AkimaInterpolation.h

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//     ____   ______ __
//    / __ \ / ____// /
//   / /_/ // /    / /
//  / ____// /___ / /___   PixInsight Class Library
// /_/     \____//_____/   PCL 2.7.0
// ----------------------------------------------------------------------------
// pcl/AkimaInterpolation.h - Released 2024-06-18T15:48:54Z
// ----------------------------------------------------------------------------
// This file is part of the PixInsight Class Library (PCL).
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// ----------------------------------------------------------------------------
 
#ifndef __PCL_AkimaInterpolation_h
#define __PCL_AkimaInterpolation_h
 
 
#include <pcl/Defs.h>
#include <pcl/Diagnostics.h>
 
#include <pcl/UnidimensionalInterpolation.h>
 
namespace pcl
{
 
// ----------------------------------------------------------------------------
 
#define m_x this->m_x
#define m_y this->m_y
 
template <typename T = double>
class PCL_CLASS AkimaInterpolation : public UnidimensionalInterpolation<T>
{
public:
 
   using vector_type = typename UnidimensionalInterpolation<T>::vector_type;
 
   using coefficient_vector = vector_type;
 
   AkimaInterpolation() = default;
 
   AkimaInterpolation( const AkimaInterpolation& ) = default;
 
   AkimaInterpolation( AkimaInterpolation&& ) = default;
 
   AkimaInterpolation& operator =( const AkimaInterpolation& ) = default;
 
   AkimaInterpolation& operator =( AkimaInterpolation&& ) = default;
 
   ~AkimaInterpolation() override
   {
   }
 
   void Initialize( const vector_type& x, const vector_type& y ) override
   {
      if ( y.Length() < 5 )
         throw Error( "AkimaInterpolation::Initialize(): Less than five data points specified." );
 
      try
      {
         Clear();
         UnidimensionalInterpolation<T>::Initialize( x, y );
 
         int n = m_y.Length();
         int N = n-1; // Number of subintervals
 
         m_b = coefficient_vector( N );
         m_c = coefficient_vector( N );
         m_d = coefficient_vector( N );
 
         // Chordal slopes
         coefficient_vector m0( N+4 ); // room for 4 additional prescribed slopes
         T* m = m0.At( 2 );            // allow negative subscripts m[-1] and m[-2]
 
         // Akima left-hand slopes to support corners
         coefficient_vector tL( n );
 
         // Calculate chordal slopes for each subinterval
         if ( m_x )
            for ( int i = 0; i < N; ++i )
            {
               T h = m_x[i+1] - m_x[i];
               if ( 1 + h*h == 1 )
                  throw Error( "AkimaInterpolation::Initialize(): Empty interpolation subinterval(s)." );
               m[i] = (m_y[i+1] - m_y[i])/h;
            }
         else
            for ( int i = 0; i < N; ++i )
               m[i] = m_y[i+1] - m_y[i];
 
         // Prescribed slopes at ending locations
         m[-2 ] = 3*m[  0] - 2*m[  1];
         m[-1 ] = 2*m[  0] -   m[  1];
         m[ N ] = 2*m[N-1] -   m[N-2];
         m[N+1] = 3*m[N-1] - 2*m[N-2];
 
         /*
          * Akima left-hand and right-hand slopes.
          * Right-hand slopes are just the interpolation coefficients bi.
          */
         for ( int i = 0; i < n; ++i )
         {
            T f = Abs( m[i-1] - m[i-2] );
            T e = Abs( m[i+1] - m[i] ) + f;
            if ( 1 + e != 1 )
            {
               tL[i] = m[i-1] + f*(m[i] - m[i-1])/e;
               if ( i < N )
                  m_b[i] = tL[i];
            }
            else
            {
               tL[i] = m[i-1];
               if ( i < N )
                  m_b[i] = m[i];
            }
         }
 
         /*
          * Interpolation coefficients m_b[i], m_c[i], m_d[i]. 'ai'
          * coefficients are the m_y[i] ordinate values.
          */
         for ( int i = 0; i < N; ++i )
         {
            m_c[i] = 3*m[i] - 2*m_b[i] - tL[i+1];
            m_d[i] = m_b[i] + tL[i+1] - 2*m[i];
 
            if ( m_x )
            {
               T h = m_x[i+1] - m_x[i];
               m_c[i] /= h;
               m_d[i] /= h*h;
            }
         }
      }
      catch ( ... )
      {
         Clear();
         throw;
      }
   }
 
   PCL_HOT_FUNCTION
   double operator()( double x ) const override
   {
      PCL_PRECONDITION( IsValid() )
 
      /*
       * Find the subinterval i0 such that m_x[i0] <= x < m_x[i0+1].
       * Find the distance dx = x - m_x[i], or dx = x - i for implicit x = {0,1,...n-1}.
       */
      int i0;
      double dx;
      if ( m_x )
      {
         i0 = 0;
         int i1 = m_x.Length() - 1;
         // if trying to extrapolate, return zero.
         if ( unlikely( x < m_x[0] || x > m_x[i1] ) )
            return 0;
         while ( i1-i0 > 1 )
         {
            int im = (i0 + i1) >> 1;
            if ( x < m_x[im] )
               i1 = im;
            else
               i0 = im;
         }
         dx = x - double( m_x[i0] );
      }
      else
      {
         if ( x <= 0 )
            return m_y[0];
         if ( x >= m_y.Length()-1 )
            return m_y[m_y.Length()-1];
         i0 = TruncInt( x );
         dx = x - i0;
      }
 
      /*
       * Use a Horner scheme to calculate b[i]*dx + c[i]*dx^2 + d[i]*dx^3.
       */
      return m_y[i0] + dx*(m_b[i0] + dx*(m_c[i0] + dx*m_d[i0]));
   }
 
   void Clear() override
   {
      m_b.Clear();
      m_c.Clear();
      m_d.Clear();
      UnidimensionalInterpolation<T>::Clear();
   }
 
   bool IsValid() const override
   {
      return m_b && m_c && m_d;
   }
 
protected:
 
   /*
    * Interpolating coefficients for each subinterval.
    * The coefficients for dx^0 are the input ordinate values in the m_y vector.
    */
   coefficient_vector m_b; // coefficients for dx^1
   coefficient_vector m_c; // coefficients for dx^2
   coefficient_vector m_d; // coefficients for dx^3
};
 
#undef m_x
#undef m_y
 
// ----------------------------------------------------------------------------
 
} // pcl
 
#endif  // __PCL_AkimaInterpolation_h
 
// ----------------------------------------------------------------------------
// EOF pcl/AkimaInterpolation.h - Released 2024-06-18T15:48:54Z