// ---------------------------------------------------------------------
//
// Copyright (C) 2012 - 2022 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------

#ifndef dealii_tensor_product_polynomials_const_h
#define dealii_tensor_product_polynomials_const_h


#include <deal.II/base/config.h>

#include <deal.II/base/exceptions.h>
#include <deal.II/base/point.h>
#include <deal.II/base/polynomial.h>
#include <deal.II/base/tensor.h>
#include <deal.II/base/tensor_product_polynomials.h>
#include <deal.II/base/utilities.h>

#include <vector>

DEAL_II_NAMESPACE_OPEN


/**
 * @addtogroup Polynomials
 * @{
 */

/**
 * Tensor product of given polynomials and a locally constant function. This
 * class inherits most of its functionality from TensorProductPolynomials. It
 * works similarly to that class but adds a constant function for the last
 * index.
 */
template <int dim>
class TensorProductPolynomialsConst : public ScalarPolynomialsBase<dim>
{
public:
  /**
   * Access to the dimension of this object, for checking and automatic
   * setting of dimension in other classes.
   */
  static constexpr unsigned int dimension = dim;

  /**
   * Constructor. <tt>pols</tt> is a vector of objects that should be derived
   * or otherwise convertible to one-dimensional polynomial objects. It will
   * be copied element by element into a private variable.
   */
  template <class Pol>
  TensorProductPolynomialsConst(const std::vector<Pol> &pols);

  /**
   * Print the list of <tt>tensor_polys</tt> indices to <tt>out</tt>.
   */
  void
  output_indices(std::ostream &out) const;

  /**
   * Set the ordering of the polynomials. Requires
   * <tt>renumber.size()==tensor_polys.n()</tt>.  Stores a copy of
   * <tt>renumber</tt>.
   */
  void
  set_numbering(const std::vector<unsigned int> &renumber);

  /**
   * Give read access to the renumber vector.
   */
  const std::vector<unsigned int> &
  get_numbering() const;

  /**
   * Give read access to the inverse renumber vector.
   */
  const std::vector<unsigned int> &
  get_numbering_inverse() const;

  /**
   * Compute the value and the first and second derivatives of each tensor
   * product polynomial at <tt>unit_point</tt>.
   *
   * The size of the vectors must either be equal 0 or equal n(). In the first
   * case, the function will not compute these values.
   *
   * If you need values or derivatives of all tensor product polynomials then
   * use this function, rather than using any of the compute_value(),
   * compute_grad() or compute_grad_grad() functions, see below, in a loop
   * over all tensor product polynomials.
   */
  void
  evaluate(const Point<dim> &           unit_point,
           std::vector<double> &        values,
           std::vector<Tensor<1, dim>> &grads,
           std::vector<Tensor<2, dim>> &grad_grads,
           std::vector<Tensor<3, dim>> &third_derivatives,
           std::vector<Tensor<4, dim>> &fourth_derivatives) const override;

  /**
   * Compute the value of the <tt>i</tt>th tensor product polynomial at
   * <tt>unit_point</tt>. Here <tt>i</tt> is given in tensor product
   * numbering.
   *
   * Note, that using this function within a loop over all tensor product
   * polynomials is not efficient, because then each point value of the
   * underlying (one-dimensional) polynomials is (unnecessarily) computed
   * several times.  Instead use the evaluate() function with
   * <tt>values.size()==</tt>n() to get the point values of all tensor
   * polynomials all at once and in a much more efficient way.
   */
  double
  compute_value(const unsigned int i, const Point<dim> &p) const override;

  /**
   * Compute the <tt>order</tt>th derivative of the <tt>i</tt>th tensor
   * product polynomial at <tt>unit_point</tt>. Here <tt>i</tt> is given in
   * tensor product numbering.
   *
   * Note, that using this function within a loop over all tensor product
   * polynomials is not efficient, because then each derivative value of the
   * underlying (one-dimensional) polynomials is (unnecessarily) computed
   * several times.  Instead use the evaluate() function, see above, with the
   * size of the appropriate parameter set to n() to get the point value of
   * all tensor polynomials all at once and in a much more efficient way.
   *
   * @tparam order The derivative order.
   */
  template <int order>
  Tensor<order, dim>
  compute_derivative(const unsigned int i, const Point<dim> &p) const;

  /**
   * @copydoc ScalarPolynomialsBase::compute_1st_derivative()
   */
  virtual Tensor<1, dim>
  compute_1st_derivative(const unsigned int i,
                         const Point<dim> & p) const override;

  /**
   * @copydoc ScalarPolynomialsBase::compute_2nd_derivative()
   */
  virtual Tensor<2, dim>
  compute_2nd_derivative(const unsigned int i,
                         const Point<dim> & p) const override;

  /**
   * @copydoc ScalarPolynomialsBase::compute_3rd_derivative()
   */
  virtual Tensor<3, dim>
  compute_3rd_derivative(const unsigned int i,
                         const Point<dim> & p) const override;

  /**
   * @copydoc ScalarPolynomialsBase::compute_4th_derivative()
   */
  virtual Tensor<4, dim>
  compute_4th_derivative(const unsigned int i,
                         const Point<dim> & p) const override;

  /**
   * Compute the grad of the <tt>i</tt>th tensor product polynomial at
   * <tt>unit_point</tt>. Here <tt>i</tt> is given in tensor product
   * numbering.
   *
   * Note, that using this function within a loop over all tensor product
   * polynomials is not efficient, because then each derivative value of the
   * underlying (one-dimensional) polynomials is (unnecessarily) computed
   * several times.  Instead use the evaluate() function, see above, with
   * <tt>grads.size()==</tt>n() to get the point value of all tensor
   * polynomials all at once and in a much more efficient way.
   */
  Tensor<1, dim>
  compute_grad(const unsigned int i, const Point<dim> &p) const override;

  /**
   * Compute the second derivative (grad_grad) of the <tt>i</tt>th tensor
   * product polynomial at <tt>unit_point</tt>. Here <tt>i</tt> is given in
   * tensor product numbering.
   *
   * Note, that using this function within a loop over all tensor product
   * polynomials is not efficient, because then each derivative value of the
   * underlying (one-dimensional) polynomials is (unnecessarily) computed
   * several times.  Instead use the evaluate() function, see above, with
   * <tt>grad_grads.size()==</tt>n() to get the point value of all tensor
   * polynomials all at once and in a much more efficient way.
   */
  Tensor<2, dim>
  compute_grad_grad(const unsigned int i, const Point<dim> &p) const override;

  /**
   * Return the number of tensor product polynomials plus the constant
   * function. For <i>n</i> 1d polynomials this is <i>n<sup>dim</sup>+1</i>.
   */
  unsigned int
  n() const;

  /**
   * Return the name of the space, which is
   * <tt>TensorProductPolynomialsConst</tt>.
   */
  std::string
  name() const override;

  /**
   * @copydoc ScalarPolynomialsBase::clone()
   */
  virtual std::unique_ptr<ScalarPolynomialsBase<dim>>
  clone() const override;

private:
  /**
   * The TensorProductPolynomials object
   */
  TensorProductPolynomials<dim> tensor_polys;

  /**
   * Index map for reordering the polynomials.
   */
  std::vector<unsigned int> index_map;

  /**
   * Index map for reordering the polynomials.
   */
  std::vector<unsigned int> index_map_inverse;
};

/** @} */


/* ---------------- template and inline functions ---------- */

#ifndef DOXYGEN

template <int dim>
template <class Pol>
inline TensorProductPolynomialsConst<dim>::TensorProductPolynomialsConst(
  const std::vector<Pol> &pols)
  : ScalarPolynomialsBase<dim>(1, Utilities::fixed_power<dim>(pols.size()) + 1)
  , tensor_polys(pols)
  , index_map(tensor_polys.n() + 1)
  , index_map_inverse(tensor_polys.n() + 1)
{}



template <int dim>
inline unsigned int
TensorProductPolynomialsConst<dim>::n() const
{
  return tensor_polys.n() + 1;
}



template <int dim>
inline const std::vector<unsigned int> &
TensorProductPolynomialsConst<dim>::get_numbering() const
{
  return index_map;
}


template <int dim>
inline const std::vector<unsigned int> &
TensorProductPolynomialsConst<dim>::get_numbering_inverse() const
{
  return index_map_inverse;
}


template <int dim>
inline std::string
TensorProductPolynomialsConst<dim>::name() const
{
  return "TensorProductPolynomialsConst";
}


template <>
inline unsigned int
TensorProductPolynomialsConst<0>::n() const
{
  return numbers::invalid_unsigned_int;
}


template <int dim>
template <int order>
Tensor<order, dim>
TensorProductPolynomialsConst<dim>::compute_derivative(
  const unsigned int i,
  const Point<dim> & p) const
{
  const unsigned int max_indices = tensor_polys.n();
  Assert(i <= max_indices, ExcInternalError());

  // treat the regular basis functions
  if (i < max_indices)
    return tensor_polys.template compute_derivative<order>(i, p);
  else
    // this is for the constant function
    return Tensor<order, dim>();
}



template <int dim>
inline Tensor<1, dim>
TensorProductPolynomialsConst<dim>::compute_1st_derivative(
  const unsigned int i,
  const Point<dim> & p) const
{
  return compute_derivative<1>(i, p);
}



template <int dim>
inline Tensor<2, dim>
TensorProductPolynomialsConst<dim>::compute_2nd_derivative(
  const unsigned int i,
  const Point<dim> & p) const
{
  return compute_derivative<2>(i, p);
}



template <int dim>
inline Tensor<3, dim>
TensorProductPolynomialsConst<dim>::compute_3rd_derivative(
  const unsigned int i,
  const Point<dim> & p) const
{
  return compute_derivative<3>(i, p);
}



template <int dim>
inline Tensor<4, dim>
TensorProductPolynomialsConst<dim>::compute_4th_derivative(
  const unsigned int i,
  const Point<dim> & p) const
{
  return compute_derivative<4>(i, p);
}

#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE

#endif
