Simulink Reference

Lookup Table (2-D)

Approximate a two-dimensional function using a selected lookup method

Library

Lookup Tables

Description

The Lookup Table (2-D) block computes an approximation to some function z=f(x,y) given x, y, z data points.

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 Matrix of output values parameter is an m-by-n matrix of z data points. Both the row and column vectors must be monotonically increasing. These vectors must be strictly monotonically increasing 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.

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

• Interpolation-Extrapolation--This is the default method; it 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.
• 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.

Note    Note that there is no difference among the Use Input Nearest, Use Input Below, and Use Input Above methods when the input x corresponds exactly to table breakpoints.

To avoid parameter saturation errors, the automatic scaling script autofixexp 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 prevents the data from being saturated to different values.

Data Type Support

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

For a discussion on the data types supported by Simulink, refer to Data Types Supported by Simulink in the Using Simulink documentation.

Parameters and Dialog Box

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

Row index input values

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

Column index input values

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

Click the Edit button to invoke the Lookup Table Editor.

Vector of output values

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

Look-up 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 Specifying Sample Time in the online documentation for more information.

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

Require all inputs to have same data type

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

Output data type mode

You can set the output signal to a built-in data type from this drop-down list, or you can choose the output data type and scaling to be the same as the input. Alternatively, you can choose to inherit the output data type and scaling by backpropagation. Lastly, if you choose Specify via dialog, the Output data type, Output scaling value, and Lock output scaling against changes by the autoscaling tool parameters become visible.

Output data type

Specify any data type, including fixed-point data types. This parameter is only visible if you select Specify via dialog for the Output data type mode parameter.

Output scaling value

Set the output scaling using binary point-only or [Slope Bias] scaling. This parameter is only visible if you select Specify via dialog for the Output data type mode parameter.

Lock output scaling against changes by the autoscaling tool

Select to lock scaling of outputs. This parameter is only visible if you select Specify via dialog for the Output data type mode parameter.

Round integer calculations toward

Select the rounding mode for fixed-point operations.

Note that block parameters such as Vector of output values are always rounded to the the nearest representable value. To direcly 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.

Examples

In this example, the block parameters are defined as

• Row:      [1 2]
  Column:   [3 4]
  Table:    [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	No

See Also

Lookup Table, Lookup Table (n-D)

Lookup Table

Lookup Table (n-D)

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