One-dimensional function y(x) defined using a grid of ordered pairs (x,y) and an interpolation rule. More...

#include <InterpolationGrid.hh>

Public Types
enum class	ExtrapolationMethod { Zero , Endpoint , Continue , Throw }
	Method to use for computing y(x) when the x value lies beyond the grid boundaries. More...

using	Grid = std::vector<OrderedPair>

using	GridConstIterator = typename std::vector<OrderedPair>::const_iterator

enum class	InterpolationMethod { Constant = 1 , LinearLinear = 2 , LinearLog = 3 , LogLinear = 4 , LogLog = 5 }
	Method to use for interpolating between (x,y) grid points. More...

using	OrderedPair = std::pair<FirstNumericType, SecondNumericType>

Public Member Functions
	InterpolationGrid (const Grid &grid, InterpolationMethod interp_method=InterpolationMethod::LinearLinear, ExtrapolationMethod extrap_method=ExtrapolationMethod::Zero)
	Create an InterpolationGrid from a vector of ordered pairs.

	InterpolationGrid (const std::vector< FirstNumericType > &xs, const std::vector< SecondNumericType > &ys, InterpolationMethod interp_method=InterpolationMethod::LinearLinear, ExtrapolationMethod extrap_method=ExtrapolationMethod::Zero)
	Create an InterpolationGrid from vectors of x and y values.

	InterpolationGrid (InterpolationMethod interp_method=InterpolationMethod::LinearLinear, ExtrapolationMethod extrap_method=ExtrapolationMethod::Zero)
	Create an InterpolationGrid without any grid points.

OrderedPair &	at (size_t j)
	Get a reference to the jth ordered pair from the grid.

const OrderedPair &	back () const
	Returns a reference to the last ordered pair.

void	clear ()
	Delete all ordered pairs from the grid.

ExtrapolationMethod	extrapolation_method () const
	Get the ExtrapolationMethod used by this InterpolationGrid.

const OrderedPair &	front () const
	Returns a reference to the first ordered pair.

std::function< SecondNumericType(FirstNumericType) >	get_function ()
	Get a std::function object that represents y(x) for this InterpolationGrid.

void	insert (FirstNumericType x, SecondNumericType y)
	Add a new ordered pair (x, y) to the grid.

SecondNumericType	interpolate (FirstNumericType x) const
	Compute y(x) using the current InterpolationMethod.

InterpolationMethod	interpolation_method () const
	Get the InterpolationMethod used by this InterpolationGrid.

GridConstIterator	lower_bound (const GridConstIterator &begin, const GridConstIterator &end, FirstNumericType x) const
	Returns a const_iterator to the first element of the grid for which the x value is not less than (i.e. greater than or equal to) x.

void	set_extrapolation_method (ExtrapolationMethod method)
	Set the ExtrapolationMethod to use.

void	set_interpolation_method (InterpolationMethod method)
	Set the InterpolationMethod to use.

size_t	size () const
	Get the number of ordered pairs on the grid.

GridConstIterator	upper_bound (const GridConstIterator &begin, const GridConstIterator &end, FirstNumericType x) const
	Returns a const_iterator to the first element of the grid for which the x value is greater than x.

Detailed Description

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>
class marley::InterpolationGrid< FirstNumericType, SecondNumericType >

One-dimensional function y(x) defined using a grid of ordered pairs (x,y) and an interpolation rule.

This class implements the one-dimensional interpolation rules described in the ENDF-6 formats manual for a grid of (x,y) pairs.

Template Parameters

FirstNumericType	type for the x values
SecondNumericType	type for the y values

Definition at line 37 of file InterpolationGrid.hh.

Member Typedef Documentation

◆ Grid

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

using marley::InterpolationGrid< FirstNumericType, SecondNumericType >::Grid = std::vector<OrderedPair>

Definition at line 42 of file InterpolationGrid.hh.

◆ GridConstIterator

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

using marley::InterpolationGrid< FirstNumericType, SecondNumericType >::GridConstIterator = typename std::vector<OrderedPair>::const_iterator

Definition at line 43 of file InterpolationGrid.hh.

◆ OrderedPair

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

using marley::InterpolationGrid< FirstNumericType, SecondNumericType >::OrderedPair = std::pair<FirstNumericType, SecondNumericType>

Definition at line 41 of file InterpolationGrid.hh.

Member Enumeration Documentation

◆ ExtrapolationMethod

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

enum class marley::InterpolationGrid::ExtrapolationMethod

strong

Method to use for computing y(x) when the x value lies beyond the grid boundaries.

The table below describes how y(x) is calculated using each of the allowed ExtrapolationMethod settings. In the notation used below, the lowest x value is called \(x_\text{left}\), the greatest x value is called \(x_\text{right}\), and their corresponding y values are called \(y_\text{left}\) and \(y_\text{right}\), respectively. The ExtrapolationMethod is only relevant when \(x < x_\text{left}\) or \(x > x_\text{right}\).

Extrapolation Methods
Method	Description
Zero	\(y = 0\)
Endpoint	\(y = \begin{cases} y_\text{left} & x < x_\text{left} \\ y_\text{right} & x > x_\text{right} \end{cases}\)
Continue	Use the usual InterpolationMethod formula with \(y = \begin{cases} y_1 = y_\text{left} \text{ and } y_2 = y_{\text{left}+1} & x < x_\text{left} \\ y_1 = y_{\text{right}-1} \text{ and } y_2 = y_\text{right} & x > x_\text{right} \end{cases}\) where \(y_{\text{left}+1}\) is the y value corresponding to the second-lowest x value, and \(y_{\text{right}-1}\) is the y value corresponding to the second-highest x value.

Definition at line 96 of file InterpolationGrid.hh.

97 { Zero, Endpoint,

◆ InterpolationMethod

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

enum class marley::InterpolationGrid::InterpolationMethod

strong

Method to use for interpolating between (x,y) grid points.

For \(x_1 \leq x < x_2\), the table below describes how the corresponding y value is calculated using each of the allowed InterpolationMethod settings.

Interpolation Methods
Method	Description
Constant	\(y = y_1\)
LinearLinear	\(y = y_1 + \frac{y_2 - y_1}{x_2 - x_1}(x - x_1) \)
LinearLog	\(y = \exp\left[\ln(y_1) + \frac{\ln(y_2) - \ln(y_1)}{x_2 - x_1}(x - x_1)\right] \)
LogLinear	\(y = y_1 + \frac{y_2 - y_1}{\ln[x_2] - \ln[x_1]}[\ln(x) - \ln(x_1)] \)
LogLog	\(y = \exp\left[\ln(y_1) + \frac{\ln(y_2) - \ln(y_1)}{\ln(x_2) - \ln(x_1)}(\ln[x] - \ln[x_1])\right] \)

Definition at line 63 of file InterpolationGrid.hh.

64 { Constant = 1,

65 LinearLinear = 2, LinearLog = 3, LogLinear = 4,

Constructor & Destructor Documentation

◆ InterpolationGrid() [1/3]

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

marley::InterpolationGrid< FirstNumericType, SecondNumericType >::InterpolationGrid	(	InterpolationMethod	interp_method = InterpolationMethod::LinearLinear,
		ExtrapolationMethod	extrap_method = ExtrapolationMethod::Zero )

inline

Create an InterpolationGrid without any grid points.

Definition at line 100 of file InterpolationGrid.hh.

                                    : interpolation_method_( interp_method ),
        extrapolation_method_( extrap_method )
      {

◆ InterpolationGrid() [2/3]

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

marley::InterpolationGrid< FirstNumericType, SecondNumericType >::InterpolationGrid	(	const Grid &	grid,
		InterpolationMethod	interp_method = InterpolationMethod::LinearLinear,
		ExtrapolationMethod	extrap_method = ExtrapolationMethod::Zero )

inline

Create an InterpolationGrid from a vector of ordered pairs.

Todo: Add error checks for the supplied grid

Definition at line 108 of file InterpolationGrid.hh.

        : interpolation_method_( interp_method ),
        extrapolation_method_( extrap_method ), ordered_pairs_( grid )
      {

◆ InterpolationGrid() [3/3]

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

marley::InterpolationGrid< FirstNumericType, SecondNumericType >::InterpolationGrid	(	const std::vector< FirstNumericType > &	xs,
		const std::vector< SecondNumericType > &	ys,
		InterpolationMethod	interp_method = InterpolationMethod::LinearLinear,
		ExtrapolationMethod	extrap_method = ExtrapolationMethod::Zero )

inline

Create an InterpolationGrid from vectors of x and y values.

Definition at line 118 of file InterpolationGrid.hh.

        : interpolation_method_( interp_method ),
        extrapolation_method_( extrap_method )
      {
        if ( xs.size() != ys.size() ) throw marley::Error(
          std::string("Vectors of x and y values passed to the constructor")
          + " of marley::InterpolationGrid have unequal sizes." );
 
        double old_x = marley_utils::minus_infinity;
        for ( size_t j = 0; j < xs.size(); ++j ) {
          double new_x = xs.at( j );
          if ( new_x <= old_x ) throw marley::Error( "The grid point x-values"
            " defined for a marley::InterpolationGrid object are not strictly"
            " increasing" );
          ordered_pairs_.push_back( OrderedPair( xs.at(j), ys.at(j) ) );
        }

Member Function Documentation

◆ at()

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

OrderedPair & marley::InterpolationGrid< FirstNumericType, SecondNumericType >::at ( size_t j )

inline

Get a reference to the jth ordered pair from the grid.

Definition at line 152 of file InterpolationGrid.hh.

◆ back()

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

const OrderedPair & marley::InterpolationGrid< FirstNumericType, SecondNumericType >::back ( ) const

inline

Returns a reference to the last ordered pair.

Definition at line 187 of file InterpolationGrid.hh.

◆ clear()

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

void marley::InterpolationGrid< FirstNumericType, SecondNumericType >::clear ( )

inline

Delete all ordered pairs from the grid.

Definition at line 149 of file InterpolationGrid.hh.

◆ extrapolation_method()

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

ExtrapolationMethod marley::InterpolationGrid< FirstNumericType, SecondNumericType >::extrapolation_method ( ) const

inline

Get the ExtrapolationMethod used by this InterpolationGrid.

Definition at line 198 of file InterpolationGrid.hh.

◆ front()

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

const OrderedPair & marley::InterpolationGrid< FirstNumericType, SecondNumericType >::front ( ) const

inline

Returns a reference to the first ordered pair.

Definition at line 184 of file InterpolationGrid.hh.

◆ get_function()

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

std::function< SecondNumericType(FirstNumericType) > marley::InterpolationGrid< FirstNumericType, SecondNumericType >::get_function ( )

inline

Get a std::function object that represents y(x) for this InterpolationGrid.

Definition at line 156 of file InterpolationGrid.hh.

      {
        return [ this ]( FirstNumericType x )
          -> SecondNumericType { return this->interpolate( x ); };

◆ insert()

template<typename FirstNumericType, typename SecondNumericType>

void marley::InterpolationGrid< FirstNumericType, SecondNumericType >::insert	(	FirstNumericType	x,
		SecondNumericType	y )

Add a new ordered pair (x, y) to the grid.

Definition at line 343 of file InterpolationGrid.hh.

  {
    // Figure out where this grid point should go in the grid. Use
    // std::upper_bound so that entries with the same x value (discontinuities)
    // are inserted in the order that they are passed to
    // InterpolationGrid::insert.
    GridConstIterator insert_point = upper_bound( ordered_pairs_.begin(),
      ordered_pairs_.end(), x );
 
    // Insert the new grid point
    ordered_pairs_.insert( insert_point, OrderedPair(x, y) );
  }

References upper_bound().

◆ interpolate()

template<typename FirstNumericType, typename SecondNumericType>

SecondNumericType marley::InterpolationGrid< FirstNumericType, SecondNumericType >::interpolate ( FirstNumericType x ) const

Compute y(x) using the current InterpolationMethod.

Definition at line 269 of file InterpolationGrid.hh.

  {
    // Find grid points just below [(x1, y1)] and just above [(x2, y2)]
    InterpolationGrid::GridConstIterator lower_point, upper_point;
    // Includes a call to check_grid()
    bool extrapolate = find_bin_limits( x, lower_point, upper_point );
 
    // If the requested x value is outside of the grid, use the correct method
    // for dealing with this situation based on the value of
    if ( extrapolate ) {
      if ( extrapolation_method_ == ExtrapolationMethod::Zero )
        return static_cast< SecondNumericType >( 0. );
      else if ( extrapolation_method_ == ExtrapolationMethod::Endpoint ) {
        if ( lower_point->first > x ) return lower_point->second;
        else return upper_point->second;
      }
      else if ( extrapolation_method_ == ExtrapolationMethod::Throw ) {
        throw marley::Error( "x = " + std::to_string( x )
          + " lies outside of the current interpolation grid object"
          " (which extends from x_min = "
          + std::to_string( ordered_pairs_.front().first )
          + " and x_max = " + std::to_string( ordered_pairs_.back().first )
          + ") and extrapolation is disabled." );
      }
    }
 
    // Either the requested point falls within the grid or
    // extrapolation_method == ExtrapolationMethod::Continue. If the "continue"
    // method for extrapolation is selected, then we continue to use the same
    // interpolation technique formula outside of the grid (for
    // InterpolationMethod::LinearLinear, this is linear-linear extrapolation).
 
    // If the constant interpolation method is selected, then use the *lower
    // bound* of each bin as the interpolated value. If we're extrapolating,
    // on the right, use the upper bound.
    if ( interpolation_method_ == InterpolationMethod::Constant ) {
      if ( !extrapolate ) return lower_point->second;
      else if ( lower_point->first > x ) return lower_point->second;
      else return upper_point->second;
    }
 
    // We'll use an interpolation formula for all other methods, so
    // get the grid point x and y values for later use.
    FirstNumericType x1 = lower_point->first;
    FirstNumericType x2 = upper_point->first;
    SecondNumericType y1 = lower_point->second;
    SecondNumericType y2 = upper_point->second;
 
    bool log_x = false, log_y = false;
    FirstNumericType x_to_use = x;
    if ( interpolation_method_ == InterpolationMethod::LinearLog )
      log_x = true;
    else if ( interpolation_method_ == InterpolationMethod::LogLinear )
      log_y = true;
    else if ( interpolation_method_ == InterpolationMethod::LogLog ) {
      log_x = true;
      log_y = true;
    }
    if ( log_x ) {
      x1 = std::log( x1 );
      x2 = std::log( x2 );
      x_to_use = std::log( x );
    }
    if ( log_y ) {
      y1 = std::log( y1 );
      y2 = std::log( y2 );
    }
 
    FirstNumericType y_interp = y1 + ( (y2 - y1)/(x2 - x1) )*( x_to_use - x1 );
    if ( log_y ) y_interp = std::exp( y_interp );
    return y_interp;
  }

References interpolate().

Referenced by marley::InterpolationMethod< double >::get_function(), and interpolate().

◆ interpolation_method()

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

InterpolationMethod marley::InterpolationGrid< FirstNumericType, SecondNumericType >::interpolation_method ( ) const

inline

Get the InterpolationMethod used by this InterpolationGrid.

Definition at line 190 of file InterpolationGrid.hh.

◆ lower_bound()

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

GridConstIterator marley::InterpolationGrid< FirstNumericType, SecondNumericType >::lower_bound	(	const GridConstIterator &	begin,
		const GridConstIterator &	end,
		FirstNumericType	x ) const

inline

Returns a const_iterator to the first element of the grid for which the x value is not less than (i.e. greater than or equal to) x.

Definition at line 164 of file InterpolationGrid.hh.

      {
        return std::lower_bound( begin, end, x,
          []( const OrderedPair& pair, const FirstNumericType& f )
          -> bool { return pair.first < f; } );

◆ set_extrapolation_method()

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

void marley::InterpolationGrid< FirstNumericType, SecondNumericType >::set_extrapolation_method ( ExtrapolationMethod method )

inline

Set the ExtrapolationMethod to use.

Definition at line 202 of file InterpolationGrid.hh.

◆ set_interpolation_method()

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

void marley::InterpolationGrid< FirstNumericType, SecondNumericType >::set_interpolation_method ( InterpolationMethod method )

inline

Set the InterpolationMethod to use.

Definition at line 194 of file InterpolationGrid.hh.

◆ size()

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

size_t marley::InterpolationGrid< FirstNumericType, SecondNumericType >::size ( ) const

inline

Get the number of ordered pairs on the grid.

Definition at line 146 of file InterpolationGrid.hh.

◆ upper_bound()

template<typename FirstNumericType, typename SecondNumericType = FirstNumericType>

GridConstIterator marley::InterpolationGrid< FirstNumericType, SecondNumericType >::upper_bound	(	const GridConstIterator &	begin,
		const GridConstIterator &	end,
		FirstNumericType	x ) const

inline

Returns a const_iterator to the first element of the grid for which the x value is greater than x.

Definition at line 174 of file InterpolationGrid.hh.

      {
        return std::upper_bound( begin, end, x,
          []( const FirstNumericType& f, const OrderedPair& pair )
          -> bool { return f < pair.first; } );

Referenced by insert().

The documentation for this class was generated from the following file:

/home/sjg/Desktop/marley/include/marley/InterpolationGrid.hh

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ Grid

◆ GridConstIterator

◆ OrderedPair

Member Enumeration Documentation

◆ ExtrapolationMethod

◆ InterpolationMethod

Constructor & Destructor Documentation

◆ InterpolationGrid() [1/3]

◆ InterpolationGrid() [2/3]

◆ InterpolationGrid() [3/3]

Member Function Documentation

◆ at()

◆ back()

◆ clear()

◆ extrapolation_method()

◆ front()

◆ get_function()

◆ insert()

◆ interpolate()

◆ interpolation_method()

◆ lower_bound()

◆ set_extrapolation_method()

◆ set_interpolation_method()

◆ size()

◆ upper_bound()