/usr/include/deal.II/lac/solver_minres.h is in libdeal.ii-dev 8.1.0-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 | // ---------------------------------------------------------------------
// $Id: solver_minres.h 31349 2013-10-20 19:07:06Z maier $
//
// Copyright (C) 2000 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__solver_minres_h
#define __deal2__solver_minres_h
#include <deal.II/base/config.h>
#include <deal.II/lac/solver.h>
#include <deal.II/lac/solver_control.h>
#include <deal.II/base/logstream.h>
#include <cmath>
#include <deal.II/base/subscriptor.h>
DEAL_II_NAMESPACE_OPEN
/*!@addtogroup Solvers */
/*@{*/
/**
* Minimal residual method for symmetric matrices.
*
* For the requirements on matrices and vectors in order to work with
* this class, see the documentation of the Solver base class.
*
* Like all other solver classes, this class has a local structure called
* @p AdditionalData which is used to pass additional parameters to the
* solver, like damping parameters or the number of temporary vectors. We
* use this additional structure instead of passing these values directly
* to the constructor because this makes the use of the @p SolverSelector and
* other classes much easier and guarantees that these will continue to
* work even if number or type of the additional parameters for a certain
* solver changes.
*
* However, since the MinRes method does not need additional data, the respective
* structure is empty and does not offer any functionality. The constructor
* has a default argument, so you may call it without the additional
* parameter.
*
* The preconditioner has to be positive definite and symmetric
*
* The algorithm is taken from the Master thesis of Astrid Batterman
* with some changes.
* The full text can be found at
* <tt>http://scholar.lib.vt.edu/theses/public/etd-12164379662151/etd-title.html</tt>
*
* @author Thomas Richter, 2000, Luca Heltai, 2006
*/
template <class VECTOR = Vector<double> >
class SolverMinRes : public Solver<VECTOR>
{
public:
/**
* Standardized data struct to
* pipe additional data to the
* solver. This solver does not
* need additional data yet.
*/
struct AdditionalData
{
};
/**
* Constructor.
*/
SolverMinRes (SolverControl &cn,
VectorMemory<VECTOR> &mem,
const AdditionalData &data=AdditionalData());
/**
* Constructor. Use an object of
* type GrowingVectorMemory as
* a default to allocate memory.
*/
SolverMinRes (SolverControl &cn,
const AdditionalData &data=AdditionalData());
/**
* Virtual destructor.
*/
virtual ~SolverMinRes ();
/**
* Solve the linear system $Ax=b$
* for x.
*/
template<class MATRIX, class PRECONDITIONER>
void
solve (const MATRIX &A,
VECTOR &x,
const VECTOR &b,
const PRECONDITIONER &precondition);
/** @addtogroup Exceptions
* @{ */
/**
* Exception
*/
DeclException0 (ExcPreconditionerNotDefinite);
//@}
protected:
/**
* Implementation of the computation of
* the norm of the residual.
*/
virtual double criterion();
/**
* Interface for derived class.
* This function gets the current
* iteration vector, the residual
* and the update vector in each
* step. It can be used for a
* graphical output of the
* convergence history.
*/
virtual void print_vectors(const unsigned int step,
const VECTOR &x,
const VECTOR &r,
const VECTOR &d) const;
/**
* Temporary vectors, allocated through
* the @p VectorMemory object at the start
* of the actual solution process and
* deallocated at the end.
*/
VECTOR *Vu0, *Vu1, *Vu2;
VECTOR *Vm0, *Vm1, *Vm2;
VECTOR *Vv;
/**
* Within the iteration loop, the
* square of the residual vector is
* stored in this variable. The
* function @p criterion uses this
* variable to compute the convergence
* value, which in this class is the
* norm of the residual vector and thus
* the square root of the @p res2 value.
*/
double res2;
};
/*@}*/
/*------------------------- Implementation ----------------------------*/
#ifndef DOXYGEN
template<class VECTOR>
SolverMinRes<VECTOR>::SolverMinRes (SolverControl &cn,
VectorMemory<VECTOR> &mem,
const AdditionalData &)
:
Solver<VECTOR>(cn,mem)
{}
template<class VECTOR>
SolverMinRes<VECTOR>::SolverMinRes (SolverControl &cn,
const AdditionalData &)
:
Solver<VECTOR>(cn)
{}
template<class VECTOR>
SolverMinRes<VECTOR>::~SolverMinRes ()
{}
template<class VECTOR>
double
SolverMinRes<VECTOR>::criterion()
{
return res2;
}
template<class VECTOR>
void
SolverMinRes<VECTOR>::print_vectors(const unsigned int,
const VECTOR &,
const VECTOR &,
const VECTOR &) const
{}
template<class VECTOR>
template<class MATRIX, class PRECONDITIONER>
void
SolverMinRes<VECTOR>::solve (const MATRIX &A,
VECTOR &x,
const VECTOR &b,
const PRECONDITIONER &precondition)
{
SolverControl::State conv=SolverControl::iterate;
deallog.push("minres");
// Memory allocation
Vu0 = this->memory.alloc();
Vu1 = this->memory.alloc();
Vu2 = this->memory.alloc();
Vv = this->memory.alloc();
Vm0 = this->memory.alloc();
Vm1 = this->memory.alloc();
Vm2 = this->memory.alloc();
// define some aliases for simpler access
typedef VECTOR *vecptr;
vecptr u[3] = {Vu0, Vu1, Vu2};
vecptr m[3] = {Vm0, Vm1, Vm2};
VECTOR &v = *Vv;
// resize the vectors, but do not set
// the values since they'd be overwritten
// soon anyway.
u[0]->reinit(b,true);
u[1]->reinit(b,true);
u[2]->reinit(b,true);
m[0]->reinit(b,true);
m[1]->reinit(b,true);
m[2]->reinit(b,true);
v.reinit(b,true);
// some values needed
double delta[3] = { 0, 0, 0 };
double f[2] = { 0, 0 };
double e[2] = { 0, 0 };
double r_l2 = 0;
double r0 = 0;
double tau = 0;
double c = 0;
double gamma = 0;
double s = 0;
double d_ = 0;
double d = 0;
// The iteration step.
unsigned int j = 1;
// Start of the solution process
A.vmult(*m[0],x);
*u[1] = b;
*u[1] -= *m[0];
// Precondition is applied.
// The preconditioner has to be
// positiv definite and symmetric
// M v = u[1]
precondition.vmult (v,*u[1]);
delta[1] = v * (*u[1]);
// Preconditioner positive
Assert (delta[1]>=0, ExcPreconditionerNotDefinite());
r0 = std::sqrt(delta[1]);
r_l2 = r0;
u[0]->reinit(b);
delta[0] = 1.;
m[0]->reinit(b);
m[1]->reinit(b);
m[2]->reinit(b);
conv = this->control().check(0,r_l2);
while (conv==SolverControl::iterate)
{
if (delta[1]!=0)
v *= 1./std::sqrt(delta[1]);
else
v.reinit(b);
A.vmult(*u[2],v);
u[2]->add (-std::sqrt(delta[1]/delta[0]), *u[0]);
gamma = *u[2] * v;
u[2]->add (-gamma / std::sqrt(delta[1]), *u[1]);
*m[0] = v;
// precondition: solve M v = u[2]
// Preconditioner has to be positiv
// definite and symmetric.
precondition.vmult(v,*u[2]);
delta[2] = v * (*u[2]);
Assert (delta[2]>=0, ExcPreconditionerNotDefinite());
if (j==1)
{
d_ = gamma;
e[1] = std::sqrt(delta[2]);
}
if (j>1)
{
d_ = s * e[0] - c * gamma;
e[0] = c * e[0] + s * gamma;
f[1] = s * std::sqrt(delta[2]);
e[1] = -c * std::sqrt(delta[2]);
}
d = std::sqrt (d_*d_ + delta[2]);
if (j>1) tau *= s / c;
c = d_ / d;
tau *= c;
s = std::sqrt(delta[2]) / d;
if (j==1)
tau = r0 * c;
m[0]->add (-e[0], *m[1]);
if (j>1)
m[0]->add (-f[0], *m[2]);
*m[0] *= 1./d;
x.add (tau, *m[0]);
r_l2 *= std::fabs(s);
conv = this->control().check(j,r_l2);
// next iteration step
++j;
// All vectors have to be shifted
// one iteration step.
// This should be changed one time.
//
// the previous code was like this:
// m[2] = m[1];
// m[1] = m[0];
// but it can be made more efficient,
// since the value of m[0] is no more
// needed in the next iteration
swap (*m[2], *m[1]);
swap (*m[1], *m[0]);
// likewise, but reverse direction:
// u[0] = u[1];
// u[1] = u[2];
swap (*u[0], *u[1]);
swap (*u[1], *u[2]);
// these are scalars, so need
// to bother
f[0] = f[1];
e[0] = e[1];
delta[0] = delta[1];
delta[1] = delta[2];
}
// Deallocation of Memory
this->memory.free(Vu0);
this->memory.free(Vu1);
this->memory.free(Vu2);
this->memory.free(Vv);
this->memory.free(Vm0);
this->memory.free(Vm1);
this->memory.free(Vm2);
// Output
deallog.pop ();
// in case of failure: throw exception
if (this->control().last_check() != SolverControl::success)
AssertThrow(false, SolverControl::NoConvergence (this->control().last_step(),
this->control().last_value()));
// otherwise exit as normal
}
#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE
#endif
|