tablelookup

Return value based on interpolating set of data points

Syntax

tablelookup(x1d, x2d, x3d, x4d, fd, x1, x2, x3, x4, interpolation = linear|smooth, extrapolation = linear|nearest|error)

Description

Use the tablelookup function in the equations section to compute an output value by interpolating the query input value against a set of data points. This functionality is similar to that of the Simulink^® and Simscape™ Lookup Table blocks. It allows you to incorporate table-driven modeling directly in your custom block, without the need of connecting an external Lookup Table block to your model.

The tablelookup function supports one-dimensional, two-dimensional, three-dimensional, and four-dimensional lookup tables. The full syntax is:

tablelookup(x1d, x2d, x3d, x4d, fd, x1, x2, x3, x4, interpolation = linear|smooth, extrapolation = linear|nearest|error)

`x1d`	Data set of input values along the first direction, specified as a one-dimensional array. The values must be strictly monotonic, either increasing or decreasing. This is a required argument.
`x2d`	Data set of input values along the second direction, specified as a one-dimensional array. The values must be strictly monotonic, either increasing or decreasing. This argument is used only for the two-dimensional, three-dimensional, and four-dimensional table lookup.
`x3d`	Data set of input values along the third direction, specified as a one-dimensional array. The values must be strictly monotonic, either increasing or decreasing. This argument is used only for the three-dimensional and four-dimensional table lookup.
`x4d`	Data set of input values along the fourth direction, specified as a one-dimensional array. The values must be strictly monotonic, either increasing or decreasing. This argument is used only for the four-dimensional table lookup.
`fd`	Data set of output values for the table lookup. This is a required argument. For one-dimensional table lookup, `fd` must be a one-dimensional array of the same size as `x1d`. For two-dimensional table lookup, `fd` must be a two-dimensional array, with the size matching the dimensions defined by the input data sets. For example, if `x1d` is a 1-by-`m` array, and `x2d` is a 1-by-`n` array, then `fd` must be an `m`-by-`n` matrix. For three-dimensional table lookup, `fd` must be a three-dimensional array, with the size matching the dimensions defined by the input data sets. For example, if `x1d` is a 1-by-`m` array, `x2d` is a 1-by-`n` array, and `x3d` is a 1-by-`p` array, then `fd` must be an `m`-by-`n`-by-`p` array. For four-dimensional table lookup, `fd` must be a four-dimensional array, with the size matching the dimensions defined by the input data sets. For example, if `x1d` is a 1-by-`m` array, `x2d` is a 1-by-`n` array, `x3d` is a 1-by-`p` array, and `x4d` is a 1-by-`q` array, then `fd` must be an `m`-by-`n`-by-`p`-by-`q` array.
`x1`	The query input value along the first direction, specified as a scalar or as a one-dimensional 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 a one-dimensional array of the same size as `x1`. Its units must be commensurate with the units of `x2d`. This argument is used only for the two-dimensional, three-dimensional, and four-dimensional table lookup.
`x3`	The query input value along the third direction, specified as a scalar or as a one-dimensional array of the same size as `x1`. Its units must be commensurate with the units of `x3d`. This argument is used only for the three-dimensional and four-dimensional table lookup.
`x4`	The query input value along the fourth direction, specified as a scalar or as a one-dimensional array of the same size as `x1`. Its units must be commensurate with the units of `x4d`. This argument is used only for the four-dimensional table lookup.
`interpolation = linear\|smooth`	Optional argument that specifies the approximation method for calculating the output value when the input value is inside the range specified in the lookup table. The default is `interpolation = linear`.
`extrapolation = linear\|nearest\|error`	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 interpolation argument values are:

linear — For one-dimensional table lookup, uses a linear function. For two-dimensional and three-dimensional table lookup, uses an extension of linear algorithm for multidimensional interpolation, by performing linear interpolation in first direction, then in second direction, and then in third direction. Use this method to get the best performance.
smooth — Uses a modified Akima algorithm. For more information, see makima. Use this method to produce a continuous curve or surface with continuous first-order derivatives.

The extrapolation argument values are:

linear— Extends from the edge of the interpolation region linearly. The slope of the linear extrapolation is equal to the slope of the interpolated curve or surface at the edge of the interpolation region. Use this method to produce a curve or surface with continuous value and continuous first-order derivatives at the boundary between the interpolation region and the extrapolation region.
nearest — Extends from the edge of the interpolation region as a constant. The value of the nearest extrapolation is equal to the value of the interpolated curve or surface at the edge of the interpolation region. Use this method to produce a curve or surface with continuous value at the boundary between the interpolation region and the extrapolation region that does not go above the highest point in the data or below the lowest point in the data.
error — Generates an error when the input value is outside the range specified in the lookup table.

The function returns an output value, in the units specified for fd, by looking up or estimating table values based on the input values:

When inputs `x1`, `x2`, `x3`, and `x4`...	The `tablelookup` function...
Match the values in the input data sets, `x1d`, `x2d`, `x3d`, and `x4d`	Outputs the corresponding table value, `fd`
Do not match the values in the input data sets, but are within range	Interpolates appropriate table values, using the method specified as the `interpolation` argument value
Do not match the values in the input data sets, and are out of range	Extrapolates the output value, using the method specified as the `extrapolation` argument value

If the query input values x1, x2, x3, and x4 are:

Scalar, then the function returns a scalar.
One-dimensional arrays, then the function returns a one-dimensional array of the same size.

Error Checking

The following rules apply to data sets x1d, x2d, x3d, x4d, and fd:

For one-dimensional table lookup, x1d and fd must be one-dimensional arrays of the same size.
For two-dimensional table lookup, x1d and x2d must be one-dimensional arrays, and fd must be a matrix, with the size matching the dimensions defined by the input data sets. For example, if x1d is a 1-by-m array, and x2d is a 1-by-n array, then fd must be an m-by-n matrix.
For three-dimensional table lookup, x1d, x2d, and x3d must be one-dimensional arrays, and fd must be a three-dimensional array, with the size matching the dimensions defined by the input data sets. For example, if x1d is a 1-by-m array, x2d is a 1-by-n array, and x3d is a 1-by-p array, then fd must be an m-by-n-by-p array.
For four-dimensional table lookup, x1d, x2d, x3d, and x4d must be one-dimensional arrays, and fd must be a four-dimensional array, with the size matching the dimensions defined by the input data sets. For example, if x1d is a 1-by-m array, x2d is a 1-by-n array, x3d is a 1-by-p array, and x4d is a 1-by-q array, then fd must be an m-by-n-by-p-by-q array.
The x1d, x2d, x3d, and x4d values must be strictly monotonic, either increasing or decreasing.
For smooth interpolation, each data set of input values must contain at least three values. For linear interpolation, two values are sufficient.

Using Enumerations for Interpolation and Extrapolation Options

The Foundation library includes built-in enumerations, interpolation.m and extrapolation.m:

classdef interpolation < int32
   enumeration
       linear (1)
       smooth (2)
   end
   methods(Static)
    function map = displayText()
      map = containers.Map;
      map('linear') = 'Linear';
      map('smooth') = 'Smooth';
    end
  end
end

classdef extrapolation < int32
   enumeration
       linear (1)
       nearest (2)
       error (3)
   end
   methods(Static)
    function map = displayText()
      map = containers.Map;
      map('linear') = 'Linear';
      map('nearest') = 'Nearest';
      map('error') = 'Error';
    end
  end
end

These enumerations are located in the directory matlabroot\toolbox\physmod\simscape\library\m\+simscape\+enum.

You can use these enumerations to declare component parameters, and then use these parameters as tablelookup function arguments. For more information, see the User-Specified Interpolation and Extrapolation Methods example and Using Enumeration in Function Arguments.

Examples

1D Lookup Table Implementation

This example implements a one-dimensional lookup table with linear interpolation and extrapolation.

component tlu_1d_linear
 inputs
   u = 0;
 end
 outputs
   y = 0;
 end
 parameters (Size=variable)
   xd = [1 2 3 4];
   yd = [1 2 3 4];
 end
 equations
   y == tablelookup(xd, yd, u);
 end
end

xd and yd are declared as variable-size parameters. This enables the block users to provide their own data sets when the component is converted to a custom block. For more information, see Using Lookup Tables in Equations.

The xd values must be strictly monotonic, either increasing or decreasing. yd must have the same size as xd.

2D Lookup Table Implementation

This example implements a two-dimensional lookup table with specific interpolation and extrapolation methods.

component tlu_2d
 inputs
   u1 = 0;
   u2 = 0;
 end
 outputs
   f = 0;
 end
 parameters (Size=variable)
   x1d = [1 2 3 4];
   x2d = [1 2 3];
   fd = [1 2 3; 3 4 5; 5 6 7; 7 8 9];
 end
 equations
   f == tablelookup(x1d, x2d, fd, u1, u2, interpolation=smooth, extrapolation=nearest);
 end
end

x1d, x2d, and fd are declared as variable-size parameters. The x1d and x2d vector values must be strictly monotonic, either increasing or decreasing. For smooth interpolation, each vector must have at least three values. The size of the fd matrix must match the dimensions of the x1d and x2d vectors.

The interpolation uses the modified Akima algorithm, makima. The extrapolation uses the nearest value of fd for out-of-range u1 and u2 values.

User-Specified Interpolation and Extrapolation Methods

This example is similar to the previous one, but it gives the block user control over the interpolation and extrapolation methods.

import simscape.enum.*
component tlu_2d_enum
 inputs
   u1 = 0;
   u2 = 0;
 end
 outputs
   f = 0;
 end
 parameters (Size=variable)
   x1d = [1 2 3 4];
   x2d = [1 2 3];
   fd = [1 2 3; 3 4 5; 5 6 7; 7 8 9];
 end
 parameters
   interp = interpolation.linear; % Interpolation method
   extrap = extrapolation.linear; % Extrapolation method
 end
 equations
   f == tablelookup(x1d, x2d, fd, u1, u2, interpolation=interp, extrapolation=extrap);
 end
end

The component imports the built-in enumerations, and then uses them to declare two additional parameters: interp (Interpolation method) and extrap (Extrapolation method). The tablelookup function uses these parameters as arguments, to specify the interpolation and extrapolation methods. For more information, see Using Enumeration in Function Arguments.

The block generated from this component will have the Interpolation method and Extrapolation method parameters, both with the default value of Linear. The block user can select any other interpolation and extrapolation options.

Using Lookup Table with Units

This example implements a one-dimensional lookup table with units, to map temperature to pressure, with linear interpolation and extrapolation.

component TtoP
 inputs
   u = {0,'K'}; % temperature
 end
 outputs
   y = {0,'Pa'}; % pressure
 end
 parameters (Size=variable)
   xd = {[100 200 300 400] 'K'};
   yd = {[1e5 2e5 3e5 4e5] 'Pa'};
 end
 equations
   y == tablelookup(xd,yd,u);
 end
end

xd and yd are declared as variable-size parameters with units. This enables the block users to provide their own data sets when the component is converted to a custom block, and also to select commensurate units from the drop-downs in the custom block dialog box. For more information, see Using Lookup Tables in Equations.