001    /*
002     * Licensed to the Apache Software Foundation (ASF) under one or more
003     * contributor license agreements.  See the NOTICE file distributed with
004     * this work for additional information regarding copyright ownership.
005     * The ASF licenses this file to You under the Apache License, Version 2.0
006     * (the "License"); you may not use this file except in compliance with
007     * the License.  You may obtain a copy of the License at
008     *
009     *      http://www.apache.org/licenses/LICENSE-2.0
010     *
011     * Unless required by applicable law or agreed to in writing, software
012     * distributed under the License is distributed on an "AS IS" BASIS,
013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014     * See the License for the specific language governing permissions and
015     * limitations under the License.
016     */
017    package org.apache.commons.math3.linear;
018    
019    import org.apache.commons.math3.exception.DimensionMismatchException;
020    import org.apache.commons.math3.exception.MaxCountExceededException;
021    import org.apache.commons.math3.exception.NullArgumentException;
022    import org.apache.commons.math3.exception.util.ExceptionContext;
023    import org.apache.commons.math3.util.IterationManager;
024    
025    /**
026     * <p>
027     * This is an implementation of the conjugate gradient method for
028     * {@link RealLinearOperator}. It follows closely the template by <a
029     * href="#BARR1994">Barrett et al. (1994)</a> (figure 2.5). The linear system at
030     * hand is A &middot; x = b, and the residual is r = b - A &middot; x.
031     * </p>
032     * <h3><a id="stopcrit">Default stopping criterion</a></h3>
033     * <p>
034     * A default stopping criterion is implemented. The iterations stop when || r ||
035     * &le; &delta; || b ||, where b is the right-hand side vector, r the current
036     * estimate of the residual, and &delta; a user-specified tolerance. It should
037     * be noted that r is the so-called <em>updated</em> residual, which might
038     * differ from the true residual due to rounding-off errors (see e.g. <a
039     * href="#STRA2002">Strakos and Tichy, 2002</a>).
040     * </p>
041     * <h3>Iteration count</h3>
042     * <p>
043     * In the present context, an iteration should be understood as one evaluation
044     * of the matrix-vector product A &middot; x. The initialization phase therefore
045     * counts as one iteration.
046     * </p>
047     * <h3><a id="context">Exception context</a></h3>
048     * <p>
049     * Besides standard {@link DimensionMismatchException}, this class might throw
050     * {@link NonPositiveDefiniteOperatorException} if the linear operator or
051     * the preconditioner are not positive definite. In this case, the
052     * {@link ExceptionContext} provides some more information
053     * <ul>
054     * <li>key {@code "operator"} points to the offending linear operator, say L,</li>
055     * <li>key {@code "vector"} points to the offending vector, say x, such that
056     * x<sup>T</sup> &middot; L &middot; x < 0.</li>
057     * </ul>
058     * </p>
059     * <h3>References</h3>
060     * <dl>
061     * <dt><a id="BARR1994">Barret et al. (1994)</a></dt>
062     * <dd>R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. M. Donato, J. Dongarra,
063     * V. Eijkhout, R. Pozo, C. Romine and H. Van der Vorst,
064     * <a href="http://www.netlib.org/linalg/html_templates/Templates.html"><em>
065     * Templates for the Solution of Linear Systems: Building Blocks for Iterative
066     * Methods</em></a>, SIAM</dd>
067     * <dt><a id="STRA2002">Strakos and Tichy (2002)
068     * <dt>
069     * <dd>Z. Strakos and P. Tichy, <a
070     * href="http://etna.mcs.kent.edu/vol.13.2002/pp56-80.dir/pp56-80.pdf">
071     * <em>On error estimation in the conjugate gradient method and why it works
072     * in finite precision computations</em></a>, Electronic Transactions on
073     * Numerical Analysis 13: 56-80, 2002</dd>
074     * </dl>
075     *
076     * @version $Id: ConjugateGradient.java 1416643 2012-12-03 19:37:14Z tn $
077     * @since 3.0
078     */
079    public class ConjugateGradient
080        extends PreconditionedIterativeLinearSolver {
081    
082        /** Key for the <a href="#context">exception context</a>. */
083        public static final String OPERATOR = "operator";
084    
085        /** Key for the <a href="#context">exception context</a>. */
086        public static final String VECTOR = "vector";
087    
088        /**
089         * {@code true} if positive-definiteness of matrix and preconditioner should
090         * be checked.
091         */
092        private boolean check;
093    
094        /** The value of &delta;, for the default stopping criterion. */
095        private final double delta;
096    
097        /**
098         * Creates a new instance of this class, with <a href="#stopcrit">default
099         * stopping criterion</a>.
100         *
101         * @param maxIterations the maximum number of iterations
102         * @param delta the &delta; parameter for the default stopping criterion
103         * @param check {@code true} if positive definiteness of both matrix and
104         * preconditioner should be checked
105         */
106        public ConjugateGradient(final int maxIterations, final double delta,
107                                 final boolean check) {
108            super(maxIterations);
109            this.delta = delta;
110            this.check = check;
111        }
112    
113        /**
114         * Creates a new instance of this class, with <a href="#stopcrit">default
115         * stopping criterion</a> and custom iteration manager.
116         *
117         * @param manager the custom iteration manager
118         * @param delta the &delta; parameter for the default stopping criterion
119         * @param check {@code true} if positive definiteness of both matrix and
120         * preconditioner should be checked
121         * @throws NullArgumentException if {@code manager} is {@code null}
122         */
123        public ConjugateGradient(final IterationManager manager,
124                                 final double delta, final boolean check)
125            throws NullArgumentException {
126            super(manager);
127            this.delta = delta;
128            this.check = check;
129        }
130    
131        /**
132         * Returns {@code true} if positive-definiteness should be checked for both
133         * matrix and preconditioner.
134         *
135         * @return {@code true} if the tests are to be performed
136         */
137        public final boolean getCheck() {
138            return check;
139        }
140    
141        /**
142         * {@inheritDoc}
143         *
144         * @throws NonPositiveDefiniteOperatorException if {@code a} or {@code m} is
145         * not positive definite
146         */
147        @Override
148        public RealVector solveInPlace(final RealLinearOperator a,
149                                       final RealLinearOperator m,
150                                       final RealVector b,
151                                       final RealVector x0)
152            throws NullArgumentException, NonPositiveDefiniteOperatorException,
153            NonSquareOperatorException, DimensionMismatchException,
154            MaxCountExceededException, NonPositiveDefiniteOperatorException {
155            checkParameters(a, m, b, x0);
156            final IterationManager manager = getIterationManager();
157            // Initialization of default stopping criterion
158            manager.resetIterationCount();
159            final double rmax = delta * b.getNorm();
160            final RealVector bro = RealVector.unmodifiableRealVector(b);
161    
162            // Initialization phase counts as one iteration.
163            manager.incrementIterationCount();
164            // p and x are constructed as copies of x0, since presumably, the type
165            // of x is optimized for the calculation of the matrix-vector product
166            // A.x.
167            final RealVector x = x0;
168            final RealVector xro = RealVector.unmodifiableRealVector(x);
169            final RealVector p = x.copy();
170            RealVector q = a.operate(p);
171    
172            final RealVector r = b.combine(1, -1, q);
173            final RealVector rro = RealVector.unmodifiableRealVector(r);
174            double rnorm = r.getNorm();
175            RealVector z;
176            if (m == null) {
177                z = r;
178            } else {
179                z = null;
180            }
181            IterativeLinearSolverEvent evt;
182            evt = new DefaultIterativeLinearSolverEvent(this,
183                manager.getIterations(), xro, bro, rro, rnorm);
184            manager.fireInitializationEvent(evt);
185            if (rnorm <= rmax) {
186                manager.fireTerminationEvent(evt);
187                return x;
188            }
189            double rhoPrev = 0.;
190            while (true) {
191                manager.incrementIterationCount();
192                evt = new DefaultIterativeLinearSolverEvent(this,
193                    manager.getIterations(), xro, bro, rro, rnorm);
194                manager.fireIterationStartedEvent(evt);
195                if (m != null) {
196                    z = m.operate(r);
197                }
198                final double rhoNext = r.dotProduct(z);
199                if (check && (rhoNext <= 0.)) {
200                    final NonPositiveDefiniteOperatorException e;
201                    e = new NonPositiveDefiniteOperatorException();
202                    final ExceptionContext context = e.getContext();
203                    context.setValue(OPERATOR, m);
204                    context.setValue(VECTOR, r);
205                    throw e;
206                }
207                if (manager.getIterations() == 2) {
208                    p.setSubVector(0, z);
209                } else {
210                    p.combineToSelf(rhoNext / rhoPrev, 1., z);
211                }
212                q = a.operate(p);
213                final double pq = p.dotProduct(q);
214                if (check && (pq <= 0.)) {
215                    final NonPositiveDefiniteOperatorException e;
216                    e = new NonPositiveDefiniteOperatorException();
217                    final ExceptionContext context = e.getContext();
218                    context.setValue(OPERATOR, a);
219                    context.setValue(VECTOR, p);
220                    throw e;
221                }
222                final double alpha = rhoNext / pq;
223                x.combineToSelf(1., alpha, p);
224                r.combineToSelf(1., -alpha, q);
225                rhoPrev = rhoNext;
226                rnorm = r.getNorm();
227                evt = new DefaultIterativeLinearSolverEvent(this,
228                    manager.getIterations(), xro, bro, rro, rnorm);
229                manager.fireIterationPerformedEvent(evt);
230                if (rnorm <= rmax) {
231                    manager.fireTerminationEvent(evt);
232                    return x;
233                }
234            }
235        }
236    }