Approximate a one-dimensional function using dynamic table
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Libraries:
Simulink / Lookup Tables
Description
How This Block Differs from Other Lookup Table Blocks
The Lookup Table Dynamic block computes an approximation of a function y= f(x) using xdat and ydatvectors. The lookup method can use interpolation, extrapolation, or the originalvalues of the input.
Using the Lookup Table Dynamic block, you can change the table data withoutstopping the simulation. For example, you can incorporate new table data if thephysical system you are simulating changes.
Inputs for Breakpoint and Table Data
The xdat vector is the breakpoint data, which must bestrictly monotonically increasing. The value of the nextelement in the vector must be greater than the value of the preceding element afterconversion to a fixed-point data type. Due to quantization, xdatcan be strictly monotonic for a floating-point data type, but not after conversionto a fixed-point data type.
The ydat vector is the table data, which is an evaluation ofthe function at the breakpoint values.
Note
The inputs to xdat and ydat cannot bescalar (one-element array) values. If you provide a scalar value to either ofthese inputs, you see an error upon simulation. Provide a 1-by-n vector to boththe xdat and ydat inputs.
Lookup Table Definition
You define the lookup table by feeding xdat and ydatas 1-by-n vectors to the block. To reduce ROM usage in the generated code for thisblock, you can use different data types for xdat andydat.
Tip
Breakpoints with even spacing can make Simulink® Coder™ generated code division-free. For more information, see fixpt_evenspace_cleanup inthe Simulink documentation and Identify questionable fixed-point operations (Embedded Coder) in the Simulink Coder documentation.
How the Block Generates Output
The block uses the input values to generate output using the method you select forLookup Method:
| Lookup Method | Block Action |
|---|---|
Interpolation-Extrapolation | Performs linear interpolation and extrapolation of theinputs.
Note If you select this lookup method, Simulink Coder software cannot generate code for thisblock. |
Interpolation-Use End Values (default) | Performs linear interpolation but does not extrapolateoutside the end points of the breakpoint data. Instead, theblock uses the end values. |
Use Input Nearest | Finds the element in |
Use Input Below | Finds the element in |
Use Input Above | Finds the element in |
Note
The Use Input Nearest, Use Input Below,and Use Input Above methods perform the same action when theinput x matches a breakpoint value.
Some continuous solvers subdivide the simulation time span into major and minortime steps. A minor time step is a subdivision of the major time step. The solverproduces a result at each major time step and uses results at minor time steps toimprove the accuracy of the result at the major time step. For continuous solvers,the output of the Lookup Table Dynamic block can appear like a stair step becausethe signal is fixed in minor time step to avoid incorrect results. For moreinformation about the effect of solvers on block output, see Compare Solvers in the Simulink documentation.
Examples
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Approximating the sinh Function Using the Lookup Table Dynamic Block
This example shows how to use the Lookup Table Dynamic block to approximate the sinh function. The breakpoint data is given by the vector [-5:5] and the table data is given by the vector sinh([-5:5]). The input x is provided by the Constant block as a 1-by-3 vector containing values that are below, within, and above the breakpoint data values.
To see how each lookup method handles input values that are below, within, and above the breakpoint data values, change the value of the Lookup Method parameter on the Lookup Table Dynamic block.
The Lookup Table Dynamic block outputs the following values when using the specified lookup methods and inputs.
Ports
Input
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x — input vector
scalar | vector | 2-D array
The block accepts real-valued or complex-valued inputs.
Example: 2:12
Dependencies
The x input vector and thexdat breakpoint data must have the same sign,bias, and fractional slope. Also, the precision and range forx must be greater than or equal to theprecision and range for xdat.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point | bus
xdat — breakpoint data
1-by-n vector of strictly monotonically increasingvalues
The xdat vector is the breakpoint data, which mustbe strictly monotonically increasing. The value of the next element inthe vector must be greater than the value of the preceding element afterconversion to a fixed-point data type. Due to quantization,xdat can be strictly monotonic for afloating-point data type, but not after conversion to a fixed-point datatype.
Tip
Breakpoints with even spacing can make Simulink Coder generated code division-free. For more information,see fixpt_evenspace_cleanup in the Simulink documentation and Identify questionable fixed-point operations (Embedded Coder) in theSimulink Coder documentation.
Example: 1:10
Dependencies
The xdat breakpoint data and thex input vector must have the same sign, bias,and fractional slope. Also, the precision and range forx must be greater than or equal to theprecision and range for xdat.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point | bus
ydat — table data
1-by-n vector
The ydat input is a 1-by-n vector of real-valued orcomplex-valued table data, which is an evaluation of the function at thebreakpoint values.
Example: [0 3 12 27 48 75 108 147 192 243 300]
Dependencies
The ydat table data and they output vector must have the same sign,bias, and fractional slope.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point | bus
Output
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y — Approximation of y = f(x) using dynamic tabledata
1-by-n vector
The block computes an approximation of a function y =f(x) using the xdat andydat input vectors. The lookup method can useinterpolation, extrapolation, or the original values of theinput.
Dependencies
The ydat table data and they output vector must have the same sign,bias, and fractional slope.
Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point
Parameters
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Main Tab
Lookup Method — Specify the lookup method
Interpolation-Use EndValues (default) | Interpolation-Extrapolation | Use Input Nearest | Use Input Below | Use Input Above
The block computes output by applying the LookupMethod you select to the input vectors of breakpoint data(xdat) and table data (ydat).For details, see How the Block Generates Output.
Programmatic Use
Block Parameter:LookUpMeth |
| Type: charactervector |
Values:'Interpolation-Extrapolation' | 'Interpolation-Use EndValues' | 'Use Input Nearest' | 'Use Input Below' | 'UseInput Above' |
Default:'Interpolation-Use End Values' |
Signal Attributes Tab
Output data type — Output data type
double (default) | 'Inherit: Inherit via back propagation' | single | int8 | uint8 | int16 | uint16 | int32 | uint32 | int64 | uint64 | boolean | fixdt(1,16,0) | fixdt(1,16,2^0,0) | <data type expression>
Specify the data type of the output signaly.
The Data Type Assistant helps you set dataattributes. To use the Data Type Assistant, click 
. For more information, see Specify Data Types Using Data Type Assistant.
Dependencies
The ydat table data and they output vector must have the same sign,bias, and fractional slope.
Programmatic Use
Block Parameter:OutDataTypeStr |
| Type: charactervector |
Values:'Inherit: Inherit via back propagation' | 'double' |'single' | 'int8' | 'uint8' | 'int16' | 'uint16' | 'int32'| 'uint32' | 'int64' | 'uint64' | 'boolean' |'fixdt(1,16,0)' | 'fixdt(1,16,2^0,0)' | <data typeexpression> |
Default:'double' |
Lock output data type setting against changes by the fixed-point tools — Option to prevent fixed-point tools from overriding Output data type
off (default) | on
Select this parameter to prevent the fixed-point tools from overriding the Output data type you specify on the block. For more information, see Use Lock Output Data Type Setting (Fixed-Point Designer).
Programmatic Use
Block Parameter: LockScale |
| Type: character vector |
Values: 'off' | 'on' |
Default: 'off' |
Integer rounding mode — Rounding mode for fixed-point operations
Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero
Specify the rounding mode for fixed-point operations. For more information, see Rounding (Fixed-Point Designer).
Block parameters 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.
Programmatic Use
Block Parameter: RndMeth |
| Type: character vector |
Values: 'Ceiling' | 'Convergent' | 'Floor' | 'Nearest' | 'Round' | 'Simplest' | 'Zero' |
Default: 'Floor' |
Saturate to max or min when overflows occur — Method of overflow action
off (default) | on
When you select this check box, overflows saturate to the maximum or minimum value that the data type can represent. Otherwise, overflows 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 this case, the code generator does not produce saturation code.
Programmatic Use
Block Parameter: DoSatur |
| Type: character vector |
Values: 'off' | 'on' |
Default: 'off' |
Block Characteristics
Data Types |
|
Direct Feedthrough |
|
Multidimensional Signals |
|
Variable-Size Signals |
|
Zero-Crossing Detection |
|
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.
The Simulink PLC Coder™ software does not support the SimulinkLookup Table Dynamic block. For your convenience, theplclib/Simulink/Lookup Tables library contains an implementation of a dynamic tablelookup block using the Prelookup and Interpolation UsingPrelookup blocks.
Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.
Version History
Introduced before R2006a
See Also
1-D Lookup Table | 2-D Lookup Table | n-D Lookup Table
Topics
- Enter Data Using Inports of Lookup Table Dynamic Block
- Nonlinearity
- About Lookup Table Blocks
- Anatomy of a Lookup Table
- Guidelines for Choosing a Lookup Table
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