Package org.hipparchus.analysis.interpolation

Class GridAxis

java.lang.Object
org.hipparchus.analysis.interpolation.GridAxis
All Implemented Interfaces:
Serializable
public class GridAxis extends Object implements Serializable
Helper for finding interpolation nodes along one axis of grid data.

This class is intended to be used for interpolating inside grids. It works on any sorted data without duplication and size at least n where n is the number of points required for interpolation (i.e. 2 for linear interpolation, 3 for quadratic...)

The method uses linear interpolation to select the nodes indices. It should be O(1) for sufficiently regular data, therefore much faster than bisection. It also features caching, which improves speed when interpolating several points in raw in the close locations, i.e. when successive calls have a high probability to return the same interpolation nodes. This occurs for example when scanning with small steps a loose grid. The method also works on non-regular grids, but may be slower in this case.

This class is thread-safe.

Since:
1.4
See Also:

  • Constructor Summary

    Constructors
    Constructor
    Description
    GridAxis(double[] grid, int n)
    Simple constructor.

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    getN()
    Get the number of points required for interpolation.
    int
    interpolationIndex(double t)
    Get the index of the first interpolation node for some coordinate along the grid.
    double
    node(int index)
    Get the interpolation node at specified index.
    int
    size()
    Get the number of points of the grid.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • GridAxis

      public GridAxis(double[] grid, int n) throws MathIllegalArgumentException
      Simple constructor.
      Parameters:
      grid - coordinates of the interpolation points, sorted in increasing order
      n - number of points required for interpolation, i.e. 2 for linear, 3 for quadratic...
      Throws:
      MathIllegalArgumentException - if grid size is smaller than n or if the grid is not sorted in strict increasing order

  • Method Details

    • size

      public int size()
      Get the number of points of the grid.
      Returns:
      number of points of the grid

    • getN

      public int getN()
      Get the number of points required for interpolation.
      Returns:
      number of points required for interpolation

    • node

      public double node(int index)
      Get the interpolation node at specified index.
      Parameters:
      index - node index
      Returns:
      coordinate of the node at specified index

    • interpolationIndex

      public int interpolationIndex(double t)
      Get the index of the first interpolation node for some coordinate along the grid.

      The index return is the one for the lowest interpolation node suitable for t. This means that if i is returned the nodes to use for interpolation at coordinate t are at indices i, i+1, ..., i+n-1, where n is the number of points required for interpolation passed at construction.

      The index is selected in order to have the subset of nodes from i to i+n-1 as balanced as possible around t:

      • if t is inside the grid and sufficiently far from the endpoints
        • if n is even, the returned nodes will be perfectly balanced: there will be n/2 nodes smaller than t and n/2 nodes larger than t
        • if n is odd, the returned nodes will be slightly unbalanced by one point: there will be (n+1)/2 nodes smaller than t and (n-1)/2 nodes larger than t
      • if t is inside the grid and close to endpoints, the returned nodes will be unbalanced: there will be less nodes on the endpoints side and more nodes on the interior side
      • if t is outside of the grid, the returned nodes will completely off balance: all nodes will be on the same side with respect to t

      It is not an error to call this method with t outside of the grid, it simply implies that the interpolation will become an extrapolation and accuracy will decrease as t goes farther from the grid points. This is intended so interpolation does not fail near the end of the grid.

      Parameters:
      t - coordinate of the point to interpolate
      Returns:
      index i such node(i), node(i+1), ... node(i+n-1) can be used for interpolating a value at coordinate t
      Since:
      1.4