# PS Lookup Table (3D)

Approximate three-dimensional function using specified lookup method

• Library:
• Simscape / Foundation Library / Physical Signals / Lookup Tables

## Description

The PS Lookup Table (3D) block computes an approximation to some function `f=f(x1,x2,x3)` given the `x1`, `x2`, `x3`, `f` data points. The three inputs and the output are physical signals.

You define the lookup table by specifying the Table grid vector 1 parameter (vector of data points along the first axis), the Table grid vector 2 parameter (vector of data points along the second axis), the Table grid vector 3 parameter (vector of data points along the third axis), and the 3D array of table values parameter (array of output values).

The `x1`, `x2`, and `x3` data vectors must be strictly monotonic, either increasing or decreasing. The array size of the tabulated function values must match the dimensions defined by the input vectors. That is, if the three input vectors have sizes 1-by-`m`, 1-by-`n`, and 1-by-`p`, respectively, supply an `m`-by-`n`-by-`p` array of output values.

The block generates output based on the input grid lookup using the selected interpolation and extrapolation methods. You have a choice of two interpolation methods and two extrapolation methods. You also have an option for the block to issue an error if any of the input signal values is outside the respective table grid vector range.

## Ports

### Input

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Input value along the first axis.

Input value along the second axis.

Input value along the third axis.

### Output

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Output function value, based on applying the lookup table to the three input values.

## Parameters

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Specify the vector of input values along the first axis as a 1-by-`m` array. The input values vector must be strictly monotonic, either increasing or decreasing. The values can be nonuniformly spaced. For smooth interpolation, the vector must contain at least three values. For linear interpolation, two values are sufficient.

Specify the vector of input values along the second axis as a 1-by-`n` array. The input values vector must be strictly monotonic, either increasing or decreasing. The values can be nonuniformly spaced. For smooth interpolation, the vector must contain at least three values. For linear interpolation, two values are sufficient.

Specify the vector of input values along the third axis as a 1-by-`p` array. The input values vector must be strictly monotonic, either increasing or decreasing. The values can be nonuniformly spaced. For smooth interpolation, the vector must contain at least three values. For linear interpolation, two values are sufficient.

Specify the output values as an `m`-by-`n`-by-`p` array, defining the function values at the input grid vertices. The output array size must match the dimensions defined by the input vectors.

Select one of the following interpolation methods for approximating the output value when the input value is between two consecutive grid points:

• `Linear` — Uses an extension of linear algorithm for multidimensional interpolation. The method performs linear interpolation first in `x1`-direction, then in `x2`-direction, and then in `x3`-direction. Select this option to get the best performance.

• `Smooth` — Uses a modified Akima interpolation algorithm. For details, see `tablelookup`. Select this option to produce a continuous surface with continuous first-order derivatives.

Select one of the following extrapolation methods for determining the output value when the input value is outside the range specified in the argument list:

• `Linear` — Extends from the edge of the interpolation region linearly. The slope of the linear extrapolation is equal to the slope of the interpolated surface at the edge of the interpolation 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 surface at the edge of the interpolation region. Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.

• `Error` — Issues an error if any of the input signals is outside the range of the table. Select this option to avoid going into the extrapolation mode when you want your data to be within the table range.