/*=========================================================================
 *
 *  Copyright NumFOCUS
 *
 *  Licensed 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.txt
 *
 *  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.
 *
 *=========================================================================*/

#include "itkFEMUtility.h"

namespace itk
{
namespace fem
{

/* Add definition for static constexpr members

Reason: You have to provide the definition of the static member as well as the
declaration. The declaration and the initializer go inside the class,
but the member definition has to be in a single separate compilation unit.
*/

constexpr double GaussIntegrate::zero;
constexpr double GaussIntegrate::one;
constexpr double GaussIntegrate::two;
constexpr double GaussIntegrate::z[110];
constexpr double GaussIntegrate::w[110];

/**
 * Numerical integration (Gauss-Legendre formula).
 * Integrates function f(x) from x=a to x=b in n points.
 */
double
GaussIntegrate::Integrate(double (*f)(double), double a, double b, int n)
{
  /**
   * This subprogram produces the gauss-legendre numerical
   * integral for

   *   b
   * int   f(x)*dx
   *    a
   *
   * The number of nodes n must satisfy
   *    2 <= n <= 20
   * The following data statements contain the gauss-legendre
   * nodes for the interval [-1,1].
   */

  double scale, t, tl, tu, sum;
  int    i, m, ibase;

  /*  Begin integration  */

  scale = (b - a) / two;
  if ((n & 1) == 0)
  {
    m = n / 2;
    ibase = m * m;
    sum = zero;
  }
  else
  {
    m = (n - 1) / 2;
    ibase = (n * n - 1) / 4;
    sum = w[ibase + m] * (*f)((a + b) / two);
  }
  for (i = 1; i <= m; i++)
  {
    t = z[ibase + i - 1];
    tl = (a * (one + t) + (one - t) * b) / two;
    tu = (a * (one - t) + (one + t) * b) / two;
    sum = sum + w[ibase + i - 1] * ((*f)(tl) + (*f)(tu));
  }

  return scale * sum;
}

} // end namespace fem
} // end namespace itk