| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.math4.legacy.linear; |
| |
| import org.apache.commons.math4.legacy.exception.DimensionMismatchException; |
| import org.apache.commons.numbers.combinatorics.BinomialCoefficient; |
| |
| /** |
| * This class implements inverses of Hilbert Matrices as |
| * {@link RealLinearOperator}. |
| */ |
| public class InverseHilbertMatrix |
| extends RealLinearOperator { |
| |
| /** The size of the matrix. */ |
| private final int n; |
| |
| /** |
| * Creates a new instance of this class. |
| * |
| * @param n Size of the matrix to be created. |
| */ |
| public InverseHilbertMatrix(final int n) { |
| this.n = n; |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public int getColumnDimension() { |
| return n; |
| } |
| |
| /** |
| * Returns the {@code (i, j)} entry of the inverse Hilbert matrix. Exact |
| * arithmetic is used; in case of overflow, an exception is thrown. |
| * |
| * @param i Row index (starts at 0). |
| * @param j Column index (starts at 0). |
| * @return The coefficient of the inverse Hilbert matrix. |
| */ |
| public long getEntry(final int i, final int j) { |
| long val = i + j + 1; |
| long aux = BinomialCoefficient.value(n + i, n - j - 1); |
| val = Math.multiplyExact(val, aux); |
| aux = BinomialCoefficient.value(n + j, n - i - 1); |
| val = Math.multiplyExact(val, aux); |
| aux = BinomialCoefficient.value(i + j, i); |
| val = Math.multiplyExact(val, aux); |
| val = Math.multiplyExact(val, aux); |
| return ((i + j) & 1) == 0 ? val : -val; |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public int getRowDimension() { |
| return n; |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public RealVector operate(final RealVector x) { |
| if (x.getDimension() != n) { |
| throw new DimensionMismatchException(x.getDimension(), n); |
| } |
| final double[] y = new double[n]; |
| for (int i = 0; i < n; i++) { |
| double pos = 0.; |
| double neg = 0.; |
| for (int j = 0; j < n; j++) { |
| final double xj = x.getEntry(j); |
| final long coeff = getEntry(i, j); |
| final double daux = coeff * xj; |
| // Positive and negative values are sorted out in order to limit |
| // catastrophic cancellations (do not forget that Hilbert |
| // matrices are *very* ill-conditioned! |
| if (daux > 0.) { |
| pos += daux; |
| } else { |
| neg += daux; |
| } |
| } |
| y[i] = pos + neg; |
| } |
| return new ArrayRealVector(y, false); |
| } |
| } |