1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.apache.commons.math4.legacy.linear;
18
19 import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
20
21 /** This class implements Hilbert Matrices as {@link RealLinearOperator}. */
22 public class HilbertMatrix
23 extends RealLinearOperator {
24
25 /** The size of the matrix. */
26 private final int n;
27
28 /**
29 * Creates a new instance of this class.
30 *
31 * @param n Size of the matrix to be created..
32 */
33 public HilbertMatrix(final int n) {
34 this.n = n;
35 }
36
37 /** {@inheritDoc} */
38 @Override
39 public int getColumnDimension() {
40 return n;
41 }
42
43 /** {@inheritDoc} */
44 @Override
45 public int getRowDimension() {
46 return n;
47 }
48
49 /** {@inheritDoc} */
50 @Override
51 public RealVector operate(final RealVector x) {
52 if (x.getDimension() != n) {
53 throw new DimensionMismatchException(x.getDimension(), n);
54 }
55 final double[] y = new double[n];
56 for (int i = 0; i < n; i++) {
57 double pos = 0.;
58 double neg = 0.;
59 for (int j = 0; j < n; j++) {
60 final double xj = x.getEntry(j);
61 final double coeff = 1. / (i + j + 1.);
62 // Positive and negative values are sorted out in order to limit
63 // catastrophic cancellations (do not forget that Hilbert
64 // matrices are *very* ill-conditioned!
65 if (xj > 0.) {
66 pos += coeff * xj;
67 } else {
68 neg += coeff * xj;
69 }
70 }
71 y[i] = pos + neg;
72 }
73 return new ArrayRealVector(y, false);
74 }
75 }