Learn more about Simulink

Lookup Table (2-D) - Approximate two-dimensional function

Library

Lookup Tables

Description

The Lookup Table (2-D) block computes an approximation to a function z = f(x,y) given x, y, z data points. The first input port corresponds to the first table dimension, x. (See How to Rotate a Block in the Simulink documentation for a description of the port order for various block orientations.)

The Row index input values parameter is a 1-by-m vector of x data points, the Column index input values parameter is a 1-by-n vector of y data points, and the Table data parameter is an m-by-n matrix of z data points. Both the row and column vectors must be monotonically increasing (i.e., the value of the next element in the vector is greater than or equal to the value of the preceding element). However, these vectors must be strictly monotonically increasing (i.e., the value of the next element in the vector is greater than the value of the preceding element) in the following cases:

The input and output data types are both fixed-point.
The input and output data types are different.
The lookup method is not Interpolation-Extrapolation.
The matrix of output values is complex.
Minimum, maximum, and overflow logging is on.

Tip Evenly-spaced breakpoints can make Real-Time Workshop generated code division-free. For more information, see fixpt_evenspace_cleanup in the Simulink documentation and Identify questionable fixed-point operations in the Real-Time Workshop documentation.

The block generates output based on the input values using one of these methods selected from the Lookup method parameter list:

Interpolation-Extrapolation — This default method performs linear interpolation and extrapolation of the inputs.

If the inputs match row and column parameter values, the output is the value at the intersection of the row and column.
If the inputs do not match row and column parameter values, then the block generates output by linearly interpolating between the appropriate row and column values. If either or both block inputs are less than the first or greater than the last row or column values, the block extrapolates using the first two or last two points.

Note If the Lookup method parameter specifies Interpolation-Extrapolation, Real-Time Workshop can generate code for this block only if its input and output signals have the same floating-point data type.

Interpolation-Use End Values — This method performs linear interpolation as described above but does not extrapolate outside the end points of x and y. Instead, the end-point values are used.
Use Input Nearest — This method does not interpolate or extrapolate. Instead, the elements in x and y nearest the current inputs are found. The corresponding element in z is then used as the output.
Use Input Below — This method does not interpolate or extrapolate. Instead, the elements in x and y nearest and below the current inputs are found. The corresponding element in z is then used as the output. If there are no elements in x or y below the current inputs, then the nearest elements are found.
Use Input Above — This method does not interpolate or extrapolate. Instead, the elements in x and y nearest and above the current inputs are found. The corresponding element in z is then used as the output. If there are no elements in x or y above the current inputs, then the nearest elements are found.

For information about creating a table with step transitions, see Representation of Discontinuities in Lookup Tables.

To avoid parameter saturation errors, the Simulink Fixed Point software's automatic scaling script employs a special rule for the Lookup Table (2-D) block. autofixexp modifies the scaling by using the output lookup values in addition to the logged minimum and maximum simulation values. The output lookup values are converted to the specified output data type. This action prevents the data from being saturated to different values.

Data Type Support

The Lookup Table (2-D) block supports all numeric data types supported by Simulink software, including fixed-point data types.

For a discussion on the data types supported by Simulink software, see Data Types Supported by Simulink in the Simulink documentation.

Parameters and Dialog Box

The Main pane of the Lookup Table (2-D) block dialog box appears as follows:

Row index input values

The row values for the table, entered as a vector. The vector values must increase monotonically.

The Row index input values parameter is converted offline to the data type of the corresponding input signal using round-to-nearest and saturation.

Column index input values

The column values for the table, entered as a vector. The vector values must increase monotonically.

The Column index input values parameter is converted offline to the data type of the corresponding input signal using round-to-nearest and saturation.

Click the Edit button to open the Lookup Table Editor (see Lookup Table Editor).

Table data

The table of output values. The matrix size must match the dimensions defined by the Row and Column parameters.

The Table data parameter is converted offline to the Output data type using round-to-nearest and saturation.

Lookup method

Specify the lookup method. See Description for a discussion of the options for this parameter.

Sample time (-1 for inherited)

Specify the time interval between samples. To inherit the sample time, set this parameter to -1. See How to Specify the Sample Time in the online documentation for more information.

The Signal Attributes pane of the Lookup Table (2-D) block dialog box appears as follows:

Output minimum

Specify the minimum value that the block should output. The default value, [], is equivalent to -Inf. Simulink software uses this value to perform:

Parameter range checking (see Checking Parameter Values)
Simulation range checking (see Checking Signal Ranges)
Automatic scaling of fixed-point data types

Output maximum

Specify the maximum value that the block should output. The default value, [], is equivalent to Inf. Simulink software uses this value to perform:

Parameter range checking (see Checking Parameter Values)
Simulation range checking (see Checking Signal Ranges)
Automatic scaling of fixed-point data types

Require all inputs to have the same data type

Select to require all inputs to have the same data type.

Output data type

Specify the output data type. You can set it to:

A rule that inherits a data type, for example, Inherit: Inherit via back propagation
The name of a built-in data type, for example, single
The name of a data type object, for example, a Simulink.NumericType object
An expression that evaluates to a data type, for example, fixdt(1,16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output data type parameter.

See Specifying Block Output Data Types for more information.

Lock output data type setting against changes by the fixed-point tools

Select to lock the output data type setting of this block against changes by the Fixed-Point Tool and the Fixed-Point Advisor. For more information, see Fixed-Point Tool and Fixed-Point Advisor in the Simulink Fixed Point documentation.

Integer rounding mode

Select the rounding mode for fixed-point operations. For more information, see Rounding in the Simulink Fixed Point User's Guide.

Block parameters such as Table data always round to the nearest representable value. To control the rounding of a block parameter, enter an expression using a MATLAB rounding function into the mask field.

Saturate on integer overflow

Select to have overflows saturate. Otherwise, they wrap.

When you select this check box, saturation applies to every internal operation on the block, not just the output or result. In general, the code generation process can detect when overflow is not possible, in which case, no saturation code is necessary.

Examples

In this example, the block parameters are:

Row index input values:     [1 2]
Column index input values:  [3 4]
Table data:                 [10 20; 30 40]

The first figure shows the block outputting a value at the intersection of block inputs that match row and column values. The first input is 1 and the second input is 4. These values select the table value at the intersection of the first row (row parameter value 1) and second column (column parameter value 4).

In the second figure, the first input is 1.7 and the second is 3.4. These values cause the block to interpolate between row and column values, as shown in the table at the left. The value at the intersection (28) is the output value.

Characteristics

Direct Feedthrough	Yes
Sample Time	Specified in the Sample time parameter
Scalar Expansion	Yes, of one input if the other is a vector
Dimensionalized	Yes
Zero-Crossing Detection	No