON<Real>()))),
59  DEFAULT_rtol_ (std::sqrt(ROL_EPSILON<Real>())),
60  DEFAULT_ltol_ (ROL_EPSILON<Real>()),
61  DEFAULT_maxit_ (5000),
62  DEFAULT_verbosity_ (0),
63  atol_ (DEFAULT_atol_),
64  rtol_ (DEFAULT_rtol_),
65  ltol_ (DEFAULT_ltol_),
66  maxit_ (DEFAULT_maxit_),
67  verbosity_ (DEFAULT_verbosity_) {
68  initialize(xprim,xdual,bnd,con,mul,res);
69 }
70 
71 template<typename Real>
72 BrentsProjection<Real>::BrentsProjection(const Vector<Real> &xprim,
73  const Vector<Real> &xdual,
74  const Ptr<BoundConstraint<Real>> &bnd,
75  const Ptr<Constraint<Real>> &con,
76  const Vector<Real> &mul,
77  const Vector<Real> &res,
78  ParameterList &list)
79  : PolyhedralProjection<Real>(xprim,xdual,bnd,con,mul,res),
80  DEFAULT_atol_ (std::sqrt(ROL_EPSILON<Real>()*std::sqrt(ROL_EPSILON<Real>()))),
81  DEFAULT_rtol_ (std::sqrt(ROL_EPSILON<Real>())),
82  DEFAULT_ltol_ (ROL_EPSILON<Real>()),
83  DEFAULT_maxit_ (5000),
84  DEFAULT_verbosity_ (0),
85  atol_ (DEFAULT_atol_),
86  rtol_ (DEFAULT_rtol_),
87  ltol_ (DEFAULT_ltol_),
88  maxit_ (DEFAULT_maxit_),
89  verbosity_ (DEFAULT_verbosity_) {
90  atol_ = list.sublist("General").sublist("Polyhedral Projection").get("Absolute Tolerance", DEFAULT_atol_);
91  rtol_ = list.sublist("General").sublist("Polyhedral Projection").get("Relative Tolerance", DEFAULT_rtol_);
92  ltol_ = list.sublist("General").sublist("Polyhedral Projection").get("Multiplier Tolerance", DEFAULT_ltol_);
93  maxit_ = list.sublist("General").sublist("Polyhedral Projection").get("Iteration Limit", DEFAULT_maxit_);
94  verbosity_ = list.sublist("General").get("Output Level", DEFAULT_verbosity_);
95  initialize(xprim,xdual,bnd,con,mul,res);
96 }
97 
98 template<typename Real>
99 void BrentsProjection<Real>::initialize(const Vector<Real> &xprim,
100  const Vector<Real> &xdual,
101  const Ptr<BoundConstraint<Real>> &bnd,
102  const Ptr<Constraint<Real>> &con,
103  const Vector<Real> &mul,
104  const Vector<Real> &res) {
105  dim_ = mul.dimension();
106  ROL_TEST_FOR_EXCEPTION(dim_!=1,std::logic_error,
107  ">>> ROL::BrentsProjection : The range of the linear constraint must be one dimensional!");
108  xnew_ = xprim.clone();
109  Px_ = xprim.clone();
110  mul1_ = static_cast<Real>(0);
111  dlam1_ = static_cast<Real>(2);
112  // con.value(x) = xprim_->dot(x) + b_
113  Real tol(std::sqrt(ROL_EPSILON<Real>()));
114  xprim_->zero();
115  con_->update(*xprim_,UpdateType::Temp);
116  con_->value(*res_,*xprim_,tol);
117  b_ = res_->dot(*res_->basis(0));
118  mul_->setScalar(static_cast<Real>(1));
119  con_->applyAdjointJacobian(*xdual_,*mul_,xprim,tol);
120  xprim_->set(xdual_->dual());
121  cdot_ = xprim_->dot(*xprim_);
122  // Set tolerance
123  //xnew_->zero();
124  //bnd_->project(*xnew_);
125  //Real res0 = std::abs(residual(*xnew_));
126  Real resl = ROL_INF<Real>(), resu = ROL_INF<Real>();
127  if (bnd_->isLowerActivated()) resl = residual(*bnd_->getLowerBound());
128  if (bnd_->isUpperActivated()) resu = residual(*bnd_->getUpperBound());
129  Real res0 = std::max(resl,resu);
130  if (res0 < atol_) res0 = static_cast<Real>(1);
131  ctol_ = std::min(atol_,rtol_*res0);
132 }
133 
134 template<typename Real>
135 void BrentsProjection<Real>::project(Vector<Real> &x, std::ostream &stream) {
136  if (con_ == nullPtr) {
137  bnd_->project(x);
138  }
139  else {
140  mul1_ = -residual(x)/cdot_;
141  //mul1_ = static_cast<Real>(0);
142  dlam1_ = static_cast<Real>(2);
143  //dlam1_ = static_cast<Real>(1)+std::abs(mul1_);
144  project_df(x, mul1_, dlam1_, stream);
145  mul_->setScalar(mul1_);
146  }
147 }
148 
149 template<typename Real>
150 Real BrentsProjection<Real>::residual(const Vector<Real> &x) const {
151  return xprim_->dot(x) + b_;
152 }
153 
154 template<typename Real>
155 void BrentsProjection<Real>::update_primal(Vector<Real> &y, const Vector<Real> &x, const Real lam) const {
156  y.set(x);
157  y.axpy(lam,*xprim_);
158  bnd_->project(y);
159 }
160 
161 template<typename Real>
162 void BrentsProjection<Real>::project_df(Vector<Real> &x, Real &lam, Real &dlam, std::ostream &stream) const {
163  const Real zero(0), one(1), c1(0.1);
164  Real lamLower(0), lamUpper(0), res(0), resLower(0), resUpper(0), s(0);
165  Real rtol = ctol_;
166  int cnt(0);
167  // Compute initial residual
168  update_primal(*xnew_,x,lam);
169  res = residual(*xnew_);
170  if (res == zero) {
171  x.set(*xnew_);
172  return;
173  }
174  std::ios_base::fmtflags streamFlags(stream.flags());
175  if (verbosity_ > 2) {
176  stream << std::scientific << std::setprecision(6);
177  stream << std::endl;
178  stream << " Polyhedral Projection using Brents' Algorithm" << std::endl;
179  stream << " Bracketing Phase" << std::endl;
180  }
181  // Bracketing phase
182  if ( res < zero ) {
183  lamLower = lam;
184  resLower = res;
185  lam += dlam;
186  update_primal(*xnew_,x,lam);
187  res = residual(*xnew_);
188  if (verbosity_ > 2) {
189  stream << " ";
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";
195  stream << std::endl;
196  stream << " ";
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;
202  stream << std::endl;
203  }
204  while ( res < zero && std::abs(res) > rtol && cnt < maxit_ ) {
205  s = std::max(resLower/res-one,c1);
206  dlam += dlam/s;
207  lamLower = lam;
208  resLower = res;
209  lam += dlam;
210  update_primal(*xnew_,x,lam);
211  res = residual(*xnew_);
212  cnt++;
213  if (verbosity_ > 2) {
214  stream << " ";
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;
220  stream << std::endl;
221  }
222  }
223  lamUpper = lam;
224  resUpper = res;
225  }
226  else {
227  lamUpper = lam;
228  resUpper = res;
229  lam -= dlam;
230  update_primal(*xnew_,x,lam);
231  res = residual(*xnew_);
232  if (verbosity_ > 2) {
233  stream << " ";
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";
239  stream << std::endl;
240  stream << " ";
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;
246  stream << std::endl;
247  }
248  while ( res > zero && std::abs(res) > rtol && cnt < maxit_ ) {
249  s = std::max(resUpper/res-one,c1);
250  dlam += dlam/s;
251  lamUpper = lam;
252  resUpper = res;
253  lam -= dlam;
254  update_primal(*xnew_,x,lam);
255  res = residual(*xnew_);
256  cnt++;
257  if (verbosity_ > 2) {
258  stream << " ";
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;
264  stream << std::endl;
265  }
266  }
267  lamLower = lam;
268  resLower = res;
269  }
270  if (verbosity_ > 2) {
271  stream << " Bracket: ";
272  stream << std::setw(15) << std::left << lamLower;
273  stream << std::setw(15) << std::left << lamUpper;
274  stream << std::endl;
275  }
276 
277  // Secant phase
278  //rtol = ctol_*std::max(one,std::min(std::abs(resLower),std::abs(resUpper)));
279  cnt = 0;
280  if (verbosity_ > 2) {
281  stream << std::endl;
282  stream << " Brents' Phase" << std::endl;
283  stream << " ";
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 low";
289  stream << std::setw(15) << std::left << "res low";
290  stream << std::setw(15) << std::left << "lam up";
291  stream << std::setw(15) << std::left << "res up";
292  stream << std::endl;
293  }
294  const Real half(0.5), two(2), three(3);
295  const Real eps(ROL_EPSILON<Real>()), tol0(rtol); // tol0(1e1*eps);
296  Real d1(1), d2(1), tol(1);
297  Real p(0), q(0), r(0), m(0);
298  lam = lamUpper; res = resUpper;
299  update_primal(*xnew_,x,lamUpper);
300  for (cnt = 0; cnt < maxit_; cnt++) {
301  if ((resUpper > zero && res > zero) || (resUpper <= zero && res <= zero)) {
302  lam = lamLower; res = resLower;
303  d1 = lamUpper-lamLower; d2 = d1;
304  }
305  if (std::abs(res) < std::abs(resUpper)) {
306  lamLower = lamUpper; lamUpper = lam; lam = lamLower;
307  resLower = resUpper; resUpper = res; res = resLower;
308  }
309  tol = two*eps*std::abs(lamUpper) + half*tol0;
310  m = half*(lam - lamUpper);
311  if (std::abs(m) <= tol || std::abs(resUpper) <= rtol) break;
312  if (std::abs(d2) < tol || std::abs(resLower) <= std::abs(resUpper)) {
313  d1 = m; d2 = d1;
314  }
315  else {
316  s = resUpper/resLower;
317  if (lamLower == lam) {
318  p = two*m*s;
319  q = one-s;
320  }
321  else {
322  q = resLower/res;
323  r = resUpper/res;
324  p = s*(two*m*q*(q-r)-(lamUpper-lamLower)*(r-one));
325  q = (q-one)*(r-one)*(s-one);
326  }
327  if (p > zero) q = -q;
328  else p = -p;
329  if (two*p < three*m*q-std::abs(tol*q) && p < std::abs(half*d2*q)) {
330  d2 = d1; d1 = p/q;
331  }
332  else {
333  d1 = m; d2 = d1;
334  }
335  }
336  lamLower = lamUpper; resLower = resUpper;
337  if (std::abs(d1) > tol) lamUpper += d1;
338  else if (m > zero) lamUpper += tol;
339  else lamUpper -= tol;
340  update_primal(*xnew_,x,lamUpper);
341  resUpper = residual(*xnew_);
342 
343  if (verbosity_ > 2) {
344  stream << " ";
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 << lamLower;
350  stream << std::setw(15) << std::left << resLower;
351  stream << std::setw(15) << std::left << lamUpper;
352  stream << std::setw(15) << std::left << resUpper;
353  stream << std::endl;
354  }
355  }
356  if (verbosity_ > 2) {
357  if (cnt < maxit_) {
358  stream << " ";
359  stream << std::setw(6) << std::left << cnt;
360  stream << std::setw(15) << std::left << rtol;
361  stream << std::setw(15) << std::left << lam;
362  stream << std::setw(15) << std::left << res;
363  stream << std::setw(15) << std::left << lamLower;
364  stream << std::setw(15) << std::left << resLower;
365  stream << std::setw(15) << std::left << lamUpper;
366  stream << std::setw(15) << std::left << resUpper;
367  stream << std::endl;
368  }
369  stream << std::endl;
370  }
371  // Return projection
372  res = resUpper;
373  x.set(*xnew_);
374  if (std::abs(res) > rtol ) {
375  //throw Exception::NotImplemented(">>> ROL::PolyhedralProjection::project : Projection failed!");
376  stream << ">>> ROL::PolyhedralProjection::project : Projection may be inaccurate! rnorm = ";
377  stream << std::abs(res) << " rtol = " << rtol << std::endl;
378  }
379  stream.flags(streamFlags);
380 }
381 
382 } // namespace ROL
383 
384 #endif
ROL::BrentsProjection::residual
Real residual(const Vector< Real > &x) const
Definition: ROL_BrentsProjection_Def.hpp:150
ROL::BrentsProjection::project_df
void project_df(Vector< Real > &x, Real &lam, Real &dlam, std::ostream &stream=std::cout) const
Definition: ROL_BrentsProjection_Def.hpp:162
ROL::BrentsProjection::BrentsProjection
BrentsProjection(const Vector< Real > &xprim, const Vector< Real > &xdual, const Ptr< BoundConstraint< Real >> &bnd, const Ptr< Constraint< Real >> &con, const Vector< Real > &mul, const Vector< Real > &res)
Definition: ROL_BrentsProjection_Def.hpp:51
ROL::Vector::clone
virtual ROL::Ptr< Vector > clone() const =0
Clone to make a new (uninitialized) vector.
ROL::Vector::dimension
virtual int dimension() const
Return dimension of the vector space.
Definition: ROL_Vector.hpp:196
ROL::Vector::axpy
virtual void axpy(const Real alpha, const Vector &x)
Compute where .
Definition: ROL_Vector.hpp:153
ROL::Vector
Defines the linear algebra or vector space interface.
Definition: ROL_Vector.hpp:80
zero
Objective_SerialSimOpt(const Ptr< Obj > &obj, const V &ui) z0_ zero()
Definition: ROL_Objective_SerialSimOpt.hpp:145
ROL::BrentsProjection::project
void project(Vector< Real > &x, std::ostream &stream=std::cout) override
Definition: ROL_BrentsProjection_Def.hpp:135
ROL::BoundConstraint
Provides the interface to apply upper and lower bound constraints.
Definition: ROL_BoundConstraint.hpp:73
ROL::BrentsProjection::initialize
void initialize(const Vector< Real > &xprim, const Vector< Real > &xdual, const Ptr< BoundConstraint< Real >> &bnd, const Ptr< Constraint< Real >> &con, const Vector< Real > &mul, const Vector< Real > &res)
Definition: ROL_BrentsProjection_Def.hpp:99
ROL::Vector::set
virtual void set(const Vector &x)
Set where .
Definition: ROL_Vector.hpp:209
ROL::ROL_EPSILON
Real ROL_EPSILON(void)
Platform-dependent machine epsilon.
Definition: ROL_Types.hpp:91
ROL::Constraint
Defines the general constraint operator interface.
Definition: ROL_Constraint.hpp:86
ROL::BrentsProjection::update_primal
void update_primal(Vector< Real > &y, const Vector< Real > &x, const Real lam) const
Definition: ROL_BrentsProjection_Def.hpp:155
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