hermite.h

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// -*- C++ -*-

#if !defined(__numerical_interpolation_hermite_h__)
#define __numerical_interpolation_hermite_h__

#include "../polynomial/evaluate.h"

#include "../../ads/array/Array.h"

#include <functional>

BEGIN_NAMESPACE_NUMERICAL



template<typename T>
T
hermiteInterpolate(T t, T value0, T value1, T derivative0, T derivative1);



template<typename T>
void
computeHermitePolynomialCoefficients(T value0, T value1, 
                                     T derivative0, T derivative1,
                                     T* coefficients);


//----------------------------------------------------------------------------



template<typename T = double>
class Hermite : 
  public std::unary_function<T,T> {
private:

  typedef std::unary_function<T,T> Base;

public:

  typedef T Number;
  typedef typename Base::argument_type argument_type;
  typedef typename Base::result_type result_type;

private:
  
  // The lower bound of the range.
  Number _lowerBound;
  // Factor that will scale the argument to the index.
  Number _scaleToIndex;
  // Polynomial coefficients.
  ads::Array<1,Number> _coefficients;

  //
  // Not implemented.
  //

  // Default constructor not implemented.
  Hermite();

public:

  template<typename Function, typename Derivative>
  Hermite(const Function& function, const Derivative& derivative,
          Number closedLowerBound, Number openUpperBound, int numberOfPatches);


  Hermite(const Hermite& other);


  Hermite&
  operator=(const Hermite& other);

  ~Hermite()
  {}

  result_type
  operator()(argument_type x) const;
};


//----------------------------------------------------------------------------



template<typename T = double>
class HermiteFunctionDerivative : 
  public std::unary_function<T,T> {
private:

  typedef std::unary_function<T,T> Base;

public:

  typedef T Number;
  typedef typename Base::argument_type argument_type;
  typedef typename Base::result_type result_type;

private:
  
  // The lower bound of the range.
  Number _lowerBound;
  // Factor that will scale the argument to the index.
  Number _scaleToIndex;
  // The function and derivative values.
  ads::Array<1,Number> _functionAndDerivativeValues;

  //
  // Not implemented.
  //

  // Default constructor not implemented.
  HermiteFunctionDerivative();
  // Copy constructor not implemented.
  HermiteFunctionDerivative(const HermiteFunctionDerivative& other);
  // Assignment operator not implemented.
  HermiteFunctionDerivative&
  operator=(const HermiteFunctionDerivative& other);

public:

  template<typename Function, typename Derivative>
  HermiteFunctionDerivative(const Function& function, const Derivative& derivative,
          Number closedLowerBound, Number openUpperBound, int numberOfPatches);

  ~HermiteFunctionDerivative()
  {}

  result_type
  operator()(argument_type x) const;
};


END_NAMESPACE_NUMERICAL

#define __numerical_interpolation_hermite_ipp__
#include "hermite.ipp"
#undef __numerical_interpolation_hermite_ipp__

#endif

---