#include <interpolation.hh>

Public Member Functions
	Interpolation (InterpolationType type, const std::vector< double > &input_x, const std::vector< double > &output_x)

	Interpolation (InterpolationType type, const double input_x, unsigned int input_x_size, const double output_x, unsigned int output_x_size)

const std::vector< int > &	left () const

const std::vector< int > &	right () const

const std::vector< double > &	alpha () const

int	left (size_t j) const

int	right (size_t j) const

double	alpha (size_t j) const

int	n_output () const

std::vector< double >	interpolate (const std::vector< double > &input_values) const
	Return interpolated values (on the output grid) given `input_values` on the input grid. More...

void	interpolate (const double input, double output) const

Private Member Functions
void	init_linear (const double input_x, unsigned int input_x_size, const double output_x, unsigned int output_x_size)

void	init_nearest (const double input_x, unsigned int input_x_size, const double output_x, unsigned int output_x_size)

void	init_piecewise_constant (const double input_x, unsigned int input_x_size, const double output_x, unsigned int output_x_size)

Private Attributes
std::vector< int >	m_left
	Interpolation indexes. More...

std::vector< int >	m_right

std::vector< double >	m_alpha
	Interpolation weights. More...

Detailed Description

Class encapsulating linear and piece-wise constant interpolation indexes and weights.

Most library interpolation routines (GSL's, for example) assume that we are working with a fixed function given on an input grid; these libraries support evaluating this function at arbitrary points. In this case an interpolation routine may use values on the input grid to create an interpolant, but has no knowledge of an "output grid."

In PISM we have a slightly different situation: we need to transfer several gridded functions between two fixed grids, so we can use both grids to compute interpolation weights, but cannot use values on the input grid.

If a point on the output grid is outside the interval defined by the input grid this code uses constant extrapolation.

This class isolates the code computing interpolation weights so that we can use these 1D weights in a 2D or 3D regridding code. This avoids code duplication: in bilinear (trilinear) interpolation X and Y (and Z) grid dimensions are treated the same. This also makes it possible to test the code computing interpolation weights in isolation.

We provide getters left(), right() and alpha().

Here left[i] is the index in the input grid (x_input) such that

input_x[left[i]] < output_x[i]

pism::Interpolation::left

const std::vector< int > & left() const

Definition: interpolation.cc:127

similar for right[i]:

input_x[right[i]] >= output_x[i]

pism::Interpolation::right

const std::vector< int > & right() const

Definition: interpolation.cc:131

When output_x[i] is outside the input interval left[i] and right[i] are adjusted so that the interpolation formula below corresponds to constant extrapolation.

alpha[i] is the linear interpolation weight used like this:

const int
  L = m_left[k],
  R = m_right[k];
const double Alpha = m_alpha[k];
result[k] = input_values[L] + Alpha * (input_values[R] - input_values[L]);

Piecewise constant 1D interpolation used for time-dependent forcing (fluxes that should be interpreted as piecewise-constant to simplify accounting of mass conservation).

Here input_x defines left end-points of intervals, For example, [0, 1] defines two intervals: [0, 1) and [1, x_e). Here the value x_e is irrelevant because we use constant extrapolation for points outside the interval covered by input data.

Definition at line 81 of file interpolation.hh.

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

src/util/interpolation.hh
src/util/interpolation.cc

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description