scatteredlookup

Return value based on interpolating unstructured set of data points

Since R2023a

Parent Section: equations

Syntax

scatteredlookup(x1d, x2d, x3d, fd, x1, x2, x3, extrapolation = linear|nearest)

Description

Use the scatteredlookup function in the equations section to compute an output value by interpolating the query input value against an unstructured, or scattered, set of data points. Unlike the tablelookup function, these data points do not need to form a table grid. You provide the coordinates of a set of input data points and the function value at each of these data points. Then, you provide the coordinates of a query point or points and the scatteredlookup function returns the corresponding interpolated function value by using Delaunay triangulation.

The scatteredlookup function supports two-dimensional and three-dimensional lookup. The full syntax is:

scatteredlookup(x1d, x2d, x3d, fd, x1, x2, x3, extrapolation = linear|nearest)

x1d	Data set of input values along the first direction, specified as a one-dimensional array. Specify at least three values for two-dimensional lookup and at least four values for three-dimensional lookup. This is a required argument.
x2d	Data set of input values along the second direction, specified as a one-dimensional array of the same size as x1d. This is a required argument.
x3d	Data set of input values along the third direction, specified as a one-dimensional array of the same size as x1d. Use this argument only for the three-dimensional lookup.
fd	Data set of function values for the lookup, specified as a one-dimensional array of the same size as x1d. This is a required argument.
x1	The query input value along the first direction, specified as a scalar or as an N-D array. Its units must be commensurate with the units of x1d. This is a required argument.
x2	The query input value along the second direction, specified as a scalar or as an N-D array of the same size as x1. Its units must be commensurate with the units of x2d. This is a required argument.
x3	The query input value along the third direction, specified as a scalar or as an N-D array of the same size as x1. Its units must be commensurate with the units of x3d. Use this argument only for the three-dimensional lookup.
extrapolation = linear|nearest	Optional argument that specifies the approximation method for calculating the output value when the input value is outside the range specified in the lookup table. The default is extrapolation = linear.

The extrapolation argument values are:

• linear— Linear extrapolation based on boundary gradients.

• nearest — Nearest neighbor extrapolation. This method evaluates to the value of the nearest neighbor on the boundary.

If the query input values x1, x2, and x3 are:

• Scalar, then the function returns a scalar.

• N-D arrays, then the function returns an N-D array of the same size.

Examples

2D Scattered Lookup Implementation

This example implements a linear function (2x + 3y) by using a two-dimensional scattered lookup.

component slu_2d
 inputs
   u1;
   u2;
 end
 outputs
   f;
 end
 parameters (Size=variable)
   x = [1 2 5 3 4 8];
   y = [1 7 10 4 4.5 8];
   % function values form a linear function 2*x + 3*y  
   fd = [5 25 40 18 21.5 40];
 end
 equations
   f == scatteredlookup(x, y, fd, u1, u2, extrapolation=nearest);
 end
end

x, y, and fd are vectors of the same size. The x and y vectors provide the coordinates of five scattered data points, and for each of these points, fd provides the function value. For example, for the first point, 2x1+3x1=5.

The scatteredlookup function triangulates the data set. For two-dimensional interpolation, each vector must have at least three values. Providing additional data points helps construct finer triangles and provides better accuracy for linear interpolation.

If the values of inputs u1 and u2 are within the convex hull of the x and y vectors, the function determines the output value by performing linear interpolation inside the corresponding triangle constructed by the triangulation, that is, interpolates the fd values at the triangle vertices.

This example specifies extrapolation=nearest. Therefore, if the values of inputs u1 and u2 are outside the convex hull of the data set, the function provides the fd value of the nearest neighbor on the boundary.

Version History

Introduced in R2023a