/*
    * 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.analysis.integration.gauss;
  
  import java.util.Arrays;
  
  import org.apache.commons.math4.legacy.analysis.polynomials.PolynomialFunction;
  import org.apache.commons.math4.legacy.analysis.polynomials.PolynomialsUtils;
  import org.apache.commons.math4.legacy.linear.EigenDecomposition;
  import org.apache.commons.math4.legacy.linear.MatrixUtils;
  import org.apache.commons.math4.legacy.linear.RealMatrix;
  import org.apache.commons.math4.legacy.core.Pair;
  
  /**
   * Factory that creates Gauss-type quadrature rule using Laguerre polynomials.
   *
   * @see <a href="http://en.wikipedia.org/wiki/Gauss%E2%80%93Laguerre_quadrature">Gauss-Laguerre quadrature (Wikipedia)</a>
   * @since 4.0
   */
  public class LaguerreRuleFactory extends BaseRuleFactory<Double> {
      /** {@inheritDoc} */
      @Override
      protected Pair<Double[], Double[]> computeRule(int numberOfPoints) {
          final RealMatrix companionMatrix = companionMatrix(numberOfPoints);
          final EigenDecomposition eigen = new EigenDecomposition(companionMatrix);
          final double[] roots = eigen.getRealEigenvalues();
          Arrays.sort(roots);
  
          final Double[] points = new Double[numberOfPoints];
          final Double[] weights = new Double[numberOfPoints];
  
          final int n1 = numberOfPoints + 1;
          final long n1Squared = n1 * (long) n1;
          final PolynomialFunction laguerreN1 = PolynomialsUtils.createLaguerrePolynomial(n1);
          for (int i = 0; i < numberOfPoints; i++) {
              final double xi = roots[i];
              points[i] = xi;
  
              final double val = laguerreN1.value(xi);
              weights[i] = xi / n1Squared / (val * val);
          }
  
          return new Pair<>(points, weights);
      }
  
      /**
       * @param degree Matrix dimension.
       * @return a square matrix.
       */
      private RealMatrix companionMatrix(final int degree) {
          final RealMatrix c = MatrixUtils.createRealMatrix(degree, degree);
  
          for (int i = 0; i < degree; i++) {
              c.setEntry(i, i, 2.0 * i + 1);
              if (i + 1 < degree) {
                  // subdiagonal
                  c.setEntry(i+1, i, -(i + 1));
              }
              if (i - 1 >= 0) {
                  // superdiagonal
                  c.setEntry(i-1, i, -i);
              }
          }
  
          return c;
      }
  }