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 }