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 * https://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
18 /*
19 * This is not the original file distributed by the Apache Software Foundation
20 * It has been modified by the Hipparchus project
21 */
22 package org.hipparchus.linear;
23
24 import org.hipparchus.exception.LocalizedCoreFormats;
25 import org.hipparchus.exception.MathIllegalArgumentException;
26
27 /** This class implements Hilbert Matrices as {@link RealLinearOperator}. */
28 public class HilbertMatrix
29 implements RealLinearOperator {
30
31 /** The size of the matrix. */
32 private final int n;
33
34 /**
35 * Creates a new instance of this class.
36 *
37 * @param n Size of the matrix to be created..
38 */
39 public HilbertMatrix(final int n) {
40 this.n = n;
41 }
42
43 /** {@inheritDoc} */
44 @Override
45 public int getColumnDimension() {
46 return n;
47 }
48
49 /** {@inheritDoc} */
50 @Override
51 public int getRowDimension() {
52 return n;
53 }
54
55 /** {@inheritDoc} */
56 @Override
57 public RealVector operate(final RealVector x) {
58 if (x.getDimension() != n) {
59 throw new MathIllegalArgumentException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
60 x.getDimension(), n);
61 }
62 final double[] y = new double[n];
63 for (int i = 0; i < n; i++) {
64 double pos = 0.;
65 double neg = 0.;
66 for (int j = 0; j < n; j++) {
67 final double xj = x.getEntry(j);
68 final double coeff = 1. / (i + j + 1.);
69 // Positive and negative values are sorted out in order to limit
70 // catastrophic cancellations (do not forget that Hilbert
71 // matrices are *very* ill-conditioned!
72 if (xj > 0.) {
73 pos += coeff * xj;
74 } else {
75 neg += coeff * xj;
76 }
77 }
78 y[i] = pos + neg;
79 }
80 return new ArrayRealVector(y, false);
81 }
82 }