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Java example source code file (InverseHilbertMatrix.java)

This example Java source code file (InverseHilbertMatrix.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

arrayrealvector, inversehilbertmatrix, override, reallinearoperator, realvector

The InverseHilbertMatrix.java Java example source code

/*
 * 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.math3.linear;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.util.ArithmeticUtils;
import org.apache.commons.math3.util.CombinatoricsUtils;

/**
 * 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 = CombinatoricsUtils.binomialCoefficient(n + i, n - j - 1);
        val = ArithmeticUtils.mulAndCheck(val, aux);
        aux = CombinatoricsUtils.binomialCoefficient(n + j, n - i - 1);
        val = ArithmeticUtils.mulAndCheck(val, aux);
        aux = CombinatoricsUtils.binomialCoefficient(i + j, i);
        val = ArithmeticUtils.mulAndCheck(val, aux);
        val = ArithmeticUtils.mulAndCheck(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);
    }
}

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